Finite Group Databasebeta

← #30622257

Subgroups — #30622257

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 876 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#21462345C211yesmaximal, characteristic, complemented
4#21462344C211yesmaximal, characteristic
5#21461969C211yesmaximal, characteristic, complemented
6#21461923C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461897C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic
10#21461804C211yesmaximal, characteristic, complemented
11#21461785C211yesmaximal, characteristic, complemented
12#21461782C211yesmaximal, characteristic, complemented
13#21461634C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#468×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923—21no—
18C2×D4×#6923C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21SD16×#6923—24no—
22#16840773—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519846C2211yescharacteristic
25C2×#14519845C2211yescharacteristic
26C2×#14519845C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31D61⋊(C22⋊C8)C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840714C2211yescharacteristic
36#16840713C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840712—21no—
39#16840712—21no—
40#16840712—21no—
41#16840711—21no—
42#16840710—21no—
43#16840709—21no—
44C4⋊C4×#6923—21no—
45C4⋊C4×#6923C2211yescharacteristic
46C4⋊C4×#6923C2211yescharacteristic
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—
77D4×#6923—44no—
78#14519856—22no—
79#14519856—41no—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923D411yescharacteristic
95C2×C22⋊#6923D411yescharacteristic
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519846—22no—
103#14519846—22no—
104#14519845—22no—
105#14519845D414yescomplemented
106#14519840—22no—
107#14519840—41no—
108#14519839—22no—
109#14519839—41no—
110#14519834—21no—
111C22⋊#92420—21no—
112#14519831—22no—
113C8×#6923—22no—
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)⋊C4—21no—
120(C2×#6923)⋊C4D411yescharacteristic
121(C2×#6923)⋊C4D411yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C2×#11758190C2×C411yescharacteristic, complemented
127C2×#11758200C2×C411yescharacteristic, complemented
128C2×#11758201C2×C411yescharacteristic, complemented
129SD16×D61—22no—
130SD16×D61—22no—
131C2×#11758194C2×C411yescharacteristic, complemented
132C2×#11758189C2×C411yescharacteristic, complemented
133C2×#11758189C2×C411yescharacteristic, complemented
134M16×D61—22no—
135M16×D61—22no—
136C2×C8×D61C2311yescharacteristic
137C2×C8×D61C2311yescharacteristic
138#14519757C2×C411yescharacteristic, complemented
139#14519756C2×C411yescharacteristic, complemented
140#14519755—21no—
141#14519754—21no—
142#14519753C2×C411yescharacteristic, complemented
143#14519752C2×C411yescharacteristic
144#14519751C2×C411yescharacteristic
145#14519750—21no—
146#14519749—21no—
147#14519748C2×C411yescharacteristic
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2311yescharacteristic
150C4⋊C4×D61C2311yescharacteristic
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153#14519711C2×C411yescharacteristic, complemented
154#14519710C2×C411yescharacteristic, complemented
155#14519710C2×C411yescharacteristic, complemented
156#14519702C2×C411yescharacteristic, complemented
157#14519701C2×C411yescharacteristic, complemented
158#14519700C2×C411yescharacteristic, complemented
159#14519699C2×C411yescharacteristic, complemented
160#14519698C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic, complemented
163C2×M16×C61C2×C411yescharacteristic, complemented
164C22⋊Q8×C61C2×C411yescharacteristic, complemented
165#121×C61C2×C411yescharacteristic
166#107×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61C2×D411yescharacteristic
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—42no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—81no—
180C22×#6923—81no—
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C22×#6923C2×D411yescharacteristic
184C22×#6923C2×D411yescharacteristic
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61#4111yescharacteristic
193Q8×D61—21no—
194Q8×D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—42no—
202D4×D61—42no—
203C2×D244—21no—
204C2×D244C22×C411yescharacteristic
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×D61—21no—
212C2×C4×D61C22×C411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61#4111yescharacteristic
215C2×C4×D61C2411yescharacteristic
216C2×Dic122—21no—
217C2×Dic122C22×C411yescharacteristic
218C22⋊#6923—22no—
219C22⋊#6923—41no—
220C22⋊#6923—42no—
221C22⋊#6923—42no—
222C22⋊#6923—42no—
223C22⋊#6923—81no—
224C2×#92420—21no—
225C2×#92420—21no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—42no—
233C4⋊#6923—42no—
234C4⋊#6923—42no—
235C4⋊#6923—42no—
236C4⋊#6923C2×D412yes—
237C4⋊#6923C2×D412yes—
238C4×#6923—21no—
239C4×#6923—21no—
240C4×#6923—21no—
241C4×#6923—21no—
242C4×#6923—42no—
243C4×#6923—42no—
244C4×#6923—42no—
245C4×#6923—42no—
246D61⋊C8—21no—
247D61⋊C8—21no—
248D61⋊C8—21no—
249D61⋊C8—21no—
250SD16×C61—22no—
251M16×C61—22no—
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C22×C411yescharacteristic
254C4⋊C4×C61—21no—
255C4⋊C4×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261#11758201—22no—
262#11758200—22no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61C22×C411yescharacteristic
269C4⋊Dic61C22×C411yescharacteristic
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758194—22no—
275C2×#92418C22×C411yescharacteristic
276C2×#92418C22×C411yescharacteristic
277#11758190—22no—
278#11758189—22no—
279#11758189—22no—
280C8×D61—21no—
281C8×D61—21no—
282C8×D61C2×D412yes—
283C8×D61#4112yes—
284C23×C61—21no—
285C23×C61C4×D411yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61C4×D411yescharacteristic
300C22×D61C22×D411yescharacteristic
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—22no—
305C2×#6923—22no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
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—41no—
324C2×#6923—84no—
325C2×#6923—84no—
326C2×#6923AGL(1,ℤ/8)12yes—
327Q8×C61—21no—
328Q8×C61—21no—
329D4×C61—21no—
330D4×C61—21no—
331D4×C61—42no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61C4×D411yescharacteristic
338C2×C4×C61C23×C411yescharacteristic
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61C4×D411yescharacteristic
349C2×Dic61C2×#4111yescharacteristic
350D244—21no—
351D244—21no—
352D244—42no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61C22×D411yescharacteristic
366C4×D61C2×#4111yescharacteristic
367C4×D61H(5,𝔽2)11yescharacteristic
368C4×D612−1+411yescharacteristic
369Dic122—21no—
370Dic122—21no—
371Dic122—41no—
372Dic122—41no—
373#92420—41no—
374#92420—41no—
375C8×C61—21no—
376C8×C61C4×D412yescomplemented
377#92418—21no—
378#92418C4×D412yescomplemented
379#23034—611nomaximal, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61C2×C4×D411yescharacteristic
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—81no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61D4211yescharacteristic
402C2×D61#54711yescharacteristic
403C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
404C2×D61#57511yescharacteristic
405C2×D61#57711yescharacteristic
406C2×D61#57811yescharacteristic
407#6923—22no—
408#6923—41no—
409#6923—41no—
410#6923—42no—
411#6923—41no—
412#6923—42no—
413#6923—81no—
414#6923—81no—
415C4×C61—21no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61C2×C4×D411yescharacteristic
420C4×C61#52011yescharacteristic
421Dic61—21no—
422Dic61—41no—
423Dic61—41no—
424Dic61—41no—
425Dic61#54811yescharacteristic
426Dic61#55311yescharacteristic
427C2×#468—611no—
428C2×C4×SD16—611no—
429C2×#428—611no—
430#2362—611no—
431#2361—611no—
432#1973—611no—
433#1942—611no—
434#1928—611no—
435#1926—611no—
436#1875—611no—
437#1872—611no—
438#1865—611no—
439#1862—611no—
440#1776—611no—
441#1753—611no—
442C2×C61—41no—
443C2×C61—81no—
444C2×C61#236111yescharacteristic
445C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C61#294711yescharacteristic
447D61—41no—
448D61—81no—
449D61#326511yescharacteristic
450D61#326911yescharacteristic
451D61#335111yescharacteristic
452D61#335311yescharacteristic
453C22×SD16—611no—
454C22×M16—611no—
455C2×C22⋊Q8—611no—
456C2×#121—611no—
457C2×C4×Q8—611no—
458C2×C4×D4—611no—
459C2×C4×D4—1221no—
460C2×#117—611no—
461C22×C4⋊C4—611no—
462#468—611no—
463#468—611no—
464#468—611no—
465#468—611no—
466#468—611no—
467#468—611no—
468#468—611no—
469#468#692311yescharacteristic, complemented
470C4×SD16—1224no—
471#428—1224no—
472C2×#107—611no—
473C2×#107—611no—
474C2×#107—611no—
475C2×#106—611no—
476C2×#106—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×C22⋊C8—611no—
484C2×#97—611no—
485C2×C4×C8—611no—
486#391—611no—
487#390—611no—
488#389—611no—
489#389—611no—
490#388—1221no—
491#388—1221no—
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#385—1221no—
496C4×C4⋊C4—611no—
497C4×C4⋊C4—611no—
498C4×C4⋊C4—1221no—
499C4×C22⋊C4—611no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504#336—611no—
505#336—611no—
506C61#2303411yescharacteristic, complemented, Sylow
507C22×Q8—611no—
508C22×D4—611no—
509C22×D4—1221no—
510C23×C4—611no—
511C23×C4—1221no—
512C23×C4—1221no—
513C2×SD16—611no—
514C2×SD16—611no—
515C2×SD16—611no—
516C2×SD16—1222no—
517C2×SD16—1222no—
518C2×SD16C2×#692311yescharacteristic, complemented
519C2×M16—611no—
520C2×M16—611no—
521C2×M16—611no—
522C2×M16—1222no—
523C2×M16—1222no—
524C2×M16C2×#692311yescharacteristic, complemented
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22⋊Q8—611no—
530C22⋊Q8—611no—
531C22⋊Q8—611no—
532C22⋊Q8—1221no—
533C22⋊Q8—1221no—
534C22⋊Q8C2×#692311yescharacteristic, complemented
535#121—611no—
536#121—611no—
537#121—611no—
538#121—1221no—
539#121—1221no—
540#121C2×#692311yescharacteristic
541C4×Q8—1222no—
542C4×Q8—2441no—
543C4×D4—1222no—
544C4×D4—2441no—
545C4×D4—2444no—
546#117—1222no—
547#117—2441no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—2441no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575#107—611no—
576#107—611no—
577#107—611no—
578#107—1222no—
579#107—1222no—
580#107C2×#692311yescharacteristic, complemented
581#106—614no—
582#106—1222no—
583#103—611no—
584#103—611no—
585#103—611no—
586#103—1222no—
587#103—2441no—
588#103C2×#692311yescharacteristic, complemented
589#102—611no—
590#102—611no—
591#102—611no—
592#102—1222no—
593#102—2441no—
594#102C2×#692311yescharacteristic, complemented
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597#97—1222no—
598C4×C8—1222no—
599#95—611no—
600#95—611no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607C24—611no—
608C24—1221no—
609C2×Q8—611no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8C22×#692311yescharacteristic
616C2×D4—21no—
617C2×D4—611no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—2442no—
627C2×D4—2442no—
628C2×D4C22×#692311yescharacteristic
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
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—1221no—
648C22×C4—1221no—
649C22×C4—4881no—
650C22×C4—4881no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4C22×#692311yescharacteristic
656SD16—22no—
657SD16—1222no—
658SD16—1222no—
659SD16—1222no—
660M16—22no—
661M16—1222no—
662M16—1222no—
663M16—1222no—
664C2×C8—611no—
665C2×C8—612no—
666C2×C8—612no—
667C2×C8—611no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8C22×#692311yescharacteristic
677C2×C8C22×#692311yescharacteristic
678C4⋊C4—21no—
679C4⋊C4—612no—
680C4⋊C4—612no—
681C4⋊C4—611no—
682C4⋊C4—611no—
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—1221no—
693C4⋊C4—1221no—
694C4⋊C4—2442no—
695C4⋊C4—2442no—
696C4⋊C4—2442no—
697C4⋊C4—2442no—
698C4⋊C4C22×#692311yescharacteristic
699C4⋊C4C22×#692311yescharacteristic
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C22⋊C4—1222no—
707C22⋊C4—1221no—
708C22⋊C4—1221no—
709C22⋊C4—4881no—
710C22⋊C4—2441no—
711C22⋊C4—2442no—
712C22⋊C4—2442no—
713C22⋊C4—2442no—
714C42—1221no—
715C42—1221no—
716C42—1221no—
717C42—1221no—
718C42—2442no—
719C42—2442no—
720C42—2442no—
721C42—2442no—
722C23—21no—
723C23—611no—
724C23—611no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23D4×#692311yescharacteristic
739Q8—21no—
740Q8—21no—
741Q8—1221no—
742Q8—1221no—
743Q8—2441no—
744Q8—2441no—
745D4—21no—
746D4—21no—
747D4—42no—
748D4—1221no—
749D4—1221no—
750D4—2442no—
751D4—2441no—
752D4—2441no—
753D4—2442no—
754D4—2442no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—612no—
766C2×C4—611no—
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—1221no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—4884no—
792C2×C4—4884no—
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×C4—2441no—
808C2×C4—2441no—
809C2×C4D4×#692311yescharacteristic
810C2×C4C23×#692311yescharacteristic
811C8—21no—
812C8—612no—
813C8—1221no—
814C8—2441no—
815C8—2441no—
816C8D4×#692312yescomplemented
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—611no—
824C22—611no—
825C22—611no—
826C22—611no—
827C22—611no—
828C22—611no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—4881no—
833C22—4881no—
834C22—4881no—
835C22—4881no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22—2441no—
842C22—2441no—
843C22C2×D4×#692311yescharacteristic
844C4—21no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—611no—
849C4—611no—
850C4—1222no—
851C4—1221no—
852C4—4881no—
853C4—4881no—
854C4—2441no—
855C4—2441no—
856C4—2441no—
857C4—2442no—
858C4—2442no—
859C4—2441no—
860C4—2441no—
861C4—2441no—
862C4C2×D4×#692311yescharacteristic
863C4#1684083111yescharacteristic
864C2—41no—
865C2—81no—
866C2—611no—
867C2—611no—
868C2—611no—
869C2—611no—
870C2—4881no—
871C2—2441no—
872C2#2146234411yescharacteristic
873C2AGL(1,ℤ/8)×#692311yescharacteristic
874C2#2146257711yescharacteristic
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#23034
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
3. #21462345C2semidirect
5. #21461969C2semidirect
6. #21461923C2semidirect
7. #21461899C2semidirect
8. #21461897C2semidirect
10. #21461804C2semidirect
11. #21461785C2semidirect
12. #21461782C2semidirect
13. #21461634C2semidirect
14. #21461559C2semidirect
58. #16840011C4semidirect
59. #16840010C4semidirect
60. #16840009C4semidirect
61. #16840008C4semidirect
62. #16840007C4semidirect
63. #16840006C4semidirect
64. #16840005C4semidirect
68. C61×#468C4semidirect
105. #14519845D4semidirect
126. C2×#11758190C2×C4semidirect
127. C2×#11758200C2×C4semidirect
128. C2×#11758201C2×C4semidirect
131. C2×#11758194C2×C4semidirect
132. C2×#11758189C2×C4semidirect
133. C2×#11758189C2×C4semidirect
138. #14519757C2×C4semidirect
139. #14519756C2×C4semidirect
142. #14519753C2×C4semidirect
153. #14519711C2×C4semidirect
154. #14519710C2×C4semidirect
155. #14519710C2×C4semidirect
156. #14519702C2×C4semidirect
157. #14519701C2×C4semidirect
158. #14519700C2×C4semidirect
159. #14519699C2×C4semidirect
160. #14519698C2×C4semidirect
161. #14519697C2×C4semidirect
162. C2×SD16×C61C2×C4semidirect
163. C2×M16×C61C2×C4semidirect
164. C22⋊Q8×C61C2×C4semidirect
166. #107×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
376. C8×C61C4×D4semidirect
378. #92418C4×D4semidirect
469. #468#6923semidirect
506. C61#23034semidirect
518. C2×SD16C2×#6923semidirect
524. C2×M16C2×#6923semidirect
534. C22⋊Q8C2×#6923semidirect
580. #107C2×#6923semidirect
588. #103C2×#6923semidirect
594. #102C2×#6923semidirect
816. C8D4×#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
#214623452
#214623442
#214619692
#214619232
#214618992
#214618972
#214618072
#214618042
#214617852
#214617822
#214616342
#214615592
#468×D612
#2303461