Finite Group Databasebeta

← #29690013

Subgroups — #29690013

Order 15616.

1242 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459111C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C2×C4×#11758196C211yesmaximal, characteristic, complemented
4#21446761C212yesmaximal, complemented
5#21446736C212yesmaximal, complemented
6#21446263C211yesmaximal, characteristic, complemented
7#21446262C211yesmaximal, characteristic, complemented
8#21446260C211yesmaximal, characteristic, complemented
9#21445838C212yesmaximal, complemented
10#21445837C212yesmaximal, complemented
11C61×#1896C211yesmaximal, characteristic, complemented
12#16840315C2211yescharacteristic
13#16840314C411yescharacteristic, complemented
14#16840314C411yescharacteristic, complemented
15#16840308C2211yescharacteristic
16#16840307C411yescharacteristic, complemented
17#16840307C411yescharacteristic, complemented
18#16840298C411yescharacteristic, complemented
19#16840298C411yescharacteristic, complemented
20#16840293C411yescharacteristic, complemented
21#16840293C411yescharacteristic, complemented
22#16840292—21no—
23#16840292—21no—
24#16840289—21no—
25#16840289—21no—
26#16840273C2211yescharacteristic
27#16840268—21no—
28#16840268—21no—
29#41×Dic61C2211yescharacteristic
30#16840230C2211yescharacteristic
31C4×#11758224—21no—
32C4×#11758224—21no—
33C22×#11758196—21no—
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839816—21no—
37#16839816—21no—
38#16839812—21no—
39#16839812—21no—
40#16839785C2212yes—
41C2×#14519705C2212yes—
42C2×#14519704C2212yes—
43C2×#14519703C2212yes—
44#16839726C2211yescharacteristic
45M16×Dic61C2212yes—
46C4×#11758196—21no—
47C4×#11758196—21no—
48C4×#11758196C2212yes—
49C4×#11758196C2212yes—
50C2×#14519684—21no—
51#16839523C2212yes—
52#16839522C2212yes—
53#16839521C2212yes—
54C61×#525C2211yescharacteristic
55C22×C42×C61C2211yescharacteristic
56C2×#104×C61C2212yes—
57C61×#407C2211yescharacteristic
58C61×#339C2212yes—
59C2×#11758222C2311yescharacteristic
60C2×#11758224—21no—
61C2×#11758224—21no—
62C23×Dic61—21no—
63C23×Dic61D411yescharacteristic
64C23×Dic61D411yescharacteristic
65C2×#11758194C2312yes—
66#14519776C2×C411yescharacteristic, complemented
67#14519776C2×C411yescharacteristic, complemented
68#14519775C2×C411yescharacteristic, complemented
69#14519773C2×C411yescharacteristic, complemented
70#14519772—21no—
71#14519772—21no—
72#14519770—21no—
73#14519770—21no—
74#14519768C2×C411yescharacteristic, complemented
75#14519768C2×C411yescharacteristic, complemented
76#14519767—21no—
77#14519767—21no—
78#14519766C2×C411yescharacteristic, complemented
79#14519764C2×C411yescharacteristic, complemented
80#14519763—21no—
81#14519763—21no—
82#14519761—21no—
83#14519761—21no—
84#14519760—21no—
85#14519758—21no—
86#14519758—21no—
87#14519756C2×C411yescharacteristic
88#14519756C2×C411yescharacteristic
89#14519754—21no—
90#14519754—21no—
91#14519754—21no—
92#14519754—21no—
93#14519751C2×C411yescharacteristic
94#14519751C2×C411yescharacteristic
95#14519749—21no—
96#14519749—21no—
97#14519749—21no—
98#14519749—21no—
99#14519746—21no—
100Q8×Dic61C2×C411yescharacteristic, complemented
101Q8×Dic61C2×C411yescharacteristic, complemented
102C4×Dic122—21no—
103C4×Dic122—21no—
104#14519742—21no—
105#14519742—21no—
106#14519742C2×C411yescharacteristic, complemented
107#14519742C2×C411yescharacteristic, complemented
108D4×Dic61—21no—
109D4×Dic61—21no—
110D4×Dic61—21no—
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic, complemented
113D4×Dic61C2×C411yescharacteristic, complemented
114#14519739C2×C411yescharacteristic, complemented
115#14519739C2×C411yescharacteristic, complemented
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519736—21no—
127#14519736C2311yescharacteristic
128#14519735—21no—
129#14519735—21no—
130#14519734—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135C2×#11758196—28no—
136C2×#11758196—22no—
137C2×#11758196—22no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—42no—
141C2×C4×Dic61C2×C411yescharacteristic
142C2×C4×Dic61C2×C411yescharacteristic
143C2×C4×Dic61C2×C411yescharacteristic
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61D411yescharacteristic
149C2×C4×Dic61D411yescharacteristic
150C2×C4×Dic61D411yescharacteristic
151C2×C4×Dic61C2312yes—
152C2×C4×Dic61C2311yescharacteristic
153C2×C4×Dic61C2311yescharacteristic
154C42×D61—21no—
155#14519706—22no—
156#14519706—22no—
157#14519705—42no—
158#14519704—42no—
159#14519703—42no—
160C22⋊#92418—21no—
161C22⋊#92418—21no—
162#14519687—22no—
163C8×Dic61—22no—
164#14519684—22no—
165#14519684—22no—
166C2×#41×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169C2×M16×C61C2312yes—
170#123×C61—21no—
171C22⋊Q8×C61C2×C411yescharacteristic
172C22⋊Q8×C61C2×C411yescharacteristic
173#121×C61C2×C411yescharacteristic
174#121×C61C2×C411yescharacteristic
175#120×C61—21no—
176C4×D4×C61—21no—
177C4×D4×C61—21no—
178#117×C61C2311yescharacteristic
179C2×C42×C61—21no—
180C2×C42×C61—42no—
181C2×C42×C61C2312yes—
182#104×C61—42no—
183C22⋊C8×C61—21no—
184C22⋊C8×C61—21no—
185C24×C61C2×D411yescharacteristic
186#41×C61—22no—
187#41×C61—22no—
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61C22×C411yescharacteristic
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—24no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—42no—
199C22×C4×C61—42no—
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—22no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—42no—
217C22×Dic61—42no—
218C22×Dic61—42no—
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C22⋊C411yescharacteristic
224C22×Dic61C22⋊C411yescharacteristic
225C22×Dic61C22⋊C411yescharacteristic
226C22×Dic61C22⋊C411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758224—44no—
232#11758224—44no—
233#11758222—22no—
234#11758222—22no—
235C2×D244C22×C411yescharacteristic
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C22×C411yescharacteristic
242M16×C61—22no—
243M16×C61—22no—
244C2×C8×C61—22no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C22×C411yescharacteristic
248C4⋊C4×C61C22×C411yescharacteristic
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C42×C61—21no—
255C42×C61—22no—
256C42×C61—22no—
257C42×C61—42no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61C22×C411yescharacteristic
276C4⋊Dic61C22×C411yescharacteristic
277#11758196—28no—
278#11758196—28no—
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289C4×Dic61—21no—
290C4×Dic61—21no—
291C4×Dic61—21no—
292C4×Dic61—21no—
293C4×Dic61—21no—
294C4×Dic61—22no—
295C4×Dic61—22no—
296C4×Dic61—42no—
297C4×Dic61C22⋊C411yescharacteristic
298C4×Dic61C22⋊C411yescharacteristic
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22⋊C411yescharacteristic
301C4×Dic61C22⋊C411yescharacteristic
302C4×Dic61C22⋊C411yescharacteristic
303C4×Dic61C22⋊C411yescharacteristic
304C4×Dic61C22⋊C411yescharacteristic
305C4×Dic61C22×C411yescharacteristic
306C4×Dic61C22×C411yescharacteristic
307C4×Dic61C22×C411yescharacteristic
308C4×Dic61C22×C411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313#11758194—22no—
314#11758194—22no—
315C2×#92418—22no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—21no—
321C23×C61C2×C22⋊C411yescharacteristic
322C23×C61C2×C22⋊C411yescharacteristic
323C23×C61C22×D411yescharacteristic
324C22×D61—21no—
325Q8×C61—22no—
326D4×C61—22no—
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—42no—
330D4×C61—42no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—24no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—48no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61H(5,𝔽2)12yes—
350C2×C4×C612−1+412yes—
351C22⋊D61—42no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—42no—
355C22⋊D61—42no—
356C22⋊D61—42no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—24no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—42no—
373C2×Dic61—48no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61#10414yescomplemented
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386D244—22no—
387C4×D61—42no—
388C4×D61—42no—
389C4×D61—42no—
390Dic122—22no—
391Dic122—42no—
392Dic122—42no—
393C8×C61—42no—
394#92418—42no—
395#21899—611nomaximal, Sylow
396C22×C61—24no—
397C22×C61—24no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61C2×#10412yes—
408C22×C61#42112yes—
409C22×C61C22×C22⋊C411yescharacteristic
410C22×C61#53511yescharacteristic
411C22×C61#53611yescharacteristic
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—44no—
418C4×C61—41no—
419C4×C61—41no—
420C4×C61—41no—
421C4×C61#52012yes—
422C4×C61#53712yes—
423Dic61—21no—
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—44no—
430Dic61—41no—
431Dic61—41no—
432Dic61—41no—
433Dic61C2×#10412yes—
434Dic61C2×#10412yes—
435#3444—611no—
436#2920—611no—
437C2×C4×C4⋊C4—611no—
438#1986—612no—
439#1980—612no—
440#1896—611no—
441#1896—611no—
442#1896—611no—
443#1896D6111yescharacteristic, complemented
444#1806—612no—
445#1806—612no—
446C2×C61—21no—
447C2×C61—21no—
448C2×C61—22no—
449C2×C61—22no—
450C2×C61—81no—
451C2×C61#231111yescharacteristic
452C2×C61C22×#10411yescharacteristic
453C2×C61C2×#42111yescharacteristic
454D61—81no—
455#533—611no—
456#533—611no—
457#533—611no—
458#532—611no—
459#532—611no—
460#532—611no—
461#529—611no—
462#529—611no—
463#529—611no—
464#529—611no—
465#529—1221no—
466#529—1221no—
467#529—1221no—
468#529—1221no—
469#525—611no—
470#525—1221no—
471#525—1221no—
472#525C2×D6111yescharacteristic
473C4×#41—611no—
474C4×#41—611no—
475C4×#41—1221no—
476C4×#41—1221no—
477C22×C4⋊C4—1221no—
478C22×C42—611no—
479C22×C42—611no—
480C22×C42C2×D6111yescharacteristic
481#432—1221no—
482#432—1221no—
483#431—1221no—
484#431—1221no—
485#423—612no—
486C2×#104—612no—
487C2×#104—612no—
488C2×#104—612no—
489C2×#104C2×D6112yes—
490#407—611no—
491#407C2×D6111yescharacteristic
492C4×M16—612no—
493C4×C4⋊C4—612no—
494C4×C4⋊C4—612no—
495C4×C4⋊C4—1221no—
496C4×C4⋊C4—1221no—
497C2×#95—1221no—
498#339—612no—
499#339—612no—
500#339—612no—
501#339C2×D6112yes—
502C61#2189911yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41C22×D6111yescharacteristic
507C23×C4—21no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—1221no—
511C23×C4C22×D6111yescharacteristic
512C2×M16—612no—
513C2×M16C22×D6112yes—
514C4⋊Q8—611no—
515C4⋊Q8—611no—
516C4⋊Q8—611no—
517#127—611no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#125—611no—
523#125—611no—
524#125—1221no—
525#125—1221no—
526#124—611no—
527#124—611no—
528#124—1221no—
529#124—1221no—
530#123—21no—
531#123—1221no—
532#123—1221no—
533#123—1221no—
534#123—1221no—
535#123—1221no—
536C22⋊Q8—611no—
537C22⋊Q8—611no—
538C22⋊Q8—1221no—
539C22⋊Q8—1221no—
540C22⋊Q8—1221no—
541C22⋊Q8—1221no—
542C22⋊Q8C4×D6111yescharacteristic
543C22⋊Q8C4×D6111yescharacteristic
544#121—611no—
545#121—611no—
546#121—1221no—
547#121—1221no—
548#121—1221no—
549#121—1221no—
550#121C4×D6111yescharacteristic
551#121C4×D6111yescharacteristic
552#120—21no—
553#120—1221no—
554C4×Q8—611no—
555C4×Q8—611no—
556C4×Q8—611no—
557C4×Q8—611no—
558C4×Q8—1221no—
559C4×Q8—1221no—
560C4×Q8—1221no—
561C4×Q8—1221no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—611no—
565C4×D4—611no—
566C4×D4—611no—
567C4×D4—611no—
568C4×D4—1221no—
569C4×D4—1221no—
570C4×D4—1221no—
571C4×D4—1221no—
572C4×D4—1221no—
573C4×D4—1221no—
574C4×D4—1221no—
575C4×D4—1221no—
576C4×D4—1221no—
577C4×D4—1221no—
578C4×D4—1221no—
579C4×D4—1221no—
580C4×D4—1221no—
581C4×D4—1221no—
582#117—611no—
583#117—1221no—
584#117—1221no—
585#117—1221no—
586#117—1221no—
587#117—1221no—
588#117—1221no—
589#117—1221no—
590#117—1221no—
591#117C22×D6111yescharacteristic
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1228no—
595C2×C42—21no—
596C2×C42—42no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—612no—
610C2×C42—1221no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—2442no—
614C2×C42C22×D6112yes—
615C4⋊C8—1222no—
616C4⋊C8—1222no—
617#104—42no—
618#104—2442no—
619#104—2442no—
620#104—2442no—
621C22⋊C8—21no—
622C22⋊C8—21no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625#97—1222no—
626C4×C8—1222no—
627#95—1222no—
628#95—1222no—
629C24D4×D6111yescharacteristic
630#41—22no—
631#41—22no—
632#41—1222no—
633#41—1222no—
634#41—2444no—
635#41—2444no—
636C2×Q8—611no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8C2×C4×D6111yescharacteristic
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—611no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4C2×C4×D6111yescharacteristic
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1224no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1224no—
675C22×C4—1222no—
676C22×C4—1221no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4C2×C4×D6111yescharacteristic
681C22×C4C2×C4×D6111yescharacteristic
682C22×C4D4×D6111yescharacteristic
683C22×C4D4×D6111yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—22no—
687M16—22no—
688M16—1222no—
689M16—1222no—
690C2×C8—22no—
691C2×C8—1222no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1228no—
709C4⋊C4—1228no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4C2×C4×D6111yescharacteristic
713C4⋊C4C2×C4×D6111yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C42—21no—
733C42—22no—
734C42—22no—
735C42—42no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—1221no—
753C42—1221no—
754C42—1221no—
755C42—1221no—
756C42—1221no—
757C42—1222no—
758C42—1222no—
759C42—2442no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—1221no—
766C23C22⋊C4×D6111yescharacteristic
767C23C22⋊C4×D6111yescharacteristic
768C23C2×D4×D6111yescharacteristic
769Q8—22no—
770Q8—1222no—
771Q8—2442no—
772Q8—2442no—
773D4—22no—
774D4—42no—
775D4—42no—
776D4—41no—
777D4—41no—
778D4—1222no—
779D4—2442no—
780D4—2442no—
781D4—2442no—
782D4—2442no—
783D4—2441no—
784D4—2441no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—614no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2442no—
827C2×C4—2448no—
828C2×C4—2442no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4C22⋊C4×D6111yescharacteristic
832C2×C4C22⋊C4×D6111yescharacteristic
833C2×C4C22×C4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4#1451982212yes—
836C2×C4#1451982412yes—
837C8—42no—
838C8—2442no—
839C22—24no—
840C22—24no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22#104×D6112yes—
854C22#1683977712yes—
855C22C2×C22⋊C4×D6111yescharacteristic
856C22#1684032711yescharacteristic
857C22#1684033411yescharacteristic
858C4—21no—
859C4—21no—
860C4—44no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—612no—
865C4—612no—
866C4—1221no—
867C4—1221no—
868C4—1221no—
869C4—1221no—
870C4—1221no—
871C4—1221no—
872C4—2444no—
873C4—2441no—
874C4—2441no—
875C4—2441no—
876C4#1684024112yes—
877C4#1684033912yes—
878C2—21no—
879C2—22no—
880C2—22no—
881C2—21no—
882C2—81no—
883C2—4881no—
884C2#2144840611yescharacteristic
885C2C2×#104×D6111yescharacteristic
886C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1896C2
socleC22×C61C22×C22⋊C4
prime radical#21459111C2
cosocleC22×C4×C61C24
hypercenter#1896D61
hypocenterC61#21899
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C2×C4×#11758196C2semidirect
4. #21446761C2semidirect
5. #21446736C2semidirect
6. #21446263C2semidirect
7. #21446262C2semidirect
8. #21446260C2semidirect
9. #21445838C2semidirect
10. #21445837C2semidirect
11. C61×#1896C2semidirect
13. #16840314C4semidirect
14. #16840314C4semidirect
16. #16840307C4semidirect
17. #16840307C4semidirect
18. #16840298C4semidirect
19. #16840298C4semidirect
20. #16840293C4semidirect
21. #16840293C4semidirect
66. #14519776C2×C4semidirect
67. #14519776C2×C4semidirect
68. #14519775C2×C4semidirect
69. #14519773C2×C4semidirect
74. #14519768C2×C4semidirect
75. #14519768C2×C4semidirect
78. #14519766C2×C4semidirect
79. #14519764C2×C4semidirect
100. Q8×Dic61C2×C4semidirect
101. Q8×Dic61C2×C4semidirect
106. #14519742C2×C4semidirect
107. #14519742C2×C4semidirect
112. D4×Dic61C2×C4semidirect
113. D4×Dic61C2×C4semidirect
114. #14519739C2×C4semidirect
115. #14519739C2×C4semidirect
377. C2×Dic61#104semidirect
443. #1896D61semidirect
502. C61#21899semidirect

Maximal subgroups

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

subgroupindex
#214591112
#214544482
C2×C4×#117581962
#214467612
#214467362
#214462632
#214462622
#214462602
#214458382
#214458372
C61×#18962
#2189961