Finite Group Databasebeta

← D61×#3509 #30588447

Subgroups — D61×#3509 #30588447

Order 15616.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459706C211yesmaximal, characteristic, complemented
2#21459705C211yesmaximal, characteristic, complemented
3#21459704C212yesmaximal, complemented
4#21459703C211yesmaximal, characteristic, complemented
5#21459702C214yesmaximal, complemented
6#21459701C214yesmaximal, complemented
7#21459700C212yesmaximal, complemented
8#21459699C214yesmaximal, complemented
9#21459698C214yesmaximal, complemented
10#21459697C218yesmaximal, complemented
11#557×D61C214yesmaximal, complemented
12#556×D61C214yesmaximal, complemented
13#552×D61C218yesmaximal, complemented
14#541×D61C214yesmaximal, complemented
15#536×D61C212yesmaximal
16#533×D61C214yesmaximal, complemented
17#533×D61C211yesmaximal, characteristic, complemented
18C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
19#519×D61C212yesmaximal, complemented
20C4×#41×D61C211yesmaximal, characteristic
21C61×#3509C211yesmaximal, characteristic, complemented
22C2×#41×D61C2211yescharacteristic
23C22×Q8×D61C2212yes—
24#16840491C2214yescomplemented
25#16840490C2218yescomplemented
26#16840490C2214yescomplemented
27#16840489C2218yescomplemented
28#16840489C22116yescomplemented
29#16840488C2218yescomplemented
30#16840487C2214yescomplemented
31#16840487C2218yescomplemented
32#16840486C2214yescomplemented
33#16840485C2214yescomplemented
34#16840484C2218yescomplemented
35#16840483C2218yescomplemented
36#16840482C2214yescomplemented
37#16840481C2218yescomplemented
38#16840480C2218yescomplemented
39#16840479C22116yescomplemented
40#16840454C2218yescomplemented
41#16840453C2218yescomplemented
42#16840452C2218yescomplemented
43#16840451C2218yescomplemented
44#16840450C2218yescomplemented
45#16840449C22116yescomplemented
46#16840448C22116yescomplemented
47#16840447C2218yescomplemented
48#16840446C2218yescomplemented
49#16840445C22116yescomplemented
50#16840444C22116yescomplemented
51#16840375C2214yescomplemented
52#16840374C2214yescomplemented
53#16840373C2214yescomplemented
54#16840372C2218yescomplemented
55#16840371C22116yescomplemented
56#16840370C2218yescomplemented
57#16840369C22116yescomplemented
58#16840338C2212yes—
59#16840337C2214yes—
60#16840336C2212yes—
61#16840335C2218yes—
62#16840334C2218yes—
63#16840333C2212yes—
64#16840332C2214yes—
65#16840319C2214yescomplemented
66#16840319C2211yescharacteristic, complemented
67#16840318C2218yescomplemented
68#16840318C2212yescomplemented
69#16840317C2212yescomplemented
70#16840317C2214yescomplemented
71#16840317C2214yescomplemented
72#16840316C2218yescomplemented
73#16840316C2214yescomplemented
74#16840316C2218yescomplemented
75#16840315C2218yescomplemented
76#16840315C2212yescomplemented
77#16840314C2214yescomplemented
78#16840314C2218yescomplemented
79#16840314C2218yescomplemented
80C2×#14519777C2211yescharacteristic, complemented
81C2×#14519776C2214yescomplemented
82C2×#14519775C2212yescomplemented
83C4⋊Q8×D61C2212yes—
84C4⋊Q8×D61C2214yes—
85C4⋊Q8×D61C2212yes—
86C4⋊Q8×D61C2212yes—
87C4⋊Q8×D61C2214yes—
88C4⋊Q8×D61C2212yescomplemented
89C4⋊Q8×D61C2214yescomplemented
90C4⋊Q8×D61C2212yescomplemented
91#126×D61C22116yes—
92#125×D61C2218yes—
93#125×D61C22116yes—
94#125×D61C2212yes—
95#124×D61C2214yes—
96#123×D61C2218yes—
97C22⋊Q8×D61C2214yes—
98C22⋊Q8×D61C2218yes—
99C22⋊Q8×D61C2218yes—
100#16840240C2212yescomplemented
101#16840239C2218yescomplemented
102#16840239C2212yescomplemented
103#16840239C2212yescomplemented
104#16840238C2218yescomplemented
105#16840238C2218yescomplemented
106#41×Dic61C2211yescharacteristic
107C4×#11758226C2212yes—
108C4×#11758222C2212yes—
109C4×#11758222C2211yescharacteristic
110#16840230C2211yescharacteristic
111#16840230C2212yes—
112C4×#11758224C2214yes—
113C4×#11758224C2212yes—
114C4×Q8×D61C2212yes—
115C4×Q8×D61C2218yes—
116C4×Q8×D61C2218yes—
117C4×Q8×D61C2218yes—
118C4×Q8×D61C2214yes—
119C4×D4×D61C2214yes—
120C4×D4×D61C2212yes—
121#117×D61C2211yescharacteristic
122#117×D61C2212yes—
123#117×D61C2218yes—
124#117×D61C2212yes—
125#117×D61C2218yes—
126C2×C4⋊C4×D61C2214yes—
127C2×C42×D61C2211yescharacteristic
128C2×C42×D61C2212yes—
129C61×#557C2214yescomplemented
130C61×#556C2214yescomplemented
131C61×#552C2218yescomplemented
132C61×#541C2214yescomplemented
133C61×#536C2212yes—
134C61×#533C2214yescomplemented
135C61×#533C2211yescharacteristic, complemented
136C2×C4⋊Q8×C61C2211yescharacteristic, complemented
137C61×#519C2212yescomplemented
138C4×#41×C61C2211yescharacteristic
139C2×#11758226C2311yescharacteristic
140C2×#11758222C2312yes—
141C2×#11758222C2311yescharacteristic
142C2×#11758224C2311yescharacteristic
143C2×#11758224C2312yes—
144#41×D61—28no—
145C22×Dic122C2312yes—
146C22×Dic122C2314yes—
147C2×Q8×D61—216no—
148C2×Q8×D61C2314yes—
149C2×Q8×D61C2314yes—
150C2×Q8×D61C2314yes—
151C2×Q8×D61C2311yescharacteristic
152C2×Q8×D61C2314yes—
153C2×Q8×D61C2314yes—
154C2×D4×D61C2312yes—
155C2×D4×D61C2311yescharacteristic
156C22×C4×D61C2312yes—
157C22×C4×D61C2314yes—
158C22×C4×D61C2312yes—
159C22×C4×D61C2314yes—
160C22×C4×D61C2311yescharacteristic
161#14519777C2314yes—
162#14519777C2314yes—
163#14519777C2312yes—
164#14519777C2312yes—
165#14519777C2312yes—
166#14519776C2318yes—
167#14519776C2318yes—
168#14519776C23116yes—
169#14519776C2318yes—
170#14519776C2318yes—
171#14519776C2314yes—
172#14519776C2314yes—
173#14519775C2318yes—
174#14519775C2314yes—
175#14519775C2314yes—
176#14519775C2314yes—
177#14519775C2314yes—
178#14519775C2314yes—
179#14519772C23116yes—
180#14519772C23116yes—
181#14519772C23116yes—
182#14519771C23116yes—
183#14519770C23116yes—
184#14519770C23116yes—
185#14519770C23116yes—
186#14519769C23116yes—
187#14519769C2318yes—
188#14519769C2312yes—
189#14519768C23116yes—
190#14519768C23116yes—
191#14519768C2318yes—
192#14519768C2318yes—
193#14519768C2314yes—
194#14519767C23116yes—
195#14519767C23116yes—
196#14519767C23116yes—
197#14519767C23116yes—
198#14519767C23116yes—
199#14519767C23116yes—
200#14519767C2318yes—
201#14519766C2314yes—
202#14519765C2314yes—
203#14519764C2314yes—
204#14519763C23116yes—
205#14519762C23116yes—
206#14519761C2318yes—
207#14519760C2318yes—
208#14519759C23116yes—
209#14519758C2318yes—
210#14519757C2314yes—
211#14519757C2318yes—
212#14519757C2318yes—
213#14519756C2318yes—
214#14519756C2314yes—
215#14519756C2318yes—
216#14519755C2318yes—
217#14519755C23116yes—
218#14519755C23116yes—
219#14519754C23116yes—
220#14519754C2318yes—
221#14519754C23116yes—
222#14519753C2314yes—
223#14519753C2318yes—
224#14519753C2318yes—
225Q8×Dic61C2318yes—
226Q8×Dic61C2318yes—
227Q8×Dic61C2314yes—
228Q8×Dic61C2312yes—
229Q8×Dic61C2318yes—
230C4×Dic122C23116yes—
231C4×Dic122C2318yes—
232C4×Dic122C23116yes—
233C4×Dic122C2318yes—
234C4×Dic122C2318yes—
235C4×Dic122C2314yes—
236C4×Dic122C2312yes—
237C4×Dic122C2314yes—
238C4×Dic122C23116yes—
239C4×Dic122C2318yes—
240#14519742C23116yes—
241#14519742C2318yes—
242#14519742C2318yes—
243#14519742C23116yes—
244#14519742C2314yes—
245#14519742C2318yes—
246#14519742C2314yes—
247#14519742C2312yes—
248#14519742C2318yes—
249#14519742C23116yes—
250C4×D244C2314yes—
251C4×D244C2312yes—
252D4×Dic61C2314yes—
253D4×Dic61C2312yes—
254#14519739C2312yes—
255#14519739C2314yes—
256C4×C22⋊D61C2314yes—
257C4×C22⋊D61C2314yes—
258C4×C22⋊D61C2314yes—
259#14519737C2314yes—
260#14519737C2314yes—
261#14519737C2314yes—
262#14519736C2318yes—
263#14519736C2318yes—
264#14519736C2311yescharacteristic
265#14519736C2312yes—
266#14519736C2312yes—
267#14519735C23116yes—
268#14519735C2318yes—
269#14519735C2318yes—
270#14519735C2312yes—
271#14519735C2314yes—
272#14519735C2314yes—
273#14519734C23116yes—
274#14519734C23116yes—
275#14519734C2312yes—
276#14519734C2312yes—
277#14519734C2312yes—
278#14519734C2314yes—
279#14519733C23116yes—
280#14519733C2318yes—
281#14519733C2318yes—
282#14519733C2312yes—
283#14519733C2314yes—
284#14519733C2314yes—
285C2×C4⋊Dic61C2314yes—
286C2×#11758196C2318yes—
287C4⋊C4×D61C2318yes—
288C4⋊C4×D61C2318yes—
289C4⋊C4×D61C2318yes—
290C4⋊C4×D61C2318yes—
291C4⋊C4×D61C2314yes—
292C4⋊C4×D61C2312yes—
293C4⋊C4×D61C2314yes—
294C4⋊C4×D61C2314yes—
295C4⋊C4×D61C23116yes—
296C4⋊C4×D61C23116yes—
297C4⋊C4×D61C2318yes—
298C22⋊C4×D61C2312yes—
299C22⋊C4×D61C2314yes—
300C22⋊C4×D61C2314yes—
301C22⋊C4×D61C23116yes—
302C2×C4×Dic61C2312yes—
303C2×C4×Dic61C2314yes—
304C2×C4×Dic61C2311yescharacteristic
305C2×C4×Dic61C2312yes—
306C42×D61C2311yescharacteristic
307C42×D61C2312yes—
308C42×D61C2311yescharacteristic
309C42×D61C2314yes—
310C42×D61C2312yes—
311C42×D61C2312yes—
312C42×D61C2314yes—
313C42×D61C2311yescharacteristic
314C42×D61C2312yes—
315C42×D61C2311yescharacteristic
316C42×D61C2312yes—
317C42×D61C23116yes—
318C42×D61C2314yes—
319C2×#41×C61C2311yescharacteristic
320C22×Q8×C61C2312yes—
321C4⋊Q8×C61C2312yes—
322C4⋊Q8×C61C2312yes—
323C4⋊Q8×C61C2314yes—
324C4⋊Q8×C61C2312yes—
325C4⋊Q8×C61C2314yes—
326#126×C61C23116yes—
327#125×C61C2318yes—
328#125×C61C2312yes—
329#125×C61C23116yes—
330#124×C61C2314yes—
331#123×C61C2318yes—
332C22⋊Q8×C61C2318yes—
333C22⋊Q8×C61C2314yes—
334C22⋊Q8×C61C2318yes—
335C4×Q8×C61C2318yes—
336C4×Q8×C61C2318yes—
337C4×Q8×C61C2314yes—
338C4×Q8×C61C2318yes—
339C4×Q8×C61C2312yes—
340C4×D4×C61C2314yes—
341C4×D4×C61C2312yes—
342#117×C61C2318yes—
343#117×C61C2312yes—
344#117×C61C2312yes—
345#117×C61C2318yes—
346#117×C61C2311yescharacteristic
347C2×C4⋊C4×C61C2314yes—
348C2×C42×C61C2311yescharacteristic
349C2×C42×C61C2312yes—
350C23×D61C2412yes—
351C23×D61C2411yescharacteristic
352#41×C61—24no—
353C2×Q8×C61—28no—
354C2×Q8×C61C2414yes—
355C2×Q8×C61C2414yes—
356C2×Q8×C61C2411yescharacteristic
357C2×Q8×C61C2414yes—
358C2×D4×C61C2412yes—
359C2×D4×C61C2411yescharacteristic
360C22×C4×C61C2414yes—
361C22×C4×C61C2412yes—
362C22×C4×C61C2412yes—
363C22×C4×C61C2414yes—
364C22×C4×C61C2411yescharacteristic
365C2×C22⋊D61C2412yes—
366C2×C22⋊D61C2412yes—
367C2×C22⋊D61C2412yes—
368C22×Dic61C2414yes—
369C22×Dic61C2412yes—
370C22×Dic61C2412yes—
371C22×Dic61C2414yes—
372C22×Dic61C2411yescharacteristic
373#11758226—24no—
374Q8×D61—216no—
375Q8×D61—216no—
376Q8×D61—216no—
377Q8×D61—216no—
378Q8×D61—24no—
379Q8×D61—216no—
380#11758224—28no—
381#11758224—24no—
382D4×D61—28no—
383D4×D61—24no—
384#11758222—24no—
385#11758222—28no—
386C2×D244C2412yes—
387C2×D244C2411yescharacteristic
388C2×C4×D61—216no—
389C2×C4×D61—28no—
390C2×C4×D61—28no—
391C2×C4×D61—216no—
392C2×C4×D61#4118yes—
393C2×C4×D61C2412yes—
394C2×C4×D61C2418yes—
395C2×C4×D61C2418yes—
396C2×C4×D61C2412yes—
397C2×C4×D61C2412yes—
398C2×C4×D61C2414yes—
399C2×C4×D61C2412yes—
400C2×C4×D61C2412yes—
401C2×C4×D61C2412yes—
402C2×C4×D61C2414yes—
403C2×C4×D61C2414yes—
404C2×C4×D61C2418yes—
405C2×C4×D61C2411yescharacteristic
406C2×C4×D61C2411yescharacteristic
407C2×C4×D61C2411yescharacteristic
408C2×C4×D61C2411yescharacteristic
409C2×C4×D61C2412yes—
410C2×Dic122—28no—
411C2×Dic122—216no—
412C2×Dic122C2418yes—
413C2×Dic122C2414yes—
414C2×Dic122C2418yes—
415C2×Dic122C2414yes—
416C2×Dic122C2411yescharacteristic
417C2×Dic122C2412yes—
418C2×Dic122C2418yes—
419C2×Dic122C2414yes—
420C4⋊C4×C61C2418yes—
421C4⋊C4×C61C2418yes—
422C4⋊C4×C61C2414yes—
423C4⋊C4×C61C2412yes—
424C4⋊C4×C61C2414yes—
425C4⋊C4×C61C2414yes—
426C4⋊C4×C61C24116yes—
427C4⋊C4×C61C24116yes—
428C4⋊C4×C61C2418yes—
429C22⋊C4×C61C2412yes—
430C22⋊C4×C61C2414yes—
431C22⋊C4×C61C2414yes—
432C22⋊C4×C61C24116yes—
433C42×C61C2411yescharacteristic
434C42×C61C2412yes—
435C42×C61C2411yescharacteristic
436C42×C61C2414yes—
437C42×C61C2412yes—
438C42×C61C24116yes—
439C42×C61C2414yes—
440C22⋊Dic61C2412yes—
441C22⋊Dic61C2414yes—
442C22⋊Dic61C2414yes—
443C22⋊Dic61C24116yes—
444#11758198C2414yes—
445#11758198C2418yes—
446#11758198C2414yes—
447#11758198C2414yes—
448#11758198C24116yes—
449#11758198C24116yes—
450C4⋊Dic61C2418yes—
451C4⋊Dic61C2418yes—
452C4⋊Dic61C2414yes—
453C4⋊Dic61C2412yes—
454C4⋊Dic61C2414yes—
455C4⋊Dic61C2414yes—
456C4⋊Dic61C24116yes—
457C4⋊Dic61C24116yes—
458C4⋊Dic61C2418yes—
459#11758196C24116yes—
460#11758196C24116yes—
461#11758196C2418yes—
462#11758196C2414yes—
463#11758196C2414yes—
464#11758196C2414yes—
465#11758196C24116yes—
466#11758196C2418yes—
467#11758196C24116yes—
468#11758196C24116yes—
469#11758196C2418yes—
470#11758196C24116yes—
471#11758196C2418yes—
472C4×Dic61C2411yescharacteristic
473C4×Dic61C2412yes—
474C4×Dic61C2414yes—
475C4×Dic61C2412yes—
476C4×Dic61C2412yes—
477C4×Dic61C2411yescharacteristic
478C4×Dic61C2412yes—
479C4×Dic61C2414yes—
480C4×Dic61C2414yes—
481C4×Dic61C2412yes—
482C4×Dic61C2414yes—
483C4×Dic61C2412yes—
484C4×Dic61C24116yes—
485C4×Dic61C24116yes—
486C4×Dic61C24116yes—
487C4×Dic61C2418yes—
488C4×Dic61C2414yes—
489C23×C61C2512yes—
490C23×C61C2511yescharacteristic
491C22×D61—24no—
492C22×D61—24no—
493C22×D61—28no—
494C22×D61C2×#4114yes—
495C22×D61C2512yes—
496C22×D61C2511yescharacteristic
497C22×D61C2511yescharacteristic
498Q8×C61—28no—
499Q8×C61—28no—
500Q8×C61—22no—
501Q8×C61—28no—
502D4×C61—24no—
503D4×C61—22no—
504C2×C4×C61—28no—
505C2×C4×C61—24no—
506C2×C4×C61—24no—
507C2×C4×C61—28no—
508C2×C4×C61C2×#4114yes—
509C2×C4×C61C2514yes—
510C2×C4×C61C2518yes—
511C2×C4×C61C2512yes—
512C2×C4×C61C2512yes—
513C2×C4×C61C2518yes—
514C2×C4×C61C2511yescharacteristic
515C2×C4×C61C2511yescharacteristic
516C2×C4×C61C2512yes—
517C22⋊D61—24no—
518C22⋊D61—24no—
519C22⋊D61—24no—
520C2×Dic61—28no—
521C2×Dic61—24no—
522C2×Dic61—24no—
523C2×Dic61—28no—
524C2×Dic61C2×#4114yes—
525C2×Dic61C2514yes—
526C2×Dic61C2518yes—
527C2×Dic61C2512yes—
528C2×Dic61C2512yes—
529C2×Dic61C2518yes—
530C2×Dic61C2511yescharacteristic
531C2×Dic61C2511yescharacteristic
532C2×Dic61C2512yes—
533D244—24no—
534D244—22no—
535C4×D61—24no—
536C4×D61—216no—
537C4×D61—216no—
538C4×D61—28no—
539C4×D61—24no—
540C4×D61—216no—
541C4×D61—24no—
542C4×D61—24no—
543C4×D61—28no—
544C4×D61—24no—
545C4×D61—24no—
546C4×D61—28no—
547C4×D61C2×#4114yes—
548C4×D61C2×#4114yes—
549C4×D61C2×#4114yes—
550C4×D61C2×#4114yes—
551C4×D612−1+418yes—
552Dic122—28no—
553Dic122—28no—
554Dic122—22no—
555Dic122—28no—
556Dic122—216no—
557Dic122—216no—
558Dic122—24no—
559Dic122—216no—
560C2×#3509—611nomaximal, Sylow
561C22×C61—22no—
562C22×C61—22no—
563C22×C61—24no—
564C22×C61C22×#4112yes—
565C22×C61C2611yescharacteristic
566C2×D61—22no—
567C2×D61—28no—
568C2×D61—22no—
569C2×D61—24no—
570C2×D61—48no—
571C2×D61C22×#4112yes—
572C2×D61C22×#4112yes—
573C2×D61C2×2−1+414yes—
574C4×C61—28no—
575C4×C61—22no—
576C4×C61—28no—
577C4×C61—24no—
578C4×C61—22no—
579C4×C61C22×#4112yes—
580C4×C61C22×#4112yes—
581C4×C61C2×2−1+414yes—
582Dic61—28no—
583Dic61—22no—
584Dic61—28no—
585Dic61—24no—
586Dic61—22no—
587Dic61C22×#4112yes—
588Dic61C22×#4112yes—
589Dic61C2×2−1+414yes—
590#3509—614no—
591#3509—614no—
592#3509—618no—
593#3509—614no—
594#3509—612no—
595#3509—614no—
596#3509—611no—
597#3509—611no—
598#3509—612no—
599#3509—611no—
600#3509D6111yescharacteristic, direct product factor
601C2×#557—614no—
602C2×#556—614no—
603C2×#552—618no—
604C2×#541—614no—
605C2×#536—612no—
606C2×#533—611no—
607C2×#533—614no—
608C22×C4⋊Q8—611no—
609C2×#519—612no—
610C2×C4×#41—611no—
611C2×C61—22no—
612C2×C61—42no—
613C2×C61C23×#4111yescharacteristic
614C2×C61C22×2−1+412yes—
615D61—22no—
616D61—42no—
617D61#350914yesdirect product factor
618C22×#41—611no—
619C23×Q8—612no—
620#557—618no—
621#557—614no—
622#557—6116no—
623#557—618no—
624#557—618no—
625#557—618no—
626#557—614no—
627#557—614no—
628#557C2×D6114yescomplemented
629#556—614no—
630#556—6116no—
631#556—618no—
632#556—618no—
633#556—618no—
634#556—614no—
635#556—614no—
636#556—618no—
637#556C2×D6114yescomplemented
638#552—6116no—
639#552—618no—
640#552—6116no—
641#552—6116no—
642#552—618no—
643#552—618no—
644#552—618no—
645#552—618no—
646#552—618no—
647#552—6116no—
648#552—618no—
649#552C2×D6118yescomplemented
650#541—614no—
651#541—6116no—
652#541—6116no—
653#541—614no—
654#541—618no—
655#541—618no—
656#541—614no—
657#541C2×D6114yescomplemented
658#536—612no—
659#536—612no—
660#536—614no—
661#536—614no—
662#536—618no—
663#536—618no—
664#536—612no—
665#536C2×D6112yes—
666#533—612no—
667#533—614no—
668#533—614no—
669#533—612no—
670#533—618no—
671#533—614no—
672#533—618no—
673#533—618no—
674#533—614no—
675#533—618no—
676#533—618no—
677#533—612no—
678#533—618no—
679#533—611no—
680#533—614no—
681#533C2×D6111yescharacteristic, complemented
682#533C2×D6114yescomplemented
683C2×C4⋊Q8—612no—
684C2×C4⋊Q8—612no—
685C2×C4⋊Q8—612no—
686C2×C4⋊Q8—614no—
687C2×C4⋊Q8—612no—
688C2×C4⋊Q8—614no—
689C2×C4⋊Q8—612no—
690C2×C4⋊Q8—612no—
691C2×C4⋊Q8—614no—
692C2×C4⋊Q8—614no—
693C2×C4⋊Q8—611no—
694C2×C4⋊Q8C2×D6111yescharacteristic, complemented
695C2×#126—6116no—
696C2×#125—612no—
697C2×#125—618no—
698C2×#125—6116no—
699C2×#124—614no—
700C2×#123—618no—
701C2×C22⋊Q8—618no—
702C2×C22⋊Q8—614no—
703C2×C22⋊Q8—618no—
704#519—612no—
705#519—618no—
706#519—618no—
707#519—612no—
708#519—612no—
709#519—618no—
710#519C2×D6112yescomplemented
711C4×#41—611no—
712C4×#41—612no—
713C4×#41—614no—
714C4×#41—612no—
715C4×#41—611no—
716C4×#41—612no—
717C4×#41—612no—
718C4×#41—611no—
719C4×#41C2×D6111yescharacteristic
720C2×C4×Q8—612no—
721C2×C4×Q8—618no—
722C2×C4×Q8—618no—
723C2×C4×Q8—618no—
724C2×C4×Q8—614no—
725C2×C4×D4—614no—
726C2×C4×D4—612no—
727C2×#117—611no—
728C2×#117—612no—
729C2×#117—612no—
730C2×#117—618no—
731C2×#117—618no—
732C22×C4⋊C4—614no—
733C22×C42—611no—
734C22×C42—612no—
735C61C2×#350911yescharacteristic, complemented, Sylow
736C2×#41—611no—
737C2×#41—612no—
738C2×#41—611no—
739C2×#41—612no—
740C2×#41—611no—
741C2×#41—1228no—
742C2×#41C22×D6111yescharacteristic
743C22×Q8—614no—
744C22×Q8—614no—
745C22×Q8—614no—
746C22×Q8—611no—
747C22×Q8—614no—
748C22×Q8—614no—
749C22×Q8—614no—
750C22×Q8—612no—
751C22×Q8—12216no—
752C22×Q8C22×D6112yes—
753C22×D4—612no—
754C22×D4—611no—
755C23×C4—611no—
756C23×C4—614no—
757C23×C4—612no—
758C23×C4—614no—
759C23×C4—612no—
760C4⋊Q8—614no—
761C4⋊Q8—614no—
762C4⋊Q8—618no—
763C4⋊Q8—614no—
764C4⋊Q8—614no—
765C4⋊Q8—614no—
766C4⋊Q8—618no—
767C4⋊Q8—618no—
768C4⋊Q8—618no—
769C4⋊Q8—618no—
770C4⋊Q8—614no—
771C4⋊Q8—614no—
772C4⋊Q8—6116no—
773C4⋊Q8—612no—
774C4⋊Q8—612no—
775C4⋊Q8—614no—
776C4⋊Q8—612no—
777C4⋊Q8—614no—
778C4⋊Q8C22×D6112yes—
779C4⋊Q8C22×D6112yes—
780C4⋊Q8C22×D6114yes—
781C4⋊Q8C22×D6112yes—
782C4⋊Q8C22×D6114yes—
783#126—6116no—
784#126—6116no—
785#126—6116no—
786#126—6116no—
787#126—6116no—
788#126—6116no—
789#126—6116no—
790#126C22×D61116yes—
791#125—618no—
792#125—614no—
793#125—6116no—
794#125—6116no—
795#125—618no—
796#125—618no—
797#125—6116no—
798#125—6116no—
799#125—6116no—
800#125—6116no—
801#125—6116no—
802#125—6116no—
803#125—612no—
804#125—618no—
805#125—6116no—
806#125C22×D6112yes—
807#125C22×D6118yes—
808#125C22×D61116yes—
809#124—614no—
810#124—614no—
811#124—6116no—
812#124—614no—
813#124C22×D6114yes—
814#123—618no—
815#123—618no—
816#123—6116no—
817#123—6116no—
818#123—618no—
819#123C22×D6118yes—
820C22⋊Q8—618no—
821C22⋊Q8—614no—
822C22⋊Q8—618no—
823C22⋊Q8—618no—
824C22⋊Q8—614no—
825C22⋊Q8—618no—
826C22⋊Q8—6116no—
827C22⋊Q8—618no—
828C22⋊Q8—618no—
829C22⋊Q8—614no—
830C22⋊Q8—6116no—
831C22⋊Q8—618no—
832C22⋊Q8—6116no—
833C22⋊Q8—618no—
834C22⋊Q8—6116no—
835C22⋊Q8C22×D6118yes—
836C22⋊Q8C22×D6114yes—
837C22⋊Q8C22×D6118yes—
838C4×Q8—612no—
839C4×Q8—618no—
840C4×Q8—618no—
841C4×Q8—618no—
842C4×Q8—614no—
843C4×Q8—614no—
844C4×Q8—612no—
845C4×Q8—6116no—
846C4×Q8—618no—
847C4×Q8—6116no—
848C4×Q8—618no—
849C4×Q8—6116no—
850C4×Q8—618no—
851C4×Q8—618no—
852C4×Q8—614no—
853C4×Q8—612no—
854C4×Q8—614no—
855C4×Q8—6116no—
856C4×Q8—618no—
857C4×Q8—618no—
858C4×Q8—6116no—
859C4×Q8—6116no—
860C4×Q8—618no—
861C4×Q8—618no—
862C4×Q8—614no—
863C4×Q8C22×D6112yes—
864C4×Q8C22×D6118yes—
865C4×Q8C22×D6118yes—
866C4×Q8C22×D6118yes—
867C4×Q8C22×D6114yes—
868C4×D4—614no—
869C4×D4—612no—
870C4×D4—614no—
871C4×D4—614no—
872C4×D4—614no—
873C4×D4—614no—
874C4×D4—612no—
875C4×D4—614no—
876C4×D4—614no—
877C4×D4—614no—
878C4×D4—614no—
879C4×D4—612no—
880C4×D4C22×D6114yes—
881C4×D4C22×D6112yes—
882#117—611no—
883#117—612no—
884#117—612no—
885#117—618no—
886#117—618no—
887#117—612no—
888#117—614no—
889#117—614no—
890#117—6116no—
891#117—618no—
892#117—618no—
893#117—612no—
894#117—614no—
895#117—614no—
896#117—618no—
897#117—618no—
898#117—6116no—
899#117—612no—
900#117—612no—
901#117—612no—
902#117—614no—
903#117—6116no—
904#117—6116no—
905#117C22×D6111yescharacteristic
906#117C22×D6112yes—
907#117C22×D6112yes—
908#117C22×D6118yes—
909#117C22×D6118yes—
910C2×C4⋊C4—618no—
911C2×C4⋊C4—614no—
912C2×C4⋊C4—618no—
913C2×C4⋊C4—618no—
914C2×C4⋊C4—618no—
915C2×C4⋊C4—618no—
916C2×C4⋊C4—614no—
917C2×C4⋊C4—612no—
918C2×C4⋊C4—614no—
919C2×C4⋊C4—614no—
920C2×C4⋊C4—6116no—
921C2×C4⋊C4—6116no—
922C2×C4⋊C4—618no—
923C2×C4⋊C4C22×D6114yes—
924C2×C22⋊C4—612no—
925C2×C22⋊C4—614no—
926C2×C22⋊C4—614no—
927C2×C22⋊C4—6116no—
928C2×C42—612no—
929C2×C42—611no—
930C2×C42—612no—
931C2×C42—614no—
932C2×C42—612no—
933C2×C42—6116no—
934C2×C42—611no—
935C2×C42—614no—
936C2×C42—614no—
937C2×C42—612no—
938C2×C42—612no—
939C2×C42—611no—
940C2×C42—611no—
941C2×C42—614no—
942C2×C42—612no—
943C2×C42—612no—
944C2×C42—611no—
945C2×C42C22×D6111yescharacteristic
946C2×C42C22×D6112yes—
947C24—611no—
948C24—612no—
949#41—24no—
950#41—1228no—
951#41—1228no—
952#41—1224no—
953#41—1224no—
954#41—1224no—
955C2×Q8—28no—
956C2×Q8—618no—
957C2×Q8—614no—
958C2×Q8—618no—
959C2×Q8—614no—
960C2×Q8—618no—
961C2×Q8—614no—
962C2×Q8—612no—
963C2×Q8—611no—
964C2×Q8—12216no—
965C2×Q8—12216no—
966C2×Q8—12216no—
967C2×Q8—12216no—
968C2×Q8—12216no—
969C2×Q8—1224no—
970C2×Q8—12216no—
971C2×Q8—1228no—
972C2×Q8C23×D6114yes—
973C2×Q8C23×D6114yes—
974C2×Q8C23×D6114yes—
975C2×Q8C23×D6111yescharacteristic
976C2×D4—612no—
977C2×D4—612no—
978C2×D4—612no—
979C2×D4—612no—
980C2×D4—611no—
981C2×D4—1224no—
982C2×D4—1228no—
983C2×D4C23×D6112yes—
984C2×D4C23×D6111yescharacteristic
985C22×C4—611no—
986C22×C4—618no—
987C22×C4—611no—
988C22×C4—612no—
989C22×C4—611no—
990C22×C4—611no—
991C22×C4—611no—
992C22×C4—612no—
993C22×C4—614no—
994C22×C4—612no—
995C22×C4—614no—
996C22×C4—614no—
997C22×C4—618no—
998C22×C4—612no—
999C22×C4—618no—
1000C22×C4—612no—
1001C22×C4—612no—
1002C22×C4—612no—
1003C22×C4—614no—
1004C22×C4—614no—
1005C22×C4—612no—
1006C22×C4—612no—
1007C22×C4—618no—
1008C22×C4—1228no—
1009C22×C4—12216no—
1010C22×C4—1228no—
1011C22×C4—12216no—
1012C22×C4C23×D6112yes—
1013C22×C4C23×D6114yes—
1014C22×C4C23×D6112yes—
1015C22×C4C23×D6114yes—
1016C22×C4C23×D6111yescharacteristic
1017C4⋊C4—6116no—
1018C4⋊C4—6116no—
1019C4⋊C4—618no—
1020C4⋊C4—618no—
1021C4⋊C4—618no—
1022C4⋊C4—614no—
1023C4⋊C4—614no—
1024C4⋊C4—614no—
1025C4⋊C4—618no—
1026C4⋊C4—6116no—
1027C4⋊C4—6116no—
1028C4⋊C4—6116no—
1029C4⋊C4—6116no—
1030C4⋊C4—618no—
1031C4⋊C4—618no—
1032C4⋊C4—614no—
1033C4⋊C4—612no—
1034C4⋊C4—614no—
1035C4⋊C4—614no—
1036C4⋊C4—6116no—
1037C4⋊C4—6116no—
1038C4⋊C4—618no—
1039C4⋊C4C23×D6118yes—
1040C4⋊C4C23×D6118yes—
1041C4⋊C4C23×D6114yes—
1042C4⋊C4C23×D6112yes—
1043C4⋊C4C23×D6114yes—
1044C4⋊C4C23×D6114yes—
1045C4⋊C4C23×D61116yes—
1046C4⋊C4C23×D61116yes—
1047C4⋊C4C23×D6118yes—
1048C22⋊C4—612no—
1049C22⋊C4—614no—
1050C22⋊C4—614no—
1051C22⋊C4—6116no—
1052C22⋊C4—614no—
1053C22⋊C4—618no—
1054C22⋊C4—614no—
1055C22⋊C4—614no—
1056C22⋊C4—6116no—
1057C22⋊C4—6116no—
1058C22⋊C4C23×D6112yes—
1059C22⋊C4C23×D6114yes—
1060C22⋊C4C23×D6114yes—
1061C22⋊C4C23×D61116yes—
1062C42—611no—
1063C42—612no—
1064C42—614no—
1065C42—612no—
1066C42—612no—
1067C42—611no—
1068C42—614no—
1069C42—614no—
1070C42—614no—
1071C42—612no—
1072C42—612no—
1073C42—612no—
1074C42—6116no—
1075C42—6116no—
1076C42—6116no—
1077C42—618no—
1078C42—614no—
1079C42C23×D6111yescharacteristic
1080C42C23×D6112yes—
1081C42C23×D6111yescharacteristic
1082C42C23×D6114yes—
1083C42C23×D6112yes—
1084C42C23×D61116yes—
1085C42C23×D6114yes—
1086C23—611no—
1087C23—614no—
1088C23—611no—
1089C23—612no—
1090C23—1224no—
1091C23—1224no—
1092C23—1228no—
1093C23C24×D6112yes—
1094C23C24×D6111yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—22no—
1098Q8—28no—
1099Q8—12216no—
1100Q8—12216no—
1101Q8—12216no—
1102Q8—1224no—
1103Q8—1228no—
1104Q8—1228no—
1105Q8—1222no—
1106Q8—1228no—
1107D4—24no—
1108D4—22no—
1109D4—1224no—
1110D4—1224no—
1111D4—1224no—
1112D4—1224no—
1113D4—1222no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—28no—
1118C2×C4—614no—
1119C2×C4—611no—
1120C2×C4—612no—
1121C2×C4—611no—
1122C2×C4—614no—
1123C2×C4—614no—
1124C2×C4—614no—
1125C2×C4—614no—
1126C2×C4—618no—
1127C2×C4—614no—
1128C2×C4—618no—
1129C2×C4—612no—
1130C2×C4—618no—
1131C2×C4—612no—
1132C2×C4—1224no—
1133C2×C4—1228no—
1134C2×C4—1224no—
1135C2×C4—1228no—
1136C2×C4—1224no—
1137C2×C4—1224no—
1138C2×C4—12216no—
1139C2×C4—12216no—
1140C2×C4—12216no—
1141C2×C4—1224no—
1142C2×C4—1228no—
1143C2×C4—1224no—
1144C2×C4—1228no—
1145C2×C4—1224no—
1146C2×C4—1224no—
1147C2×C4—1228no—
1148C2×C4#41×D6114yes—
1149C2×C4C24×D6114yes—
1150C2×C4C24×D6118yes—
1151C2×C4C24×D6112yes—
1152C2×C4C24×D6118yes—
1153C2×C4C24×D6112yes—
1154C2×C4C24×D6111yescharacteristic
1155C2×C4C24×D6111yescharacteristic
1156C2×C4C24×D6112yes—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—612no—
1161C22—614no—
1162C22—612no—
1163C22—1228no—
1164C22—1222no—
1165C22—1222no—
1166C22—1224no—
1167C22—2448no—
1168C22C2×#41×D6112yes—
1169C22C25×D6111yescharacteristic
1170C4—22no—
1171C4—28no—
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—612no—
1176C4—612no—
1177C4—614no—
1178C4—1222no—
1179C4—1228no—
1180C4—1224no—
1181C4—1222no—
1182C4—1228no—
1183C4C2×#41×D6112yes—
1184C4C2×#41×D6112yes—
1185C42−1+4×D6114yes—
1186C2—22no—
1187C2—42no—
1188C2—614no—
1189C2—1222no—
1190C2—2442no—
1191C2C22×#41×D6111yescharacteristic
1192C2C2×2−1+4×D6112yes—
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3509C2
prime radicalC2×#41×D61C22
hypercenter#3509D61
hypocenterC61C2×#3509
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #21459706C2semidirect
2. #21459705C2semidirect
3. #21459704C2semidirect
4. #21459703C2semidirect
5. #21459702C2semidirect
6. #21459701C2semidirect
7. #21459700C2semidirect
8. #21459699C2semidirect
9. #21459698C2semidirect
10. #21459697C2semidirect
11. #557×D61C2semidirect
12. #556×D61C2semidirect
13. #552×D61C2semidirect
14. #541×D61C2semidirect
16. #533×D61C2semidirect
17. #533×D61C2semidirect
18. C2×C4⋊Q8×D61C2semidirect
19. #519×D61C2semidirect
21. C61×#3509C2semidirect
24. #16840491C22semidirect
25. #16840490C22semidirect
26. #16840490C22semidirect
27. #16840489C22semidirect
28. #16840489C22semidirect
29. #16840488C22semidirect
30. #16840487C22semidirect
31. #16840487C22semidirect
32. #16840486C22semidirect
33. #16840485C22semidirect
34. #16840484C22semidirect
35. #16840483C22semidirect
36. #16840482C22semidirect
37. #16840481C22semidirect
38. #16840480C22semidirect
39. #16840479C22semidirect
40. #16840454C22semidirect
41. #16840453C22semidirect
42. #16840452C22semidirect
43. #16840451C22semidirect
44. #16840450C22semidirect
45. #16840449C22semidirect
46. #16840448C22semidirect
47. #16840447C22semidirect
48. #16840446C22semidirect
49. #16840445C22semidirect
50. #16840444C22semidirect
51. #16840375C22semidirect
52. #16840374C22semidirect
53. #16840373C22semidirect
54. #16840372C22semidirect
55. #16840371C22semidirect
56. #16840370C22semidirect
57. #16840369C22semidirect
65. #16840319C22semidirect
66. #16840319C22semidirect
67. #16840318C22semidirect
68. #16840318C22semidirect
69. #16840317C22semidirect
70. #16840317C22semidirect
71. #16840317C22semidirect
72. #16840316C22semidirect
73. #16840316C22semidirect
74. #16840316C22semidirect
75. #16840315C22semidirect
76. #16840315C22semidirect
77. #16840314C22semidirect
78. #16840314C22semidirect
79. #16840314C22semidirect
80. C2×#14519777C22semidirect
81. C2×#14519776C22semidirect
82. C2×#14519775C22semidirect
88. C4⋊Q8×D61C22semidirect
89. C4⋊Q8×D61C22semidirect
90. C4⋊Q8×D61C22semidirect
100. #16840240C22semidirect
101. #16840239C22semidirect
102. #16840239C22semidirect
103. #16840239C22semidirect
104. #16840238C22semidirect
105. #16840238C22semidirect
129. C61×#557C22semidirect
130. C61×#556C22semidirect
131. C61×#552C22semidirect
132. C61×#541C22semidirect
134. C61×#533C22semidirect
135. C61×#533C22semidirect
136. C2×C4⋊Q8×C61C22semidirect
137. C61×#519C22semidirect
600. #3509D61direct (N × H)
617. D61#3509direct (N × H)
628. #557C2×D61semidirect
637. #556C2×D61semidirect
649. #552C2×D61semidirect
657. #541C2×D61semidirect
681. #533C2×D61semidirect
682. #533C2×D61semidirect
694. C2×C4⋊Q8C2×D61semidirect
710. #519C2×D61semidirect
735. C61C2×#3509semidirect

Maximal subgroups

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

subgroupindex
#214597062
#214597052
#214597042
#214597032
#214597022
#214597012
#214597002
#214596992
#214596982
#214596972
#557×D612
#556×D612
#552×D612
#541×D612
#536×D612
#533×D612
C2×C4⋊Q8×D612
#519×D612
C4×#41×D612
C61×#35092
C2×#350961