Finite Group Databasebeta

← #30621753

Subgroups — #30621753

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×#6923C211yesmaximal, characteristic, complemented
2C2×#16840753C211yesmaximal, characteristic, complemented
3#21462344C211yesmaximal, characteristic, complemented
4#21462322C211yesmaximal, characteristic, complemented
5#21461969C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461835C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461782C211yesmaximal, characteristic, complemented
12#21461768C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#449×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×D4×#6923—21no—
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×D4×#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22D8×#6923—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519846C2211yescharacteristic
25#16840753—24no—
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35(C2×#6923)⋊Q8C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840712—21no—
39#16840710—21no—
40#16840710—21no—
41#16840710—21no—
42#16840709—21no—
43#16840705—21no—
44#16840704C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C4×C22⋊#6923C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×D8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839910C411yescharacteristic, complemented
59#16839909C411yescharacteristic, complemented
60#16839908C411yescharacteristic, complemented
61#16839907C411yescharacteristic, complemented
62#16839906C411yescharacteristic, complemented
63#16839905C411yescharacteristic, complemented
64#16839904C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#449C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C23×#6923—21no—
73C2×#11758213—21no—
74D61⋊M16—22no—
75D61⋊M16—41no—
76C2×#11758217—21no—
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—22no—
82D4×#6923—41no—
83D4×#6923—41no—
84D4×#6923—41no—
85D4×#6923—44no—
86C2×C4⋊#6923—22no—
87C2×C4⋊#6923—21no—
88C2×C4⋊#6923—21no—
89C2×C4⋊#6923—41no—
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C4⋊#6923C2311yescharacteristic
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×C22⋊#6923D411yescharacteristic
101C2×C22⋊#6923D411yescharacteristic
102C2×C4×#6923—21no—
103C2×C4×#6923C2311yescharacteristic
104C2×C4×#6923C2311yescharacteristic
105#14519846—22no—
106#14519846—41no—
107#14519840—22no—
108#14519840—22no—
109#14519839—22no—
110#14519839—22no—
111#14519839—41no—
112#14519839D414yescomplemented
113#14519831—41no—
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)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4D411yescharacteristic
123(C2×#6923)⋊C4D411yescharacteristic
124C2×#11758226C2×C411yescharacteristic, complemented
125C2×#11758222—21no—
126C2×#11758222C2×C411yescharacteristic, complemented
127C2×#11758224—21no—
128C2×#11758224C2×C411yescharacteristic, complemented
129#41×D61—22no—
130#41×D61—22no—
131#41×D61—41no—
132#41×D61—41no—
133C2×Q8×D61C2311yescharacteristic
134C2×D4×D61—21no—
135C2×D4×D61—21no—
136C2×D4×D61C2311yescharacteristic
137C2×D4×D61C2311yescharacteristic
138C22×C4×D61—21no—
139C22×C4×D61C2311yescharacteristic
140C2×#11758190C2×C411yescharacteristic, complemented
141C2×#11758200C2×C411yescharacteristic, complemented
142C2×#11758201C2×C411yescharacteristic, complemented
143SD16×D61—41no—
144SD16×D61—41no—
145C2×D488C2×C411yescharacteristic, complemented
146C2×#11758199C2×C411yescharacteristic, complemented
147C2×#11758199C2×C411yescharacteristic, complemented
148D8×D61—22no—
149D8×D61—22no—
150C2×C8×D61C2311yescharacteristic
151C2×C8×D61C2311yescharacteristic
152#14519752C2×C411yescharacteristic, complemented
153#14519751C2×C411yescharacteristic, complemented
154#14519750—21no—
155#14519749—21no—
156#14519748C2×C411yescharacteristic, complemented
157C4⋊C4×D61C2311yescharacteristic
158C22⋊C4×D61—21no—
159#14519702C2×C411yescharacteristic, complemented
160#14519701C2×C411yescharacteristic, complemented
161#14519700C2×C411yescharacteristic, complemented
162#14519699C2×C411yescharacteristic, complemented
163#14519698C2×C411yescharacteristic, complemented
164#14519697C2×C411yescharacteristic, complemented
165C22⋊#92418C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167#14519689C2×C411yescharacteristic, complemented
168C2×#41×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic, complemented
170C2×D8×C61C2×C411yescharacteristic, complemented
171#121×C61C2×C411yescharacteristic, complemented
172#103×C61C2×C411yescharacteristic, complemented
173#102×C61C2×C411yescharacteristic, complemented
174C22⋊C8×C61C2×C411yescharacteristic, complemented
175C23×D61—21no—
176C23×D61—21no—
177C23×D61C2×D411yescharacteristic
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—42no—
185C22×#6923—42no—
186C22×#6923—42no—
187C22×#6923—42no—
188C22×#6923—42no—
189C22×#6923—42no—
190C22×#6923—81no—
191C22×#6923—81no—
192C22×#6923—81no—
193C22×#6923—81no—
194C22×#6923C2×D411yescharacteristic
195C22×#6923C2×D411yescharacteristic
196C22×#6923C2×D411yescharacteristic
197C22×#6923C2×D411yescharacteristic
198#41×C61—22no—
199#41×C61—41no—
200C2×Q8×C61C22×C411yescharacteristic
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61C22×C411yescharacteristic
204C2×D4×C61C22×C411yescharacteristic
205C22×C4×C61—21no—
206C22×C4×C61C22×C411yescharacteristic
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C22×Dic61—21no—
214C22×Dic61#4111yescharacteristic
215#11758226—22no—
216#11758226—41no—
217Q8×D61—21no—
218Q8×D61—21no—
219Q8×D61—21no—
220Q8×D61—21no—
221#11758224—22no—
222#11758224—41no—
223#11758224—42no—
224#11758224—42no—
225D4×D61—21no—
226D4×D61—21no—
227D4×D61—21no—
228D4×D61—21no—
229D4×D61—21no—
230D4×D61—21no—
231D4×D61—42no—
232D4×D61—42no—
233D4×D61—42no—
234D4×D61—42no—
235D4×D61C2×D412yes—
236D4×D61#4112yes—
237#11758222—22no—
238#11758222—41no—
239#11758222—42no—
240#11758222—42no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244C22×C411yescharacteristic
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61#4111yescharacteristic
258C2×C4×D61C2411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22×C411yescharacteristic
261C22⋊#6923—22no—
262C22⋊#6923—41no—
263C22⋊#6923—42no—
264C22⋊#6923—42no—
265C22⋊#6923—42no—
266C22⋊#6923—42no—
267C22⋊#6923—81no—
268C22⋊#6923—81no—
269#11758217—42no—
270C2×#92420—21no—
271C2×#92420—21no—
272C4⋊#6923—21no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—21no—
276C4⋊#6923—21no—
277C4⋊#6923—21no—
278C4⋊#6923—21no—
279C4⋊#6923—42no—
280C4⋊#6923—42no—
281C4⋊#6923C2×D412yes—
282C4×#6923—21no—
283C4×#6923—21no—
284C4×#6923—21no—
285C4×#6923—21no—
286C4×#6923—42no—
287#11758213—42no—
288D61⋊C8—21no—
289D61⋊C8—21no—
290D61⋊C8—21no—
291D61⋊C8C2×D412yes—
292SD16×C61—41no—
293D8×C61—22no—
294C2×C8×C61C22×C411yescharacteristic
295C2×C8×C61C22×C411yescharacteristic
296C4⋊C4×C61C22×C411yescharacteristic
297C22⋊C4×C61—21no—
298C22⋊Dic61—21no—
299#11758201—41no—
300#11758200—41no—
301#11758199—22no—
302#11758199—22no—
303#11758198—21no—
304#11758198—21no—
305C4⋊Dic61C22×C411yescharacteristic
306#11758196—21no—
307C2×#92418C22×C411yescharacteristic
308C2×#92418C22×C411yescharacteristic
309D488—22no—
310#11758190—41no—
311C8×D61—21no—
312C8×D61—21no—
313C8×D61—21no—
314C8×D61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61C4×D411yescharacteristic
318C22×D61—21no—
319C22×D61—22no—
320C22×D61—21no—
321C22×D61—22no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61C4×D411yescharacteristic
339C22×D61C22×D411yescharacteristic
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—22no—
344C2×#6923—21no—
345C2×#6923—21no—
346C2×#6923—21no—
347C2×#6923—21no—
348C2×#6923—21no—
349C2×#6923—21no—
350C2×#6923—21no—
351C2×#6923—21no—
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—41no—
362C2×#6923—41no—
363C2×#6923—84no—
364C2×#6923—84no—
365C2×#6923—84no—
366C2×#6923—84no—
367C2×#6923AGL(1,ℤ/8)12yes—
368Q8×C61—21no—
369Q8×C61—21no—
370D4×C61—21no—
371D4×C61—21no—
372D4×C61—21no—
373D4×C61—42no—
374D4×C61—42no—
375D4×C61C4×D412yescomplemented
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—42no—
381C2×C4×C61C4×D411yescharacteristic
382C2×C4×C61C23×C411yescharacteristic
383C22⋊D61—22no—
384C22⋊D61—22no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—41no—
390C22⋊D61—41no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—42no—
396C2×Dic61C4×D411yescharacteristic
397C2×Dic61C2×#4111yescharacteristic
398D244—21no—
399D244—21no—
400D244—21no—
401D244—42no—
402D244—42no—
403D244C4×D412yescomplemented
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—42no—
411C4×D61—42no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61C22×D411yescharacteristic
417C4×D61C2×#4111yescharacteristic
418C4×D61H(5,𝔽2)11yescharacteristic
419C4×D61H(5,𝔽2)11yescharacteristic
420Dic122—21no—
421Dic122—21no—
422Dic122—41no—
423Dic122—41no—
424#92420—22no—
425#92420—41no—
426C8×C61—21no—
427C8×C61—21no—
428#92418—21no—
429#92418—21no—
430#22878—611nomaximal, Sylow
431C22×C61—21no—
432C22×C61—22no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61C2×C4×D411yescharacteristic
441C2×D61—21no—
442C2×D61—22no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—42no—
449C2×D61—41no—
450C2×D61—42no—
451C2×D61—41no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—81no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61—81no—
462C2×D61D4211yescharacteristic
463C2×D61#54611yescharacteristic
464C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
465C2×D61#57511yescharacteristic
466C2×D61#57611yescharacteristic
467C2×D61#57811yescharacteristic
468#6923—22no—
469#6923—41no—
470#6923—42no—
471#6923—41no—
472#6923—41no—
473#6923—81no—
474#6923—81no—
475#6923—81no—
476C4×C61—21no—
477C4×C61—41no—
478C4×C61—41no—
479C4×C61C2×C4×D411yescharacteristic
480C4×C61#51811yescharacteristic
481Dic61—21no—
482Dic61—41no—
483Dic61—41no—
484Dic61#54611yescharacteristic
485Dic61#55111yescharacteristic
486C2×#449—611no—
487C2×C4×D8—611no—
488C2×#417—611no—
489#2361—611no—
490#2339—611no—
491#1973—611no—
492#1933—611no—
493#1928—611no—
494#1895—611no—
495#1879—611no—
496#1877—611no—
497#1862—611no—
498#1852—611no—
499#1762—611no—
500#1753—611no—
501C2×C61—41no—
502C2×C61—42no—
503C2×C61—81no—
504C2×C61#235811yescharacteristic
505C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
506C2×C61#295111yescharacteristic
507D61—41no—
508D61—42no—
509D61—81no—
510D61#326411yescharacteristic
511D61#326911yescharacteristic
512D61#332211yescharacteristic
513D61#333011yescharacteristic
514C22×#41—611no—
515C22×SD16—611no—
516C22×D8—611no—
517C22×M16—611no—
518C2×#121—611no—
519C2×C4×D4—611no—
520C2×C4×D4—611no—
521C2×C4×D4—611no—
522C2×C4×D4—1221no—
523C22×C4⋊C4—611no—
524#449—611no—
525#449—611no—
526#449—611no—
527#449—611no—
528#449—611no—
529#449—611no—
530#449—611no—
531#449#692311yescharacteristic, complemented
532C4×D8—1224no—
533C2×#107—611no—
534C2×#107—611no—
535#417—1224no—
536C2×#103—611no—
537C2×#103—611no—
538C2×#103—611no—
539C2×#102—611no—
540C2×#102—611no—
541C2×#102—611no—
542C2×#102—611no—
543C2×#102—611no—
544C2×C22⋊C8—611no—
545C2×#97—611no—
546C2×C4×C8—611no—
547#391—611no—
548#391—611no—
549#390—611no—
550#389—611no—
551#388—1221no—
552#386—1221no—
553#386—1221no—
554#386—1221no—
555#385—1221no—
556#381—1221no—
557#380—611no—
558C4×C4⋊C4—611no—
559C4×C22⋊C4—611no—
560C2×#95—1221no—
561#340—611no—
562#340—611no—
563#340—611no—
564#340—611no—
565#336—611no—
566#336—611no—
567C61#2287811yescharacteristic, complemented, Sylow
568C2×#41—611no—
569C2×#41—611no—
570C2×#41—611no—
571C2×#41—1221no—
572C2×#41—1221no—
573C2×#41—1222no—
574C2×#41—1222no—
575C2×#41—2441no—
576C2×#41—2441no—
577C2×#41C2×#692311yescharacteristic, complemented
578C22×Q8—611no—
579C22×D4—611no—
580C22×D4—611no—
581C22×D4—1221no—
582C22×D4—1221no—
583C23×C4—611no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4—1221no—
587C23×C4—1221no—
588C23×C4—1221no—
589C2×SD16—611no—
590C2×SD16—611no—
591C2×SD16—611no—
592C2×SD16—2441no—
593C2×SD16—2441no—
594C2×SD16C2×#692311yescharacteristic, complemented
595C2×D8—611no—
596C2×D8—611no—
597C2×D8—611no—
598C2×D8—1222no—
599C2×D8—1222no—
600C2×D8C2×#692311yescharacteristic, complemented
601C2×M16—1222no—
602C2×M16—1221no—
603C2×M16—1221no—
604C2×M16—2441no—
605C22×C8—611no—
606C22×C8—611no—
607C22×C8—611no—
608C22×C8—611no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—1221no—
613#121—1221no—
614#121C2×#692311yescharacteristic, complemented
615C4×D4—1222no—
616C4×D4—1222no—
617C4×D4—1222no—
618C4×D4—2441no—
619C4×D4—2441no—
620C4×D4—2441no—
621C4×D4—2444no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—1222no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—2441no—
631C2×C22⋊C4—611no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C42—611no—
641C2×C42—611no—
642C2×C42—1221no—
643#107—1222no—
644#107—2441no—
645#103—611no—
646#103—611no—
647#103—611no—
648#103—1222no—
649#103—1222no—
650#103C2×#692311yescharacteristic, complemented
651#102—614no—
652#102—611no—
653#102—611no—
654#102—611no—
655#102—1222no—
656#102—1222no—
657#102—2441no—
658#102C2×#692311yescharacteristic, complemented
659C22⋊C8—611no—
660C22⋊C8—611no—
661C22⋊C8—611no—
662C22⋊C8C2×#692311yescharacteristic, complemented
663#97—2441no—
664C4×C8—1222no—
665#95—611no—
666#95—611no—
667#95—1221no—
668#95—1221no—
669#95—1221no—
670#95—1221no—
671#95—1221no—
672#95—1221no—
673#95—1221no—
674C24—611no—
675C24—1221no—
676C24—1221no—
677#41—22no—
678#41—41no—
679#41—1222no—
680#41—1222no—
681#41—1222no—
682#41—2441no—
683#41—2442no—
684#41—2442no—
685#41—2441no—
686#41—2442no—
687#41—2442no—
688#41—2441no—
689C2×Q8—611no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8C22×#692311yescharacteristic
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—612no—
699C2×D4—612no—
700C2×D4—611no—
701C2×D4—611no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—2442no—
717C2×D4—2442no—
718C2×D4—2442no—
719C2×D4—2442no—
720C2×D4C22×#692311yescharacteristic
721C2×D4C22×#692311yescharacteristic
722C22×C4—21no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—4881no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4—4881no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4—2442no—
752C22×C4—2442no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2442no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4C22×#692311yescharacteristic
760SD16—41no—
761SD16—2441no—
762SD16—2441no—
763SD16—2441no—
764D8—22no—
765D8—1222no—
766D8—1222no—
767D8—1222no—
768M16—2442no—
769M16—2442no—
770C2×C8—612no—
771C2×C8—611no—
772C2×C8—611no—
773C2×C8—1221no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8C22×#692311yescharacteristic
783C2×C8C22×#692311yescharacteristic
784C4⋊C4—612no—
785C4⋊C4—611no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—2442no—
795C4⋊C4—2442no—
796C4⋊C4C22×#692311yescharacteristic
797C22⋊C4—21no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1222no—
801C22⋊C4—1221no—
802C22⋊C4—4881no—
803C22⋊C4—4881no—
804C22⋊C4—2441no—
805C22⋊C4—2442no—
806C22⋊C4—2442no—
807C22⋊C4—2442no—
808C22⋊C4—2442no—
809C42—1221no—
810C42—1221no—
811C42—1221no—
812C42—1221no—
813C42—2442no—
814C23—21no—
815C23—21no—
816C23—611no—
817C23—611no—
818C23—1221no—
819C23—1221no—
820C23—1222no—
821C23—1222no—
822C23—1221no—
823C23—1221no—
824C23—1221no—
825C23—1221no—
826C23—1221no—
827C23—1221no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23D4×#692311yescharacteristic
839Q8—21no—
840Q8—21no—
841Q8—1221no—
842Q8—1221no—
843Q8—2441no—
844Q8—2441no—
845D4—21no—
846D4—21no—
847D4—21no—
848D4—42no—
849D4—42no—
850D4—612no—
851D4—1222no—
852D4—1222no—
853D4—1221no—
854D4—1221no—
855D4—1221no—
856D4—2442no—
857D4—2442no—
858D4—2441no—
859D4—2441no—
860D4—2442no—
861D4—2442no—
862D4—2442no—
863D4—2442no—
864D4D4×#692312yescomplemented
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—42no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—612no—
876C2×C4—611no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
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—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1222no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—4884no—
900C2×C4—4884no—
901C2×C4—4884no—
902C2×C4—4884no—
903C2×C4—2442no—
904C2×C4—2442no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2442no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4D4×#692311yescharacteristic
922C2×C4C23×#692311yescharacteristic
923C8—21no—
924C8—21no—
925C8—1222no—
926C8—1221no—
927C8—1221no—
928C8—2441no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—22no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—611no—
939C22—611no—
940C22—611no—
941C22—611no—
942C22—611no—
943C22—611no—
944C22—1221no—
945C22—1221no—
946C22—1221no—
947C22—1222no—
948C22—4881no—
949C22—4881no—
950C22—4881no—
951C22—4881no—
952C22—2441no—
953C22—2442no—
954C22—2442no—
955C22—2441no—
956C22—2441no—
957C22—2441no—
958C22—2442no—
959C22—2442no—
960C22—2441no—
961C22—2441no—
962C22—2441no—
963C22—2441no—
964C22—2441no—
965C22C2×D4×#692311yescharacteristic
966C4—21no—
967C4—41no—
968C4—41no—
969C4—611no—
970C4—611no—
971C4—1222no—
972C4—1221no—
973C4—4881no—
974C4—4881no—
975C4—4881no—
976C4—2441no—
977C4—2441no—
978C4—2441no—
979C4—2442no—
980C4—2441no—
981C4—2441no—
982C4C2×D4×#692311yescharacteristic
983C4#1684082911yescharacteristic
984C2—41no—
985C2—42no—
986C2—81no—
987C2—611no—
988C2—611no—
989C2—611no—
990C2—611no—
991C2—4881no—
992C2—2441no—
993C2—2442no—
994C2#2146234111yescharacteristic
995C2AGL(1,ℤ/8)×#692311yescharacteristic
996C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#449×D61C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#22878
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×D8×#6923C2semidirect
2. C2×#16840753C2semidirect
3. #21462344C2semidirect
4. #21462322C2semidirect
5. #21461969C2semidirect
6. #21461908C2semidirect
7. #21461899C2semidirect
8. #21461835C2semidirect
9. #21461814C2semidirect
10. #21461812C2semidirect
11. #21461782C2semidirect
12. #21461768C2semidirect
13. #21461590C2semidirect
14. #21461562C2semidirect
58. #16839910C4semidirect
59. #16839909C4semidirect
60. #16839908C4semidirect
61. #16839907C4semidirect
62. #16839906C4semidirect
63. #16839905C4semidirect
64. #16839904C4semidirect
68. C61×#449C4semidirect
112. #14519839D4semidirect
124. C2×#11758226C2×C4semidirect
126. C2×#11758222C2×C4semidirect
128. C2×#11758224C2×C4semidirect
140. C2×#11758190C2×C4semidirect
141. C2×#11758200C2×C4semidirect
142. C2×#11758201C2×C4semidirect
145. C2×D488C2×C4semidirect
146. C2×#11758199C2×C4semidirect
147. C2×#11758199C2×C4semidirect
152. #14519752C2×C4semidirect
153. #14519751C2×C4semidirect
156. #14519748C2×C4semidirect
159. #14519702C2×C4semidirect
160. #14519701C2×C4semidirect
161. #14519700C2×C4semidirect
162. #14519699C2×C4semidirect
163. #14519698C2×C4semidirect
164. #14519697C2×C4semidirect
165. C22⋊#92418C2×C4semidirect
166. #14519689C2×C4semidirect
167. #14519689C2×C4semidirect
168. C2×#41×C61C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
170. C2×D8×C61C2×C4semidirect
171. #121×C61C2×C4semidirect
172. #103×C61C2×C4semidirect
173. #102×C61C2×C4semidirect
174. C22⋊C8×C61C2×C4semidirect
375. D4×C61C4×D4semidirect
403. D244C4×D4semidirect
531. #449#6923semidirect
567. C61#22878semidirect
577. C2×#41C2×#6923semidirect
594. C2×SD16C2×#6923semidirect
600. C2×D8C2×#6923semidirect
614. #121C2×#6923semidirect
650. #103C2×#6923semidirect
658. #102C2×#6923semidirect
662. C22⋊C8C2×#6923semidirect
864. D4D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D8×#69232
C2×#168407532
#214623442
#214623222
#214619692
#214619082
#214618992
#214618352
#214618142
#214618122
#214617822
#214617682
#214615902
#214615622
#449×D612
#2287861