Finite Group Databasebeta

← #29646942

Subgroups — #29646942

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11758222C211yesmaximal, characteristic
2#21454783C211yesmaximal, characteristic
3#21454480C211yesmaximal, characteristic
4#21444293C211yesmaximal, characteristic, complemented
5#21444290C211yesmaximal, characteristic, complemented
6#21444272C211yesmaximal, characteristic, complemented
7#21444266C211yesmaximal, characteristic, complemented
8#21444264C211yesmaximal, characteristic, complemented
9#21444246C211yesmaximal, characteristic, complemented
10#21444239C211yesmaximal, characteristic, complemented
11#21444238C211yesmaximal, characteristic, complemented
12#21444220C211yesmaximal, characteristic, complemented
13#21444212C211yesmaximal, characteristic, complemented
14Q8⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1479C211yesmaximal, characteristic, complemented
16Q8×Dic122C411yescharacteristic
17#16840490—21no—
18#16840490C411yescharacteristic
19#16840472—21no—
20#16840472C411yescharacteristic
21#16840467—21no—
22#16840467—21no—
23#16840467C411yescharacteristic
24#16840467C411yescharacteristic
25Q8×D244C411yescharacteristic
26Q8×C22⋊D61C411yescharacteristic
27Q8×C22⋊D61C411yescharacteristic
28#16840319—21no—
29#16840319C2211yescharacteristic
30#16840316—21no—
31#16840316—21no—
32#16840316C2211yescharacteristic
33#16840316C2211yescharacteristic
34C4×#11758222—21no—
35C4×#11758222C2211yescharacteristic
36C4×Q8×D61C2211yescharacteristic
37C4×Q8×D61C2211yescharacteristic
38#16839891—21no—
39#16839837—21no—
40#16839836—21no—
41#16839832—21no—
42#16839821—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic
45#16839818C2211yescharacteristic
46#16839814C2211yescharacteristic
47#16839813C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839784C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic
51#16839727—21no—
52#16839716—21no—
53C4×#11758194C2211yescharacteristic
54C4×#11758189C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58#16839494C2211yescharacteristic
59#16839494C2211yescharacteristic
60Q8⋊#92418C2211yescharacteristic
61Q8⋊#92418C2211yescharacteristic
62Q8⋊#92418C2211yescharacteristic
63Q8⋊#92418C2211yescharacteristic
64#16839492C2211yescharacteristic
65#16839492C2211yescharacteristic
66#16839492C2211yescharacteristic
67#16839492C2211yescharacteristic
68C2×C4×Q8×C61C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×Q8⋊C8C2211yescharacteristic
74C61×Q8⋊C8C2211yescharacteristic
75C2×#11758222D411yescharacteristic
76C2×Q8×D61C2×C411yescharacteristic
77C2×Q8×D61C2×C411yescharacteristic
78C2×#11758194—21no—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83#14519777—21no—
84#14519777—21no—
85#14519777C2×C411yescharacteristic
86#14519777C2×C411yescharacteristic
87#14519776—21no—
88#14519776—21no—
89#14519776C2×C411yescharacteristic
90#14519776C2×C411yescharacteristic
91#14519775—21no—
92#14519775—21no—
93#14519775C2×C411yescharacteristic
94#14519775C2×C411yescharacteristic
95#14519769—21no—
96#14519769—21no—
97#14519769—21no—
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519767—21no—
102#14519767—21no—
103#14519767—21no—
104#14519757—21no—
105#14519757—21no—
106#14519757C2×C411yescharacteristic
107#14519757C2×C411yescharacteristic
108#14519756—21no—
109#14519756—21no—
110#14519756—21no—
111#14519756—21no—
112#14519756—21no—
113#14519756C2×C411yescharacteristic
114#14519756C2×C411yescharacteristic
115#14519755—21no—
116#14519755—21no—
117#14519755—21no—
118#14519755—21no—
119#14519755—21no—
120#14519755—21no—
121#14519753—21no—
122#14519753—21no—
123#14519753C2×C411yescharacteristic
124#14519753C2×C411yescharacteristic
125Q8×Dic61C2×C411yescharacteristic
126Q8×Dic61C2×C411yescharacteristic
127C4×Dic122—21no—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122D411yescharacteristic
136C4×Dic122C2311yescharacteristic
137C4×Dic122C2311yescharacteristic
138#14519742—21no—
139#14519742—21no—
140#14519742C2×C411yescharacteristic
141#14519742C2×C411yescharacteristic
142C4×D244—21no—
143C4×D244—21no—
144C4×D244C2×C411yescharacteristic
145C4×D244D411yescharacteristic
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61C2×C411yescharacteristic
151C4×C22⋊D61C2×C411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154#14519736—21no—
155#14519736D411yescharacteristic
156#14519734—21no—
157#14519734—21no—
158#14519734D411yescharacteristic
159#14519734D411yescharacteristic
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61C2×C411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic
164C42×D61—21no—
165C42×D61—21no—
166C42×D61C2311yescharacteristic
167C42×D61C2311yescharacteristic
168C4⋊#92418C2311yescharacteristic
169C4⋊#92418C2311yescharacteristic
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519688—21no—
180#14519688—21no—
181#14519687—21no—
182#14519687—21no—
183C4×#92418C2311yescharacteristic
184C4×#92418C2311yescharacteristic
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×Q8×C61C2×C411yescharacteristic
188C4×Q8×C61—21no—
189C4×Q8×C61—21no—
190C4×Q8×C61C2×C411yescharacteristic
191C4×Q8×C61C2×C411yescharacteristic
192C4×Q8×C61C2311yescharacteristic
193C4×Q8×C61C2311yescharacteristic
194C2×C4⋊C4×C61—21no—
195C2×C4⋊C4×C61C2×C411yescharacteristic
196C2×C42×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61C2311yescharacteristic
200C4⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61—21no—
202C22⋊C8×C61—21no—
203C4×C8×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—22no—
208C2×Q8×C61—41no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×Q8×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C2×C22⋊D61C22⋊C411yescharacteristic
217C2×C22⋊D61C22⋊C411yescharacteristic
218Q8×D61—22no—
219Q8×D61—22no—
220Q8×D61—41no—
221Q8×D61—41no—
222#11758222—22no—
223#11758222—22no—
224C2×D244C22⋊C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122C22⋊C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C2×Dic122C22×C411yescharacteristic
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C22×C411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C42×C61—21no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61C22×C411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2411yescharacteristic
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61C22⋊C411yescharacteristic
265C22⋊Dic61C22⋊C411yescharacteristic
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198C22⋊C411yescharacteristic
271#11758198C22⋊C411yescharacteristic
272#11758198C22⋊C411yescharacteristic
273#11758198C22⋊C411yescharacteristic
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22×C411yescharacteristic
284C4⋊Dic61C22×C411yescharacteristic
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61C22×C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317#11758194—42no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322#11758189—42no—
323#11758189—42no—
324C8×D61—42no—
325C8×D61—42no—
326C23×C61C2×C22⋊C411yescharacteristic
327C22×D61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329Q8×C61—21no—
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—42no—
333Q8×C61#13112yes—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—41no—
343C2×C4×C61—42no—
344C2×C4×C61—81no—
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C22⋊D61—22no—
352C22⋊D61—22no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363D244—22no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—42no—
373C4×D61—42no—
374C4×D61—81no—
375C4×D61—81no—
376C4×D61#13712yes—
377C4×D61#13712yes—
378Dic122—22no—
379Dic122—21no—
380Dic122—21no—
381Dic122—21no—
382Dic122—21no—
383Dic122—42no—
384Dic122—42no—
385Dic122—81no—
386Dic122—81no—
387Dic122—81no—
388C8×C61—41no—
389C8×C61—41no—
390C8×C61—41no—
391C8×C61—41no—
392#92418—22no—
393#92418—41no—
394#92418—41no—
395#92418—41no—
396#17514—611nomaximal, Sylow
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61C22×C22⋊C411yescharacteristic
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61#41912yes—
407C4×C61—22no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C2×#13111yescharacteristic
416C4×C61#56811yescharacteristic
417C4×C61C2×#13711yescharacteristic
418C4×C61C2×#13711yescharacteristic
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—21no—
423Dic61—21no—
424Dic61—41no—
425Dic61—41no—
426Dic61—41no—
427Dic61—41no—
428Dic61#41912yes—
429Q8×#41—611no—
430#2965—611no—
431#2925—611no—
432#1497—611no—
433#1497—611no—
434#1493—611no—
435#1491—611no—
436#1491—611no—
437#1487—611no—
438#1485—611no—
439#1485—611no—
440#1481—611no—
441#1479—611no—
442#1479D6111yescharacteristic, complemented
443C2×Q8⋊C8—611no—
444C2×C61—41no—
445C2×C61#288011yescharacteristic
446C2×C61C2×#41911yescharacteristic
447C2×C61#290111yescharacteristic
448D61—22no—
449D61—41no—
450Q82—611no—
451#557—611no—
452#557—1221no—
453#554—611no—
454#554—611no—
455#554—611no—
456#554—1221no—
457#554—1221no—
458#554—1221no—
459D4×Q8—611no—
460D4×Q8—611no—
461D4×Q8—611no—
462#533—611no—
463#533—611no—
464#533—611no—
465#533—1221no—
466#533—1221no—
467#533—1221no—
468C4×#41—611no—
469C4×#41—1221no—
470C2×C4×Q8—611no—
471C2×C4×Q8—611no—
472C2×C4×Q8C2×D6111yescharacteristic
473#446—1221no—
474#436—1221no—
475#435—1221no—
476#435—1221no—
477#433—1221no—
478#433—1221no—
479#432—611no—
480#432—611no—
481#431—611no—
482#431—611no—
483#431—611no—
484#431C2×D6111yescharacteristic
485#431C2×D6111yescharacteristic
486#423—611no—
487C2×C4⋊C8—611no—
488#408—1221no—
489#405—1221no—
490C4×M16—611no—
491C4×M16—611no—
492C2×C4×C8—611no—
493Q8⋊C8—611no—
494Q8⋊C8—611no—
495Q8⋊C8—611no—
496Q8⋊C8—611no—
497Q8⋊C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8C2×D6111yescharacteristic
506Q8⋊C8C2×D6111yescharacteristic
507Q8⋊C8C2×D6111yescharacteristic
508Q8⋊C8C2×D6111yescharacteristic
509C61#1751411yescharacteristic, complemented, Sylow
510C2×#41—611no—
511C22×Q8—611no—
512C22×Q8—611no—
513C22×Q8C4×D6111yescharacteristic
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16—1221no—
517C22×C8—1221no—
518C22×C8—1221no—
519C4⋊Q8—611no—
520C4⋊Q8—611no—
521C4⋊Q8—611no—
522C4⋊Q8—611no—
523C4⋊Q8—611no—
524C4⋊Q8—611no—
525C4⋊Q8—1221no—
526C4⋊Q8—1221no—
527C4⋊Q8—1221no—
528C4⋊Q8—1221no—
529C4⋊Q8—1221no—
530C4⋊Q8—1221no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125—1221no—
536#125—1221no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540C22⋊Q8—611no—
541C22⋊Q8—611no—
542C22⋊Q8—611no—
543C22⋊Q8—611no—
544C22⋊Q8—611no—
545C22⋊Q8—611no—
546C22⋊Q8—1221no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8C4×D6111yescharacteristic
581C4×Q8C4×D6111yescharacteristic
582C4×Q8C22×D6111yescharacteristic
583C4×Q8C22×D6111yescharacteristic
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596#117—611no—
597#117—611no—
598#117—611no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4C4×D6111yescharacteristic
608C2×C42—21no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42C22×D6111yescharacteristic
614C4⋊C8—21no—
615C4⋊C8—611no—
616C4⋊C8—611no—
617C4⋊C8—1221no—
618C4⋊C8—1221no—
619C4⋊C8—1221no—
620C4⋊C8—1221no—
621C4⋊C8C22×D6111yescharacteristic
622C4⋊C8C22×D6111yescharacteristic
623C22⋊C8—21no—
624C22⋊C8—21no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627C22⋊C8—1221no—
628C22⋊C8—1221no—
629C22⋊C8—1221no—
630#97—1221no—
631#97—1221no—
632#97—1221no—
633#97—1221no—
634C4×C8—21no—
635C4×C8—611no—
636C4×C8—611no—
637C4×C8—1221no—
638C4×C8—1221no—
639C4×C8C22×D6111yescharacteristic
640C4×C8C22×D6111yescharacteristic
641#41—1222no—
642#41—1222no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—41no—
646C2×Q8—611no—
647C2×Q8—611no—
648C2×Q8—611no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1222no—
655C2×Q8—1222no—
656C2×Q8—2441no—
657C2×Q8—2441no—
658C2×Q8C2×C4×D6111yescharacteristic
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—611no—
661C2×D4—611no—
662C2×D4—611no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4C2×C4×D6111yescharacteristic
676C22×C4D4×D6111yescharacteristic
677C22×C4D4×D6111yescharacteristic
678M16—2442no—
679M16—2442no—
680M16—2442no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—2442no—
690C2×C8—2442no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—611no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4C2×C4×D6111yescharacteristic
728C4⋊C4C2×C4×D6111yescharacteristic
729C22⋊C4—611no—
730C22⋊C4—611no—
731C22⋊C4—611no—
732C22⋊C4—611no—
733C22⋊C4—611no—
734C22⋊C4—611no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42—1221no—
755C42—1221no—
756C42—1221no—
757C42C2×C4×D6111yescharacteristic
758C42D4×D6111yescharacteristic
759C42D4×D6111yescharacteristic
760C42C23×D6111yescharacteristic
761C23—611no—
762C23—611no—
763C23C22⋊C4×D6111yescharacteristic
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—42no—
768Q8—1222no—
769Q8—1221no—
770Q8—1221no—
771Q8—1221no—
772Q8—1221no—
773Q8—4881no—
774Q8—4881no—
775Q8—4881no—
776Q8—2442no—
777Q8—2442no—
778Q8#1451978312yes—
779D4—1222no—
780D4—1222no—
781D4—1222no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—81no—
793C2×C4—611no—
794C2×C4—612no—
795C2×C4—612no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—4881no—
812C2×C4—4881no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4C22⋊C4×D6111yescharacteristic
818C2×C4C22⋊C4×D6111yescharacteristic
819C2×C4C22⋊C4×D6111yescharacteristic
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C8—41no—
824C8—41no—
825C8—41no—
826C8—41no—
827C8—1222no—
828C8—2441no—
829C8—2441no—
830C8—2441no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—612no—
835C22—1221no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22—1221no—
840C22C2×C22⋊C4×D6111yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—612no—
850C4—1221no—
851C4—1221no—
852C4—1221no—
853C4—1221no—
854C4—1221no—
855C4—2441no—
856C4—2441no—
857C4—2441no—
858C4—2441no—
859C4C2×#1451978311yescharacteristic
860C4#1684052811yescharacteristic
861C4#137×D6111yescharacteristic
862C4#137×D6111yescharacteristic
863C2—41no—
864C2—1222no—
865C2—2441no—
866C2#2145426511yescharacteristic
867C2#419×D6111yescharacteristic
868C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1479C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222D4
cosocleC42×C61C24
hypercenter#1479D61
hypocenterC61#17514
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #21444293C2semidirect
5. #21444290C2semidirect
6. #21444272C2semidirect
7. #21444266C2semidirect
8. #21444264C2semidirect
9. #21444246C2semidirect
10. #21444239C2semidirect
11. #21444238C2semidirect
12. #21444220C2semidirect
13. #21444212C2semidirect
14. Q8⋊C8×D61C2semidirect
15. C61×#1479C2semidirect
442. #1479D61semidirect
509. C61#17514semidirect

Maximal subgroups

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

subgroupindex
Q8×#117582222
#214547832
#214544802
#214442932
#214442902
#214442722
#214442662
#214442642
#214442462
#214442392
#214442382
#214442202
#214442122
Q8⋊C8×D612
C61×#14792
#1751461