Finite Group Databasebeta

← D61×#3548 #30587802

Subgroups — D61×#3548 #30587802

Order 15616.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460219C211yesmaximal, characteristic, complemented
2#21460218C214yesmaximal, complemented
3#21460217C212yesmaximal, complemented
4#21460216C214yesmaximal, complemented
5#21460215C214yesmaximal, complemented
6#21460214C218yesmaximal, complemented
7#21460213C214yesmaximal, complemented
8#21460212C214yesmaximal, complemented
9#562×D61C214yesmaximal, complemented
10#554×D61C214yesmaximal, complemented
11#550×D61C214yesmaximal, complemented
12#547×D61C214yesmaximal, complemented
13#540×D61C214yesmaximal, complemented
14#537×D61C218yesmaximal, complemented
15#533×D61C211yesmaximal, characteristic, complemented
16#532×D61C212yesmaximal, complemented
17C61×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D61C2218yes—
19C2×#41×D61C2214yes—
20#16840510C2214yescomplemented
21#16840509C22116yescomplemented
22#16840508C22116yescomplemented
23#16840507C22116yescomplemented
24#16840506C2218yescomplemented
25#16840473C2214yescomplemented
26#16840472C2214yescomplemented
27#16840471C2218yescomplemented
28#16840470C2218yescomplemented
29#16840469C2214yescomplemented
30#16840468C2218yescomplemented
31#16840467C2218yescomplemented
32#16840466C22116yescomplemented
33#16840434C2214yescomplemented
34#16840433C2218yescomplemented
35#16840433C2214yescomplemented
36#16840432C2218yescomplemented
37#16840432C2214yescomplemented
38#16840431C2218yescomplemented
39#16840430C22116yescomplemented
40#16840430C2218yescomplemented
41#16840417C2214yescomplemented
42#16840416C2214yescomplemented
43#16840415C2214yescomplemented
44#16840414C2218yescomplemented
45#16840413C2218yescomplemented
46#16840412C2218yescomplemented
47#16840411C2218yescomplemented
48#16840410C22116yescomplemented
49#16840368C2214yescomplemented
50#16840367C2214yescomplemented
51#16840366C2214yescomplemented
52#16840365C2218yescomplemented
53#16840364C22116yescomplemented
54#16840363C2218yescomplemented
55#16840362C22116yescomplemented
56#16840343C2218yescomplemented
57#16840342C2218yescomplemented
58#16840342C22116yescomplemented
59#16840342C2218yescomplemented
60#16840341C2218yescomplemented
61#16840341C22116yescomplemented
62#16840341C2218yescomplemented
63#16840340C2218yescomplemented
64#16840340C2218yescomplemented
65#16840339C22116yescomplemented
66#16840339C22116yescomplemented
67#16840319C2211yescharacteristic, complemented
68#16840318C2212yescomplemented
69#16840317C2212yescomplemented
70#16840316C2214yescomplemented
71#16840315C2212yescomplemented
72#16840314C2214yescomplemented
73#16840313C2212yescomplemented
74#16840312C2212yescomplemented
75#16840311C2214yescomplemented
76#16840310C2212yescomplemented
77#16840309C2214yescomplemented
78#16840309C2214yescomplemented
79#16840308C2214yescomplemented
80#16840307C2214yescomplemented
81#16840307C2214yescomplemented
82C4⋊Q8×D61C2212yes—
83C4⋊Q8×D61C2212yes—
84#127×D61C2212yes—
85#127×D61C2214yes—
86#125×D61C2214yes—
87#125×D61C2212yes—
88#124×D61C2214yes—
89#123×D61C22116yes—
90C22⋊Q8×D61C2218yes—
91C22⋊Q8×D61C22116yes—
92C22⋊Q8×D61C2214yes—
93#121×D61C2218yes—
94#121×D61C22116yes—
95#121×D61C2214yes—
96#121×D61C2214yes—
97#121×D61C22116yes—
98C4×Q8×D61C2214yes—
99C4×D4×D61C2214yes—
100C4×D4×D61C2214yes—
101C4×D4×D61C2218yes—
102#117×D61C2212yes—
103C2×C4⋊C4×D61C2218yes—
104C2×C42×D61C2211yescharacteristic
105C61×#562C2214yescomplemented
106C61×#554C2214yescomplemented
107C61×#550C2214yescomplemented
108C61×#547C2214yescomplemented
109C61×#540C2214yescomplemented
110C61×#537C2218yescomplemented
111C61×#533C2211yescharacteristic, complemented
112C61×#532C2212yescomplemented
113C2×#11758226C2314yes—
114C2×#11758226C2318yes—
115C2×#11758222C2314yes—
116C2×#11758222C2318yes—
117C2×#11758222C2318yes—
118C2×#11758222C23116yes—
119C2×#11758224C2318yes—
120C2×#11758224C2314yes—
121C2×#11758224C23116yes—
122C2×#11758224C2318yes—
123#41×D61—416no—
124#41×D61—432no—
125C2×Q8×D61C2314yes—
126C2×Q8×D61C2314yes—
127C2×D4×D61C2314yes—
128C2×D4×D61C2314yes—
129C2×D4×D61C2318yes—
130C2×D4×D61C23116yes—
131C2×D4×D61C2314yes—
132C22×C4×D61C2311yescharacteristic
133C22×C4×D61C2312yes—
134C22×C4×D61C2318yes—
135C22×C4×D61C23116yes—
136#14519777C2312yes—
137#14519777C2312yes—
138#14519776C2314yes—
139#14519776C2314yes—
140#14519776C2314yes—
141#14519776C2314yes—
142#14519775C2314yes—
143#14519775C2314yes—
144#14519774C2312yes—
145#14519774C2314yes—
146#14519773C2314yes—
147#14519773C2314yes—
148#14519773C2314yes—
149#14519773C23116yes—
150#14519773C2318yes—
151#14519769C2314yes—
152#14519769C2312yes—
153#14519768C2318yes—
154#14519768C2314yes—
155#14519767C23116yes—
156#14519767C2318yes—
157#14519766C2314yes—
158#14519765C2314yes—
159#14519764C2314yes—
160#14519763C2318yes—
161#14519763C2318yes—
162#14519762C23116yes—
163#14519762C23116yes—
164#14519761C23116yes—
165#14519760C23116yes—
166#14519759C23116yes—
167#14519759C23116yes—
168#14519758C23116yes—
169#14519757C2318yes—
170#14519757C23116yes—
171#14519757C2314yes—
172#14519756C2318yes—
173#14519756C23116yes—
174#14519756C2314yes—
175#14519755C23116yes—
176#14519755C23116yes—
177#14519755C23116yes—
178#14519755C2318yes—
179#14519754C23116yes—
180#14519754C23116yes—
181#14519754C23116yes—
182#14519754C2318yes—
183#14519753C23116yes—
184#14519753C2318yes—
185#14519753C2314yes—
186#14519752C23116yes—
187#14519752C2314yes—
188#14519752C2314yes—
189#14519752C23116yes—
190#14519752C2318yes—
191#14519751C23116yes—
192#14519751C2314yes—
193#14519751C2314yes—
194#14519751C23116yes—
195#14519751C2318yes—
196#14519750C23116yes—
197#14519750C23116yes—
198#14519750C2318yes—
199#14519750C2318yes—
200#14519750C23116yes—
201#14519750C23116yes—
202#14519750C23116yes—
203#14519749C23116yes—
204#14519749C23116yes—
205#14519749C2318yes—
206#14519749C2318yes—
207#14519749C23116yes—
208#14519749C23116yes—
209#14519749C23116yes—
210#14519748C23116yes—
211#14519748C2314yes—
212#14519748C2314yes—
213#14519748C23116yes—
214#14519748C2318yes—
215Q8×Dic61C2314yes—
216C4×Dic122C2318yes—
217C4×Dic122C2314yes—
218#14519742C2318yes—
219#14519742C2314yes—
220C4×D244C2318yes—
221C4×D244C2314yes—
222C4×D244C2314yes—
223D4×Dic61C2318yes—
224D4×Dic61C2314yes—
225D4×Dic61C2314yes—
226#14519739C2314yes—
227#14519739C2318yes—
228#14519739C2314yes—
229C4×C22⋊D61C23116yes—
230C4×C22⋊D61C2318yes—
231C4×C22⋊D61C2318yes—
232#14519737C2318yes—
233#14519737C23116yes—
234#14519737C2318yes—
235#14519736C2312yes—
236#14519735C2314yes—
237#14519734C2314yes—
238#14519733C2314yes—
239C2×C4⋊Dic61C2318yes—
240C2×#11758196C23116yes—
241C4⋊C4×D61C23116yes—
242C4⋊C4×D61C2314yes—
243C4⋊C4×D61C2314yes—
244C4⋊C4×D61C2318yes—
245C4⋊C4×D61C2318yes—
246C4⋊C4×D61C23116yes—
247C4⋊C4×D61C2314yes—
248C4⋊C4×D61C2314yes—
249C4⋊C4×D61C2318yes—
250C22⋊C4×D61C2314yes—
251C22⋊C4×D61C23116yes—
252C22⋊C4×D61C2318yes—
253C22⋊C4×D61C2318yes—
254C2×C4×Dic61C2311yescharacteristic
255C2×C4×Dic61C2312yes—
256C42×D61C2311yescharacteristic
257C42×D61C2312yes—
258C42×D61C2311yescharacteristic
259C42×D61C2311yescharacteristic
260C42×D61C2312yes—
261C42×D61C2311yescharacteristic
262C42×D61C2314yes—
263C2×#41×C61C2314yes—
264C2×#41×C61C2318yes—
265C4⋊Q8×C61C2312yes—
266C4⋊Q8×C61C2312yes—
267#127×C61C2312yes—
268#127×C61C2314yes—
269#125×C61C2312yes—
270#125×C61C2314yes—
271#124×C61C2314yes—
272#123×C61C23116yes—
273C22⋊Q8×C61C2314yes—
274C22⋊Q8×C61C2318yes—
275C22⋊Q8×C61C23116yes—
276#121×C61C2314yes—
277#121×C61C2314yes—
278#121×C61C23116yes—
279#121×C61C2318yes—
280#121×C61C23116yes—
281C4×Q8×C61C2314yes—
282C4×D4×C61C2314yes—
283C4×D4×C61C2314yes—
284C4×D4×C61C2318yes—
285#117×C61C2312yes—
286C2×C4⋊C4×C61C2318yes—
287C2×C42×C61C2311yescharacteristic
288C23×D61C2411yescharacteristic
289C23×D61C2418yes—
290#41×C61—48no—
291#41×C61—416no—
292C2×Q8×C61C2414yes—
293C2×Q8×C61C2414yes—
294C2×D4×C61C2414yes—
295C2×D4×C61C2414yes—
296C2×D4×C61C2418yes—
297C2×D4×C61C24116yes—
298C2×D4×C61C2414yes—
299C22×C4×C61C2412yes—
300C22×C4×C61C2418yes—
301C22×C4×C61C2411yescharacteristic
302C22×C4×C61C24116yes—
303C2×C22⋊D61C2418yes—
304C2×C22⋊D61C2418yes—
305C2×C22⋊D61C2418yes—
306C2×C22⋊D61C2418yes—
307C2×C22⋊D61C24116yes—
308C2×C22⋊D61C2418yes—
309C2×C22⋊D61C24116yes—
310C22×Dic61C2412yes—
311C22×Dic61C2418yes—
312C22×Dic61C2411yescharacteristic
313C22×Dic61C24116yes—
314#11758226—48no—
315#11758226—416no—
316Q8×D61—216no—
317Q8×D61—48no—
318#11758224—416no—
319#11758224—432no—
320#11758224—416no—
321#11758224—48no—
322D4×D61—216no—
323D4×D61—216no—
324D4×D61—416no—
325D4×D61—48no—
326D4×D61—432no—
327#11758222—432no—
328#11758222—416no—
329#11758222—416no—
330#11758222—48no—
331C2×D244C2414yes—
332C2×D244C2414yes—
333C2×D244C2418yes—
334C2×D244C2414yes—
335C2×D244C24116yes—
336C2×C4×D61—232no—
337C2×C4×D61—28no—
338C2×C4×D61—24no—
339C2×C4×D61—432no—
340C2×C4×D61C2418yes—
341C2×C4×D61C2418yes—
342C2×C4×D61C2412yes—
343C2×C4×D61C2412yes—
344C2×C4×D61C2418yes—
345C2×C4×D61C2418yes—
346C2×C4×D61C2412yes—
347C2×C4×D61C2411yescharacteristic
348C2×C4×D61C2411yescharacteristic
349C2×C4×D61C2411yescharacteristic
350C2×C4×D61C24116yes—
351C2×C4×D61C24116yes—
352C2×C4×D61C2412yes—
353C2×C4×D61C2411yescharacteristic
354C2×Dic122C2418yes—
355C2×Dic122C2414yes—
356C2×Dic122C2414yes—
357C2×Dic122C2418yes—
358C4⋊C4×C61C2414yes—
359C4⋊C4×C61C2414yes—
360C4⋊C4×C61C24116yes—
361C4⋊C4×C61C2414yes—
362C4⋊C4×C61C2414yes—
363C4⋊C4×C61C2418yes—
364C22⋊C4×C61C2414yes—
365C22⋊C4×C61C24116yes—
366C22⋊C4×C61C2418yes—
367C22⋊C4×C61C2418yes—
368C42×C61C2411yescharacteristic
369C42×C61C2412yes—
370C42×C61C2411yescharacteristic
371C42×C61C2414yes—
372C22⋊Dic61C2414yes—
373C22⋊Dic61C24116yes—
374C22⋊Dic61C2418yes—
375C22⋊Dic61C2418yes—
376#11758198C2418yes—
377#11758198C2418yes—
378#11758198C24116yes—
379#11758198C2418yes—
380#11758198C24116yes—
381#11758198C2418yes—
382#11758198C2418yes—
383C4⋊Dic61C2414yes—
384C4⋊Dic61C2414yes—
385C4⋊Dic61C24116yes—
386C4⋊Dic61C2414yes—
387C4⋊Dic61C2414yes—
388C4⋊Dic61C2418yes—
389#11758196C2418yes—
390#11758196C2418yes—
391#11758196C24116yes—
392#11758196C24116yes—
393#11758196C2418yes—
394#11758196C2418yes—
395#11758196C2418yes—
396#11758196C2418yes—
397C4×Dic61C2411yescharacteristic
398C4×Dic61C2412yes—
399C4×Dic61C2412yes—
400C4×Dic61C2412yes—
401C4×Dic61C2412yes—
402C4×Dic61C2411yescharacteristic
403C4×Dic61C2412yes—
404C4×Dic61C2418yes—
405C4×Dic61C2414yes—
406C23×C61C2511yescharacteristic
407C23×C61C2518yes—
408C22×D61—24no—
409C22×D61—216no—
410C22×D61—216no—
411C22×D61—22no—
412C22×D61—216no—
413C22×D61C2511yescharacteristic
414C22×D61C2518yes—
415C22×D61C2511yescharacteristic
416Q8×C61—28no—
417Q8×C61—44no—
418D4×C61—28no—
419D4×C61—28no—
420D4×C61—416no—
421D4×C61—44no—
422D4×C61—48no—
423C2×C4×C61—24no—
424C2×C4×C61—216no—
425C2×C4×C61—22no—
426C2×C4×C61—416no—
427C2×C4×C61C2512yes—
428C2×C4×C61C2511yescharacteristic
429C2×C4×C61C2518yes—
430C2×C4×C61C2518yes—
431C2×C4×C61C2512yes—
432C2×C4×C61C2511yescharacteristic
433C22⋊D61—216no—
434C22⋊D61—216no—
435C22⋊D61—416no—
436C22⋊D61—416no—
437C22⋊D61—48no—
438C22⋊D61—48no—
439C22⋊D61—48no—
440C2×Dic61—24no—
441C2×Dic61—216no—
442C2×Dic61—22no—
443C2×Dic61—416no—
444C2×Dic61C2511yescharacteristic
445C2×Dic61C2512yes—
446C2×Dic61C2518yes—
447C2×Dic61C2518yes—
448C2×Dic61C2512yes—
449C2×Dic61C2511yescharacteristic
450D244—28no—
451D244—28no—
452D244—416no—
453D244—44no—
454D244—48no—
455C4×D61—216no—
456C4×D61—24no—
457C4×D61—216no—
458C4×D61—22no—
459C4×D61—24no—
460C4×D61—216no—
461C4×D61—22no—
462C4×D61—216no—
463C4×D61—24no—
464C4×D61—22no—
465C4×D61—416no—
466C4×D61—416no—
467C4×D61H(5,𝔽2)18yes—
468C4×D612−1+414yes—
469Dic122—28no—
470Dic122—216no—
471Dic122—48no—
472Dic122—44no—
473C2×#3548—611nomaximal, Sylow
474C22×C61—22no—
475C22×C61—28no—
476C22×C61—28no—
477C22×C61—21no—
478C22×C61—28no—
479C22×C61C2611yescharacteristic
480C2×D61—22no—
481C2×D61—28no—
482C2×D61—28no—
483C2×D61—21no—
484C2×D61—28no—
485C2×D61—44no—
486C2×D61—432no—
487C2×D61C2×H(5,𝔽2)14yes—
488C2×D61C2×2−1+412yes—
489C4×C61—28no—
490C4×C61—22no—
491C4×C61—28no—
492C4×C61—21no—
493C4×C61C2×H(5,𝔽2)14yes—
494C4×C61C2×2−1+412yes—
495Dic61—28no—
496Dic61—22no—
497Dic61—28no—
498Dic61—21no—
499Dic61C2×H(5,𝔽2)14yes—
500Dic61C2×2−1+412yes—
501#3548—614no—
502#3548—614no—
503#3548—614no—
504#3548—614no—
505#3548—614no—
506#3548—618no—
507#3548—611no—
508#3548—612no—
509#3548D6111yescharacteristic, direct product factor
510C2×#562—614no—
511C2×#554—614no—
512C2×#550—614no—
513C2×#547—614no—
514C2×#540—614no—
515C2×#537—618no—
516C2×#533—611no—
517C2×#532—612no—
518C2×C61—41no—
519C2×C61—48no—
520C2×C61C22×H(5,𝔽2)12yes—
521C2×C61C22×2−1+411yescharacteristic
522D61—41no—
523D61—48no—
524D61#354814yesdirect product factor
525C22×#41—614no—
526C22×#41—618no—
527#562—614no—
528#562—618no—
529#562—6116no—
530#562—6116no—
531#562—6116no—
532#562C2×D6114yescomplemented
533#554—614no—
534#554—618no—
535#554—6116no—
536#554—618no—
537#554—614no—
538#554—614no—
539#554—618no—
540#554—618no—
541#554C2×D6114yescomplemented
542#550—618no—
543#550—618no—
544#550—614no—
545#550—618no—
546#550—6116no—
547#550—614no—
548#550—618no—
549#550—614no—
550#550C2×D6114yescomplemented
551#547—618no—
552#547—614no—
553#547—6116no—
554#547—618no—
555#547—618no—
556#547—614no—
557#547—614no—
558#547—618no—
559#547C2×D6114yescomplemented
560#540—614no—
561#540—614no—
562#540—6116no—
563#540—6116no—
564#540—618no—
565#540—618no—
566#540—614no—
567#540C2×D6114yescomplemented
568#537—618no—
569#537—618no—
570#537—618no—
571#537—6116no—
572#537—618no—
573#537—6116no—
574#537—6116no—
575#537—618no—
576#537—6116no—
577#537—618no—
578#537—618no—
579#537C2×D6118yescomplemented
580#533—612no—
581#533—612no—
582#533—614no—
583#533—614no—
584#533—612no—
585#533—611no—
586#533C2×D6111yescharacteristic, complemented
587#532—614no—
588#532—612no—
589#532—612no—
590#532—614no—
591#532—614no—
592#532—614no—
593#532—614no—
594#532—614no—
595#532—612no—
596#532C2×D6112yescomplemented
597C2×C4⋊Q8—612no—
598C2×C4⋊Q8—612no—
599C2×#127—612no—
600C2×#127—614no—
601C2×#125—612no—
602C2×#125—614no—
603C2×#124—614no—
604C2×#123—6116no—
605C2×C22⋊Q8—614no—
606C2×C22⋊Q8—618no—
607C2×C22⋊Q8—6116no—
608C2×#121—614no—
609C2×#121—614no—
610C2×#121—6116no—
611C2×#121—618no—
612C2×#121—6116no—
613C2×C4×Q8—614no—
614C2×C4×D4—614no—
615C2×C4×D4—614no—
616C2×C4×D4—618no—
617C2×#117—612no—
618C22×C4⋊C4—618no—
619C22×C42—611no—
620C61C2×#354811yescharacteristic, complemented, Sylow
621C2×#41—614no—
622C2×#41—618no—
623C2×#41—618no—
624C2×#41—614no—
625C2×#41—6116no—
626C2×#41—618no—
627C2×#41—618no—
628C2×#41—614no—
629C2×#41—6116no—
630C2×#41—618no—
631C2×#41—24416no—
632C2×#41—24432no—
633C2×#41C22×D6114yes—
634C2×#41C22×D6118yes—
635C22×Q8—614no—
636C22×Q8—614no—
637C22×D4—614no—
638C22×D4—614no—
639C22×D4—618no—
640C22×D4—6116no—
641C22×D4—614no—
642C23×C4—618no—
643C23×C4—611no—
644C23×C4—612no—
645C23×C4—6116no—
646C4⋊Q8—614no—
647C4⋊Q8—614no—
648C4⋊Q8—614no—
649C4⋊Q8—614no—
650C4⋊Q8—614no—
651C4⋊Q8—614no—
652C4⋊Q8—612no—
653C4⋊Q8—612no—
654C4⋊Q8C22×D6112yes—
655C4⋊Q8C22×D6112yes—
656#127—614no—
657#127—614no—
658#127—614no—
659#127—6116no—
660#127—618no—
661#127—612no—
662#127—614no—
663#127C22×D6112yes—
664#127C22×D6114yes—
665#125—618no—
666#125—614no—
667#125—6116no—
668#125—618no—
669#125—612no—
670#125—614no—
671#125C22×D6112yes—
672#125C22×D6114yes—
673#124—614no—
674#124—614no—
675#124—618no—
676#124—618no—
677#124—614no—
678#124C22×D6114yes—
679#123—6116no—
680#123—6116no—
681#123—6116no—
682#123—6116no—
683#123—6116no—
684#123—6116no—
685#123—6116no—
686#123C22×D61116yes—
687C22⋊Q8—614no—
688C22⋊Q8—618no—
689C22⋊Q8—6116no—
690C22⋊Q8—614no—
691C22⋊Q8—618no—
692C22⋊Q8—6116no—
693C22⋊Q8—618no—
694C22⋊Q8—614no—
695C22⋊Q8—6116no—
696C22⋊Q8—618no—
697C22⋊Q8—6116no—
698C22⋊Q8—6116no—
699C22⋊Q8—6116no—
700C22⋊Q8—618no—
701C22⋊Q8—6116no—
702C22⋊Q8—6116no—
703C22⋊Q8—6116no—
704C22⋊Q8C22×D6114yes—
705C22⋊Q8C22×D6118yes—
706C22⋊Q8C22×D61116yes—
707#121—614no—
708#121—618no—
709#121—614no—
710#121—618no—
711#121—6116no—
712#121—6116no—
713#121—6116no—
714#121—618no—
715#121—6116no—
716#121—6116no—
717#121—6116no—
718#121—6116no—
719#121—614no—
720#121—614no—
721#121—6116no—
722#121—618no—
723#121—6116no—
724#121—614no—
725#121—614no—
726#121—6116no—
727#121—618no—
728#121—6116no—
729#121—618no—
730#121—618no—
731#121—6116no—
732#121—6116no—
733#121—6116no—
734#121—6116no—
735#121—6116no—
736#121C22×D6114yes—
737#121C22×D6114yes—
738#121C22×D61116yes—
739#121C22×D6118yes—
740#121C22×D61116yes—
741C4×Q8—614no—
742C4×Q8—618no—
743C4×Q8—614no—
744C4×Q8—618no—
745C4×Q8—614no—
746C4×Q8C22×D6114yes—
747C4×D4—614no—
748C4×D4—614no—
749C4×D4—618no—
750C4×D4—618no—
751C4×D4—618no—
752C4×D4—6116no—
753C4×D4—614no—
754C4×D4—614no—
755C4×D4—618no—
756C4×D4—618no—
757C4×D4—618no—
758C4×D4—6116no—
759C4×D4—614no—
760C4×D4—614no—
761C4×D4—618no—
762C4×D4C22×D6114yes—
763C4×D4C22×D6114yes—
764C4×D4C22×D6118yes—
765#117—612no—
766#117—614no—
767#117—614no—
768#117—614no—
769#117C22×D6112yes—
770C2×C4⋊C4—6116no—
771C2×C4⋊C4—618no—
772C2×C4⋊C4—614no—
773C2×C4⋊C4—614no—
774C2×C4⋊C4—6116no—
775C2×C4⋊C4—6116no—
776C2×C4⋊C4—618no—
777C2×C4⋊C4—618no—
778C2×C4⋊C4—614no—
779C2×C4⋊C4—614no—
780C2×C4⋊C4—618no—
781C2×C4⋊C4C22×D6118yes—
782C2×C22⋊C4—614no—
783C2×C22⋊C4—6116no—
784C2×C22⋊C4—618no—
785C2×C22⋊C4—618no—
786C2×C42—612no—
787C2×C42—611no—
788C2×C42—614no—
789C2×C42—611no—
790C2×C42—612no—
791C2×C42—611no—
792C2×C42—611no—
793C2×C42—612no—
794C2×C42—611no—
795C2×C42C22×D6111yescharacteristic
796C24—611no—
797C24—618no—
798#41—48no—
799#41—416no—
800#41—24416no—
801#41—2448no—
802#41—24416no—
803#41—24432no—
804#41—24416no—
805#41—2448no—
806#41—2448no—
807#41—24416no—
808#41—24432no—
809#41—24416no—
810C2×Q8—618no—
811C2×Q8—614no—
812C2×Q8—618no—
813C2×Q8—614no—
814C2×Q8—12216no—
815C2×Q8—2448no—
816C2×Q8C23×D6114yes—
817C2×Q8C23×D6114yes—
818C2×D4—618no—
819C2×D4—618no—
820C2×D4—618no—
821C2×D4—618no—
822C2×D4—6116no—
823C2×D4—6116no—
824C2×D4—618no—
825C2×D4—614no—
826C2×D4—614no—
827C2×D4—618no—
828C2×D4—6116no—
829C2×D4—614no—
830C2×D4—12216no—
831C2×D4—12216no—
832C2×D4—24416no—
833C2×D4—2448no—
834C2×D4—24432no—
835C2×D4C23×D6114yes—
836C2×D4C23×D6114yes—
837C2×D4C23×D6118yes—
838C2×D4C23×D61116yes—
839C2×D4C23×D6114yes—
840C22×C4—611no—
841C22×C4—612no—
842C22×C4—611no—
843C22×C4—612no—
844C22×C4—618no—
845C22×C4—6116no—
846C22×C4—611no—
847C22×C4—612no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—618no—
853C22×C4—618no—
854C22×C4—618no—
855C22×C4—618no—
856C22×C4—6116no—
857C22×C4—6116no—
858C22×C4—1224no—
859C22×C4—12232no—
860C22×C4—1228no—
861C22×C4—24432no—
862C22×C4C23×D6111yescharacteristic
863C22×C4C23×D6112yes—
864C22×C4C23×D6118yes—
865C22×C4C23×D61116yes—
866C4⋊C4—618no—
867C4⋊C4—618no—
868C4⋊C4—614no—
869C4⋊C4—614no—
870C4⋊C4—6116no—
871C4⋊C4—6116no—
872C4⋊C4—6116no—
873C4⋊C4—618no—
874C4⋊C4—618no—
875C4⋊C4—618no—
876C4⋊C4—618no—
877C4⋊C4—614no—
878C4⋊C4—614no—
879C4⋊C4—618no—
880C4⋊C4C23×D6114yes—
881C4⋊C4C23×D6114yes—
882C4⋊C4C23×D61116yes—
883C4⋊C4C23×D6114yes—
884C4⋊C4C23×D6114yes—
885C4⋊C4C23×D6118yes—
886C22⋊C4—614no—
887C22⋊C4—6116no—
888C22⋊C4—618no—
889C22⋊C4—618no—
890C22⋊C4—618no—
891C22⋊C4—6116no—
892C22⋊C4—6116no—
893C22⋊C4—618no—
894C22⋊C4—618no—
895C22⋊C4—618no—
896C22⋊C4—618no—
897C22⋊C4C23×D6114yes—
898C22⋊C4C23×D61116yes—
899C22⋊C4C23×D6118yes—
900C22⋊C4C23×D6118yes—
901C42—611no—
902C42—612no—
903C42—612no—
904C42—612no—
905C42—612no—
906C42—612no—
907C42—611no—
908C42—618no—
909C42—614no—
910C42C23×D6111yescharacteristic
911C42C23×D6112yes—
912C42C23×D6111yescharacteristic
913C42C23×D6114yes—
914C23—611no—
915C23—611no—
916C23—618no—
917C23—1224no—
918C23—12216no—
919C23—1222no—
920C23—12216no—
921C23—12216no—
922C23C24×D6111yescharacteristic
923C23C24×D6118yes—
924Q8—28no—
925Q8—44no—
926Q8—12216no—
927Q8—1228no—
928Q8—2448no—
929Q8—2444no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—12216no—
936D4—12216no—
937D4—1228no—
938D4—1228no—
939D4—2448no—
940D4—2444no—
941D4—24416no—
942D4—2448no—
943D4—2448no—
944D4—2448no—
945D4—24416no—
946D4—24416no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—611no—
952C2×C4—612no—
953C2×C4—618no—
954C2×C4—614no—
955C2×C4—611no—
956C2×C4—612no—
957C2×C4—618no—
958C2×C4—618no—
959C2×C4—1222no—
960C2×C4—12216no—
961C2×C4—1224no—
962C2×C4—1222no—
963C2×C4—12216no—
964C2×C4—1224no—
965C2×C4—12216no—
966C2×C4—1222no—
967C2×C4—12216no—
968C2×C4—1224no—
969C2×C4—12216no—
970C2×C4—1224no—
971C2×C4—1222no—
972C2×C4—24416no—
973C2×C4—24416no—
974C2×C4—24416no—
975C2×C4C24×D6111yescharacteristic
976C2×C4C24×D6112yes—
977C2×C4C24×D6118yes—
978C2×C4C24×D6118yes—
979C2×C4C24×D6112yes—
980C2×C4C24×D6111yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—614no—
987C22—612no—
988C22—1222no—
989C22—1228no—
990C22—1228no—
991C22—1221no—
992C22—1228no—
993C22—2444no—
994C22—24432no—
995C22C25×D6111yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—614no—
1001C4—612no—
1002C4—1228no—
1003C4—1222no—
1004C4—1228no—
1005C4—1221no—
1006C4H(5,𝔽2)×D6114yes—
1007C42−1+4×D6112yes—
1008C2—41no—
1009C2—48no—
1010C2—614no—
1011C2—2441no—
1012C2—2448no—
1013C2C2×H(5,𝔽2)×D6112yes—
1014C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3548C2
hypercenter#3548D61
hypocenterC61C2×#3548
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #21460219C2semidirect
2. #21460218C2semidirect
3. #21460217C2semidirect
4. #21460216C2semidirect
5. #21460215C2semidirect
6. #21460214C2semidirect
7. #21460213C2semidirect
8. #21460212C2semidirect
9. #562×D61C2semidirect
10. #554×D61C2semidirect
11. #550×D61C2semidirect
12. #547×D61C2semidirect
13. #540×D61C2semidirect
14. #537×D61C2semidirect
15. #533×D61C2semidirect
16. #532×D61C2semidirect
17. C61×#3548C2semidirect
20. #16840510C22semidirect
21. #16840509C22semidirect
22. #16840508C22semidirect
23. #16840507C22semidirect
24. #16840506C22semidirect
25. #16840473C22semidirect
26. #16840472C22semidirect
27. #16840471C22semidirect
28. #16840470C22semidirect
29. #16840469C22semidirect
30. #16840468C22semidirect
31. #16840467C22semidirect
32. #16840466C22semidirect
33. #16840434C22semidirect
34. #16840433C22semidirect
35. #16840433C22semidirect
36. #16840432C22semidirect
37. #16840432C22semidirect
38. #16840431C22semidirect
39. #16840430C22semidirect
40. #16840430C22semidirect
41. #16840417C22semidirect
42. #16840416C22semidirect
43. #16840415C22semidirect
44. #16840414C22semidirect
45. #16840413C22semidirect
46. #16840412C22semidirect
47. #16840411C22semidirect
48. #16840410C22semidirect
49. #16840368C22semidirect
50. #16840367C22semidirect
51. #16840366C22semidirect
52. #16840365C22semidirect
53. #16840364C22semidirect
54. #16840363C22semidirect
55. #16840362C22semidirect
56. #16840343C22semidirect
57. #16840342C22semidirect
58. #16840342C22semidirect
59. #16840342C22semidirect
60. #16840341C22semidirect
61. #16840341C22semidirect
62. #16840341C22semidirect
63. #16840340C22semidirect
64. #16840340C22semidirect
65. #16840339C22semidirect
66. #16840339C22semidirect
67. #16840319C22semidirect
68. #16840318C22semidirect
69. #16840317C22semidirect
70. #16840316C22semidirect
71. #16840315C22semidirect
72. #16840314C22semidirect
73. #16840313C22semidirect
74. #16840312C22semidirect
75. #16840311C22semidirect
76. #16840310C22semidirect
77. #16840309C22semidirect
78. #16840309C22semidirect
79. #16840308C22semidirect
80. #16840307C22semidirect
81. #16840307C22semidirect
105. C61×#562C22semidirect
106. C61×#554C22semidirect
107. C61×#550C22semidirect
108. C61×#547C22semidirect
109. C61×#540C22semidirect
110. C61×#537C22semidirect
111. C61×#533C22semidirect
112. C61×#532C22semidirect
509. #3548D61direct (N × H)
524. D61#3548direct (N × H)
532. #562C2×D61semidirect
541. #554C2×D61semidirect
550. #550C2×D61semidirect
559. #547C2×D61semidirect
567. #540C2×D61semidirect
579. #537C2×D61semidirect
586. #533C2×D61semidirect
596. #532C2×D61semidirect
620. C61C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#214602192
#214602182
#214602172
#214602162
#214602152
#214602142
#214602132
#214602122
#562×D612
#554×D612
#550×D612
#547×D612
#540×D612
#537×D612
#533×D612
#532×D612
C61×#35482
C2×#354861