Finite Group Databasebeta

← #30620613

Subgroups — #30620613

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462330C211yesmaximal, characteristic, complemented
2D4×C22⋊#6923C211yesmaximal, characteristic
3#21461911C211yesmaximal, characteristic, complemented
4#21461909C211yesmaximal, characteristic, complemented
5#21461897C211yesmaximal, characteristic, complemented
6#21461896C211yesmaximal, characteristic, complemented
7#21461784C211yesmaximal, characteristic, complemented
8#21461782C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461697C211yesmaximal, characteristic, complemented
11#21461657C211yesmaximal, characteristic
12#21461590C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#418×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C22×C22⋊#6923—21no—
19C2×#14519846C2211yescharacteristic, complemented
20C2×#14519845C2211yescharacteristic, complemented
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26C2×#14519831C2211yescharacteristic, complemented
27C2×C8×#6923C2211yescharacteristic, complemented
28#16840714C2211yescharacteristic
29#16840714C2211yescharacteristic
30#16840713C2211yescharacteristic, complemented
31#16840713C2211yescharacteristic, complemented
32#16840712—21no—
33#16840712—21no—
34#16840710—21no—
35#16840710—21no—
36#16840707—21no—
37#16840704C2211yescharacteristic
38#16840704C2211yescharacteristic
39#16840703—21no—
40C4⋊C4×#6923C2211yescharacteristic, complemented
41C4⋊C4×#6923C2211yescharacteristic, complemented
42C4×C4⋊#6923—21no—
43C4×C22⋊#6923C2211yescharacteristic
44#16840636C2211yescharacteristic, complemented
45#16840636C2211yescharacteristic, complemented
46#16840635C2211yescharacteristic, complemented
47#16840635C2211yescharacteristic, complemented
48#16840635C2211yescharacteristic, complemented
49#16840635C2211yescharacteristic, complemented
50(C2×#6923)⋊C8C2211yescharacteristic, complemented
51(C2×#6923)⋊C8C2211yescharacteristic, complemented
52C22×D4×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54#117×D61C2211yescharacteristic
55#16839768C411yescharacteristic, complemented
56#16839767C411yescharacteristic, complemented
57#16839766C411yescharacteristic, complemented
58#16839765C411yescharacteristic, complemented
59#16839765C411yescharacteristic, complemented
60#16839765C411yescharacteristic, complemented
61#16839765C411yescharacteristic, complemented
62#102×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#418C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—41no—
74D4×#6923—41no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—44no—
90C2×C22⋊#6923D411yescharacteristic
91C2×C22⋊#6923D411yescharacteristic
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—41no—
97#14519845—41no—
98#14519839—22no—
99#14519839—22no—
100#14519839—41no—
101#14519839—41no—
102#14519834—21no—
103C22⋊#92420—21no—
104#14519831—41no—
105C8×#6923—41no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4D411yescharacteristic
113(C2×#6923)⋊C4D411yescharacteristic
114C24×D61—21no—
115C22×D244C2×C411yescharacteristic
116C22×C22⋊D61—21no—
117C2×D4×D61—22no—
118C2×D4×D61—22no—
119C2×D4×D61—21no—
120C2×D4×D61—21no—
121C2×D4×D61—41no—
122C2×D4×D61—41no—
123C2×D4×D61C2×C411yescharacteristic
124C2×D4×D61C2×C411yescharacteristic
125C2×D4×D61C2311yescharacteristic
126C2×D4×D61C2311yescharacteristic
127C22×C4×D61C2311yescharacteristic
128C2×#11758194C2×C411yescharacteristic, complemented
129C2×#11758189C2×C411yescharacteristic, complemented
130C2×#11758189C2×C411yescharacteristic, complemented
131M16×D61—41no—
132M16×D61—41no—
133C2×C8×D61C2311yescharacteristic
134C2×C8×D61C2311yescharacteristic
135#14519736C2×C411yescharacteristic, complemented
136#14519735C2×C411yescharacteristic, complemented
137#14519735C2×C411yescharacteristic, complemented
138#14519734—21no—
139#14519733—21no—
140C4⋊C4×D61C2311yescharacteristic
141C4⋊C4×D61C2311yescharacteristic
142C22⋊C4×D61—21no—
143C42×D61—21no—
144#14519699C2×C411yescharacteristic
145#14519699C2×C411yescharacteristic
146#14519699C2×C411yescharacteristic, complemented
147#14519699C2×C411yescharacteristic, complemented
148#14519698C2×C411yescharacteristic
149#14519698C2×C411yescharacteristic
150#14519698C2×C411yescharacteristic, complemented
151#14519698C2×C411yescharacteristic, complemented
152#14519697C2×C411yescharacteristic
153#14519697C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic, complemented
155#14519697C2×C411yescharacteristic, complemented
156C22×D4×C61C2×C411yescharacteristic
157C2×M16×C61C2×C411yescharacteristic, complemented
158#117×C61C2×C411yescharacteristic, complemented
159#102×C61C2×C411yescharacteristic
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic, complemented
163C24×C61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61C2×D411yescharacteristic
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—81no—
185C22×#6923—81no—
186C22×#6923C2×D411yescharacteristic
187C22×#6923C2×D411yescharacteristic
188C22×#6923C2×D411yescharacteristic
189C22×#6923C2×D411yescharacteristic
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—41no—
193C2×D4×C61C22×C411yescharacteristic
194C2×D4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C22×Dic61#4111yescharacteristic
203D4×D61—22no—
204D4×D61—22no—
205D4×D61—21no—
206D4×D61—21no—
207D4×D61—21no—
208D4×D61—21no—
209D4×D61—21no—
210D4×D61—21no—
211D4×D61—41no—
212D4×D61—41no—
213D4×D61—42no—
214D4×D61—42no—
215D4×D61—42no—
216D4×D61—42no—
217D4×D61#4112yes—
218D4×D61#4112yes—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244—41no—
222C2×D244C22×C411yescharacteristic
223C2×D244C22×C411yescharacteristic
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61#4111yescharacteristic
233C2×C4×D61C2411yescharacteristic
234C22⋊#6923—22no—
235C22⋊#6923—41no—
236C22⋊#6923—42no—
237C22⋊#6923—42no—
238C22⋊#6923—42no—
239C22⋊#6923—42no—
240C22⋊#6923—42no—
241C22⋊#6923—81no—
242C22⋊#6923—81no—
243C22⋊#6923—81no—
244C2×#92420—21no—
245C2×#92420—21no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—21no—
249C4⋊#6923—21no—
250C4⋊#6923—21no—
251C4⋊#6923—21no—
252C4⋊#6923—21no—
253C4⋊#6923—21no—
254C4⋊#6923—42no—
255C4⋊#6923—42no—
256C4×#6923—21no—
257C4×#6923—21no—
258C4×#6923—21no—
259C4×#6923—21no—
260C4×#6923—81no—
261C4×#6923—81no—
262D61⋊C8—21no—
263D61⋊C8—21no—
264D61⋊C8—21no—
265D61⋊C8—21no—
266M16×C61—41no—
267C2×C8×C61C22×C411yescharacteristic
268C2×C8×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C22⋊C4×C61—21no—
272C42×C61—21no—
273C22⋊Dic61—21no—
274#11758198—21no—
275#11758198—21no—
276C4⋊Dic61C22×C411yescharacteristic
277C4⋊Dic61C22×C411yescharacteristic
278#11758196—21no—
279#11758196—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283#11758194—41no—
284C2×#92418C22×C411yescharacteristic
285C2×#92418C22×C411yescharacteristic
286#11758189—41no—
287#11758189—41no—
288C8×D61—21no—
289C8×D61—21no—
290C8×D61—21no—
291C8×D61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—81no—
297C23×C61C4×D411yescharacteristic
298C22×D61—21no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—42no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—81no—
325C22×D61—81no—
326C22×D61—81no—
327C22×D61—84no—
328C22×D61—84no—
329C22×D61—84no—
330C22×D61—84no—
331C22×D61C4×D411yescharacteristic
332C22×D61C22×D411yescharacteristic
333C2×#6923—21no—
334C2×#6923—21no—
335C2×#6923—21no—
336C2×#6923—21no—
337C2×#6923—21no—
338C2×#6923—21no—
339C2×#6923—21no—
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—21no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—84no—
357C2×#6923—84no—
358C2×#6923AGL(1,ℤ/8)12yes—
359D4×C61—21no—
360D4×C61—21no—
361D4×C61—21no—
362D4×C61—42no—
363D4×C61#11712yes—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61C4×D411yescharacteristic
369C2×C4×C61C23×C411yescharacteristic
370C22⋊D61—22no—
371C22⋊D61—22no—
372C22⋊D61—42no—
373C22⋊D61—42no—
374C22⋊D61—41no—
375C22⋊D61—41no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61C4×D411yescharacteristic
381C2×Dic61C2×#4111yescharacteristic
382D244—21no—
383D244—21no—
384D244—21no—
385D244—42no—
386D244#11712yes—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61C2×#4111yescharacteristic
398C4×D61C2×#4111yescharacteristic
399C4×D61H(5,𝔽2)11yescharacteristic
400C4×D61H(5,𝔽2)11yescharacteristic
401#92420—41no—
402#92420—41no—
403C8×C61—21no—
404C8×C61—21no—
405#92418—21no—
406#92418—21no—
407#22580—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—22no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—84no—
418C22×C61C2×C4×D411yescharacteristic
419C2×D61—21no—
420C2×D61—22no—
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—41no—
429C2×D61—41no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—84no—
437C2×D61—84no—
438C2×D61—84no—
439C2×D61—81no—
440C2×D61—81no—
441C2×D61—81no—
442C2×D61—81no—
443C2×D61#54611yescharacteristic
444C2×D61#54611yescharacteristic
445C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
446C2×D61#57511yescharacteristic
447C2×D61#57611yescharacteristic
448C2×D61#57711yescharacteristic
449#6923—22no—
450#6923—41no—
451#6923—41no—
452#6923—41no—
453#6923—81no—
454#6923—81no—
455#6923—81no—
456#6923—81no—
457C4×C61—21no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61C2×#11711yescharacteristic
461C4×C61#51811yescharacteristic
462Dic61—21no—
463Dic61—41no—
464Dic61—41no—
465Dic61#55111yescharacteristic
466Dic61#55111yescharacteristic
467C2×#418—611no—
468#2347—611no—
469D4×C22⋊C4—611no—
470#1936—611no—
471#1934—611no—
472#1926—611no—
473#1925—611no—
474#1864—611no—
475#1862—611no—
476#1825—611no—
477#1809—611no—
478#1786—611no—
479#1762—611no—
480C4×#102—611no—
481#1753—611no—
482C2×C61—41no—
483C2×C61—42no—
484C2×C61—81no—
485C2×C61#234211yescharacteristic
486C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
487C2×C61#294611yescharacteristic
488D61—41no—
489D61—42no—
490D61—81no—
491D61#331111yescharacteristic
492D61#331811yescharacteristic
493D61#332211yescharacteristic
494D61#332411yescharacteristic
495C23×D4—611no—
496C22×M16—611no—
497C2×C4×D4—611no—
498C2×C4×D4—611no—
499C2×#117—611no—
500C22×C22⋊C4—1221no—
501C2×#107—611no—
502C2×#106—611no—
503#418—611no—
504#418—611no—
505#418—611no—
506#418—611no—
507#418—611no—
508#418—611no—
509#418—611no—
510#418#692311yescharacteristic, complemented
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×C22⋊C8—611no—
520C2×#97—611no—
521C2×C4×C8—611no—
522#390—611no—
523#390—611no—
524#389—611no—
525#389—611no—
526#388—1221no—
527#388—1221no—
528#386—1221no—
529#386—1221no—
530#383—1221no—
531#380—611no—
532#380—611no—
533#379—1221no—
534C4×C4⋊C4—611no—
535C4×C4⋊C4—611no—
536C4×C4⋊C4—1221no—
537C4×C22⋊C4—611no—
538#340—611no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340—611no—
543#340—611no—
544#336—611no—
545#336—611no—
546C61#2258011yescharacteristic, complemented, Sylow
547C25—1221no—
548C22×D4—611no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—611no—
553C22×D4—1221no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1222no—
557C22×D4—1222no—
558C22×D4—2441no—
559C22×D4—2441no—
560C22×D4C2×#692311yescharacteristic
561C23×C4—611no—
562C23×C4—1221no—
563C23×C4—1221no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—611no—
567C2×M16—2441no—
568C2×M16—2441no—
569C2×M16C2×#692311yescharacteristic, complemented
570C22×C8—611no—
571C22×C8—611no—
572C22×C8—611no—
573C22×C8—611no—
574C4×D4—1222no—
575C4×D4—1222no—
576C4×D4—2441no—
577C4×D4—2441no—
578#117—611no—
579#117—611no—
580#117—611no—
581#117—1221no—
582#117—1221no—
583#117C2×#692311yescharacteristic, complemented
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C22⋊C4—611no—
593C2×C22⋊C4—611no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—2444no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—1221no—
607C2×C42—1221no—
608C2×C42—1221no—
609#107—2441no—
610#106—2441no—
611#102—611no—
612#102—611no—
613#102—611no—
614#102—611no—
615#102—611no—
616#102—611no—
617#102—611no—
618#102—611no—
619#102—611no—
620#102—611no—
621#102—611no—
622#102—611no—
623#102—1222no—
624#102—1222no—
625#102—2441no—
626#102—2441no—
627#102C2×#692311yescharacteristic
628#102C2×#692311yescharacteristic
629#102C2×#692311yescharacteristic, complemented
630#102C2×#692311yescharacteristic, complemented
631C22⋊C8—1221no—
632C22⋊C8—1221no—
633#97—2441no—
634C4×C8—2441no—
635#95—611no—
636#95—611no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641#95—1221no—
642#95—1221no—
643C24—21no—
644C24—611no—
645C24—1221no—
646C24—1221no—
647C24—1221no—
648C24—1221no—
649C24—1221no—
650C24—4881no—
651C24—4881no—
652C24—2442no—
653C24—2442no—
654C24—2442no—
655C24—2442no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—41no—
659C2×D4—612no—
660C2×D4—612no—
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—1222no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1221no—
677C2×D4—2441no—
678C2×D4—2441no—
679C2×D4—2441no—
680C2×D4—2442no—
681C2×D4—2442no—
682C2×D4—2442no—
683C2×D4—2442no—
684C2×D4—2442no—
685C2×D4—2442no—
686C2×D4C22×#692311yescharacteristic
687C2×D4C22×#692311yescharacteristic
688C22×C4—611no—
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—1221no—
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—1221no—
707C22×C4—4881no—
708C22×C4—4881no—
709C22×C4—2442no—
710C22×C4—2442no—
711C22×C4—2442no—
712C22×C4—2442no—
713C22×C4C22×#692311yescharacteristic
714M16—41no—
715M16—2441no—
716M16—2441no—
717M16—2441no—
718C2×C8—611no—
719C2×C8—611no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8C22×#692311yescharacteristic
731C2×C8C22×#692311yescharacteristic
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—2442no—
745C4⋊C4—2442no—
746C4⋊C4C22×#692311yescharacteristic
747C4⋊C4C22×#692311yescharacteristic
748C22⋊C4—21no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1222no—
752C22⋊C4—1221no—
753C22⋊C4—4881no—
754C22⋊C4—4881no—
755C22⋊C4—4881no—
756C22⋊C4—2442no—
757C22⋊C4—2441no—
758C22⋊C4—2442no—
759C22⋊C4—2442no—
760C22⋊C4—2442no—
761C22⋊C4—2442no—
762C42—21no—
763C42—1221no—
764C42—1221no—
765C42—1221no—
766C42—1221no—
767C42—1221no—
768C42—1221no—
769C42—1221no—
770C42—4881no—
771C42—4881no—
772C23—21no—
773C23—21no—
774C23—42no—
775C23—42no—
776C23—81no—
777C23—611no—
778C23—611no—
779C23—1221no—
780C23—1221no—
781C23—1222no—
782C23—1222no—
783C23—1221no—
784C23—1221no—
785C23—1221no—
786C23—1221no—
787C23—1221no—
788C23—1221no—
789C23—4881no—
790C23—4881no—
791C23—4881no—
792C23—4884no—
793C23—4884no—
794C23—4884no—
795C23—4884no—
796C23—2442no—
797C23—2442no—
798C23—2442no—
799C23—2441no—
800C23—2441no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23—2441no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23D4×#692311yescharacteristic
813D4—21no—
814D4—21no—
815D4—21no—
816D4—42no—
817D4—612no—
818D4—1222no—
819D4—1222no—
820D4—1221no—
821D4—1221no—
822D4—1221no—
823D4—2442no—
824D4—2441no—
825D4—2441no—
826D4—2442no—
827D4—2442no—
828D4#1451985612yes—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—612no—
839C2×C4—611no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
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—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—4884no—
862C2×C4—4884no—
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×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4D4×#692311yescharacteristic
880C2×C4C23×#692311yescharacteristic
881C8—21no—
882C8—21no—
883C8—1221no—
884C8—1221no—
885C8—2441no—
886C8—2441no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—22no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—84no—
897C22—611no—
898C22—611no—
899C22—611no—
900C22—611no—
901C22—611no—
902C22—611no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—1222no—
907C22—4884no—
908C22—4884no—
909C22—4881no—
910C22—4881no—
911C22—4881no—
912C22—4881no—
913C22—4884no—
914C22—2442no—
915C22—2442no—
916C22—2441no—
917C22—2441no—
918C22—2441no—
919C22—2441no—
920C22—2442no—
921C22—2442no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22—2441no—
926C22—2441no—
927C22C2×D4×#692311yescharacteristic
928C4—21no—
929C4—41no—
930C4—41no—
931C4—611no—
932C4—611no—
933C4—1222no—
934C4—1221no—
935C4—4881no—
936C4—4881no—
937C4—4881no—
938C4—4881no—
939C4—2441no—
940C4—2441no—
941C4—2441no—
942C4—2441no—
943C4—2441no—
944C4C2×#1451985611yescharacteristic
945C4#1684082911yescharacteristic
946C2—41no—
947C2—42no—
948C2—81no—
949C2—611no—
950C2—611no—
951C2—611no—
952C2—611no—
953C2—4881no—
954C2—2441no—
955C2—2442no—
956C2#2146232511yescharacteristic
957C2AGL(1,ℤ/8)×#692311yescharacteristic
958C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#418C4
socleC22×C61C2×C4×D4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenter#418#6923
hypocenterC61#22580
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #21462330C2semidirect
3. #21461911C2semidirect
4. #21461909C2semidirect
5. #21461897C2semidirect
6. #21461896C2semidirect
7. #21461784C2semidirect
8. #21461782C2semidirect
9. #21461724C2semidirect
10. #21461697C2semidirect
12. #21461590C2semidirect
13. #102×#6923C2semidirect
14. #21461559C2semidirect
19. C2×#14519846C22semidirect
20. C2×#14519845C22semidirect
26. C2×#14519831C22semidirect
27. C2×C8×#6923C22semidirect
30. #16840713C22semidirect
31. #16840713C22semidirect
40. C4⋊C4×#6923C22semidirect
41. C4⋊C4×#6923C22semidirect
44. #16840636C22semidirect
45. #16840636C22semidirect
46. #16840635C22semidirect
47. #16840635C22semidirect
48. #16840635C22semidirect
49. #16840635C22semidirect
50. (C2×#6923)⋊C8C22semidirect
51. (C2×#6923)⋊C8C22semidirect
55. #16839768C4semidirect
56. #16839767C4semidirect
57. #16839766C4semidirect
58. #16839765C4semidirect
59. #16839765C4semidirect
60. #16839765C4semidirect
61. #16839765C4semidirect
66. C61×#418C4semidirect
128. C2×#11758194C2×C4semidirect
129. C2×#11758189C2×C4semidirect
130. C2×#11758189C2×C4semidirect
135. #14519736C2×C4semidirect
136. #14519735C2×C4semidirect
137. #14519735C2×C4semidirect
146. #14519699C2×C4semidirect
147. #14519699C2×C4semidirect
150. #14519698C2×C4semidirect
151. #14519698C2×C4semidirect
154. #14519697C2×C4semidirect
155. #14519697C2×C4semidirect
157. C2×M16×C61C2×C4semidirect
158. #117×C61C2×C4semidirect
161. #102×C61C2×C4semidirect
162. #102×C61C2×C4semidirect
510. #418#6923semidirect
546. C61#22580semidirect
569. C2×M16C2×#6923semidirect
583. #117C2×#6923semidirect
629. #102C2×#6923semidirect
630. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623302
D4×C22⋊#69232
#214619112
#214619092
#214618972
#214618962
#214617842
#214617822
#214617242
#214616972
#214616572
#214615902
#102×#69232
#214615592
#418×D612
#2258061