Finite Group Databasebeta

← #30616879

Subgroups — #30616879

Order 15616.

1400 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840830C211yesmaximal, characteristic, complemented
2C2×#16840801C211yesmaximal, characteristic, complemented
3C2×SD16×#6923C211yesmaximal, characteristic, complemented
4#21462307C211yesmaximal, characteristic
5#21461815C211yesmaximal, characteristic, complemented
6#21461815C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic
8#21461785C211yesmaximal, characteristic, complemented
9#21461783C211yesmaximal, characteristic, complemented
10#21461770C211yesmaximal, characteristic, complemented
11#21461658C211yesmaximal, characteristic, complemented
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#448×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×D4×#6923C2211yescharacteristic
25C2×#14519856—21no—
26C2×#14519856—21no—
27C2×#14519856C2211yescharacteristic
28C2×#14519856C2211yescharacteristic
29#16840801—24no—
30SD16×#6923—24no—
31C2×#14519846C2211yescharacteristic
32C2×#14519845C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519840C2211yescharacteristic
36C2×#14519840C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C2×C8×#6923C2211yescharacteristic
42#16840714—21no—
43#16840714C2211yescharacteristic
44#16840713C2211yescharacteristic
45#16840712—21no—
46#16840710—21no—
47#16840709—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×SD16×D61C2211yescharacteristic
58C2×SD16×D61C2211yescharacteristic
59#121×D61C2211yescharacteristic
60#16839903C411yescharacteristic, complemented
61#16839902C411yescharacteristic, complemented
62#16839902C411yescharacteristic, complemented
63#16839901C411yescharacteristic, complemented
64#16839900C411yescharacteristic, complemented
65#16839899C411yescharacteristic, complemented
66#16839899C411yescharacteristic, complemented
67#103×D61C2211yescharacteristic
68#103×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#448C411yescharacteristic, complemented
71C23×#6923—21no—
72C2×D61⋊C8C2311yescharacteristic
73C2×D61⋊C8C2311yescharacteristic
74Q8×#6923—28no—
75Q8×#6923—28no—
76Q8×#6923—22no—
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—22no—
80Q8×#6923—22no—
81Q8×#6923—22no—
82Q8×#6923D414yescomplemented
83Q8×#6923D414yescomplemented
84D4×#6923—22no—
85D4×#6923—22no—
86#14519856—28no—
87#14519856—28no—
88#14519856—22no—
89#14519856—22no—
90#14519856—22no—
91#14519856—22no—
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⋊#6923—21no—
106C2×C22⋊#6923—21no—
107C2×C22⋊#6923—21no—
108C2×C22⋊#6923D411yescharacteristic
109C2×C22⋊#6923D411yescharacteristic
110C2×C4×#6923—21no—
111C2×C4×#6923—21no—
112C2×C4×#6923—21no—
113C2×C4×#6923—21no—
114C2×C4×#6923—21no—
115C2×C4×#6923—21no—
116C2×C4×#6923C2311yescharacteristic
117C2×C4×#6923C2311yescharacteristic
118#14519846—22no—
119#14519845—22no—
120#14519840—22no—
121#14519840—22no—
122#14519840—22no—
123#14519840—22no—
124#14519839—22no—
125#14519839—22no—
126#14519834—21no—
127C22⋊#92420—21no—
128#14519831—22no—
129C8×#6923—22no—
130(C2×#6923)⋊C4—21no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133C22×Dic122—21no—
134C22×Dic122C2×C411yescharacteristic, complemented
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, complemented
142C2×Q8×D61C2×C411yescharacteristic, complemented
143C2×Q8×D61C2311yescharacteristic
144C2×Q8×D61C2311yescharacteristic
145C2×D4×D61—21no—
146C2×D4×D61C2311yescharacteristic
147C22×C4×D61—21no—
148C22×C4×D61C2311yescharacteristic
149C2×#11758190C2×C411yescharacteristic
150C2×#11758190C2×C411yescharacteristic
151C2×#11758200C2×C411yescharacteristic
152C2×#11758200C2×C411yescharacteristic
153C2×#11758201C2×C411yescharacteristic
154C2×#11758201C2×C411yescharacteristic
155SD16×D61—22no—
156SD16×D61—22no—
157SD16×D61—22no—
158SD16×D61—22no—
159C2×C8×D61C2311yescharacteristic
160C2×C8×D61C2311yescharacteristic
161#14519752C2×C411yescharacteristic
162#14519751C2×C411yescharacteristic
163#14519750—21no—
164#14519749—21no—
165#14519748C2×C411yescharacteristic
166C4⋊C4×D61C2311yescharacteristic
167C22⋊C4×D61—21no—
168#14519702C2×C411yescharacteristic, complemented
169#14519702C2×C411yescharacteristic, complemented
170#14519701C2×C411yescharacteristic, complemented
171#14519701C2×C411yescharacteristic, complemented
172#14519700C2×C411yescharacteristic, complemented
173#14519700C2×C411yescharacteristic, complemented
174C22⋊#92418C2×C411yescharacteristic, complemented
175#14519689C2×C411yescharacteristic, complemented
176#14519689C2×C411yescharacteristic, complemented
177C22×Q8×C61C2×C411yescharacteristic, complemented
178C2×SD16×C61C2×C411yescharacteristic
179C2×SD16×C61C2×C411yescharacteristic
180#121×C61C2×C411yescharacteristic
181#103×C61C2×C411yescharacteristic, complemented
182#103×C61C2×C411yescharacteristic, complemented
183C22⋊C8×C61C2×C411yescharacteristic, complemented
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—42no—
191C22×#6923—81no—
192C22×#6923—81no—
193C22×#6923C2×D411yescharacteristic
194C22×#6923C2×D411yescharacteristic
195C22×#6923C2×D411yescharacteristic
196C22×#6923C2×D411yescharacteristic
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61—21no—
200C2×Q8×C61C22×C411yescharacteristic
201C2×Q8×C61C22×C411yescharacteristic
202C2×D4×C61—21no—
203C2×D4×C61C22×C411yescharacteristic
204C22×C4×C61—21no—
205C22×C4×C61C22×C411yescharacteristic
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C22×Dic61—21no—
210C22×Dic61#4111yescharacteristic
211Q8×D61—24no—
212Q8×D61—24no—
213Q8×D61—24no—
214Q8×D61—24no—
215Q8×D61—22no—
216Q8×D61—22no—
217Q8×D61—21no—
218Q8×D61—21no—
219Q8×D61—21no—
220Q8×D61—21no—
221Q8×D61—22no—
222Q8×D61—22no—
223Q8×D61C2×D412yes—
224Q8×D61C2×D412yes—
225Q8×D61#4112yes—
226Q8×D61#4112yes—
227D4×D61—21no—
228D4×D61—21no—
229D4×D61—21no—
230D4×D61—21no—
231D4×D61—81no—
232D4×D61—81no—
233C2×D244—21no—
234C2×D244C22×C411yescharacteristic
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61C22×C411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61#4111yescharacteristic
249C2×C4×D61C2411yescharacteristic
250C2×Dic122—24no—
251C2×Dic122—24no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—22no—
258C2×Dic122—22no—
259C2×Dic122C22×C411yescharacteristic
260C2×Dic122C22×C411yescharacteristic
261C22⋊#6923—24no—
262C22⋊#6923—22no—
263C22⋊#6923—22no—
264C22⋊#6923—42no—
265C22⋊#6923—81no—
266C22⋊#6923—81no—
267C22⋊#6923—81no—
268C2×#92420—21no—
269C2×#92420—21no—
270C4⋊#6923—24no—
271C4⋊#6923—24no—
272C4⋊#6923—24no—
273C4⋊#6923—24no—
274C4⋊#6923—22no—
275C4⋊#6923—22no—
276C4⋊#6923—21no—
277C4⋊#6923—21no—
278C4⋊#6923—21no—
279C4⋊#6923—21no—
280C4⋊#6923—21no—
281C4⋊#6923—21no—
282C4⋊#6923—81no—
283C4⋊#6923C2×D412yes—
284C4⋊#6923C2×D412yes—
285C4×#6923—24no—
286C4×#6923—24no—
287C4×#6923—24no—
288C4×#6923—24no—
289C4×#6923—24no—
290C4×#6923—21no—
291C4×#6923—21no—
292C4×#6923—81no—
293C4×#6923C2×D412yes—
294C4×#6923C2×D412yes—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299SD16×C61—22no—
300SD16×C61—22no—
301C2×C8×C61C22×C411yescharacteristic
302C2×C8×C61C22×C411yescharacteristic
303C4⋊C4×C61C22×C411yescharacteristic
304C22⋊C4×C61—21no—
305C22⋊Dic61—21no—
306#11758201—22no—
307#11758201—22no—
308#11758200—22no—
309#11758200—22no—
310#11758198—21no—
311#11758198—21no—
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314C2×#92418C22×C411yescharacteristic
315C2×#92418C22×C411yescharacteristic
316#11758190—22no—
317#11758190—22no—
318C8×D61—21no—
319C8×D61—21no—
320C8×D61—21no—
321C8×D61—21no—
322C23×C61—21no—
323C23×C61C4×D411yescharacteristic
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61C4×D411yescharacteristic
338C22×D61C22×D411yescharacteristic
339C2×#6923—21no—
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—21no—
344C2×#6923—21no—
345C2×#6923—22no—
346C2×#6923—22no—
347C2×#6923—21no—
348C2×#6923—21no—
349C2×#6923—21no—
350C2×#6923—21no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—84no—
362C2×#6923#12012yes—
363C2×#6923#12012yes—
364Q8×C61—24no—
365Q8×C61—21no—
366Q8×C61—21no—
367Q8×C61C4×D412yes—
368Q8×C61C4×D412yes—
369D4×C61—21no—
370D4×C61—21no—
371D4×C61—81no—
372C2×C4×C61—24no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61C4×D411yescharacteristic
379C2×C4×C61C23×C411yescharacteristic
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—24no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61C4×D411yescharacteristic
391C2×Dic61C2×#4111yescharacteristic
392D244—21no—
393D244—21no—
394D244—81no—
395C4×D61—24no—
396C4×D61—24no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—21no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61C22×D411yescharacteristic
410C4×D61C22×D411yescharacteristic
411C4×D61C2×#4111yescharacteristic
412C4×D61C2×#4111yescharacteristic
413Dic122—24no—
414Dic122—24no—
415Dic122—24no—
416Dic122—21no—
417Dic122—21no—
418Dic122—22no—
419Dic122—22no—
420Dic122—22no—
421Dic122—22no—
422Dic122C4×D412yes—
423Dic122C4×D412yes—
424#92420—41no—
425#92420—41no—
426C8×C61—21no—
427C8×C61—21no—
428#92418—21no—
429#92418—21no—
430#21462—611nomaximal, Sylow
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61C2×C4×D411yescharacteristic
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61C2×#12011yescharacteristic
453C2×D61#52511yescharacteristic
454C2×D61#57711yescharacteristic
455C2×D61#57711yescharacteristic
456C2×D61#57711yescharacteristic
457C2×D61#57811yescharacteristic
458#6923—22no—
459#6923—22no—
460#6923—41no—
461#6923—42no—
462#6923—41no—
463#6923—42no—
464#6923—81no—
465#6923—81no—
466C4×C61—22no—
467C4×C61—22no—
468C4×C61—21no—
469C4×C61—41no—
470C4×C61C2×C4×D411yescharacteristic
471C4×C61C2×C4×D411yescharacteristic
472Dic61—21no—
473Dic61—22no—
474Dic61—22no—
475Dic61—41no—
476Dic61#52511yescharacteristic
477Dic61#52511yescharacteristic
478C2×#519—611no—
479C2×#448—611no—
480C2×#440—611no—
481C2×C4×SD16—611no—
482#2324—611no—
483#1880—611no—
484#1880—611no—
485#1875—611no—
486#1865—611no—
487#1863—611no—
488#1854—611no—
489#1787—611no—
490#1763—611no—
491C4×#103—611no—
492#1750—611no—
493C2×C61—41no—
494C2×C61—81no—
495C2×C61C4×#12011yescharacteristic
496C2×C61#294711yescharacteristic
497C2×C61#294911yescharacteristic
498D61—41no—
499D61—81no—
500D61#301011yescharacteristic
501D61#301311yescharacteristic
502D61#312111yescharacteristic
503D61#312611yescharacteristic
504C23×Q8—611no—
505C22×SD16—611no—
506C22×SD16—611no—
507C2×#121—611no—
508#519—1224no—
509#519—1224no—
510C2×C4×Q8—611no—
511C2×C4×Q8—611no—
512C2×C4×Q8—611no—
513C2×C4×Q8—611no—
514C2×C4×Q8—1221no—
515C2×C4×Q8—1221no—
516C2×C4×D4—611no—
517C2×#117—611no—
518C2×#117—611no—
519C2×#117—1221no—
520C2×#117—1221no—
521#448—611no—
522#448—611no—
523#448—611no—
524#448—611no—
525#448—611no—
526#448—611no—
527#448—611no—
528#448#692311yescharacteristic, complemented
529#440—1224no—
530C4×SD16—1224no—
531C2×#107—611no—
532C2×#106—611no—
533C2×#103—611no—
534C2×#103—611no—
535C2×#103—611no—
536C2×#103—611no—
537C2×#103—611no—
538C2×#103—611no—
539C2×#102—611no—
540C2×#102—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543C2×#97—611no—
544C2×C4×C8—611no—
545#390—611no—
546#390—1221no—
547#389—611no—
548#388—1221no—
549#386—1221no—
550#385—1221no—
551#380—611no—
552C4×C4⋊C4—611no—
553#340—611no—
554#340—611no—
555#340—611no—
556#340—611no—
557#336—611no—
558#336—611no—
559C61#2146211yescharacteristic, complemented, Sylow
560C22×Q8—611no—
561C22×Q8—611no—
562C22×Q8—611no—
563C22×Q8—611no—
564C22×Q8—611no—
565C22×Q8—1221no—
566C22×Q8—1221no—
567C22×Q8—1221no—
568C22×Q8—1222no—
569C22×Q8—1222no—
570C22×Q8—1222no—
571C22×Q8—1222no—
572C22×Q8C2×#692311yescharacteristic, complemented
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—1221no—
577C23×C4—1221no—
578C2×SD16—611no—
579C2×SD16—611no—
580C2×SD16—611no—
581C2×SD16—611no—
582C2×SD16—611no—
583C2×SD16—611no—
584C2×SD16—1222no—
585C2×SD16—1222no—
586C2×SD16—1222no—
587C2×SD16—1222no—
588C2×SD16C2×#692311yescharacteristic
589C2×SD16C2×#692311yescharacteristic
590C22×C8—611no—
591C22×C8—611no—
592C22×C8—611no—
593C22×C8—611no—
594#121—611no—
595#121—611no—
596#121—611no—
597#121—1221no—
598#121—1221no—
599#121C2×#692311yescharacteristic
600C4×Q8—614no—
601C4×Q8—614no—
602C4×Q8—1222no—
603C4×Q8—1222no—
604C4×Q8—1222no—
605C4×Q8—1222no—
606C4×Q8—1222no—
607C4×Q8—1222no—
608C4×Q8—1228no—
609C4×Q8—1228no—
610C4×D4—1222no—
611C4×D4—1222no—
612#117—1222no—
613#117—1222no—
614#117—1222no—
615#117—1222no—
616#117—1228no—
617#117—1228no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C22⋊C4—611no—
631C2×C22⋊C4—611no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C42—611no—
639C2×C42—611no—
640C2×C42—1221no—
641C2×C42—1221no—
642C2×C42—1221no—
643C2×C42—1221no—
644C2×C42—1221no—
645C2×C42—1221no—
646#107—1222no—
647#106—1222no—
648#103—611no—
649#103—611no—
650#103—611no—
651#103—611no—
652#103—611no—
653#103—611no—
654#103—1222no—
655#103—1222no—
656#103—1222no—
657#103—1222no—
658#103C2×#692311yescharacteristic, complemented
659#103C2×#692311yescharacteristic, complemented
660#102—1222no—
661#102—1222no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667C22⋊C8C2×#692311yescharacteristic, complemented
668#97—1222no—
669C4×C8—1222no—
670#95—1221no—
671#95—1221no—
672#95—1221no—
673C24—611no—
674C24—1221no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—21no—
678C2×Q8—612no—
679C2×Q8—612no—
680C2×Q8—612no—
681C2×Q8—612no—
682C2×Q8—611no—
683C2×Q8—611no—
684C2×Q8—1221no—
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8—1222no—
689C2×Q8—1222no—
690C2×Q8—1224no—
691C2×Q8—1224no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8—1222no—
697C2×Q8—1222no—
698C2×Q8—1224no—
699C2×Q8—1224no—
700C2×Q8—1224no—
701C2×Q8—1224no—
702C2×Q8—1222no—
703C2×Q8—1222no—
704C2×Q8—1221no—
705C2×Q8C22×#692311yescharacteristic
706C2×Q8C22×#692311yescharacteristic
707C2×D4—21no—
708C2×D4—611no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—4881no—
718C2×D4—4881no—
719C2×D4C22×#692311yescharacteristic
720C22×C4—21no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1224no—
739C22×C4—1224no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4—2442no—
749C22×C4C22×#692311yescharacteristic
750SD16—22no—
751SD16—22no—
752SD16—1222no—
753SD16—1222no—
754SD16—1222no—
755SD16—1222no—
756SD16—1222no—
757SD16—1222no—
758C2×C8—611no—
759C2×C8—611no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8C22×#692311yescharacteristic
771C2×C8C22×#692311yescharacteristic
772C4⋊C4—612no—
773C4⋊C4—612no—
774C4⋊C4—611no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1222no—
779C4⋊C4—1222no—
780C4⋊C4—1224no—
781C4⋊C4—1224no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1224no—
787C4⋊C4—1224no—
788C4⋊C4—4881no—
789C4⋊C4C22×#692311yescharacteristic
790C22⋊C4—21no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1222no—
794C22⋊C4—1222no—
795C22⋊C4—1224no—
796C22⋊C4—1221no—
797C22⋊C4—4881no—
798C22⋊C4—4881no—
799C22⋊C4—4881no—
800C22⋊C4—2442no—
801C42—612no—
802C42—612no—
803C42—1221no—
804C42—1221no—
805C42—1224no—
806C42—1224no—
807C42—1224no—
808C42—1224no—
809C42—1224no—
810C42—4881no—
811C23—21no—
812C23—611no—
813C23—611no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23D4×#692311yescharacteristic
828Q8—24no—
829Q8—21no—
830Q8—21no—
831Q8—612no—
832Q8—612no—
833Q8—1222no—
834Q8—1222no—
835Q8—1222no—
836Q8—1222no—
837Q8—1224no—
838Q8—1224no—
839Q8—1224no—
840Q8—1221no—
841Q8—1221no—
842Q8D4×#692312yes—
843Q8D4×#692312yes—
844D4—21no—
845D4—21no—
846D4—81no—
847D4—1221no—
848D4—1221no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2441no—
854C2×C4—24no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—612no—
866C2×C4—612no—
867C2×C4—611no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1221no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1224no—
877C2×C4—1224no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1224no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—4884no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4D4×#692311yescharacteristic
912C2×C4C23×#692311yescharacteristic
913C8—21no—
914C8—21no—
915C8—1221no—
916C8—1221no—
917C8—2441no—
918C8—2441no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—611no—
926C22—611no—
927C22—611no—
928C22—611no—
929C22—611no—
930C22—611no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—4881no—
935C22—4881no—
936C22—4881no—
937C22—4881no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22—2441no—
943C22—2441no—
944C22—2441no—
945C22C2×D4×#692311yescharacteristic
946C4—22no—
947C4—22no—
948C4—21no—
949C4—41no—
950C4—611no—
951C4—611no—
952C4—1222no—
953C4—1222no—
954C4—1221no—
955C4—1222no—
956C4—1222no—
957C4—4881no—
958C4—4881no—
959C4—2441no—
960C4—2441no—
961C4—2442no—
962C4—2442no—
963C4—2441no—
964C4C2×D4×#692311yescharacteristic
965C4C2×D4×#692311yescharacteristic
966C2—41no—
967C2—81no—
968C2—611no—
969C2—611no—
970C2—611no—
971C2—611no—
972C2—4881no—
973C2—2441no—
974C2#120×#692311yescharacteristic
975C2#2146257711yescharacteristic
976C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#448C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#448#6923
hypocenterC61#21462
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#16840830C2semidirect
2. C2×#16840801C2semidirect
3. C2×SD16×#6923C2semidirect
5. #21461815C2semidirect
6. #21461815C2semidirect
8. #21461785C2semidirect
9. #21461783C2semidirect
10. #21461770C2semidirect
11. #21461658C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
14. #21461550C2semidirect
60. #16839903C4semidirect
61. #16839902C4semidirect
62. #16839902C4semidirect
63. #16839901C4semidirect
64. #16839900C4semidirect
65. #16839899C4semidirect
66. #16839899C4semidirect
70. C61×#448C4semidirect
82. Q8×#6923D4semidirect
83. Q8×#6923D4semidirect
134. C22×Dic122C2×C4semidirect
141. C2×Q8×D61C2×C4semidirect
142. C2×Q8×D61C2×C4semidirect
168. #14519702C2×C4semidirect
169. #14519702C2×C4semidirect
170. #14519701C2×C4semidirect
171. #14519701C2×C4semidirect
172. #14519700C2×C4semidirect
173. #14519700C2×C4semidirect
174. C22⋊#92418C2×C4semidirect
175. #14519689C2×C4semidirect
176. #14519689C2×C4semidirect
177. C22×Q8×C61C2×C4semidirect
181. #103×C61C2×C4semidirect
182. #103×C61C2×C4semidirect
183. C22⋊C8×C61C2×C4semidirect
528. #448#6923semidirect
559. C61#21462semidirect
572. C22×Q8C2×#6923semidirect
658. #103C2×#6923semidirect
659. #103C2×#6923semidirect
667. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408302
C2×#168408012
C2×SD16×#69232
#214623072
#214618152
#214618072
#214617852
#214617832
#214617702
#214616582
#214615922
#103×#69232
#214615502
#448×D612
#2146261