Finite Group Databasebeta

← #30622198

Subgroups — #30622198

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840803C211yesmaximal, characteristic, complemented
2C2×D8×#6923C211yesmaximal, characteristic, complemented
3#21462349C211yesmaximal, characteristic, complemented
4#21462332C211yesmaximal, characteristic, complemented
5#21461951C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461911C211yesmaximal, characteristic, complemented
8#21461909C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461782C211yesmaximal, characteristic, complemented
13#21461620C211yesmaximal, characteristic, complemented
14#21461589C211yesmaximal, characteristic, complemented
15#459×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×D4×#6923C2211yescharacteristic
21#16840803—24no—
22D8×#6923—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31#16840721C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34#16840714—21no—
35#16840714C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840713C2211yescharacteristic
39#16840710—21no—
40#16840710—21no—
41#16840709—21no—
42#16840709—21no—
43#16840706C2211yescharacteristic
44#16840704—21no—
45C4×C4⋊#6923C2211yescharacteristic
46C4×C4⋊#6923C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×D8×D61C2211yescharacteristic
55C2×D8×D61C2211yescharacteristic
56#127×D61C2211yescharacteristic
57C4×D4×D61C2211yescharacteristic
58#16839958C411yescharacteristic, complemented
59#16839957C411yescharacteristic, complemented
60#16839956C411yescharacteristic, complemented
61#16839956C411yescharacteristic, complemented
62#16839955C411yescharacteristic, complemented
63#16839955C411yescharacteristic, complemented
64#16839954C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#459C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C23×#6923—21no—
73C2×D61⋊C8C2311yescharacteristic
74C2×D61⋊C8C2311yescharacteristic
75D4×#6923—22no—
76D4×#6923—22no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—41no—
80D4×#6923—41no—
81D4×#6923—41no—
82D4×#6923—41no—
83D4×#6923—44no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923D411yescharacteristic
87C2×C4⋊#6923D411yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923C2311yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103#14519846—22no—
104#14519845—22no—
105#14519839—22no—
106#14519839—22no—
107#14519839—22no—
108#14519839—41no—
109#14519839—41no—
110#14519839D414yescomplemented
111#14519832—21no—
112#14519832—21no—
113#14519831—22no—
114C8×#6923—22no—
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×D4×D61—21no—
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C2×D4×D61C2311yescharacteristic
126C2×D4×D61C2311yescharacteristic
127C22×C4×D61—21no—
128C2×D488C2×C411yescharacteristic, complemented
129C2×D488C2×C411yescharacteristic, complemented
130C2×#11758199C2×C411yescharacteristic, complemented
131C2×#11758199C2×C411yescharacteristic, complemented
132C2×#11758199C2×C411yescharacteristic, complemented
133C2×#11758199C2×C411yescharacteristic, complemented
134D8×D61—22no—
135D8×D61—22no—
136D8×D61—22no—
137D8×D61—22no—
138C2×C8×D61C2311yescharacteristic
139C2×C8×D61C2311yescharacteristic
140#14519774C2×C411yescharacteristic, complemented
141#14519773—21no—
142#14519773—21no—
143#14519773C2×C411yescharacteristic, complemented
144#14519773C2×C411yescharacteristic, complemented
145C4×D244C2×C411yescharacteristic, complemented
146D4×Dic61C2×C411yescharacteristic, complemented
147#14519739C2×C411yescharacteristic, complemented
148C4×C22⋊D61—21no—
149#14519737—21no—
150C4⋊C4×D61C2311yescharacteristic
151C22⋊C4×D61—21no—
152C42×D61C2311yescharacteristic
153C4⋊#92418C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519706C2×C411yescharacteristic, complemented
156#14519699C2×C411yescharacteristic, complemented
157#14519699C2×C411yescharacteristic, complemented
158#14519698C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162C2×D8×C61C2×C411yescharacteristic, complemented
163C2×D8×C61C2×C411yescharacteristic, complemented
164#127×C61C2×C411yescharacteristic, complemented
165C4×D4×C61C2×C411yescharacteristic, complemented
166C4⋊C8×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—42no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—81no—
185C22×#6923—81no—
186C22×#6923—81no—
187C22×#6923—81no—
188C22×#6923C2×D411yescharacteristic
189C22×#6923C2×D411yescharacteristic
190C22×#6923C2×D411yescharacteristic
191C22×#6923C2×D411yescharacteristic
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61C22×C411yescharacteristic
195C2×D4×C61C22×C411yescharacteristic
196C2×D4×C61C22×C411yescharacteristic
197C22×C4×C61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C22×Dic61—21no—
206D4×D61—21no—
207D4×D61—21no—
208D4×D61—21no—
209D4×D61—21no—
210D4×D61—21no—
211D4×D61—21no—
212D4×D61—21no—
213D4×D61—21no—
214D4×D61—21no—
215D4×D61—21no—
216D4×D61—42no—
217D4×D61—42no—
218D4×D61—81no—
219D4×D61—81no—
220D4×D61C2×D412yes—
221D4×D61#4112yes—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244C22×C411yescharacteristic
225C2×D244C22×C411yescharacteristic
226C2×D244C22×C411yescharacteristic
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—81no—
231C2×C4×D61—81no—
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2411yescharacteristic
235C22⋊#6923—42no—
236C22⋊#6923—42no—
237C22⋊#6923—42no—
238C22⋊#6923—42no—
239C22⋊#6923—42no—
240C22⋊#6923—42no—
241C22⋊#6923—81no—
242C22⋊#6923—81no—
243C2×#92420—21no—
244C2×#92420—21no—
245C4⋊#6923—22no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—21no—
249C4⋊#6923—21no—
250C4⋊#6923—21no—
251C4⋊#6923—21no—
252C4⋊#6923—21no—
253C4⋊#6923—41no—
254C4⋊#6923—81no—
255C4⋊#6923—81no—
256C4⋊#6923C2×D412yes—
257C4×#6923—21no—
258C4×#6923—21no—
259C4×#6923—21no—
260C4×#6923—21no—
261C4×#6923—42no—
262D61⋊C8—21no—
263D61⋊C8—21no—
264D61⋊C8—21no—
265D61⋊C8C2×D412yes—
266D8×C61—22no—
267D8×C61—22no—
268C2×C8×C61C22×C411yescharacteristic
269C2×C8×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C22⋊C4×C61—21no—
272C42×C61C22×C411yescharacteristic
273C22⋊Dic61—21no—
274#11758199—22no—
275#11758199—22no—
276#11758199—22no—
277#11758199—22no—
278#11758198—21no—
279#11758198—21no—
280C4⋊Dic61C22×C411yescharacteristic
281#11758196—21no—
282C4×Dic61C22×C411yescharacteristic
283C4×Dic61#4111yescharacteristic
284C4×Dic61#4111yescharacteristic
285C2×#92418C22×C411yescharacteristic
286C2×#92418C22×C411yescharacteristic
287D488—22no—
288D488—22no—
289C8×D61—21no—
290C8×D61—21no—
291C8×D61—21no—
292C8×D61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C22×D61—21no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61C22×D411yescharacteristic
318C2×#6923—21no—
319C2×#6923—21no—
320C2×#6923—21no—
321C2×#6923—21no—
322C2×#6923—21no—
323C2×#6923—22no—
324C2×#6923—21no—
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—21no—
329C2×#6923—21no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—84no—
342C2×#6923—84no—
343C2×#6923—84no—
344C2×#6923—84no—
345C2×#6923AGL(1,ℤ/8)12yes—
346D4×C61—21no—
347D4×C61—21no—
348D4×C61—21no—
349D4×C61—21no—
350D4×C61—21no—
351D4×C61—42no—
352D4×C61—81no—
353D4×C61C4×D412yescomplemented
354C2×C4×C61—21no—
355C2×C4×C61—81no—
356C2×C4×C61C4×D411yescharacteristic
357C2×C4×C61C4×D411yescharacteristic
358C2×C4×C61C23×C411yescharacteristic
359C22⋊D61—22no—
360C22⋊D61—22no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—41no—
364C22⋊D61—41no—
365C22⋊D61—41no—
366C22⋊D61—41no—
367C22⋊D61—81no—
368C22⋊D61—81no—
369C2×Dic61—21no—
370C2×Dic61—81no—
371C2×Dic61C4×D411yescharacteristic
372C2×Dic61C4×D411yescharacteristic
373C2×Dic61C2×#4111yescharacteristic
374D244—21no—
375D244—21no—
376D244—21no—
377D244—21no—
378D244—21no—
379D244—42no—
380D244—81no—
381D244C4×D412yescomplemented
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—41no—
387C4×D61—41no—
388C4×D61—81no—
389C4×D61—81no—
390C4×D61C22×D411yescharacteristic
391C4×D61C2×#4111yescharacteristic
392C4×D61H(5,𝔽2)11yescharacteristic
393C4×D612−1+411yescharacteristic
394#92420—22no—
395#92420—41no—
396C8×C61—21no—
397C8×C61—21no—
398#92418—21no—
399#92418—21no—
400#23008—611nomaximal, Sylow
401C22×C61—22no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61C2×C4×D411yescharacteristic
411C2×D61—22no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61—81no—
428C2×D61—81no—
429C2×D61—81no—
430C2×D61—81no—
431C2×D61—81no—
432C2×D61D4211yescharacteristic
433C2×D61#54811yescharacteristic
434C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
435C2×D61#57511yescharacteristic
436C2×D61#57611yescharacteristic
437C2×D61#57611yescharacteristic
438#6923—22no—
439#6923—41no—
440#6923—42no—
441#6923—41no—
442#6923—41no—
443#6923—81no—
444#6923—81no—
445#6923—81no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—41no—
449C4×C61C2×C4×D411yescharacteristic
450C4×C61#52011yescharacteristic
451Dic61—21no—
452Dic61—21no—
453Dic61—41no—
454Dic61#54711yescharacteristic
455Dic61#55311yescharacteristic
456C2×#459—611no—
457C2×#442—611no—
458C2×C4×D8—611no—
459#2366—611no—
460#2349—611no—
461#1961—611no—
462#1949—611no—
463#1936—611no—
464#1934—611no—
465#1879—611no—
466#1879—611no—
467#1864—611no—
468#1862—611no—
469#1771—611no—
470#1762—611no—
471C2×C61—42no—
472C2×C61—81no—
473C2×C61—81no—
474C2×C61#236111yescharacteristic
475C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
476C2×C61#294811yescharacteristic
477D61—42no—
478D61—81no—
479D61—81no—
480D61#326411yescharacteristic
481D61#326811yescharacteristic
482D61#336611yescharacteristic
483D61#337011yescharacteristic
484C22×D8—611no—
485C22×D8—611no—
486C2×#127—611no—
487C2×C4×D4—611no—
488C2×C4×D4—611no—
489C2×C4×D4—611no—
490C2×C4×D4—611no—
491C2×C4×D4—611no—
492C2×C4×D4—1221no—
493#459—611no—
494#459—611no—
495#459—611no—
496#459—611no—
497#459—611no—
498#459—611no—
499#459—611no—
500#459#692311yescharacteristic, complemented
501#442—1224no—
502C4×D8—1224no—
503C2×#107—611no—
504C2×#106—611no—
505C2×C4⋊C8—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#97—611no—
515C2×#97—611no—
516C2×C4×C8—611no—
517#390—611no—
518#390—611no—
519#390—1221no—
520#389—611no—
521#389—611no—
522#386—1221no—
523#386—1221no—
524#385—1221no—
525#385—1221no—
526#382—611no—
527#380—1221no—
528C4×C4⋊C4—611no—
529C4×C4⋊C4—611no—
530C2×#95—1221no—
531#340—611no—
532#340—611no—
533#340—611no—
534#340—611no—
535#336—611no—
536#336—611no—
537C61#2300811yescharacteristic, complemented, Sylow
538C22×D4—611no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—1221no—
542C22×D4—1221no—
543C23×C4—1221no—
544C23×C4—1221no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548C2×D8—611no—
549C2×D8—611no—
550C2×D8—611no—
551C2×D8—611no—
552C2×D8—611no—
553C2×D8—611no—
554C2×D8—1222no—
555C2×D8—1222no—
556C2×D8—1222no—
557C2×D8—1222no—
558C2×D8C2×#692311yescharacteristic, complemented
559C2×D8C2×#692311yescharacteristic, complemented
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564#127—611no—
565#127—611no—
566#127—611no—
567#127—1221no—
568#127—1221no—
569#127C2×#692311yescharacteristic, complemented
570C4×D4—611no—
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—1221no—
574C4×D4—1221no—
575C4×D4—1222no—
576C4×D4—1222no—
577C4×D4—1222no—
578C4×D4—1222no—
579C4×D4—2441no—
580C4×D4—2441no—
581C4×D4—2441no—
582C4×D4—2441no—
583C4×D4—2444no—
584C4×D4C2×#692311yescharacteristic, complemented
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
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×C42—611no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—1221no—
607#107—1222no—
608#106—1222no—
609C4⋊C8—611no—
610C4⋊C8—611no—
611C4⋊C8—611no—
612C4⋊C8C2×#692311yescharacteristic, complemented
613#102—614no—
614#102—611no—
615#102—611no—
616#102—611no—
617#102—611no—
618#102—611no—
619#102—611no—
620#102—1222no—
621#102—1222no—
622#102—1222no—
623#102—2441no—
624#102—2441no—
625#102C2×#692311yescharacteristic, complemented
626#102C2×#692311yescharacteristic, complemented
627#97—1221no—
628#97—1221no—
629#97—1222no—
630C4×C8—1222no—
631#95—611no—
632#95—611no—
633#95—1221no—
634#95—1221no—
635#95—1221no—
636#95—1221no—
637#95—1221no—
638C24—1221no—
639C24—1221no—
640C24—1221no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—612no—
644C2×D4—612no—
645C2×D4—611no—
646C2×D4—611no—
647C2×D4—611no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—4881no—
668C2×D4—4881no—
669C2×D4—2442no—
670C2×D4—2442no—
671C2×D4C22×#692311yescharacteristic
672C2×D4C22×#692311yescharacteristic
673C2×D4C22×#692311yescharacteristic
674C22×C4—21no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—4881no—
691C22×C4—4881no—
692C22×C4—4881no—
693C22×C4—4881no—
694C22×C4—4881no—
695C22×C4—4881no—
696C22×C4—2442no—
697C22×C4—2442no—
698C22×C4—2442no—
699C22×C4—2442no—
700C22×C4—2442no—
701C22×C4—2442no—
702C22×C4—2442no—
703C22×C4—2442no—
704D8—22no—
705D8—22no—
706D8—1222no—
707D8—1222no—
708D8—1222no—
709D8—1222no—
710D8—1222no—
711D8—1222no—
712C2×C8—612no—
713C2×C8—611no—
714C2×C8—611no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8C22×#692311yescharacteristic
725C2×C8C22×#692311yescharacteristic
726C4⋊C4—612no—
727C4⋊C4—611no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1222no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—4881no—
738C4⋊C4—4881no—
739C4⋊C4—2441no—
740C4⋊C4C22×#692311yescharacteristic
741C22⋊C4—21no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—4881no—
746C22⋊C4—4881no—
747C22⋊C4—2442no—
748C22⋊C4—2442no—
749C22⋊C4—2442no—
750C22⋊C4—2442no—
751C22⋊C4—2442no—
752C22⋊C4—2442no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—2442no—
761C42C22×#692311yescharacteristic
762C23—21no—
763C23—21no—
764C23—21no—
765C23—611no—
766C23—1222no—
767C23—1222no—
768C23—1221no—
769C23—1221no—
770C23—1221no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—42no—
793D4—81no—
794D4—612no—
795D4—1222no—
796D4—1222no—
797D4—1221no—
798D4—1221no—
799D4—1221no—
800D4—1221no—
801D4—1221no—
802D4—4881no—
803D4—4881no—
804D4—4881no—
805D4—2442no—
806D4—2441no—
807D4—2441no—
808D4—2441no—
809D4—2441no—
810D4—2442no—
811D4—2442no—
812D4D4×#692312yescomplemented
813C2×C4—21no—
814C2×C4—81no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—612no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1222no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—4881no—
841C2×C4—4881no—
842C2×C4—4884no—
843C2×C4—4881no—
844C2×C4—4884no—
845C2×C4—4884no—
846C2×C4—4884no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4D4×#692311yescharacteristic
861C2×C4D4×#692311yescharacteristic
862C2×C4C23×#692311yescharacteristic
863C8—21no—
864C8—21no—
865C8—1222no—
866C8—1221no—
867C8—1221no—
868C8—2441no—
869C22—22no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—611no—
879C22—611no—
880C22—611no—
881C22—611no—
882C22—611no—
883C22—611no—
884C22—1222no—
885C22—4881no—
886C22—4881no—
887C22—4881no—
888C22—4881no—
889C22—4881no—
890C22—4881no—
891C22—4881no—
892C22—4881no—
893C22—2442no—
894C22—2442no—
895C22—2442no—
896C22—2442no—
897C22—2441no—
898C22—2441no—
899C22—2441no—
900C22—2441no—
901C22—2441no—
902C22—2441no—
903C22—2441no—
904C22—2441no—
905C22C2×D4×#692311yescharacteristic
906C4—21no—
907C4—21no—
908C4—41no—
909C4—611no—
910C4—611no—
911C4—1222no—
912C4—1221no—
913C4—1221no—
914C4—4881no—
915C4—4881no—
916C4—4881no—
917C4—2441no—
918C4—2441no—
919C4—2441no—
920C4—2442no—
921C4—2441no—
922C4C2×D4×#692311yescharacteristic
923C4#1684083111yescharacteristic
924C2—42no—
925C2—81no—
926C2—81no—
927C2—611no—
928C2—611no—
929C2—611no—
930C2—611no—
931C2—4881no—
932C2—4881no—
933C2—2442no—
934C2#2146234411yescharacteristic
935C2AGL(1,ℤ/8)×#692311yescharacteristic
936C2#2146257811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#459×D61C2
cosocleC2×C4×D61C24
hypercenter#459#6923
hypocenterC61#23008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#16840803C2semidirect
2. C2×D8×#6923C2semidirect
3. #21462349C2semidirect
4. #21462332C2semidirect
5. #21461951C2semidirect
6. #21461932C2semidirect
7. #21461911C2semidirect
8. #21461909C2semidirect
9. #21461814C2semidirect
10. #21461814C2semidirect
11. #21461784C2semidirect
12. #21461782C2semidirect
13. #21461620C2semidirect
14. #21461589C2semidirect
58. #16839958C4semidirect
59. #16839957C4semidirect
60. #16839956C4semidirect
61. #16839956C4semidirect
62. #16839955C4semidirect
63. #16839955C4semidirect
64. #16839954C4semidirect
68. C61×#459C4semidirect
110. #14519839D4semidirect
128. C2×D488C2×C4semidirect
129. C2×D488C2×C4semidirect
130. C2×#11758199C2×C4semidirect
131. C2×#11758199C2×C4semidirect
132. C2×#11758199C2×C4semidirect
133. C2×#11758199C2×C4semidirect
140. #14519774C2×C4semidirect
143. #14519773C2×C4semidirect
144. #14519773C2×C4semidirect
145. C4×D244C2×C4semidirect
146. D4×Dic61C2×C4semidirect
147. #14519739C2×C4semidirect
153. C4⋊#92418C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519706C2×C4semidirect
156. #14519699C2×C4semidirect
157. #14519699C2×C4semidirect
158. #14519698C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519697C2×C4semidirect
161. #14519697C2×C4semidirect
162. C2×D8×C61C2×C4semidirect
163. C2×D8×C61C2×C4semidirect
164. #127×C61C2×C4semidirect
165. C4×D4×C61C2×C4semidirect
166. C4⋊C8×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
353. D4×C61C4×D4semidirect
381. D244C4×D4semidirect
500. #459#6923semidirect
537. C61#23008semidirect
558. C2×D8C2×#6923semidirect
559. C2×D8C2×#6923semidirect
569. #127C2×#6923semidirect
584. C4×D4C2×#6923semidirect
612. C4⋊C8C2×#6923semidirect
625. #102C2×#6923semidirect
626. #102C2×#6923semidirect
812. D4D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408032
C2×D8×#69232
#214623492
#214623322
#214619512
#214619322
#214619112
#214619092
#214618142
#214617842
#214617822
#214616202
#214615892
#459×D612
#2300861