Finite Group Databasebeta

← #29646908

Subgroups — #29646908

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459305C211yesmaximal, characteristic
2#21454781C211yesmaximal, characteristic, complemented
3#21454480C211yesmaximal, characteristic, complemented
4#21444288C211yesmaximal, characteristic, complemented
5#21444286C211yesmaximal, characteristic, complemented
6#21444268C211yesmaximal, characteristic, complemented
7#21444263C211yesmaximal, characteristic, complemented
8#21444260C211yesmaximal, characteristic, complemented
9#21444242C211yesmaximal, characteristic, complemented
10#21444234C211yesmaximal, characteristic, complemented
11#21444216C211yesmaximal, characteristic, complemented
12#21444209C211yesmaximal, characteristic, complemented
13#21444208C211yesmaximal, characteristic, complemented
14D4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1484C211yesmaximal, characteristic, complemented
16C2×#41×D61—21no—
17#16840432C411yescharacteristic
18#16840427C411yescharacteristic
19#16840420—21no—
20#16840415C411yescharacteristic
21#16840412C411yescharacteristic
22#16840412C411yescharacteristic
23#16840405—21no—
24#16840401—21no—
25#16840401—21no—
26#16840397C411yescharacteristic
27#16840396C411yescharacteristic
28#16840396C411yescharacteristic
29#16840309C2211yescharacteristic
30#16840309C2211yescharacteristic
31#16840271—21no—
32#16840271—21no—
33#16840269—21no—
34C4×#11758222C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37C4×D4×D61C2211yescharacteristic
38#16839890—21no—
39#16839838—21no—
40#16839835—21no—
41#16839831—21no—
42#16839821—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic, complemented
45#16839818C2211yescharacteristic, complemented
46#16839815C2211yescharacteristic, complemented
47#16839814C2211yescharacteristic, complemented
48#16839813C2211yescharacteristic, complemented
49#16839813C2211yescharacteristic, complemented
50#16839784C2211yescharacteristic, complemented
51C4⋊C8×D61C2211yescharacteristic, complemented
52#16839727—21no—
53#16839716—21no—
54C4×#11758189C2211yescharacteristic, complemented
55C4×C8×D61C2211yescharacteristic, complemented
56#16839491C2211yescharacteristic
57#16839491C2211yescharacteristic
58#16839491C2211yescharacteristic, complemented
59#16839491C2211yescharacteristic, complemented
60D4⋊#92418C2211yescharacteristic, complemented
61D4⋊#92418C2211yescharacteristic, complemented
62D4⋊#92418C2211yescharacteristic, complemented
63D4⋊#92418C2211yescharacteristic, complemented
64#16839489C2211yescharacteristic
65#16839489C2211yescharacteristic
66#16839489C2211yescharacteristic, complemented
67#16839489C2211yescharacteristic, complemented
68C61×#532C2211yescharacteristic
69C61×#431C2211yescharacteristic, complemented
70C4×M16×C61C2211yescharacteristic, complemented
71C61×D4⋊C8C2211yescharacteristic, complemented
72C61×D4⋊C8C2211yescharacteristic, complemented
73C61×D4⋊C8C2211yescharacteristic, complemented
74C61×D4⋊C8C2211yescharacteristic, complemented
75C2×#11758226—21no—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222D411yescharacteristic
79C2×#11758224—21no—
80C2×#11758224—21no—
81C2×#11758224—21no—
82#41×D61—44no—
83#41×D61—44no—
84C2×Q8×D61—21no—
85C22×D244C2×C411yescharacteristic
86C2×D4×D61—21no—
87C2×D4×D61—21no—
88C2×D4×D61—21no—
89C2×D4×D61C2×C411yescharacteristic
90C2×D4×D61C2×C411yescharacteristic
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C2×#11758189—21no—
95C2×#11758189—21no—
96C2×C8×D61—21no—
97C2×C8×D61—21no—
98#14519776C2×C411yescharacteristic
99#14519776C2×C411yescharacteristic
100#14519773C2×C411yescharacteristic
101#14519773C2×C411yescharacteristic
102#14519763—21no—
103#14519763—21no—
104#14519762—21no—
105#14519762—21no—
106#14519759—21no—
107#14519759—21no—
108#14519758—21no—
109#14519758—21no—
110#14519755—21no—
111#14519755—21no—
112#14519754—21no—
113#14519754—21no—
114#14519753—21no—
115#14519753—21no—
116#14519752C2×C411yescharacteristic
117#14519752C2×C411yescharacteristic
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519749—21no—
123#14519749—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic
127#14519748C2×C411yescharacteristic
128#14519747—21no—
129#14519747—21no—
130#14519745—21no—
131#14519745—21no—
132#14519745—21no—
133#14519745—21no—
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122D411yescharacteristic
136C4×D244—21no—
137C4×D244—21no—
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141C4×D244D411yescharacteristic
142C4×D244C2311yescharacteristic
143C4×D244C2311yescharacteristic
144D4×Dic61C2×C411yescharacteristic
145D4×Dic61C2×C411yescharacteristic
146#14519739C2×C411yescharacteristic
147#14519739C2×C411yescharacteristic
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152C4×C22⋊D61C2×C411yescharacteristic
153C4×C22⋊D61C2×C411yescharacteristic
154C4×C22⋊D61D411yescharacteristic
155C4×C22⋊D61D411yescharacteristic
156#14519737—21no—
157#14519737—21no—
158#14519736D411yescharacteristic
159#14519734D411yescharacteristic
160#14519734D411yescharacteristic
161C2×C4⋊Dic61C2×C411yescharacteristic
162C4⋊C4×D61C2×C411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic
164C2×#11758198—21no—
165C22⋊C4×D61—21no—
166C22⋊C4×D61—21no—
167C42×D61C2311yescharacteristic
168C42×D61C2311yescharacteristic
169C4⋊#92418—21no—
170C4⋊#92418C2311yescharacteristic
171C4⋊#92418C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174#14519706—21no—
175#14519706—21no—
176C22⋊#92418—21no—
177C22⋊#92418—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519688—21no—
183#14519687—21no—
184#14519687—21no—
185C4×#92418C2311yescharacteristic
186C4×#92418C2311yescharacteristic
187C8×Dic61—21no—
188C8×Dic61—21no—
189C2×#41×C61—21no—
190C2×M16×C61—21no—
191C4⋊Q8×C61C2×C411yescharacteristic
192#127×C61C2×C411yescharacteristic
193#124×C61—21no—
194#121×C61—21no—
195#121×C61C2×C411yescharacteristic
196#121×C61C2×C411yescharacteristic
197C4×D4×C61—21no—
198C4×D4×C61C2311yescharacteristic
199C4×D4×C61C2311yescharacteristic
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61C2311yescharacteristic
202C4⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61—21no—
204#97×C61—21no—
205C4×C8×C61—21no—
206C4×C8×C61C2311yescharacteristic
207C4×C8×C61C2311yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211#41×C61—42no—
212#41×C61—42no—
213C2×Q8×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61C22×C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238#11758226—44no—
239Q8×D61—44no—
240#11758224—44no—
241#11758224—44no—
242#11758224—44no—
243D4×D61—22no—
244D4×D61—22no—
245D4×D61—41no—
246D4×D61—41no—
247D4×D61—44no—
248D4×D61—44no—
249D4×D61—44no—
250#11758222—22no—
251#11758222—22no—
252#11758222—42no—
253#11758222—42no—
254#11758222—42no—
255#11758222—42no—
256C2×D244—22no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—41no—
261C2×D244C22⋊C411yescharacteristic
262C2×D244C22×C411yescharacteristic
263C2×D244C22×C411yescharacteristic
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—42no—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61—42no—
277C2×C4×D61—42no—
278C2×C4×D61C22×C411yescharacteristic
279C2×C4×D61C22×C411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×Dic122—21no—
285C2×Dic122—21no—
286C2×Dic122C22⋊C411yescharacteristic
287M16×C61—42no—
288C2×C8×C61—21no—
289C2×C8×C61—21no—
290C2×C8×C61—21no—
291C2×C8×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61C22×C411yescharacteristic
294C4⋊C4×C61C22×C411yescharacteristic
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C42×C61C22×C411yescharacteristic
300C42×C61C2×D411yescharacteristic
301C42×C61C2×D411yescharacteristic
302C42×C61C2411yescharacteristic
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61C22⋊C411yescharacteristic
308C22⋊Dic61C22⋊C411yescharacteristic
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319#11758198C22⋊C411yescharacteristic
320#11758198C22⋊C411yescharacteristic
321C4⋊Dic61—21no—
322C4⋊Dic61C22⋊C411yescharacteristic
323C4⋊Dic61C22⋊C411yescharacteristic
324C4⋊Dic61C22×C411yescharacteristic
325C4⋊Dic61C22×C411yescharacteristic
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196C22⋊C411yescharacteristic
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61C22×C411yescharacteristic
335C4×Dic61C22×C411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C2×#92418—21no—
341C2×#92418—21no—
342C2×#92418—21no—
343C2×#92418—21no—
344#11758189—42no—
345#11758189—42no—
346C8×D61—42no—
347C8×D61—42no—
348C23×C61—21no—
349C23×C61—21no—
350C23×C61C2×C22⋊C411yescharacteristic
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—81no—
360C22×D61—81no—
361C22×D61—81no—
362C22×D61C2×C22⋊C411yescharacteristic
363C22×D61C2×C22⋊C411yescharacteristic
364Q8×C61—42no—
365D4×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—42no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—81no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C23×C411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C22⋊D61—22no—
391C22⋊D61—22no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—42no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—42no—
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411D244—22no—
412D244—21no—
413D244—21no—
414D244—21no—
415D244—42no—
416D244—42no—
417D244—42no—
418D244#13112yes—
419C4×D61—21no—
420C4×D61—21no—
421C4×D61—21no—
422C4×D61—21no—
423C4×D61—21no—
424C4×D61—21no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61—42no—
430C4×D61—42no—
431C4×D61—42no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—42no—
437C4×D61AGL(1,ℤ/8)12yes—
438C4×D61AGL(1,ℤ/8)12yes—
439Dic122—22no—
440Dic122—42no—
441Dic122—42no—
442C8×C61—22no—
443C8×C61—41no—
444C8×C61—41no—
445C8×C61—41no—
446#92418—41no—
447#92418—41no—
448#92418—41no—
449#92418—41no—
450#17511—611nomaximal, Sylow
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61C22×C22⋊C411yescharacteristic
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—22no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—84no—
473C2×D61—84no—
474C2×D61—84no—
475C2×D61#41812yes—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61C2×#13111yescharacteristic
483C4×C61#56811yescharacteristic
484C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
485C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—41no—
492Dic61—41no—
493Dic61#41812yes—
494D4×#41—611no—
495#2965—611no—
496#2925—611no—
497#1496—611no—
498#1496—611no—
499#1492—611no—
500#1490—611no—
501#1490—611no—
502#1486—611no—
503#1484—611no—
504#1484D6111yescharacteristic, complemented
505#1480—611no—
506#1478—611no—
507#1478—611no—
508C2×D4⋊C8—611no—
509C2×C61—41no—
510C2×C61—81no—
511C2×C61—81no—
512C2×C61#288011yescharacteristic
513C2×C61C2×#41811yescharacteristic
514C2×C61#290111yescharacteristic
515D61—22no—
516D61—41no—
517D61—42no—
518D61—81no—
519C22×#41—1221no—
520#550—611no—
521D4×Q8—611no—
522#548—1221no—
523#547—611no—
524#547—611no—
525#547—611no—
526#546—1221no—
527#546—1221no—
528#546—1221no—
529D42—611no—
530D42—611no—
531D42—611no—
532#532—611no—
533#532—611no—
534#532C2×D6111yescharacteristic
535#525—1221no—
536#525—1221no—
537#525—1221no—
538C4×#41—611no—
539C2×C4×D4—611no—
540C2×C4×D4—611no—
541C2×C4×D4—611no—
542#446—1221no—
543#436—1221no—
544#435—1221no—
545#435—1221no—
546#433—1221no—
547#433—1221no—
548#432—611no—
549#432—611no—
550#431—611no—
551#431—611no—
552#431—611no—
553#431—611no—
554#431C2×D6111yescharacteristic, complemented
555#423—611no—
556C2×C4⋊C8—611no—
557#408—1221no—
558#405—1221no—
559C4×M16—611no—
560C4×M16C2×D6111yescharacteristic, complemented
561C2×C4×C8—611no—
562D4⋊C8—611no—
563D4⋊C8—611no—
564D4⋊C8—611no—
565D4⋊C8—611no—
566D4⋊C8—611no—
567D4⋊C8—611no—
568D4⋊C8—611no—
569D4⋊C8—611no—
570D4⋊C8—611no—
571D4⋊C8—611no—
572D4⋊C8—611no—
573D4⋊C8—611no—
574D4⋊C8C2×D6111yescharacteristic, complemented
575D4⋊C8C2×D6111yescharacteristic, complemented
576D4⋊C8C2×D6111yescharacteristic, complemented
577D4⋊C8C2×D6111yescharacteristic, complemented
578C61#1751111yescharacteristic, complemented, Sylow
579C2×#41—21no—
580C2×#41—611no—
581C2×#41—1221no—
582C2×#41—1221no—
583C2×#41—1221no—
584C2×#41—1221no—
585C2×#41—1221no—
586C2×#41—1221no—
587C2×#41—2444no—
588C2×#41—2444no—
589C22×Q8—1221no—
590C22×D4—611no—
591C22×D4—611no—
592C22×D4—611no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4—1221no—
596C23×C4—1221no—
597C23×C4—1221no—
598C23×C4—1221no—
599C2×M16—21no—
600C2×M16—1221no—
601C2×M16—1221no—
602C22×C8—1221no—
603C22×C8—1221no—
604C4⋊Q8—611no—
605C4⋊Q8—611no—
606C4⋊Q8C4×D6111yescharacteristic
607#127—611no—
608#127—611no—
609#127C4×D6111yescharacteristic
610#124—21no—
611#124—1221no—
612#124—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625#121—21no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—611no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121C4×D6111yescharacteristic
639#121C4×D6111yescharacteristic
640#120—1221no—
641#120—1221no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646C4×Q8—611no—
647C4×Q8—611no—
648C4×D4—21no—
649C4×D4—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4C22×D6111yescharacteristic
672C4×D4C22×D6111yescharacteristic
673#117—611no—
674#117—611no—
675#117—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C22⋊C4—1221no—
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1221no—
682C2×C42—611no—
683C2×C42—611no—
684C2×C42C22×D6111yescharacteristic
685C4⋊C8—611no—
686C4⋊C8—611no—
687C4⋊C8—1221no—
688C4⋊C8—1221no—
689C4⋊C8—1221no—
690C4⋊C8—1221no—
691C4⋊C8—1221no—
692C4⋊C8C22×D6111yescharacteristic
693C4⋊C8C22×D6111yescharacteristic
694C22⋊C8—21no—
695C22⋊C8—1221no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—21no—
702#97—1221no—
703#97—1221no—
704#97—1221no—
705C4×C8—21no—
706C4×C8—611no—
707C4×C8—611no—
708C4×C8—1221no—
709C4×C8—1221no—
710C4×C8C22×D6111yescharacteristic
711C4×C8C22×D6111yescharacteristic
712C24—1221no—
713C24—1221no—
714C24—1221no—
715#41—42no—
716#41—42no—
717#41—1222no—
718#41—1222no—
719#41—2442no—
720#41—2442no—
721#41—2442no—
722#41—2442no—
723#41—2444no—
724#41—2444no—
725#41—2444no—
726#41—2444no—
727C2×Q8—21no—
728C2×Q8—611no—
729C2×Q8—1221no—
730C2×Q8—1221no—
731C2×Q8—2444no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—611no—
737C2×D4—611no—
738C2×D4—611no—
739C2×D4—611no—
740C2×D4—611no—
741C2×D4—1222no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1222no—
751C2×D4—1222no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—2441no—
756C2×D4—2441no—
757C2×D4—2441no—
758C2×D4—2444no—
759C2×D4—2444no—
760C2×D4—2444no—
761C2×D4C2×C4×D6111yescharacteristic
762C2×D4C2×C4×D6111yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—2442no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4—2442no—
788C22×C4C2×C4×D6111yescharacteristic
789C22×C4D4×D6111yescharacteristic
790C22×C4D4×D6111yescharacteristic
791M16—42no—
792M16—2442no—
793M16—2442no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—2442no—
803C2×C8—2442no—
804C4⋊C4—21no—
805C4⋊C4—611no—
806C4⋊C4—611no—
807C4⋊C4—611no—
808C4⋊C4—611no—
809C4⋊C4—611no—
810C4⋊C4—611no—
811C4⋊C4—611no—
812C4⋊C4—611no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4C2×C4×D6111yescharacteristic
819C4⋊C4C2×C4×D6111yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—611no—
828C22⋊C4—611no—
829C22⋊C4—611no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C42—611no—
843C42—611no—
844C42—611no—
845C42—611no—
846C42—611no—
847C42—611no—
848C42C2×C4×D6111yescharacteristic
849C42D4×D6111yescharacteristic
850C42D4×D6111yescharacteristic
851C42C23×D6111yescharacteristic
852C23—21no—
853C23—21no—
854C23—611no—
855C23—611no—
856C23—1221no—
857C23—1221no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—2442no—
862C23—2442no—
863C23—2442no—
864C23—2442no—
865C23—2442no—
866C23—2442no—
867C23C22⋊C4×D6111yescharacteristic
868Q8—42no—
869Q8—1222no—
870Q8—2442no—
871Q8—2442no—
872D4—21no—
873D4—21no—
874D4—21no—
875D4—21no—
876D4—42no—
877D4—42no—
878D4—42no—
879D4—81no—
880D4—612no—
881D4—1222no—
882D4—1222no—
883D4—1222no—
884D4—1221no—
885D4—1221no—
886D4—1221no—
887D4—4881no—
888D4—4881no—
889D4—2442no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—611no—
910C2×C4—612no—
911C2×C4—612no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2442no—
928C2×C4—2442no—
929C2×C4—2442no—
930C2×C4—2442no—
931C2×C4—2442no—
932C2×C4—2442no—
933C2×C4—2442no—
934C2×C4—2442no—
935C2×C4—2442no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4C22⋊C4×D6111yescharacteristic
941C2×C4C22⋊C4×D6111yescharacteristic
942C2×C4C22⋊C4×D6111yescharacteristic
943C2×C4C22×C4×D6111yescharacteristic
944C2×C4C2×D4×D6111yescharacteristic
945C2×C4C2×D4×D6111yescharacteristic
946C8—22no—
947C8—41no—
948C8—41no—
949C8—41no—
950C8—2441no—
951C8—2441no—
952C8—2441no—
953C8—2441no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—612no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—1222no—
969C22—1221no—
970C22—4884no—
971C22—4884no—
972C22—4884no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22—2441no—
978C22C2×C22⋊C4×D6111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—41no—
984C4—41no—
985C4—612no—
986C4—1221no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—2441no—
992C4—2441no—
993C4#131×D6111yescharacteristic
994C4#1684052711yescharacteristic
995C4AGL(1,ℤ/8)×D6111yescharacteristic
996C4AGL(1,ℤ/8)×D6111yescharacteristic
997C2—41no—
998C2—81no—
999C2—81no—
1000C2—1222no—
1001C2—4881no—
1002C2—2441no—
1003C2—2442no—
1004C2#2145426711yescharacteristic
1005C2#418×D6111yescharacteristic
1006C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1484C2
socleC22×C61C22×C22⋊C4
prime radical#21459305C2
cosocleC42×C61C24
hypercenter#1484D61
hypocenterC61#17511
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1484

Complements

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

NH ≅ G/Ntype
2. #21454781C2semidirect
3. #21454480C2semidirect
4. #21444288C2semidirect
5. #21444286C2semidirect
6. #21444268C2semidirect
7. #21444263C2semidirect
8. #21444260C2semidirect
9. #21444242C2semidirect
10. #21444234C2semidirect
11. #21444216C2semidirect
12. #21444209C2semidirect
13. #21444208C2semidirect
14. D4⋊C8×D61C2semidirect
15. C61×#1484C2semidirect
44. #16839819C22semidirect
45. #16839818C22semidirect
46. #16839815C22semidirect
47. #16839814C22semidirect
48. #16839813C22semidirect
49. #16839813C22semidirect
50. #16839784C22semidirect
51. C4⋊C8×D61C22semidirect
54. C4×#11758189C22semidirect
55. C4×C8×D61C22semidirect
58. #16839491C22semidirect
59. #16839491C22semidirect
60. D4⋊#92418C22semidirect
61. D4⋊#92418C22semidirect
62. D4⋊#92418C22semidirect
63. D4⋊#92418C22semidirect
66. #16839489C22semidirect
67. #16839489C22semidirect
69. C61×#431C22semidirect
70. C4×M16×C61C22semidirect
71. C61×D4⋊C8C22semidirect
72. C61×D4⋊C8C22semidirect
73. C61×D4⋊C8C22semidirect
74. C61×D4⋊C8C22semidirect
504. #1484D61semidirect
554. #431C2×D61semidirect
560. C4×M16C2×D61semidirect
574. D4⋊C8C2×D61semidirect
575. D4⋊C8C2×D61semidirect
576. D4⋊C8C2×D61semidirect
577. D4⋊C8C2×D61semidirect
578. C61#17511semidirect

Maximal subgroups

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

subgroupindex
#214593052
#214547812
#214544802
#214442882
#214442862
#214442682
#214442632
#214442602
#214442422
#214442342
#214442162
#214442092
#214442082
D4⋊C8×D612
C61×#14842
#1751161