Finite Group Databasebeta

← #30616880

Subgroups — #30616880

Order 15616.

1344 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840830C211yesmaximal, characteristic
2C2×#16840802C211yesmaximal, characteristic, complemented
3C2×Q16×#6923C211yesmaximal, characteristic, complemented
4#21462306C211yesmaximal, characteristic
5#21461813C211yesmaximal, characteristic, complemented
6#21461813C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic
8#21461785C211yesmaximal, characteristic, complemented
9#21461783C211yesmaximal, characteristic, complemented
10#21461770C211yesmaximal, characteristic
11#21461658C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic
15#451×D61C211yesmaximal, characteristic
16#16840830—24no—
17#16840830—24no—
18C2×Q8×#6923—21no—
19C2×Q8×#6923—21no—
20C2×Q8×#6923C2211yescharacteristic
21C2×Q8×#6923C2211yescharacteristic
22C2×Q8×#6923C2211yescharacteristic
23C2×Q8×#6923C2211yescharacteristic
24C2×Q8×#6923C2211yescharacteristic
25C2×#14519856—21no—
26C2×#14519856—21no—
27C2×#14519856C2211yescharacteristic
28C2×#14519856C2211yescharacteristic
29#16840802—24no—
30Q16×#6923—24no—
31C2×#14519846C2211yescharacteristic
32C2×#14519845C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519840C2211yescharacteristic
36C2×#14519840C2211yescharacteristic
37C2×#14519840C2211yescharacteristic
38C2×#14519840C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C2×C8×#6923C2211yescharacteristic
42(C2×#6923)⋊Q8C2211yescharacteristic
43#16840713—21no—
44#16840713C2211yescharacteristic
45#16840712—21no—
46#16840712—21no—
47#16840711—21no—
48#16840704C2211yescharacteristic
49C4⋊C4×#6923C2211yescharacteristic
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54(C2×#6923)⋊C8C2211yescharacteristic
55(C2×#6923)⋊C8C2211yescharacteristic
56C22×Q8×D61C2211yescharacteristic
57C2×Q16×D61C2211yescharacteristic
58C2×Q16×D61C2211yescharacteristic
59C22⋊Q8×D61C2211yescharacteristic
60#16839920C411yescharacteristic, complemented
61#16839919C411yescharacteristic, complemented
62#16839919C411yescharacteristic, complemented
63#16839918C411yescharacteristic, complemented
64#16839917C411yescharacteristic, complemented
65#16839916C411yescharacteristic, complemented
66#16839916C411yescharacteristic, complemented
67#103×D61C2211yescharacteristic
68#103×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#451C411yescharacteristic, complemented
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—28no—
74Q8×#6923—28no—
75Q8×#6923—22no—
76Q8×#6923—22no—
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—22no—
80Q8×#6923—22no—
81Q8×#6923—22no—
82Q8×#6923—22no—
83Q8×#6923D414yes—
84Q8×#6923D414yes—
85#14519856—28no—
86#14519856—28no—
87#14519856—22no—
88#14519856—22no—
89#14519856—22no—
90#14519856—22no—
91C2×C4⋊#6923—21no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—21no—
96C2×C4⋊#6923—21no—
97C2×C4⋊#6923D411yescharacteristic
98C2×C4⋊#6923D411yescharacteristic
99C2×C4⋊#6923C2311yescharacteristic
100C2×C4⋊#6923C2311yescharacteristic
101C2×C4⋊#6923C2311yescharacteristic
102C2×C4⋊#6923C2311yescharacteristic
103C2×C22⋊#6923—21no—
104C2×C22⋊#6923—21no—
105C2×C22⋊#6923D411yescharacteristic
106C2×C22⋊#6923D411yescharacteristic
107C2×C4×#6923—21no—
108C2×C4×#6923—21no—
109C2×C4×#6923—21no—
110C2×C4×#6923—21no—
111C2×C4×#6923—21no—
112C2×C4×#6923—21no—
113C2×C4×#6923—21no—
114C2×C4×#6923C2311yescharacteristic
115C2×C4×#6923C2311yescharacteristic
116#14519846—22no—
117#14519845—22no—
118#14519840—22no—
119#14519840—22no—
120#14519840—22no—
121#14519840—22no—
122#14519840—22no—
123#14519840—22no—
124#14519834—21no—
125C22⋊#92420—21no—
126#14519831—22no—
127C8×#6923—22no—
128(C2×#6923)⋊C4—21no—
129(C2×#6923)⋊C4—21no—
130(C2×#6923)⋊C4—21no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133C22×Dic122—21no—
134C22×Dic122C2×C411yescharacteristic
135C2×Q8×D61—22no—
136C2×Q8×D61—22no—
137C2×Q8×D61—22no—
138C2×Q8×D61—22no—
139C2×Q8×D61—21no—
140C2×Q8×D61—21no—
141C2×Q8×D61C2×C411yescharacteristic
142C2×Q8×D61C2×C411yescharacteristic
143C2×Q8×D61C2311yescharacteristic
144C2×Q8×D61C2311yescharacteristic
145C2×Q8×D61C2311yescharacteristic
146C22×C4×D61—21no—
147C22×C4×D61C2311yescharacteristic
148C2×Dic244C2×C411yescharacteristic
149C2×Dic244C2×C411yescharacteristic
150C2×#11758202C2×C411yescharacteristic
151C2×#11758202C2×C411yescharacteristic
152C2×#11758202C2×C411yescharacteristic
153C2×#11758202C2×C411yescharacteristic
154Q16×D61—22no—
155Q16×D61—22no—
156Q16×D61—22no—
157Q16×D61—22no—
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519757C2×C411yescharacteristic
161#14519756C2×C411yescharacteristic
162#14519755—21no—
163#14519754—21no—
164#14519753C2×C411yescharacteristic
165C4⋊C4×D61—21no—
166C4⋊C4×D61C2311yescharacteristic
167C22⋊C4×D61—21no—
168#14519702C2×C411yescharacteristic
169#14519702C2×C411yescharacteristic
170#14519701C2×C411yescharacteristic
171#14519701C2×C411yescharacteristic
172#14519700C2×C411yescharacteristic
173#14519700C2×C411yescharacteristic
174C22⋊#92418C2×C411yescharacteristic
175#14519689C2×C411yescharacteristic
176#14519689C2×C411yescharacteristic
177C22×Q8×C61C2×C411yescharacteristic
178C2×Q16×C61C2×C411yescharacteristic
179C2×Q16×C61C2×C411yescharacteristic
180C22⋊Q8×C61C2×C411yescharacteristic
181#103×C61C2×C411yescharacteristic
182#103×C61C2×C411yescharacteristic
183C22⋊C8×C61C2×C411yescharacteristic
184C23×D61C2×D411yescharacteristic
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923C2×D411yescharacteristic
190C22×#6923C2×D411yescharacteristic
191C22×#6923C2×D411yescharacteristic
192C22×#6923C2×D411yescharacteristic
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61—21no—
196C2×Q8×C61C22×C411yescharacteristic
197C2×Q8×C61C22×C411yescharacteristic
198C2×Q8×C61C22×C411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61C22×C411yescharacteristic
201C22×Dic61—21no—
202C22×Dic61#4111yescharacteristic
203Q8×D61—24no—
204Q8×D61—24no—
205Q8×D61—24no—
206Q8×D61—24no—
207Q8×D61—22no—
208Q8×D61—22no—
209Q8×D61—21no—
210Q8×D61—21no—
211Q8×D61—21no—
212Q8×D61—21no—
213Q8×D61—22no—
214Q8×D61—22no—
215Q8×D61—21no—
216Q8×D61—21no—
217Q8×D61—21no—
218Q8×D61—21no—
219Q8×D61C2×D412yes—
220Q8×D61C2×D412yes—
221Q8×D61#4112yes—
222Q8×D61#4112yes—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61#4111yescharacteristic
238C2×C4×D61C2411yescharacteristic
239C2×Dic122—24no—
240C2×Dic122—24no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—21no—
249C2×Dic122C22×C411yescharacteristic
250C2×Dic122C22×C411yescharacteristic
251C2×Dic122C22×C411yescharacteristic
252C22⋊#6923—24no—
253C22⋊#6923—22no—
254C22⋊#6923—22no—
255C22⋊#6923—81no—
256C2×#92420—21no—
257C2×#92420—21no—
258C4⋊#6923—24no—
259C4⋊#6923—24no—
260C4⋊#6923—24no—
261C4⋊#6923—24no—
262C4⋊#6923—22no—
263C4⋊#6923—22no—
264C4⋊#6923—21no—
265C4⋊#6923—21no—
266C4⋊#6923—21no—
267C4⋊#6923—21no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—42no—
271C4⋊#6923—81no—
272C4⋊#6923C2×D412yes—
273C4⋊#6923C2×D412yes—
274C4×#6923—24no—
275C4×#6923—24no—
276C4×#6923—24no—
277C4×#6923—24no—
278C4×#6923—24no—
279C4×#6923—21no—
280C4×#6923—21no—
281C4×#6923—42no—
282C4×#6923—81no—
283C4×#6923C2×D412yes—
284C4×#6923C2×D412yes—
285D61⋊C8—21no—
286D61⋊C8—21no—
287D61⋊C8—21no—
288D61⋊C8—21no—
289Q16×C61—22no—
290Q16×C61—22no—
291C2×C8×C61C22×C411yescharacteristic
292C2×C8×C61C22×C411yescharacteristic
293C4⋊C4×C61—21no—
294C4⋊C4×C61C22×C411yescharacteristic
295C22⋊C4×C61—21no—
296C22⋊Dic61—21no—
297#11758202—22no—
298#11758202—22no—
299#11758202—22no—
300#11758202—22no—
301#11758198—21no—
302#11758198—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C22×C411yescharacteristic
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308C2×#92418C22×C411yescharacteristic
309C2×#92418C22×C411yescharacteristic
310Dic244—22no—
311Dic244—22no—
312C8×D61—21no—
313C8×D61—21no—
314C8×D61—21no—
315C8×D61—21no—
316C23×C61C4×D411yescharacteristic
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61C4×D411yescharacteristic
324C22×D61C22×D411yescharacteristic
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—21no—
329C2×#6923—21no—
330C2×#6923—21no—
331C2×#6923—22no—
332C2×#6923—22no—
333C2×#6923—21no—
334C2×#6923—21no—
335C2×#6923—21no—
336C2×#6923—21no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923#12012yes—
348C2×#6923#12012yes—
349Q8×C61—24no—
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—21no—
353Q8×C61—21no—
354Q8×C61C4×D412yes—
355Q8×C61C4×D412yes—
356C2×C4×C61—24no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61C4×D411yescharacteristic
364C2×C4×C61C23×C411yescharacteristic
365C2×Dic61—24no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61C4×D411yescharacteristic
373C2×Dic61C2×#4111yescharacteristic
374C4×D61—24no—
375C4×D61—24no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—21no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—41no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61C22×D411yescharacteristic
391C4×D61C22×D411yescharacteristic
392C4×D61C2×#4111yescharacteristic
393C4×D61C2×#4111yescharacteristic
394Dic122—24no—
395Dic122—24no—
396Dic122—24no—
397Dic122—21no—
398Dic122—21no—
399Dic122—22no—
400Dic122—22no—
401Dic122—22no—
402Dic122—22no—
403Dic122—21no—
404Dic122—21no—
405Dic122—41no—
406Dic122—41no—
407Dic122C4×D412yes—
408Dic122C4×D412yes—
409#92420—41no—
410#92420—41no—
411C8×C61—21no—
412C8×C61—21no—
413#92418—21no—
414#92418—21no—
415#21463—611nomaximal, Sylow
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—21no—
419C22×C61C2×C4×D411yescharacteristic
420C2×D61—21no—
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61C2×#12011yescharacteristic
428C2×D61#52511yescharacteristic
429C2×D61#57711yescharacteristic
430C2×D61#57811yescharacteristic
431C2×D61#57811yescharacteristic
432C2×D61#57811yescharacteristic
433#6923—22no—
434#6923—22no—
435#6923—41no—
436#6923—42no—
437#6923—41no—
438#6923—42no—
439#6923—81no—
440#6923—81no—
441C4×C61—22no—
442C4×C61—22no—
443C4×C61—21no—
444C4×C61—41no—
445C4×C61—41no—
446C4×C61C2×C4×D411yescharacteristic
447C4×C61C2×C4×D411yescharacteristic
448Dic61—21no—
449Dic61—22no—
450Dic61—22no—
451Dic61—41no—
452Dic61—41no—
453Dic61#52511yescharacteristic
454Dic61#52511yescharacteristic
455C2×#519—611no—
456C2×#451—611no—
457C2×#441—611no—
458C2×C4×Q16—611no—
459#2323—611no—
460#1878—611no—
461#1878—611no—
462#1873—611no—
463#1865—611no—
464#1863—611no—
465#1854—611no—
466#1787—611no—
467#1763—611no—
468C4×#103—611no—
469#1750—611no—
470C2×C61—41no—
471C2×C61C4×#12011yescharacteristic
472C2×C61#294711yescharacteristic
473C2×C61#295011yescharacteristic
474D61—41no—
475D61#301111yescharacteristic
476D61#301311yescharacteristic
477D61#312111yescharacteristic
478D61#312711yescharacteristic
479C23×Q8—611no—
480C22×Q16—611no—
481C22×Q16—611no—
482C2×C22⋊Q8—611no—
483#519—1224no—
484#519—1224no—
485C2×C4×Q8—611no—
486C2×C4×Q8—611no—
487C2×C4×Q8—611no—
488C2×C4×Q8—611no—
489C2×C4×Q8—611no—
490C2×C4×Q8—1221no—
491C2×C4×Q8—1221no—
492C2×#117—611no—
493C2×#117—611no—
494C2×#117—1221no—
495C2×#117—1221no—
496#451—611no—
497#451—611no—
498#451—611no—
499#451—611no—
500#451—611no—
501#451—611no—
502#451—611no—
503#451#692311yescharacteristic, complemented
504#441—1224no—
505C4×Q16—1224no—
506C2×#107—611no—
507C2×#106—611no—
508C2×#103—611no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#103—611no—
512C2×#103—611no—
513C2×#103—611no—
514C2×#103—611no—
515C2×#103—611no—
516C2×C22⋊C8—611no—
517C2×C22⋊C8—611no—
518C2×#97—611no—
519C2×C4×C8—611no—
520#391—611no—
521#389—611no—
522#389—1221no—
523#388—1221no—
524#388—1221no—
525#387—1221no—
526#380—611no—
527C4×C4⋊C4—611no—
528#340—611no—
529#340—611no—
530#340—611no—
531#340—611no—
532#336—611no—
533#336—611no—
534C61#2146311yescharacteristic, complemented, Sylow
535C22×Q8—611no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—611no—
539C22×Q8—611no—
540C22×Q8—611no—
541C22×Q8—1221no—
542C22×Q8—1221no—
543C22×Q8—1221no—
544C22×Q8—1222no—
545C22×Q8—1222no—
546C22×Q8—1222no—
547C22×Q8—1222no—
548C22×Q8C2×#692311yescharacteristic
549C23×C4—611no—
550C23×C4—1221no—
551C2×Q16—611no—
552C2×Q16—611no—
553C2×Q16—611no—
554C2×Q16—611no—
555C2×Q16—611no—
556C2×Q16—611no—
557C2×Q16—1222no—
558C2×Q16—1222no—
559C2×Q16—1222no—
560C2×Q16—1222no—
561C2×Q16C2×#692311yescharacteristic
562C2×Q16C2×#692311yescharacteristic
563C22×C8—611no—
564C22×C8—611no—
565C22×C8—611no—
566C22×C8—611no—
567C22⋊Q8—611no—
568C22⋊Q8—611no—
569C22⋊Q8—611no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8C2×#692311yescharacteristic
573C4×Q8—614no—
574C4×Q8—614no—
575C4×Q8—1222no—
576C4×Q8—1222no—
577C4×Q8—1222no—
578C4×Q8—1222no—
579C4×Q8—1222no—
580C4×Q8—1222no—
581C4×Q8—1222no—
582C4×Q8—1222no—
583C4×Q8—1228no—
584C4×Q8—1228no—
585#117—1222no—
586#117—1222no—
587#117—1222no—
588#117—1222no—
589#117—1228no—
590#117—1228no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619#107—1222no—
620#106—1222no—
621#103—611no—
622#103—611no—
623#103—611no—
624#103—611no—
625#103—611no—
626#103—611no—
627#103—1222no—
628#103—1222no—
629#103—1222no—
630#103—1222no—
631#103—1222no—
632#103—1222no—
633#103C2×#692311yescharacteristic
634#103C2×#692311yescharacteristic
635C22⋊C8—611no—
636C22⋊C8—611no—
637C22⋊C8—611no—
638C22⋊C8—1221no—
639C22⋊C8—1221no—
640C22⋊C8C2×#692311yescharacteristic
641#97—1222no—
642C4×C8—1222no—
643#95—1221no—
644#95—1221no—
645#95—1221no—
646#95—1221no—
647#95—1221no—
648C24—611no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—21no—
652C2×Q8—612no—
653C2×Q8—612no—
654C2×Q8—612no—
655C2×Q8—612no—
656C2×Q8—611no—
657C2×Q8—611no—
658C2×Q8—611no—
659C2×Q8—1221no—
660C2×Q8—1221no—
661C2×Q8—1221no—
662C2×Q8—1221no—
663C2×Q8—1221no—
664C2×Q8—1222no—
665C2×Q8—1222no—
666C2×Q8—1224no—
667C2×Q8—1224no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—1221no—
674C2×Q8—1221no—
675C2×Q8—1221no—
676C2×Q8—1222no—
677C2×Q8—1222no—
678C2×Q8—1224no—
679C2×Q8—1224no—
680C2×Q8—1224no—
681C2×Q8—1224no—
682C2×Q8—1222no—
683C2×Q8—1222no—
684C2×Q8—1221no—
685C2×Q8C22×#692311yescharacteristic
686C2×Q8C22×#692311yescharacteristic
687C2×Q8C22×#692311yescharacteristic
688C22×C4—21no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1224no—
707C22×C4—1224no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4C22×#692311yescharacteristic
716Q16—22no—
717Q16—22no—
718Q16—1222no—
719Q16—1222no—
720Q16—1222no—
721Q16—1222no—
722Q16—1222no—
723Q16—1222no—
724C2×C8—611no—
725C2×C8—611no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8C22×#692311yescharacteristic
737C2×C8C22×#692311yescharacteristic
738C4⋊C4—21no—
739C4⋊C4—612no—
740C4⋊C4—612no—
741C4⋊C4—611no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1222no—
748C4⋊C4—1222no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1224no—
756C4⋊C4—1224no—
757C4⋊C4—1221no—
758C4⋊C4—4881no—
759C4⋊C4—2442no—
760C4⋊C4C22×#692311yescharacteristic
761C22⋊C4—21no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1222no—
765C22⋊C4—1222no—
766C22⋊C4—1224no—
767C22⋊C4—1221no—
768C22⋊C4—4881no—
769C42—612no—
770C42—612no—
771C42—1221no—
772C42—1221no—
773C42—1224no—
774C42—1224no—
775C42—1224no—
776C42—1224no—
777C42—1224no—
778C42—4881no—
779C42—2442no—
780C23—611no—
781C23—611no—
782C23—1221no—
783C23—1221no—
784C23—1221no—
785C23—1221no—
786C23—1221no—
787C23—1221no—
788C23D4×#692311yescharacteristic
789Q8—24no—
790Q8—21no—
791Q8—21no—
792Q8—21no—
793Q8—21no—
794Q8—612no—
795Q8—612no—
796Q8—1222no—
797Q8—1222no—
798Q8—1222no—
799Q8—1222no—
800Q8—1224no—
801Q8—1224no—
802Q8—1224no—
803Q8—1221no—
804Q8—1221no—
805Q8—1221no—
806Q8—1221no—
807Q8—2441no—
808Q8—2441no—
809Q8D4×#692312yes—
810Q8D4×#692312yes—
811C2×C4—24no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—612no—
824C2×C4—612no—
825C2×C4—611no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1221no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1224no—
835C2×C4—1224no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1224no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4D4×#692311yescharacteristic
872C2×C4C23×#692311yescharacteristic
873C8—21no—
874C8—21no—
875C8—1221no—
876C8—1221no—
877C8—2441no—
878C8—2441no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—611no—
883C22—611no—
884C22—611no—
885C22—611no—
886C22—611no—
887C22—611no—
888C22—1221no—
889C22—1221no—
890C22—1221no—
891C22—2441no—
892C22—2441no—
893C22—2441no—
894C22—2441no—
895C22C2×D4×#692311yescharacteristic
896C4—22no—
897C4—22no—
898C4—21no—
899C4—41no—
900C4—41no—
901C4—611no—
902C4—611no—
903C4—1222no—
904C4—1222no—
905C4—1221no—
906C4—1222no—
907C4—1222no—
908C4—4881no—
909C4—4881no—
910C4—2441no—
911C4—2441no—
912C4—2442no—
913C4—2442no—
914C4—2441no—
915C4—2441no—
916C4C2×D4×#692311yescharacteristic
917C4C2×D4×#692311yescharacteristic
918C2—41no—
919C2—611no—
920C2—611no—
921C2—611no—
922C2—611no—
923C2—2441no—
924C2#120×#692311yescharacteristic
925C2#2146257711yescharacteristic
926C2#2146258011yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#451C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#451#6923
hypocenterC61#21463
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#16840802C2semidirect
3. C2×Q16×#6923C2semidirect
5. #21461813C2semidirect
6. #21461813C2semidirect
8. #21461785C2semidirect
9. #21461783C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
60. #16839920C4semidirect
61. #16839919C4semidirect
62. #16839919C4semidirect
63. #16839918C4semidirect
64. #16839917C4semidirect
65. #16839916C4semidirect
66. #16839916C4semidirect
70. C61×#451C4semidirect
503. #451#6923semidirect
534. C61#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#168408302
C2×#168408022
C2×Q16×#69232
#214623062
#214618132
#214618052
#214617852
#214617832
#214617702
#214616582
#214615922
#103×#69232
#214615502
#451×D612
#2146361