Finite Group Databasebeta

← #30587883

Subgroups — #30587883

Order 15616.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460481C218yesmaximal, complemented
2#21460465C214yesmaximal, complemented
3#21460401C214yesmaximal, complemented
4#21460310C212yesmaximal, complemented
5#21460278C212yesmaximal, complemented
6#21460209C212yesmaximal, complemented
7#21460187C212yesmaximal, complemented
8#21460083C214yesmaximal, complemented
9#21460076C214yesmaximal, complemented
10#21459957C214yesmaximal, complemented
11#21459443C211yesmaximal, characteristic, complemented
12#21459441C212yesmaximal, complemented
13#21459410C214yesmaximal, complemented
14#21459377C214yesmaximal, complemented
15#21459244C214yesmaximal, complemented
16#21459241C214yesmaximal, complemented
17#21459207C214yesmaximal, complemented
18#21459114C211yesmaximal, characteristic, complemented
19#21459112C212yesmaximal, complemented
20C61×#3481C211yesmaximal, characteristic, complemented
21#16840515C2214yescomplemented
22#16840513C2218yescomplemented
23#16840509C2218yescomplemented
24#16840508C2218yescomplemented
25#16840507C2218yescomplemented
26#16840505C2214yescomplemented
27#16840502C2214yescomplemented
28#16840501C2218yes—
29#16840501C2214yescomplemented
30#16840500C2218yescomplemented
31#16840496C2218yescomplemented
32#16840494C2214yescomplemented
33#16840492C2211yescharacteristic, complemented
34#16840491C2212yescomplemented
35#16840489C2214yescomplemented
36#16840483C2214yescomplemented
37#16840482C2214yescomplemented
38#16840482C2212yescomplemented
39#16840482C2214yescomplemented
40#16840479C2218yescomplemented
41#16840478C2211yescharacteristic, complemented
42#16840477C2214yes—
43#16840476C2214yescomplemented
44#16840474C2214yescomplemented
45#16840469C2214yescomplemented
46#16840465C2214yescomplemented
47#16840463C2218yescomplemented
48#16840459C2214yescomplemented
49#16840458C2218yescomplemented
50#16840457C2218yescomplemented
51#16840452C2218yescomplemented
52#16840451C2218yescomplemented
53#16840451C2214yescomplemented
54#16840447C2214yescomplemented
55#16840447C2214yescomplemented
56#16840438C2218yescomplemented
57#16840438C2218yescomplemented
58#16840432C2212yescomplemented
59#16840430C2214yes—
60#16840430C2214yescomplemented
61Q8×D244C2212yescomplemented
62#16840422C2214yescomplemented
63#16840420C2214yescomplemented
64#16840419C2214yes—
65#16840417C2214yescomplemented
66#16840417C2212yescomplemented
67#16840416C2214yescomplemented
68#16840406C2214yes—
69#16840406C2214yescomplemented
70#16840393C2214yescomplemented
71#16840392C2214yescomplemented
72#16840385C2218yescomplemented
73#16840381C2214yescomplemented
74#16840380C2218yescomplemented
75#16840379C2218yescomplemented
76#16840379C2214yescomplemented
77#16840377C2214yes—
78#16840377C2218yescomplemented
79#16840377C2214yescomplemented
80#16840375C2214yescomplemented
81#16840372C2218yescomplemented
82#16840372C2214yescomplemented
83#16840369C2218yescomplemented
84#16840365C2218yescomplemented
85#16840363C2218yescomplemented
86#16840363C2214yescomplemented
87#16840363C2214yescomplemented
88#16840356C2218yescomplemented
89#16840356C2218yescomplemented
90#16840355C2218yescomplemented
91#16840353C2218yescomplemented
92#16840350C2218yescomplemented
93#16840350C2218yescomplemented
94#16840347C2218yescomplemented
95#16840347C2218yescomplemented
96#16840343C2214yescomplemented
97#16840341C2214yes—
98#16840335C2214yescomplemented
99#16840332C2214yescomplemented
100#16840329C2214yes—
101#16840329C2214yescomplemented
102#16840319C2214yescomplemented
103#16840319C2211yescharacteristic, complemented
104#16840317C2212yescomplemented
105#16840316C2212yescomplemented
106#16840316C2212yescomplemented
107#16840315C2214yescomplemented
108#16840315C2212yescomplemented
109#16840310C2212yes—
110#16840309C2212yes—
111#16840309C2212yes—
112#16840309C2214yescomplemented
113#16840309C2218yescomplemented
114#16840308C2212yes—
115#16840308C2214yescomplemented
116#16840299C2212yescomplemented
117#16840299C2212yescomplemented
118#16840294C2212yes—
119#16840294C2212yes—
120#16840294C2218yescomplemented
121#16840294C2218yescomplemented
122#16840294C2214yescomplemented
123#16840294C2214yescomplemented
124#16840293C2214yescomplemented
125#16840292C2214yescomplemented
126#16840292C2218yescomplemented
127#16840292C2218yescomplemented
128#16840292C2214yescomplemented
129#16840291C2214yescomplemented
130#16840290C2214yescomplemented
131#16840290C2214yescomplemented
132#16840290C2218yescomplemented
133#16840274C2212yescomplemented
134#16840273C2214yescomplemented
135#16840273C2218yescomplemented
136#16840272C2214yescomplemented
137#16840271C2214yescomplemented
138#16840271C2214yescomplemented
139#16840269C2212yes—
140#16840269C2212yescomplemented
141#41×Dic61C2212yescomplemented
142C4×#11758222C2214yescomplemented
143C4×#11758222C2214yescomplemented
144C4×#11758222C2214yescomplemented
145C4×#11758222C2212yescomplemented
146#16840230C2214yescomplemented
147C4×#11758224C2214yescomplemented
148C4×#11758224C2214yescomplemented
149C4×Q8×D61C2214yescomplemented
150C2×#14519736C2214yescomplemented
151C2×C42×D61C2211yescharacteristic, complemented
152C61×#559C2211yescharacteristic, complemented
153C61×#554C2212yescomplemented
154C61×#553C2214yes—
155C61×#551C2214yescomplemented
156C61×#546C2214yes—
157D42×C61C2211yescharacteristic, complemented
158C61×#532C2211yescharacteristic
159C61×#529C2214yescomplemented
160C61×#525C2214yes—
161C4×#41×C61C2212yes—
162C2×C4×D4×C61C2214yescomplemented
163C2×#11758222C2314yes—
164C2×#11758222C2314yes—
165C2×#11758222C2314yes—
166C2×#11758222C2312yes—
167C2×#11758222C2314yes—
168C2×#11758224C2314yes—
169C2×#11758224C2314yes—
170C2×Q8×D61C2314yes—
171C22×C4×D61C2312yes—
172C22×C4×D61C2311yescharacteristic
173#14519777C2314yes—
174#14519777C2312yes—
175#14519777C2314yes—
176#14519776C2314yes—
177#14519776C2318yes—
178#14519776C2312yes—
179#14519776C2312yes—
180#14519776C2318yes—
181#14519775C2314yes—
182#14519775C2312yes—
183#14519773C2314yes—
184#14519773C2318yes—
185#14519773C2314yes—
186#14519773C2312yes—
187#14519772C2314yes—
188#14519772C2318yes—
189#14519772C2318yes—
190#14519772C2318yes—
191#14519772C2314yes—
192#14519770C2318yes—
193#14519770C2318yes—
194#14519770C2318yes—
195#14519770C2314yes—
196#14519770C2318yes—
197#14519770C2318yes—
198#14519770C2318yes—
199#14519770C2314yes—
200#14519770C2318yes—
201#14519770C2318yes—
202#14519770C2318yes—
203#14519769C2312yes—
204#14519769C2318yes—
205#14519768C2314yes—
206#14519768C2318yes—
207#14519768C2312yes—
208#14519768C2312yes—
209#14519768C2314yes—
210#14519768C2318yes—
211#14519768C2318yes—
212#14519767C2318yes—
213#14519767C2318yes—
214#14519767C2318yes—
215#14519767C2314yes—
216#14519767C2314yes—
217#14519766C2314yes—
218#14519766C2312yes—
219#14519764C2314yes—
220#14519764C2312yes—
221#14519764C2314yes—
222#14519764C2318yes—
223#14519764C2314yes—
224#14519764C2318yes—
225#14519763C2318yes—
226#14519763C2318yes—
227#14519763C2318yes—
228#14519763C2318yes—
229#14519763C2318yes—
230#14519763C2318yes—
231#14519763C2314yes—
232#14519763C2314yes—
233#14519762C2314yes—
234#14519762C2318yes—
235#14519762C2314yes—
236#14519761C2318yes—
237#14519761C2318yes—
238#14519761C2314yes—
239#14519760C2318yes—
240#14519760C2318yes—
241#14519760C2318yes—
242#14519759C2318yes—
243#14519759C2318yes—
244#14519759C2318yes—
245#14519759C2318yes—
246#14519759C2314yes—
247#14519759C2314yes—
248#14519759C2318yes—
249#14519759C2318yes—
250#14519759C2318yes—
251#14519758C2318yes—
252#14519758C2318yes—
253#14519758C2314yes—
254#14519758C2314yes—
255#14519757C2318yes—
256#14519757C2314yes—
257#14519757C2314yes—
258#14519757C2312yes—
259#14519757C2312yes—
260#14519757C2318yes—
261#14519756C2314yes—
262#14519756C2318yes—
263#14519756C2318yes—
264#14519756C2318yes—
265#14519756C2314yes—
266#14519756C2314yes—
267#14519756C2318yes—
268#14519755C2318yes—
269#14519755C2314yes—
270#14519755C2314yes—
271#14519754C2318yes—
272#14519754C2318yes—
273#14519754C2314yes—
274#14519754C2314yes—
275#14519754C2318yes—
276#14519754C2318yes—
277#14519753C2312yes—
278#14519753C2314yes—
279#14519753C2312yes—
280#14519752C2318yes—
281#14519752C2312yes—
282#14519752C2314yes—
283#14519752C2312yes—
284#14519751C2318yes—
285#14519751C2318yes—
286#14519751C2318yes—
287#14519750C2318yes—
288#14519750C2318yes—
289#14519750C2318yes—
290#14519750C2318yes—
291#14519750C2314yes—
292#14519750C2314yes—
293#14519749C2318yes—
294#14519749C2318yes—
295#14519749C2318yes—
296#14519749C2318yes—
297#14519749C2314yes—
298#14519749C2314yes—
299#14519748C2318yes—
300#14519748C2314yes—
301#14519748C2312yes—
302#14519748C2314yes—
303#14519748C2318yes—
304#14519748C2314yes—
305#14519748C2312yes—
306#14519748C2314yes—
307#14519748C2318yes—
308#14519747C2314yes—
309#14519746C2318yes—
310#14519746C2318yes—
311#14519746C2318yes—
312#14519745C2314yes—
313#14519745C2314yes—
314Q8×Dic61C2314yes—
315Q8×Dic61C2314yes—
316C4×Dic122C2314yes—
317C4×Dic122C2314yes—
318C4×Dic122C2314yes—
319C4×Dic122C2318yes—
320C4×Dic122C2314yes—
321C4×Dic122C2312yes—
322C4×Dic122C2312yes—
323C4×Dic122C2314yes—
324C4×Dic122C2314yes—
325#14519742C2318yes—
326#14519742C2314yes—
327#14519742C2318yes—
328#14519742C2314yes—
329#14519742C2314yes—
330C4×D244C2314yes—
331C4×D244C2314yes—
332C4×D244C2314yes—
333C4×D244C2312yes—
334C4×D244C2312yes—
335C4×D244C2314yes—
336C4×D244C2314yes—
337D4×Dic61C2314yes—
338D4×Dic61C2314yes—
339D4×Dic61C2318yes—
340D4×Dic61C2314yes—
341#14519739C2318yes—
342C4×C22⋊D61C2318yes—
343C4×C22⋊D61C2314yes—
344C4×C22⋊D61C2314yes—
345C4×C22⋊D61C2314yes—
346C4×C22⋊D61C2314yes—
347C4×C22⋊D61C2318yes—
348C4×C22⋊D61C2318yes—
349C4×C22⋊D61C2314yes—
350C4×C22⋊D61C2314yes—
351C4×C22⋊D61C2314yes—
352C4×C22⋊D61C2314yes—
353C4×C22⋊D61C2314yes—
354C4×C22⋊D61C2318yes—
355C4×C22⋊D61C2314yes—
356#14519737C2318yes—
357#14519737C2318yes—
358#14519737C2318yes—
359#14519737C2318yes—
360#14519736C2318yes—
361#14519736C2318yes—
362#14519736C2314yes—
363#14519736C2314yes—
364#14519736C2318yes—
365#14519736C2312yes—
366#14519736C2314yes—
367#14519736C2312yes—
368#14519736C2314yes—
369#14519735C2314yes—
370#14519735C2314yes—
371#14519734C2318yes—
372#14519734C2314yes—
373#14519734C2314yes—
374#14519734C2314yes—
375#14519734C2314yes—
376#14519734C2314yes—
377#14519733C2318yes—
378#14519733C2318yes—
379C2×C4⋊Dic61C2318yes—
380C4⋊C4×D61C2318yes—
381C4⋊C4×D61C2314yes—
382C2×C22⋊Dic61C2318yes—
383C2×C4×Dic61C2311yescharacteristic
384C2×C4×Dic61C2312yes—
385C2×C4×Dic61C2314yes—
386C2×C4×Dic61C2314yes—
387C42×D61C2312yes—
388C42×D61C2312yes—
389C42×D61C2312yes—
390C42×D61C2312yes—
391C42×D61C2314yes—
392C42×D61C2318yes—
393C2×#41×C61C2312yes—
394C2×#41×C61C2312yes—
395C22×D4×C61C2314yes—
396C23×C4×C61C2314yes—
397C4⋊Q8×C61C2311yescharacteristic
398#127×C61C2311yescharacteristic
399#126×C61C2318yes—
400#125×C61C2314yes—
401#124×C61C2312yes—
402#124×C61C2314yes—
403#123×C61C2318yes—
404#123×C61C2314yes—
405#123×C61C2314yes—
406C22⋊Q8×C61C2314yes—
407C22⋊Q8×C61C2318yes—
408#121×C61C2314yes—
409#121×C61C2314yes—
410#121×C61C2318yes—
411#120×C61C2314yes—
412#120×C61C2314yes—
413C4×Q8×C61C2312yes—
414C4×Q8×C61C2312yes—
415C4×D4×C61C2314yes—
416C4×D4×C61C2318yes—
417C4×D4×C61C2312yes—
418C4×D4×C61C2314yes—
419C4×D4×C61C2314yes—
420C4×D4×C61C2314yes—
421C4×D4×C61C2314yes—
422C4×D4×C61C2318yes—
423C4×D4×C61C2312yes—
424#117×C61C2314yes—
425#117×C61C2312yes—
426#117×C61C2314yes—
427C2×C4⋊C4×C61C2314yes—
428C2×C22⋊C4×C61C2318yes—
429C2×C42×C61C2311yescharacteristic
430C2×C42×C61C2314yes—
431C24×C61C2414yes—
432C23×D61C2411yescharacteristic
433#41×C61—44no—
434#41×C61—44no—
435C2×Q8×C61C2412yes—
436C2×Q8×C61C2412yes—
437C2×D4×C61—48no—
438C2×D4×C61C2414yes—
439C2×D4×C61C2412yes—
440C2×D4×C61C2414yes—
441C2×D4×C61C2418yes—
442C2×D4×C61C2412yes—
443C2×D4×C61C2414yes—
444C22×C4×C61—48no—
445C22×C4×C61C2412yes—
446C22×C4×C61C2411yescharacteristic
447C22×C4×C61C2414yes—
448C22×C4×C61C2414yes—
449C22×C4×C61C2414yes—
450C22×C4×C61C2414yes—
451C22×C4×C61C2418yes—
452C22×C4×C61C2414yes—
453C2×C22⋊D61C2418yes—
454C2×C22⋊D61C2418yes—
455C2×C22⋊D61C2418yes—
456C2×C22⋊D61C2414yes—
457C2×C22⋊D61C2414yes—
458C2×C22⋊D61C2414yes—
459C2×C22⋊D61C2414yes—
460C2×C22⋊D61C2418yes—
461C2×C22⋊D61C2414yes—
462C22×Dic61C2412yes—
463C22×Dic61C2411yescharacteristic
464C22×Dic61C2418yes—
465C22×Dic61C2418yes—
466Q8×D61—48no—
467#11758224—48no—
468#11758224—48no—
469#11758222—44no—
470#11758222—48no—
471#11758222—48no—
472#11758222—48no—
473#11758222—48no—
474C2×D244C2412yes—
475C2×D244C2414yes—
476C2×D244C2414yes—
477C2×D244C2414yes—
478C2×C4×D61—42no—
479C2×C4×D61—44no—
480C2×C4×D61C2412yes—
481C2×C4×D61C2412yes—
482C2×C4×D61C2412yes—
483C2×C4×D61C2414yes—
484C2×C4×D61C2414yes—
485C2×C4×D61C2412yes—
486C2×C4×D61C2412yes—
487C2×C4×D61C2412yes—
488C2×C4×D61C2418yes—
489C2×C4×D61C2414yes—
490C2×C4×D61C2418yes—
491C2×Dic122C2414yes—
492C2×Dic122C2412yes—
493C2×Dic122C2418yes—
494C2×Dic122C2414yes—
495C2×Dic122C2414yes—
496C2×Dic122C2414yes—
497C4⋊C4×C61C2412yes—
498C4⋊C4×C61C2414yes—
499C4⋊C4×C61C2418yes—
500C4⋊C4×C61C2412yes—
501C4⋊C4×C61C2414yes—
502C4⋊C4×C61C2414yes—
503C4⋊C4×C61C2418yes—
504C22⋊C4×C61C2414yes—
505C22⋊C4×C61C2418yes—
506C22⋊C4×C61C2418yes—
507C22⋊C4×C61C2418yes—
508C22⋊C4×C61C2414yes—
509C22⋊C4×C61C2414yes—
510C22⋊C4×C61C2414yes—
511C22⋊C4×C61C2414yes—
512C42×C61C2412yes—
513C42×C61C2411yescharacteristic
514C42×C61C2414yes—
515C42×C61C2414yes—
516C42×C61C2414yes—
517C42×C61C2411yescharacteristic
518C22⋊Dic61C2414yes—
519C22⋊Dic61C2414yes—
520C22⋊Dic61C2418yes—
521C22⋊Dic61C2418yes—
522C22⋊Dic61C2418yes—
523C22⋊Dic61C2418yes—
524C22⋊Dic61C2414yes—
525C22⋊Dic61C2418yes—
526C22⋊Dic61C2414yes—
527C22⋊Dic61C2414yes—
528C22⋊Dic61C2414yes—
529C22⋊Dic61C2418yes—
530#11758198C2414yes—
531#11758198C2414yes—
532#11758198C2414yes—
533#11758198C2414yes—
534#11758198C2414yes—
535#11758198C2414yes—
536#11758198C2414yes—
537#11758198C2414yes—
538#11758198C2414yes—
539#11758198C2418yes—
540#11758198C2414yes—
541#11758198C2418yes—
542#11758198C2418yes—
543C4⋊Dic61C2414yes—
544C4⋊Dic61C2418yes—
545C4⋊Dic61C2414yes—
546C4⋊Dic61C2414yes—
547C4⋊Dic61C2418yes—
548C4⋊Dic61C2418yes—
549C4⋊Dic61C2412yes—
550C4⋊Dic61C2412yes—
551C4⋊Dic61C2414yes—
552C4⋊Dic61C2418yes—
553C4⋊Dic61C2414yes—
554C4⋊Dic61C2414yes—
555#11758196C2418yes—
556#11758196C2418yes—
557#11758196C2418yes—
558#11758196C2414yes—
559#11758196C2418yes—
560#11758196C2418yes—
561#11758196C2414yes—
562#11758196C2414yes—
563#11758196C2414yes—
564#11758196C2414yes—
565#11758196C2414yes—
566#11758196C2414yes—
567#11758196C2418yes—
568#11758196C2414yes—
569#11758196C2414yes—
570#11758196C2414yes—
571C4×Dic61C2411yescharacteristic
572C4×Dic61C2412yes—
573C4×Dic61C2412yes—
574C4×Dic61C2411yescharacteristic
575C4×Dic61C2414yes—
576C4×Dic61C2412yes—
577C4×Dic61C2412yes—
578C4×Dic61C2412yes—
579C4×Dic61C2414yes—
580C4×Dic61C2414yes—
581C4×Dic61C2418yes—
582C4×Dic61C2414yes—
583C4×Dic61C2418yes—
584C4×Dic61C2414yes—
585C4×Dic61C2418yes—
586C4×Dic61C2414yes—
587C23×C61—44no—
588C23×C61—48no—
589C23×C61C2514yes—
590C23×C61C2511yescharacteristic
591C23×C61C2514yes—
592C22×D61—41no—
593C22×D61—42no—
594C22×D61C2512yes—
595C22×D61C2514yes—
596Q8×C61—24no—
597Q8×C61—42no—
598D4×C61—28no—
599D4×C61—24no—
600D4×C61—48no—
601D4×C61—44no—
602D4×C61—44no—
603D4×C61—42no—
604C2×C4×C61—24no—
605C2×C4×C61—22no—
606C2×C4×C61—28no—
607C2×C4×C61—28no—
608C2×C4×C61—28no—
609C2×C4×C61—44no—
610C2×C4×C61—48no—
611C2×C4×C61—44no—
612C2×C4×C61C2512yes—
613C2×C4×C61C2514yes—
614C2×C4×C61C2514yes—
615C2×C4×C61C2511yescharacteristic
616C2×C4×C61C2514yes—
617C2×C4×C61C2514yes—
618C2×C4×C61C2512yes—
619C2×C4×C61C2511yescharacteristic
620C22⋊D61—48no—
621C22⋊D61—44no—
622C22⋊D61—44no—
623C22⋊D61—44no—
624C22⋊D61—48no—
625C22⋊D61—44no—
626C22⋊D61—44no—
627C22⋊D61—48no—
628C22⋊D61—48no—
629C2×Dic61—41no—
630C2×Dic61—42no—
631C2×Dic61—48no—
632C2×Dic61—48no—
633C2×Dic61C2512yes—
634C2×Dic61C2514yes—
635C2×Dic61C2512yes—
636C2×Dic61C2514yes—
637C2×Dic61C2518yes—
638C2×Dic61C2512yes—
639C2×Dic61C2514yes—
640D244—24no—
641D244—44no—
642D244—44no—
643D244—44no—
644C4×D61—24no—
645C4×D61—24no—
646C4×D61—24no—
647C4×D61—28no—
648C4×D61—28no—
649C4×D61—42no—
650C4×D61—42no—
651C4×D61—42no—
652C4×D61—48no—
653C4×D61—44no—
654C4×D61—48no—
655Dic122—24no—
656Dic122—28no—
657Dic122—44no—
658Dic122—44no—
659Dic122—44no—
660Dic122—48no—
661#62762—611nomaximal, Sylow
662C22×C61—28no—
663C22×C61—22no—
664C22×C61—21no—
665C22×C61—24no—
666C22×C61—24no—
667C22×C61—24no—
668C22×C61—24no—
669C22×C61—88no—
670C22×C61C2611yescharacteristic
671C2×D61—24no—
672C2×D61—22no—
673C2×D61—22no—
674C2×D61—22no—
675C2×D61—24no—
676C2×D61—24no—
677C2×D61—44no—
678C4×C61—24no—
679C4×C61—24no—
680C4×C61—24no—
681C4×C61—24no—
682C4×C61—22no—
683C4×C61—21no—
684C4×C61#58512yes—
685C4×C61#58514yes—
686Dic61—28no—
687Dic61—24no—
688Dic61—24no—
689Dic61—24no—
690Dic61—22no—
691Dic61—22no—
692Dic61—22no—
693#3566—618no—
694#3565—614no—
695#3562—614no—
696#3555—612no—
697#3554—612no—
698#3547—612no—
699#3546—612no—
700#3540—614no—
701#3539—614no—
702#3529—614no—
703#3483—611no—
704#3482—612no—
705#3481D6111yescharacteristic, complemented
706#3480—614no—
707#3475—614no—
708#3461—614no—
709#3460—614no—
710#3455—614no—
711#3444—611no—
712#3444—612no—
713C2×C61—41no—
714C2×C61—44no—
715C2×C61—44no—
716C2×C61C2×#58511yescharacteristic
717C2×C61C2×#58512yes—
718D61—44no—
719D61—42no—
720#563—614no—
721#563—618no—
722#562—618no—
723#562—618no—
724#562—618no—
725H(3,𝔽4)—614no—
726#560—614no—
727#560—618no—
728#560—618no—
729#560—614no—
730#559—614no—
731#559—618no—
732#559C2×D6111yescharacteristic, complemented
733Q82—611no—
734#557—614no—
735#557—612no—
736#556—618no—
737#556—614no—
738#556—614no—
739#556—614no—
740#556—612no—
741#555—611no—
742#555—614no—
743#555—614no—
744#555—614no—
745#554—614no—
746#554C2×D6112yescomplemented
747#553—618no—
748#553—614no—
749#553—618no—
750#553—614no—
751#553—618no—
752#553C2×D6114yes—
753#552—618no—
754#552—614no—
755#552—618no—
756#552—614no—
757#552—614no—
758#551—618no—
759#551—618no—
760#551C2×D6114yescomplemented
761#550—612no—
762#550—614no—
763#550—614no—
764D4×Q8—612no—
765#548—614no—
766#548—614no—
767#548—614no—
768#547—614no—
769#547—614no—
770#547—612no—
771#546—614no—
772#546—614no—
773#546C2×D6114yes—
774D42C2×D6111yescharacteristic, complemented
775#544—614no—
776#544—614no—
777#542—614no—
778#542—618no—
779#542—618no—
780#542—618no—
781#542—614no—
782#542—614no—
783#542—614no—
784#542—618no—
785#541—618no—
786#541—614no—
787#541—618no—
788#541—614no—
789#540—618no—
790#540—614no—
791#540—618no—
792#540—614no—
793#539—618no—
794#539—618no—
795#539—618no—
796#539—618no—
797#538—618no—
798#538—618no—
799#538—618no—
800#538—618no—
801#537—614no—
802#537—614no—
803#536—614no—
804#536—614no—
805#535—614no—
806#535—614no—
807#533—612no—
808#533—612no—
809#533—612no—
810#533—612no—
811#533—614no—
812#533—611no—
813#533—614no—
814#532—612no—
815#532—614no—
816#532—612no—
817#532—612no—
818#532—612no—
819#532—614no—
820#532—618no—
821#532C2×D6111yescharacteristic
822#529—614no—
823#529—614no—
824#529—612no—
825#529—612no—
826#529—614no—
827#529—614no—
828#529—618no—
829#529—618no—
830#529—612no—
831#529—612no—
832#529—614no—
833#529—618no—
834#529—618no—
835#529—614no—
836#529—614no—
837#529—614no—
838#529—618no—
839#529C2×D6114yescomplemented
840#525—612no—
841#525—612no—
842#525—614no—
843#525—618no—
844#525—614no—
845#525—614no—
846#525—614no—
847#525—612no—
848#525C2×D6114yes—
849C4×#41—612no—
850C4×#41—614no—
851C4×#41—614no—
852C4×#41—614no—
853C4×#41—614no—
854C4×#41—614no—
855C4×#41—612no—
856C4×#41—614no—
857C4×#41C2×D6112yes—
858C2×C4×Q8—614no—
859C2×C4×D4C2×D6114yescomplemented
860C2×#117—614no—
861C22×C42—611no—
862C61#6276211yescharacteristic, complemented, Sylow
863C2×#41—614no—
864C2×#41—614no—
865C2×#41—614no—
866C2×#41—614no—
867C2×#41—614no—
868C2×#41—612no—
869C2×#41—614no—
870C2×#41C22×D6112yes—
871C2×#41C22×D6112yes—
872C22×Q8—614no—
873C22×D4C22×D6114yes—
874C23×C4—612no—
875C23×C4—611no—
876C23×C4C22×D6114yes—
877C4⋊Q8—612no—
878C4⋊Q8—614no—
879C4⋊Q8—612no—
880C4⋊Q8—612no—
881C4⋊Q8—614no—
882C4⋊Q8—618no—
883C4⋊Q8—618no—
884C4⋊Q8—612no—
885C4⋊Q8—614no—
886C4⋊Q8—614no—
887C4⋊Q8C22×D6111yescharacteristic
888#127—612no—
889#127—614no—
890#127—618no—
891#127—614no—
892#127C22×D6111yescharacteristic
893#126—614no—
894#126—614no—
895#126—618no—
896#126—618no—
897#126—618no—
898#126—614no—
899#126—618no—
900#126—614no—
901#126—618no—
902#126—618no—
903#126—618no—
904#126—618no—
905#126—618no—
906#126—618no—
907#126—618no—
908#126—618no—
909#126C22×D6118yes—
910#125—614no—
911#125—614no—
912#125—614no—
913#125—612no—
914#125—612no—
915#125—618no—
916#125—618no—
917#125—618no—
918#125—614no—
919#125—618no—
920#125—618no—
921#125—618no—
922#125—612no—
923#125—618no—
924#125C22×D6114yes—
925#124—612no—
926#124—614no—
927#124—614no—
928#124—612no—
929#124—618no—
930#124—614no—
931#124—618no—
932#124—614no—
933#124—614no—
934#124—614no—
935#124—618no—
936#124—618no—
937#124—618no—
938#124—618no—
939#124—618no—
940#124—618no—
941#124C22×D6112yes—
942#124C22×D6114yes—
943#123—614no—
944#123—614no—
945#123—618no—
946#123—618no—
947#123—618no—
948#123—618no—
949#123—618no—
950#123—614no—
951#123—614no—
952#123—618no—
953#123—618no—
954#123—614no—
955#123—614no—
956#123—614no—
957#123—618no—
958#123—618no—
959#123—618no—
960#123—618no—
961#123—618no—
962#123—618no—
963#123—618no—
964#123—618no—
965#123C22×D6114yes—
966#123C22×D6114yes—
967#123C22×D6118yes—
968C22⋊Q8—612no—
969C22⋊Q8—612no—
970C22⋊Q8—614no—
971C22⋊Q8—614no—
972C22⋊Q8—618no—
973C22⋊Q8—618no—
974C22⋊Q8—618no—
975C22⋊Q8—614no—
976C22⋊Q8—614no—
977C22⋊Q8—618no—
978C22⋊Q8—614no—
979C22⋊Q8—612no—
980C22⋊Q8—614no—
981C22⋊Q8—612no—
982C22⋊Q8—614no—
983C22⋊Q8—618no—
984C22⋊Q8—614no—
985C22⋊Q8—618no—
986C22⋊Q8—618no—
987C22⋊Q8—614no—
988C22⋊Q8—614no—
989C22⋊Q8—618no—
990C22⋊Q8—618no—
991C22⋊Q8—618no—
992C22⋊Q8—618no—
993C22⋊Q8C22×D6118yes—
994C22⋊Q8C22×D6114yes—
995#121—612no—
996#121—614no—
997#121—614no—
998#121—612no—
999#121—614no—
1000#121—614no—
1001#121—618no—
1002#121—614no—
1003#121—618no—
1004#121—618no—
1005#121—618no—
1006#121—614no—
1007#121—618no—
1008#121—618no—
1009#121—618no—
1010#121—618no—
1011#121—618no—
1012#121—618no—
1013#121—612no—
1014#121—612no—
1015#121—614no—
1016#121—618no—
1017#121—614no—
1018#121—614no—
1019#121—618no—
1020#121—618no—
1021#121—618no—
1022#121—618no—
1023#121C22×D6114yes—
1024#121C22×D6118yes—
1025#121C22×D6114yes—
1026#120—618no—
1027#120—618no—
1028#120—618no—
1029#120—614no—
1030#120—614no—
1031#120—614no—
1032#120C22×D6114yes—
1033#120C22×D6114yes—
1034C4×Q8—614no—
1035C4×Q8—614no—
1036C4×Q8—614no—
1037C4×Q8—618no—
1038C4×Q8—614no—
1039C4×Q8—614no—
1040C4×Q8—618no—
1041C4×Q8—614no—
1042C4×Q8—618no—
1043C4×Q8—612no—
1044C4×Q8—614no—
1045C4×Q8—614no—
1046C4×Q8—612no—
1047C4×Q8—614no—
1048C4×Q8—614no—
1049C4×Q8—614no—
1050C4×Q8C22×D6112yes—
1051C4×Q8C22×D6112yes—
1052C4×D4—618no—
1053C4×D4—614no—
1054C4×D4—614no—
1055C4×D4—614no—
1056C4×D4—614no—
1057C4×D4—614no—
1058C4×D4—618no—
1059C4×D4—618no—
1060C4×D4—618no—
1061C4×D4—614no—
1062C4×D4—614no—
1063C4×D4—614no—
1064C4×D4—614no—
1065C4×D4—614no—
1066C4×D4—614no—
1067C4×D4—614no—
1068C4×D4—614no—
1069C4×D4—618no—
1070C4×D4—618no—
1071C4×D4—618no—
1072C4×D4—618no—
1073C4×D4—618no—
1074C4×D4—618no—
1075C4×D4—612no—
1076C4×D4—614no—
1077C4×D4—614no—
1078C4×D4—614no—
1079C4×D4—614no—
1080C4×D4—612no—
1081C4×D4—614no—
1082C4×D4C22×D6112yes—
1083C4×D4C22×D6114yes—
1084C4×D4C22×D6118yes—
1085C4×D4C22×D6114yes—
1086C4×D4C22×D6114yes—
1087C4×D4C22×D6118yes—
1088C4×D4C22×D6114yes—
1089C4×D4C22×D6114yes—
1090C4×D4C22×D6112yes—
1091#117—614no—
1092#117—618no—
1093#117—618no—
1094#117—618no—
1095#117—614no—
1096#117—612no—
1097#117—612no—
1098#117—614no—
1099#117—614no—
1100#117—614no—
1101#117—614no—
1102#117—618no—
1103#117—618no—
1104#117—614no—
1105#117—614no—
1106#117—614no—
1107#117—614no—
1108#117—614no—
1109#117—618no—
1110#117C22×D6114yes—
1111#117C22×D6112yes—
1112#117C22×D6114yes—
1113C2×C4⋊C4—618no—
1114C2×C4⋊C4—614no—
1115C2×C4⋊C4—618no—
1116C2×C4⋊C4C22×D6114yes—
1117C2×C22⋊C4—618no—
1118C2×C22⋊C4C22×D6118yes—
1119C2×C42—614no—
1120C2×C42—614no—
1121C2×C42—611no—
1122C2×C42—612no—
1123C2×C42—614no—
1124C2×C42—618no—
1125C2×C42—612no—
1126C2×C42—612no—
1127C2×C42—612no—
1128C2×C42—612no—
1129C2×C42C22×D6114yes—
1130C2×C42C22×D6111yescharacteristic
1131C24—611no—
1132C24C23×D6114yes—
1133#41—44no—
1134#41—44no—
1135#41—2448no—
1136#41—2448no—
1137#41—2448no—
1138#41—2444no—
1139#41—2448no—
1140#41—2448no—
1141#41—2448no—
1142C2×Q8—614no—
1143C2×Q8—612no—
1144C2×Q8—618no—
1145C2×Q8—614no—
1146C2×Q8—614no—
1147C2×Q8—614no—
1148C2×Q8—2448no—
1149C2×Q8C23×D6112yes—
1150C2×Q8C23×D6112yes—
1151C2×D4—48no—
1152C2×D4—614no—
1153C2×D4—614no—
1154C2×D4—618no—
1155C2×D4—614no—
1156C2×D4—618no—
1157C2×D4—614no—
1158C2×D4—614no—
1159C2×D4—618no—
1160C2×D4—618no—
1161C2×D4—612no—
1162C2×D4—614no—
1163C2×D4—614no—
1164C2×D4—614no—
1165C2×D4C23×D6114yes—
1166C2×D4C23×D6112yes—
1167C2×D4C23×D6114yes—
1168C2×D4C23×D6112yes—
1169C2×D4C23×D6114yes—
1170C2×D4C23×D6118yes—
1171C22×C4—48no—
1172C22×C4—612no—
1173C22×C4—611no—
1174C22×C4—618no—
1175C22×C4—618no—
1176C22×C4—612no—
1177C22×C4—612no—
1178C22×C4—614no—
1179C22×C4—614no—
1180C22×C4—612no—
1181C22×C4—612no—
1182C22×C4—612no—
1183C22×C4—612no—
1184C22×C4—614no—
1185C22×C4—618no—
1186C22×C4—618no—
1187C22×C4—2442no—
1188C22×C4—2444no—
1189C22×C4C23×D6112yes—
1190C22×C4C23×D6114yes—
1191C22×C4C23×D6114yes—
1192C22×C4C23×D6111yescharacteristic
1193C22×C4C23×D6114yes—
1194C22×C4C23×D6114yes—
1195C22×C4C23×D6118yes—
1196C22×C4C23×D6114yes—
1197C4⋊C4—614no—
1198C4⋊C4—614no—
1199C4⋊C4—618no—
1200C4⋊C4—618no—
1201C4⋊C4—618no—
1202C4⋊C4—614no—
1203C4⋊C4—618no—
1204C4⋊C4—618no—
1205C4⋊C4—618no—
1206C4⋊C4—614no—
1207C4⋊C4—614no—
1208C4⋊C4—614no—
1209C4⋊C4—618no—
1210C4⋊C4—614no—
1211C4⋊C4—614no—
1212C4⋊C4—618no—
1213C4⋊C4—614no—
1214C4⋊C4—618no—
1215C4⋊C4—614no—
1216C4⋊C4—614no—
1217C4⋊C4—614no—
1218C4⋊C4—614no—
1219C4⋊C4—612no—
1220C4⋊C4—612no—
1221C4⋊C4—614no—
1222C4⋊C4—614no—
1223C4⋊C4—618no—
1224C4⋊C4—614no—
1225C4⋊C4C23×D6112yes—
1226C4⋊C4C23×D6114yes—
1227C4⋊C4C23×D6112yes—
1228C4⋊C4C23×D6114yes—
1229C4⋊C4C23×D6118yes—
1230C4⋊C4C23×D6118yes—
1231C4⋊C4C23×D6114yes—
1232C22⋊C4—614no—
1233C22⋊C4—614no—
1234C22⋊C4—618no—
1235C22⋊C4—618no—
1236C22⋊C4—614no—
1237C22⋊C4—614no—
1238C22⋊C4—618no—
1239C22⋊C4—614no—
1240C22⋊C4—618no—
1241C22⋊C4—618no—
1242C22⋊C4—614no—
1243C22⋊C4—618no—
1244C22⋊C4—614no—
1245C22⋊C4—614no—
1246C22⋊C4—614no—
1247C22⋊C4—614no—
1248C22⋊C4—614no—
1249C22⋊C4—618no—
1250C22⋊C4—614no—
1251C22⋊C4—614no—
1252C22⋊C4—614no—
1253C22⋊C4—618no—
1254C22⋊C4—618no—
1255C22⋊C4—614no—
1256C22⋊C4—614no—
1257C22⋊C4C23×D6114yes—
1258C22⋊C4C23×D6118yes—
1259C22⋊C4C23×D6118yes—
1260C22⋊C4C23×D6118yes—
1261C22⋊C4C23×D6114yes—
1262C22⋊C4C23×D6114yes—
1263C22⋊C4C23×D6114yes—
1264C22⋊C4C23×D6114yes—
1265C42—612no—
1266C42—612no—
1267C42—612no—
1268C42—612no—
1269C42—612no—
1270C42—614no—
1271C42—618no—
1272C42—614no—
1273C42—614no—
1274C42—614no—
1275C42—618no—
1276C42—618no—
1277C42—611no—
1278C42—614no—
1279C42—614no—
1280C42—611no—
1281C42C23×D6111yescharacteristic
1282C42C23×D6111yescharacteristic
1283C42C23×D6114yes—
1284C42C23×D6114yes—
1285C42C23×D6112yes—
1286C42C23×D6114yes—
1287C23—44no—
1288C23—48no—
1289C23—612no—
1290C23—614no—
1291C23—2441no—
1292C23—2442no—
1293C23C24×D6114yes—
1294C23C24×D6111yescharacteristic
1295C23C24×D6114yes—
1296Q8—24no—
1297Q8—42no—
1298Q8—1228no—
1299Q8—1224no—
1300Q8—2448no—
1301Q8—2444no—
1302Q8—2444no—
1303Q8—2444no—
1304D4—24no—
1305D4—28no—
1306D4—48no—
1307D4—44no—
1308D4—42no—
1309D4—44no—
1310D4—1224no—
1311D4—2444no—
1312D4—2444no—
1313D4—2444no—
1314D4—2444no—
1315D4—2444no—
1316D4—2448no—
1317D4—2444no—
1318D4—2444no—
1319D4—2444no—
1320D4—2448no—
1321D4—2448no—
1322D4—2448no—
1323C2×C4—28no—
1324C2×C4—28no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—28no—
1328C2×C4—44no—
1329C2×C4—48no—
1330C2×C4—44no—
1331C2×C4—612no—
1332C2×C4—614no—
1333C2×C4—614no—
1334C2×C4—612no—
1335C2×C4—612no—
1336C2×C4—618no—
1337C2×C4—614no—
1338C2×C4—1224no—
1339C2×C4—1228no—
1340C2×C4—1224no—
1341C2×C4—1224no—
1342C2×C4—1228no—
1343C2×C4—2442no—
1344C2×C4—2442no—
1345C2×C4—2442no—
1346C2×C4—2448no—
1347C2×C4—2444no—
1348C2×C4—2448no—
1349C2×C4—2441no—
1350C2×C4—2442no—
1351C2×C4—2448no—
1352C2×C4—2448no—
1353C2×C4C24×D6112yes—
1354C2×C4C24×D6114yes—
1355C2×C4C24×D6114yes—
1356C2×C4C24×D6111yescharacteristic
1357C2×C4C24×D6114yes—
1358C2×C4C24×D6114yes—
1359C2×C4C24×D6112yes—
1360C2×C4C24×D6111yescharacteristic
1361C22—24no—
1362C22—24no—
1363C22—21no—
1364C22—22no—
1365C22—24no—
1366C22—24no—
1367C22—28no—
1368C22—88no—
1369C22—1222no—
1370C22—1224no—
1371C22—1224no—
1372C22—1222no—
1373C22—1222no—
1374C22—1224no—
1375C22—2444no—
1376C22C25×D6111yescharacteristic
1377C4—24no—
1378C4—24no—
1379C4—21no—
1380C4—22no—
1381C4—24no—
1382C4—24no—
1383C4—1222no—
1384C4—1224no—
1385C4—1222no—
1386C4—1222no—
1387C4—1224no—
1388C4—1224no—
1389C4—1228no—
1390C4#1684059712yes—
1391C4#1684059814yes—
1392C2—44no—
1393C2—44no—
1394C2—41no—
1395C2—2442no—
1396C2—2444no—
1397C2C2×#1684059711yescharacteristic
1398C2C2×#1684059812yes—
subgroupG/H
centerC2×C4C24×D61
commutator, socle, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC61×#3481C2
hypercenter#3481D61
hypocenterC61#62762
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #3481

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21460481C2semidirect
2. #21460465C2semidirect
3. #21460401C2semidirect
4. #21460310C2semidirect
5. #21460278C2semidirect
6. #21460209C2semidirect
7. #21460187C2semidirect
8. #21460083C2semidirect
9. #21460076C2semidirect
10. #21459957C2semidirect
11. #21459443C2semidirect
12. #21459441C2semidirect
13. #21459410C2semidirect
14. #21459377C2semidirect
15. #21459244C2semidirect
16. #21459241C2semidirect
17. #21459207C2semidirect
18. #21459114C2semidirect
19. #21459112C2semidirect
20. C61×#3481C2semidirect
21. #16840515C22semidirect
22. #16840513C22semidirect
23. #16840509C22semidirect
24. #16840508C22semidirect
25. #16840507C22semidirect
26. #16840505C22semidirect
27. #16840502C22semidirect
29. #16840501C22semidirect
30. #16840500C22semidirect
31. #16840496C22semidirect
32. #16840494C22semidirect
33. #16840492C22semidirect
34. #16840491C22semidirect
35. #16840489C22semidirect
36. #16840483C22semidirect
37. #16840482C22semidirect
38. #16840482C22semidirect
39. #16840482C22semidirect
40. #16840479C22semidirect
41. #16840478C22semidirect
43. #16840476C22semidirect
44. #16840474C22semidirect
45. #16840469C22semidirect
46. #16840465C22semidirect
47. #16840463C22semidirect
48. #16840459C22semidirect
49. #16840458C22semidirect
50. #16840457C22semidirect
51. #16840452C22semidirect
52. #16840451C22semidirect
53. #16840451C22semidirect
54. #16840447C22semidirect
55. #16840447C22semidirect
56. #16840438C22semidirect
57. #16840438C22semidirect
58. #16840432C22semidirect
60. #16840430C22semidirect
61. Q8×D244C22semidirect
62. #16840422C22semidirect
63. #16840420C22semidirect
65. #16840417C22semidirect
66. #16840417C22semidirect
67. #16840416C22semidirect
69. #16840406C22semidirect
70. #16840393C22semidirect
71. #16840392C22semidirect
72. #16840385C22semidirect
73. #16840381C22semidirect
74. #16840380C22semidirect
75. #16840379C22semidirect
76. #16840379C22semidirect
78. #16840377C22semidirect
79. #16840377C22semidirect
80. #16840375C22semidirect
81. #16840372C22semidirect
82. #16840372C22semidirect
83. #16840369C22semidirect
84. #16840365C22semidirect
85. #16840363C22semidirect
86. #16840363C22semidirect
87. #16840363C22semidirect
88. #16840356C22semidirect
89. #16840356C22semidirect
90. #16840355C22semidirect
91. #16840353C22semidirect
92. #16840350C22semidirect
93. #16840350C22semidirect
94. #16840347C22semidirect
95. #16840347C22semidirect
96. #16840343C22semidirect
98. #16840335C22semidirect
99. #16840332C22semidirect
101. #16840329C22semidirect
102. #16840319C22semidirect
103. #16840319C22semidirect
104. #16840317C22semidirect
105. #16840316C22semidirect
106. #16840316C22semidirect
107. #16840315C22semidirect
108. #16840315C22semidirect
112. #16840309C22semidirect
113. #16840309C22semidirect
115. #16840308C22semidirect
116. #16840299C22semidirect
117. #16840299C22semidirect
120. #16840294C22semidirect
121. #16840294C22semidirect
122. #16840294C22semidirect
123. #16840294C22semidirect
124. #16840293C22semidirect
125. #16840292C22semidirect
126. #16840292C22semidirect
127. #16840292C22semidirect
128. #16840292C22semidirect
129. #16840291C22semidirect
130. #16840290C22semidirect
131. #16840290C22semidirect
132. #16840290C22semidirect
133. #16840274C22semidirect
134. #16840273C22semidirect
135. #16840273C22semidirect
136. #16840272C22semidirect
137. #16840271C22semidirect
138. #16840271C22semidirect
140. #16840269C22semidirect
141. #41×Dic61C22semidirect
142. C4×#11758222C22semidirect
143. C4×#11758222C22semidirect
144. C4×#11758222C22semidirect
145. C4×#11758222C22semidirect
146. #16840230C22semidirect
147. C4×#11758224C22semidirect
148. C4×#11758224C22semidirect
149. C4×Q8×D61C22semidirect
150. C2×#14519736C22semidirect
151. C2×C42×D61C22semidirect
152. C61×#559C22semidirect
153. C61×#554C22semidirect
155. C61×#551C22semidirect
157. D42×C61C22semidirect
159. C61×#529C22semidirect
162. C2×C4×D4×C61C22semidirect
705. #3481D61semidirect
732. #559C2×D61semidirect
746. #554C2×D61semidirect
760. #551C2×D61semidirect
774. D42C2×D61semidirect
839. #529C2×D61semidirect
859. C2×C4×D4C2×D61semidirect
862. C61#62762semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214604812
#214604652
#214604012
#214603102
#214602782
#214602092
#214601872
#214600832
#214600762
#214599572
#214594432
#214594412
#214594102
#214593772
#214592442
#214592412
#214592072
#214591142
#214591122
C61×#34812
#6276261