Finite Group Databasebeta

← #30622258

Subgroups — #30622258

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840773C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic
4#21462343C211yesmaximal, characteristic, complemented
5#21461969C211yesmaximal, characteristic, complemented
6#21461923C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461806C211yesmaximal, characteristic
10#21461805C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461783C211yesmaximal, characteristic, complemented
13#21461634C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#468×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20SD16×#6923—24no—
21#16840773—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519845C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34#16840714—21no—
35#16840714C2211yescharacteristic
36#16840713—21no—
37#16840713C2211yescharacteristic
38#16840713C2211yescharacteristic
39#16840712—21no—
40#16840711—21no—
41#16840710—21no—
42#16840709—21no—
43C4⋊C4×#6923C2211yescharacteristic
44C4⋊C4×#6923C2211yescharacteristic
45C22⋊C4×#6923—21no—
46C22⋊C4×#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×M16×D61C2211yescharacteristic
56C22⋊Q8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16840011C411yescharacteristic, complemented
59#16840010C411yescharacteristic, complemented
60#16840009C411yescharacteristic, complemented
61#16840008C411yescharacteristic, complemented
62#16840007C411yescharacteristic, complemented
63#16840006C411yescharacteristic, complemented
64#16840005C411yescharacteristic, complemented
65#107×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#468C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—41no—
75D4×#6923—22no—
76D4×#6923—41no—
77#14519856—22no—
78#14519856—41no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923D411yescharacteristic
94C2×C22⋊#6923D411yescharacteristic
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923C2311yescharacteristic
100C2×C4×#6923C2311yescharacteristic
101#14519846—22no—
102#14519846—22no—
103#14519845—22no—
104#14519845D414yescomplemented
105#14519840—22no—
106#14519840—41no—
107#14519839—22no—
108#14519839—41no—
109#14519834—21no—
110C22⋊#92420—21no—
111#14519831—22no—
112C8×#6923—22no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×D4×D61—21no—
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C2×#11758190C2×C411yescharacteristic, complemented
126C2×#11758200C2×C411yescharacteristic, complemented
127C2×#11758201C2×C411yescharacteristic, complemented
128SD16×D61—22no—
129SD16×D61—22no—
130C2×#11758194C2×C411yescharacteristic, complemented
131C2×#11758189C2×C411yescharacteristic, complemented
132C2×#11758189C2×C411yescharacteristic, complemented
133M16×D61—22no—
134M16×D61—22no—
135C2×C8×D61C2311yescharacteristic
136C2×C8×D61C2311yescharacteristic
137#14519757C2×C411yescharacteristic, complemented
138#14519756C2×C411yescharacteristic, complemented
139#14519755—21no—
140#14519754—21no—
141#14519753C2×C411yescharacteristic, complemented
142#14519752C2×C411yescharacteristic
143#14519751C2×C411yescharacteristic
144#14519750—21no—
145#14519749—21no—
146#14519748C2×C411yescharacteristic
147C4⋊C4×D61—21no—
148C4⋊C4×D61C2311yescharacteristic
149C4⋊C4×D61C2311yescharacteristic
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152#14519711C2×C411yescharacteristic, complemented
153#14519710C2×C411yescharacteristic, complemented
154#14519710C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519701C2×C411yescharacteristic, complemented
157#14519700C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161C2×SD16×C61C2×C411yescharacteristic, complemented
162C2×M16×C61C2×C411yescharacteristic, complemented
163C22⋊Q8×C61C2×C411yescharacteristic, complemented
164#121×C61C2×C411yescharacteristic
165#107×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168C23×D61—21no—
169C23×D61C2×D411yescharacteristic
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—42no—
175C22×#6923—42no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—81no—
179C22×#6923—81no—
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C22×#6923C2×D411yescharacteristic
184C2×Q8×C61C22×C411yescharacteristic
185C2×D4×C61—21no—
186C2×D4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61#4111yescharacteristic
192Q8×D61—21no—
193Q8×D61—21no—
194Q8×D61—21no—
195Q8×D61—21no—
196D4×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—81no—
201D4×D61—81no—
202C2×D244—21no—
203C2×D244C22×C411yescharacteristic
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61C22×C411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61#4111yescharacteristic
214C2×C4×D61C2411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122C22×C411yescharacteristic
217C22⋊#6923—22no—
218C22⋊#6923—41no—
219C22⋊#6923—42no—
220C22⋊#6923—42no—
221C22⋊#6923—42no—
222C22⋊#6923—81no—
223C2×#92420—21no—
224C2×#92420—21no—
225C4⋊#6923—21no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—42no—
232C4⋊#6923—42no—
233C4⋊#6923—81no—
234C4⋊#6923—81no—
235C4⋊#6923C2×D412yes—
236C4⋊#6923C2×D412yes—
237C4×#6923—21no—
238C4×#6923—21no—
239C4×#6923—21no—
240C4×#6923—21no—
241C4×#6923—42no—
242C4×#6923—42no—
243C4×#6923—81no—
244C4×#6923—81no—
245D61⋊C8—21no—
246D61⋊C8—21no—
247D61⋊C8—21no—
248D61⋊C8—21no—
249SD16×C61—22no—
250M16×C61—22no—
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C22×C411yescharacteristic
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22×C411yescharacteristic
255C4⋊C4×C61C22×C411yescharacteristic
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260#11758201—22no—
261#11758200—22no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61C22×C411yescharacteristic
268C4⋊Dic61C22×C411yescharacteristic
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758194—22no—
274C2×#92418C22×C411yescharacteristic
275C2×#92418C22×C411yescharacteristic
276#11758190—22no—
277#11758189—22no—
278#11758189—22no—
279C8×D61—21no—
280C8×D61—21no—
281C8×D61C2×D412yes—
282C8×D61#4112yes—
283C23×C61—21no—
284C23×C61C4×D411yescharacteristic
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61C4×D411yescharacteristic
299C22×D61C22×D411yescharacteristic
300C2×#6923—21no—
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—22no—
304C2×#6923—22no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—84no—
324C2×#6923—84no—
325C2×#6923#13712yes—
326Q8×C61—21no—
327Q8×C61—21no—
328D4×C61—21no—
329D4×C61—21no—
330D4×C61—81no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61C4×D411yescharacteristic
337C2×C4×C61C23×C411yescharacteristic
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—81no—
341C22⋊D61—81no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61C4×D411yescharacteristic
348C2×Dic61C2×#4111yescharacteristic
349D244—21no—
350D244—21no—
351D244—81no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61C22×D411yescharacteristic
365C4×D61C2×#4111yescharacteristic
366C4×D61H(5,𝔽2)11yescharacteristic
367C4×D612−1+411yescharacteristic
368Dic122—21no—
369Dic122—21no—
370Dic122—41no—
371Dic122—41no—
372#92420—41no—
373#92420—41no—
374C8×C61—21no—
375C8×C61C4×D412yes—
376#92418—21no—
377#92418C4×D412yes—
378#23035—611nomaximal, Sylow
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61C2×C4×D411yescharacteristic
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—81no—
397C2×D61—81no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61D4211yescharacteristic
401C2×D61#54711yescharacteristic
402C2×D61C2×#13711yescharacteristic
403C2×D61#57511yescharacteristic
404C2×D61#57611yescharacteristic
405C2×D61#57711yescharacteristic
406#6923—22no—
407#6923—41no—
408#6923—41no—
409#6923—42no—
410#6923—41no—
411#6923—42no—
412#6923—81no—
413#6923—81no—
414C4×C61—21no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61C2×C4×D411yescharacteristic
419C4×C61#52011yescharacteristic
420Dic61—21no—
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424Dic61#54811yescharacteristic
425Dic61#55311yescharacteristic
426C2×#468—611no—
427C2×C4×SD16—611no—
428C2×#428—611no—
429#2363—611no—
430#2360—611no—
431#1973—611no—
432#1942—611no—
433#1927—611no—
434#1925—611no—
435#1874—611no—
436#1873—611no—
437#1864—611no—
438#1863—611no—
439#1776—611no—
440#1753—611no—
441C2×C61—41no—
442C2×C61—81no—
443C2×C61#236111yescharacteristic
444C2×C61C4×#13711yescharacteristic
445C2×C61#294611yescharacteristic
446D61—41no—
447D61—81no—
448D61#326611yescharacteristic
449D61#326811yescharacteristic
450D61#335111yescharacteristic
451D61#335711yescharacteristic
452C22×SD16—611no—
453C22×M16—611no—
454C2×C22⋊Q8—611no—
455C2×#121—611no—
456C2×C4×Q8—611no—
457C2×C4×D4—611no—
458C2×#117—611no—
459C22×C4⋊C4—611no—
460#468—611no—
461#468—611no—
462#468—611no—
463#468—611no—
464#468—611no—
465#468—611no—
466#468—611no—
467#468#692311yescharacteristic, complemented
468C4×SD16—1224no—
469#428—1224no—
470C2×#107—611no—
471C2×#107—611no—
472C2×#107—611no—
473C2×#106—611no—
474C2×#106—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×C22⋊C8—611no—
482C2×#97—611no—
483C2×C4×C8—611no—
484#391—611no—
485#390—611no—
486#390—1221no—
487#389—611no—
488#389—611no—
489#389—1221no—
490#388—1221no—
491#387—1221no—
492#386—1221no—
493#385—1221no—
494C4×C4⋊C4—611no—
495C4×C4⋊C4—611no—
496C4×C22⋊C4—611no—
497C4×C22⋊C4—1221no—
498C4×C22⋊C4—1221no—
499#340—611no—
500#340—611no—
501#340—611no—
502#340—611no—
503#336—611no—
504#336—611no—
505C61#2303511yescharacteristic, complemented, Sylow
506C22×Q8—611no—
507C22×D4—611no—
508C22×D4—1221no—
509C23×C4—611no—
510C23×C4—1221no—
511C23×C4—1221no—
512C2×SD16—611no—
513C2×SD16—611no—
514C2×SD16—611no—
515C2×SD16—1222no—
516C2×SD16—1222no—
517C2×SD16C2×#692311yescharacteristic, complemented
518C2×M16—611no—
519C2×M16—611no—
520C2×M16—611no—
521C2×M16—1222no—
522C2×M16—1222no—
523C2×M16C2×#692311yescharacteristic, complemented
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22⋊Q8—611no—
529C22⋊Q8—611no—
530C22⋊Q8—611no—
531C22⋊Q8—1221no—
532C22⋊Q8—1221no—
533C22⋊Q8C2×#692311yescharacteristic, complemented
534#121—611no—
535#121—611no—
536#121—611no—
537#121—1221no—
538#121—1221no—
539#121C2×#692311yescharacteristic
540C4×Q8—1222no—
541C4×Q8—2441no—
542C4×D4—1222no—
543C4×D4—2441no—
544#117—1222no—
545#117—2441no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1222no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—2441no—
559C2×C22⋊C4—611no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—1221no—
570C2×C42—1221no—
571C2×C42—1221no—
572C2×C42—1221no—
573#107—611no—
574#107—611no—
575#107—611no—
576#107—1222no—
577#107—1222no—
578#107C2×#692311yescharacteristic, complemented
579#106—614no—
580#106—1222no—
581#103—611no—
582#103—611no—
583#103—611no—
584#103—1222no—
585#103—2441no—
586#103C2×#692311yescharacteristic, complemented
587#102—611no—
588#102—611no—
589#102—611no—
590#102—1222no—
591#102—2441no—
592#102C2×#692311yescharacteristic, complemented
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595#97—1222no—
596C4×C8—1222no—
597#95—611no—
598#95—611no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—611no—
606C24—1221no—
607C2×Q8—611no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8C22×#692311yescharacteristic
614C2×D4—21no—
615C2×D4—611no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—4881no—
625C2×D4—4881no—
626C2×D4C22×#692311yescharacteristic
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4—2442no—
650C22×C4—2442no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4C22×#692311yescharacteristic
654SD16—22no—
655SD16—1222no—
656SD16—1222no—
657SD16—1222no—
658M16—22no—
659M16—1222no—
660M16—1222no—
661M16—1222no—
662C2×C8—611no—
663C2×C8—612no—
664C2×C8—612no—
665C2×C8—611no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8C22×#692311yescharacteristic
675C2×C8C22×#692311yescharacteristic
676C4⋊C4—21no—
677C4⋊C4—612no—
678C4⋊C4—612no—
679C4⋊C4—611no—
680C4⋊C4—611no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—4881no—
693C4⋊C4—4881no—
694C4⋊C4—2442no—
695C4⋊C4—2442no—
696C4⋊C4C22×#692311yescharacteristic
697C4⋊C4C22×#692311yescharacteristic
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1222no—
705C22⋊C4—1221no—
706C22⋊C4—1221no—
707C22⋊C4—4881no—
708C22⋊C4—2441no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C22⋊C4—2442no—
712C42—1221no—
713C42—1221no—
714C42—1221no—
715C42—1221no—
716C42—4881no—
717C42—4881no—
718C42—2442no—
719C42—2442no—
720C23—21no—
721C23—611no—
722C23—611no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23D4×#692311yescharacteristic
737Q8—21no—
738Q8—21no—
739Q8—1221no—
740Q8—1221no—
741Q8—2441no—
742Q8—2441no—
743D4—21no—
744D4—21no—
745D4—81no—
746D4—1221no—
747D4—1221no—
748D4—4881no—
749D4—4881no—
750D4—4881no—
751D4—2441no—
752D4—2441no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—612no—
764C2×C4—611no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—4884no—
790C2×C4—4884no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4D4×#692311yescharacteristic
808C2×C4C23×#692311yescharacteristic
809C8—21no—
810C8—612no—
811C8—1221no—
812C8—2441no—
813C8—2441no—
814C8D4×#692312yes—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—611no—
822C22—611no—
823C22—611no—
824C22—611no—
825C22—611no—
826C22—611no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—4881no—
831C22—4881no—
832C22—4881no—
833C22—4881no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22C2×D4×#692311yescharacteristic
842C4—21no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—611no—
847C4—611no—
848C4—1222no—
849C4—1221no—
850C4—4881no—
851C4—4881no—
852C4—2441no—
853C4—2441no—
854C4—2441no—
855C4—2442no—
856C4—2442no—
857C4—2441no—
858C4—2441no—
859C4—2441no—
860C4C2×D4×#692311yescharacteristic
861C4#1684083111yescharacteristic
862C2—41no—
863C2—81no—
864C2—611no—
865C2—611no—
866C2—611no—
867C2—611no—
868C2—4881no—
869C2—2441no—
870C2#2146234411yescharacteristic
871C2#137×#692311yescharacteristic
872C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#468C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#468#6923
hypocenterC61#23035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
2. C2×#16840773C2semidirect
4. #21462343C2semidirect
5. #21461969C2semidirect
6. #21461923C2semidirect
7. #21461898C2semidirect
8. #21461896C2semidirect
10. #21461805C2semidirect
11. #21461784C2semidirect
12. #21461783C2semidirect
13. #21461634C2semidirect
14. #21461559C2semidirect
58. #16840011C4semidirect
59. #16840010C4semidirect
60. #16840009C4semidirect
61. #16840008C4semidirect
62. #16840007C4semidirect
63. #16840006C4semidirect
64. #16840005C4semidirect
68. C61×#468C4semidirect
104. #14519845D4semidirect
125. C2×#11758190C2×C4semidirect
126. C2×#11758200C2×C4semidirect
127. C2×#11758201C2×C4semidirect
130. C2×#11758194C2×C4semidirect
131. C2×#11758189C2×C4semidirect
132. C2×#11758189C2×C4semidirect
137. #14519757C2×C4semidirect
138. #14519756C2×C4semidirect
141. #14519753C2×C4semidirect
152. #14519711C2×C4semidirect
153. #14519710C2×C4semidirect
154. #14519710C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519701C2×C4semidirect
157. #14519700C2×C4semidirect
158. #14519699C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519697C2×C4semidirect
161. C2×SD16×C61C2×C4semidirect
162. C2×M16×C61C2×C4semidirect
163. C22⋊Q8×C61C2×C4semidirect
165. #107×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
467. #468#6923semidirect
505. C61#23035semidirect
517. C2×SD16C2×#6923semidirect
523. C2×M16C2×#6923semidirect
533. C22⋊Q8C2×#6923semidirect
578. #107C2×#6923semidirect
586. #103C2×#6923semidirect
592. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407732
#214623462
#214623432
#214619692
#214619232
#214618982
#214618962
#214618062
#214618052
#214617842
#214617832
#214616342
#214615592
#468×D612
#2303561