Finite Group Databasebeta

← #29646489

Subgroups — #29646489

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519822C211yesmaximal, characteristic
2#21454938C211yesmaximal, characteristic, complemented
3#21454781C211yesmaximal, characteristic, complemented
4#21444260C211yesmaximal, characteristic, complemented
5#21444259C211yesmaximal, characteristic, complemented
6#21444255C211yesmaximal, characteristic, complemented
7#21444251C211yesmaximal, characteristic, complemented
8#21444250C211yesmaximal, characteristic, complemented
9#21444244C211yesmaximal, characteristic, complemented
10#21444242C211yesmaximal, characteristic, complemented
11#21444208C211yesmaximal, characteristic, complemented
12#21444203C211yesmaximal, characteristic, complemented
13#21444198C211yesmaximal, characteristic, complemented
14D4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1490C211yesmaximal, characteristic, complemented
16C2×#14519822C411yescharacteristic
17#16840243C411yescharacteristic
18#16840243C411yescharacteristic
19#16840241—21no—
20#16840241C411yescharacteristic
21#16840241C411yescharacteristic
22#16840237C411yescharacteristic
23#16840235—21no—
24#16840235—21no—
25#16840234—21no—
26#16840234C411yescharacteristic
27#16840234C411yescharacteristic
28C4×#11758222C2211yescharacteristic
29C4×#11758222C2211yescharacteristic
30C4×#11758224—21no—
31C4×#11758224C2211yescharacteristic
32C4×#11758224C2211yescharacteristic
33C2×C4×C22⋊D61—21no—
34C2×C4×C22⋊D61—21no—
35C4×D4×D61—21no—
36C4×D4×D61C2211yescharacteristic
37C4×D4×D61C2211yescharacteristic
38#16839890—21no—
39#16839890—21no—
40#16839838—21no—
41#16839837—21no—
42#16839836—21no—
43#16839835—21no—
44#16839835—21no—
45#16839831—21no—
46#16839818C2211yescharacteristic, complemented
47#16839815C2211yescharacteristic, complemented
48#16839814C2211yescharacteristic, complemented
49#16839813C2211yescharacteristic, complemented
50#16839813C2211yescharacteristic, complemented
51#16839786C2211yescharacteristic, complemented
52#16839784C2211yescharacteristic, complemented
53C4⋊C8×D61C2211yescharacteristic, complemented
54C4×#11758189C2211yescharacteristic, complemented
55C4×C8×D61C2211yescharacteristic, complemented
56#16839494C2211yescharacteristic, complemented
57#16839494C2211yescharacteristic, complemented
58#16839492C2211yescharacteristic, complemented
59#16839492C2211yescharacteristic, complemented
60#16839491C2211yescharacteristic, complemented
61#16839491C2211yescharacteristic, complemented
62D4⋊#92418C2211yescharacteristic, complemented
63D4⋊#92418C2211yescharacteristic, complemented
64D4⋊#92418C2211yescharacteristic, complemented
65D4⋊#92418C2211yescharacteristic, complemented
66#16839489C2211yescharacteristic, complemented
67#16839489C2211yescharacteristic, complemented
68C2×C4×D4×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C4×M16×C61C2211yescharacteristic, complemented
71C61×D4⋊C8C2211yescharacteristic, complemented
72C61×D4⋊C8C2211yescharacteristic, complemented
73C61×D4⋊C8C2211yescharacteristic, complemented
74C61×D4⋊C8C2211yescharacteristic, complemented
75#14519822—24no—
76#14519822—24no—
77C2×#11758222C2×C411yescharacteristic
78C2×#11758222C2×C411yescharacteristic
79C2×#11758224—21no—
80C2×#11758224C2×C411yescharacteristic
81C2×#11758224C2×C411yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C2×D4×D61—21no—
85C2×D4×D61C2×C411yescharacteristic
86C2×D4×D61C2×C411yescharacteristic
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C2×#11758194—21no—
90C2×#11758189—21no—
91C2×#11758189—21no—
92C2×C8×D61—21no—
93C2×C8×D61—21no—
94C4×Dic122C2×C411yescharacteristic
95C4×Dic122D411yescharacteristic
96C4×Dic122D411yescharacteristic
97C4×Dic122C2311yescharacteristic
98#14519742—21no—
99#14519742C2×C411yescharacteristic
100#14519742C2×C411yescharacteristic
101C4×D244C2×C411yescharacteristic
102C4×D244D411yescharacteristic
103C4×D244D411yescharacteristic
104C4×D244C2311yescharacteristic
105D4×Dic61—21no—
106D4×Dic61—21no—
107D4×Dic61C2×C411yescharacteristic
108D4×Dic61C2×C411yescharacteristic
109D4×Dic61C2×C411yescharacteristic
110D4×Dic61C2×C411yescharacteristic
111#14519739—21no—
112#14519739C2×C411yescharacteristic
113#14519739C2×C411yescharacteristic
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61D411yescharacteristic
129C4×C22⋊D61D411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131C4×C22⋊D61D411yescharacteristic
132#14519737—21no—
133#14519737—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519736C2×C411yescharacteristic
141#14519736C2×C411yescharacteristic
142#14519735—21no—
143#14519735C2×C411yescharacteristic
144#14519735C2×C411yescharacteristic
145#14519734—21no—
146#14519734C2×C411yescharacteristic
147#14519734C2×C411yescharacteristic
148#14519733—21no—
149#14519733—21no—
150#14519733—21no—
151#14519733—21no—
152C2×#11758196—21no—
153C2×#11758196—21no—
154C4⋊C4×D61—21no—
155C4⋊C4×D61C2×C411yescharacteristic
156C4⋊C4×D61C2×C411yescharacteristic
157C2×C22⋊Dic61—21no—
158C2×C22⋊Dic61—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61—21no—
167C42×D61—21no—
168C42×D61C2311yescharacteristic
169C42×D61C2311yescharacteristic
170C4⋊#92418—21no—
171C4⋊#92418—21no—
172C4⋊#92418C2311yescharacteristic
173C4⋊#92418C2311yescharacteristic
174#14519706—21no—
175#14519706—21no—
176#14519706—21no—
177#14519706—21no—
178C22⋊#92418—21no—
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519689—21no—
183#14519687—21no—
184#14519687—21no—
185C4×#92418C2311yescharacteristic
186C4×#92418C2311yescharacteristic
187C8×Dic61—21no—
188C8×Dic61—21no—
189C22×D4×C61C2×C411yescharacteristic
190C23×C4×C61—21no—
191C2×M16×C61—21no—
192C4×D4×C61—21no—
193C4×D4×C61—21no—
194C4×D4×C61C2×C411yescharacteristic
195C4×D4×C61C2×C411yescharacteristic
196C4×D4×C61C2311yescharacteristic
197C4×D4×C61C2311yescharacteristic
198C2×C4⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61C2311yescharacteristic
202C4⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61—21no—
204#97×C61—21no—
205#97×C61—21no—
206C4×C8×C61C2311yescharacteristic
207C4×C8×C61C2311yescharacteristic
208C24×C61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—81no—
222C22×C4×C61—81no—
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C2×C22⋊D61—28no—
227C2×C22⋊D61—28no—
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—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241#11758224—28no—
242#11758224—22no—
243#11758224—22no—
244#11758224—22no—
245#11758224M1614yescomplemented
246D4×D61—28no—
247D4×D61—22no—
248D4×D61—22no—
249D4×D61—22no—
250D4×D61M1614yescomplemented
251#11758222—22no—
252#11758222—22no—
253#11758222—22no—
254#11758222—22no—
255C2×D244C22⋊C411yescharacteristic
256C2×D244C22×C411yescharacteristic
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×C4×D61—81no—
267C2×C4×D61—81no—
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122C22⋊C411yescharacteristic
275C2×Dic122C22×C411yescharacteristic
276M16×C61—42no—
277C2×C8×C61—21no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C42×C61C22×C411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C42×C61C2×D411yescharacteristic
291C42×C61C2411yescharacteristic
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309C4⋊Dic61C22⋊C411yescharacteristic
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61C22×C411yescharacteristic
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336#11758194—81no—
337C2×#92418—21no—
338C2×#92418—21no—
339C2×#92418—21no—
340C2×#92418—21no—
341#11758189—42no—
342#11758189—81no—
343C8×D61—42no—
344C8×D61—81no—
345C23×C61—24no—
346C23×C61—21no—
347C23×C61—21no—
348C23×C61—81no—
349C23×C61—81no—
350C23×C61C2×C22⋊C411yescharacteristic
351C22×D61—21no—
352C22×D61—24no—
353C22×D61—24no—
354C22×D61—81no—
355C22×D61—81no—
356C22×D61—81no—
357C22×D61—81no—
358C22×D61C2×C22⋊C411yescharacteristic
359C22×D61C2×C22⋊C411yescharacteristic
360D4×C61—24no—
361D4×C61—21no—
362D4×C61—21no—
363D4×C61C2×M1612yes—
364D4×C61C2×M1612yes—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—81no—
377C2×C4×C61—81no—
378C2×C4×C61—81no—
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C23×C411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C22⋊D61—24no—
386C22⋊D61—24no—
387C22⋊D61—24no—
388C22⋊D61—22no—
389C22⋊D61—24no—
390C22⋊D61—22no—
391C22⋊D61—24no—
392C2×Dic61—24no—
393C2×Dic61—21no—
394C2×Dic61—24no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—81no—
398C2×Dic61—81no—
399C2×Dic61—81no—
400C2×Dic61—81no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407D244—22no—
408D244—21no—
409D244C2×M1612yes—
410C4×D61—24no—
411C4×D61—21no—
412C4×D61—21no—
413C4×D61—21no—
414C4×D61—21no—
415C4×D61—21no—
416C4×D61—21no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—81no—
422C4×D61—81no—
423C4×D61—81no—
424C4×D61—81no—
425C4×D61—81no—
426C4×D61C2×M1612yes—
427C4×D61C2×M1612yes—
428Dic122—21no—
429Dic122—22no—
430Dic122C2×M1612yes—
431C8×C61—22no—
432C8×C61—41no—
433C8×C61—41no—
434C8×C61—41no—
435#92418—41no—
436#92418—41no—
437#92418—41no—
438#92418—41no—
439#17453—611nomaximal, Sylow
440C22×C61—22no—
441C22×C61—22no—
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—84no—
450C22×C61C22×C22⋊C411yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—22no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—84no—
460C2×D61—84no—
461C2×D61#40712yes—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61C22×M1611yescharacteristic
469C4×C61C22×M1611yescharacteristic
470C4×C61#57611yescharacteristic
471C4×C61#57711yescharacteristic
472Dic61—21no—
473Dic61—22no—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—41no—
479Dic61—41no—
480Dic61#40712yes—
481C4×H(5,𝔽2)—611no—
482#2989—611no—
483#2965—611no—
484#1490—611no—
485#1490D6111yescharacteristic, complemented
486#1489—611no—
487#1489—611no—
488#1488—611no—
489#1488—611no—
490#1486—611no—
491#1486—611no—
492#1478—611no—
493#1477—611no—
494#1476—611no—
495C2×D4⋊C8—611no—
496C2×C61—42no—
497C2×C61—42no—
498C2×C61—41no—
499C2×C61C2×#40711yescharacteristic
500C2×C61#289711yescharacteristic
501C2×C61#290111yescharacteristic
502D61—22no—
503D61—41no—
504D61—42no—
505C2×H(5,𝔽2)—611no—
506#520—611no—
507#520—611no—
508#520—611no—
509#520—611no—
510#520—1221no—
511#518—611no—
512#518—611no—
513#518—611no—
514#518—1221no—
515#518—1221no—
516#518—1221no—
517C4×#41—611no—
518C4×#41—611no—
519C4×#41—611no—
520C4×#41—611no—
521C4×#41—1221no—
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×C4×D4—1221no—
525C2×C4×D4—1221no—
526C2×C4×D4—1221no—
527C2×C4×D4C2×D6111yescharacteristic
528#446—1221no—
529#446—1221no—
530#436—1221no—
531#436—1221no—
532#435—1221no—
533#435—1221no—
534#435—1221no—
535#435—1221no—
536#432—611no—
537#432C2×D6111yescharacteristic, complemented
538#431—611no—
539#431—611no—
540#431—611no—
541#431—611no—
542#423—611no—
543#423—611no—
544C2×C4⋊C8—611no—
545C4×M16—611no—
546C4×M16C2×D6111yescharacteristic, complemented
547C2×C4×C8—611no—
548Q8⋊C8—611no—
549Q8⋊C8—611no—
550Q8⋊C8—611no—
551Q8⋊C8—611no—
552D4⋊C8—611no—
553D4⋊C8—611no—
554D4⋊C8—611no—
555D4⋊C8—611no—
556D4⋊C8—611no—
557D4⋊C8—611no—
558D4⋊C8—611no—
559D4⋊C8—611no—
560D4⋊C8C2×D6111yescharacteristic, complemented
561D4⋊C8C2×D6111yescharacteristic, complemented
562D4⋊C8C2×D6111yescharacteristic, complemented
563D4⋊C8C2×D6111yescharacteristic, complemented
564C61#1745311yescharacteristic, complemented, Sylow
565H(5,𝔽2)—1224no—
566H(5,𝔽2)—1224no—
567C2×#41—611no—
568C2×#41—611no—
569C2×#41—611no—
570C2×#41—611no—
571C2×#41—1221no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4C4×D6111yescharacteristic
578C23×C4—21no—
579C23×C4—1221no—
580C23×C4—1221no—
581C2×M16—21no—
582C2×M16—1221no—
583C2×M16—1221no—
584C2×M16—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C4×Q8—611no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—1221no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4C4×D6111yescharacteristic
636C4×D4C4×D6111yescharacteristic
637C4×D4C22×D6111yescharacteristic
638C4×D4C22×D6111yescharacteristic
639#117—611no—
640#117—611no—
641#117—611no—
642#117—611no—
643#117—611no—
644#117—611no—
645#117—1221no—
646#117—1221no—
647#117—1221no—
648#117—1221no—
649#117—1221no—
650#117—1221no—
651C2×C4⋊C4—611no—
652C2×C4⋊C4—611no—
653C2×C4⋊C4—1221no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4C4×D6111yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C42—611no—
667C2×C42—611no—
668C2×C42—1221no—
669C2×C42—1221no—
670C2×C42—1221no—
671C2×C42C22×D6111yescharacteristic
672C4⋊C8—611no—
673C4⋊C8—611no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C4⋊C8—1221no—
677C4⋊C8—1221no—
678C4⋊C8—1221no—
679C4⋊C8—1221no—
680C4⋊C8C22×D6111yescharacteristic
681C4⋊C8C22×D6111yescharacteristic
682C22⋊C8—21no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688#97—21no—
689#97—21no—
690#97—1221no—
691#97—1221no—
692C4×C8—611no—
693C4×C8—611no—
694C4×C8—1221no—
695C4×C8—1221no—
696C4×C8C22×D6111yescharacteristic
697C4×C8C22×D6111yescharacteristic
698C24—21no—
699C24—1221no—
700C24—1221no—
701#41—614no—
702#41—1222no—
703#41—1222no—
704#41—1222no—
705#41—1222no—
706#41—1222no—
707#41—1222no—
708#41—1228no—
709#41—1222no—
710C2×Q8—611no—
711C2×Q8—611no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—21no—
715C2×D4—614no—
716C2×D4—611no—
717C2×D4—611no—
718C2×D4—611no—
719C2×D4—611no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1222no—
724C2×D4—1228no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1228no—
728C2×D4—1228no—
729C2×D4—1221no—
730C2×D4—1222no—
731C2×D4C2×C4×D6111yescharacteristic
732C2×D4C2×C4×D6111yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—81no—
739C22×C4—81no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—4881no—
760C22×C4—4881no—
761C22×C4—4881no—
762C22×C4—4881no—
763C22×C4C2×C4×D6111yescharacteristic
764C22×C4D4×D6111yescharacteristic
765C22×C4D4×D6111yescharacteristic
766M16—42no—
767M16—4881no—
768M16—4881no—
769M16—2442no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—4881no—
779C2×C8—2442no—
780C4⋊C4—21no—
781C4⋊C4—611no—
782C4⋊C4—611no—
783C4⋊C4—611no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—611no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4C2×C4×D6111yescharacteristic
796C4⋊C4C2×C4×D6111yescharacteristic
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—611no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—1221no—
825C42—1221no—
826C42—1221no—
827C42—1221no—
828C42—1221no—
829C42—1221no—
830C42—1221no—
831C42C2×C4×D6111yescharacteristic
832C42D4×D6111yescharacteristic
833C42D4×D6111yescharacteristic
834C42C23×D6111yescharacteristic
835C23—24no—
836C23—21no—
837C23—21no—
838C23—81no—
839C23—81no—
840C23—611no—
841C23—611no—
842C23—1224no—
843C23—1224no—
844C23—1221no—
845C23—4881no—
846C23—4881no—
847C23—4881no—
848C23—4881no—
849C23C22⋊C4×D6111yescharacteristic
850Q8—612no—
851Q8—1222no—
852Q8—1221no—
853D4—24no—
854D4—21no—
855D4—21no—
856D4—612no—
857D4—1222no—
858D4—1222no—
859D4—1224no—
860D4—1222no—
861D4—1224no—
862D4—1224no—
863D4—1224no—
864D4—1224no—
865D4—1221no—
866D4M16×D6112yes—
867D4M16×D6112yes—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—611no—
883C2×C4—612no—
884C2×C4—612no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—1224no—
891C2×C4—1224no—
892C2×C4—1224no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—4881no—
903C2×C4—4881no—
904C2×C4—4881no—
905C2×C4—4881no—
906C2×C4—4881no—
907C2×C4—4881no—
908C2×C4—4881no—
909C2×C4—4881no—
910C2×C4—4881no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4C22⋊C4×D6111yescharacteristic
916C2×C4C22⋊C4×D6111yescharacteristic
917C2×C4C22⋊C4×D6111yescharacteristic
918C2×C4C22×C4×D6111yescharacteristic
919C2×C4C2×D4×D6111yescharacteristic
920C2×C4C2×D4×D6111yescharacteristic
921C8—22no—
922C8—41no—
923C8—41no—
924C8—41no—
925C8—2441no—
926C8—2441no—
927C8—2441no—
928C8—2441no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—84no—
939C22—612no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—1221no—
944C22—1222no—
945C22—1221no—
946C22—4884no—
947C22—4884no—
948C22—2441no—
949C22—2441no—
950C22C2×C22⋊C4×D6111yescharacteristic
951C4—21no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—41no—
956C4—41no—
957C4—612no—
958C4—1221no—
959C4—1221no—
960C4—1221no—
961C4—1221no—
962C4—1221no—
963C4—1222no—
964C4—2441no—
965C4—2441no—
966C4C2×M16×D6111yescharacteristic
967C4C2×M16×D6111yescharacteristic
968C4#1684056611yescharacteristic
969C4#1684057211yescharacteristic
970C2—41no—
971C2—42no—
972C2—42no—
973C2—1222no—
974C2—2441no—
975C2—2442no—
976C2#407×D6111yescharacteristic
977C2#2145434411yescharacteristic
978C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1490C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519822C4
cosocleC42×C61C24
hypercenter#1490D61
hypocenterC61#17453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #21454938C2semidirect
3. #21454781C2semidirect
4. #21444260C2semidirect
5. #21444259C2semidirect
6. #21444255C2semidirect
7. #21444251C2semidirect
8. #21444250C2semidirect
9. #21444244C2semidirect
10. #21444242C2semidirect
11. #21444208C2semidirect
12. #21444203C2semidirect
13. #21444198C2semidirect
14. D4⋊C8×D61C2semidirect
15. C61×#1490C2semidirect
46. #16839818C22semidirect
47. #16839815C22semidirect
48. #16839814C22semidirect
49. #16839813C22semidirect
50. #16839813C22semidirect
51. #16839786C22semidirect
52. #16839784C22semidirect
53. C4⋊C8×D61C22semidirect
54. C4×#11758189C22semidirect
55. C4×C8×D61C22semidirect
56. #16839494C22semidirect
57. #16839494C22semidirect
58. #16839492C22semidirect
59. #16839492C22semidirect
60. #16839491C22semidirect
61. #16839491C22semidirect
62. D4⋊#92418C22semidirect
63. D4⋊#92418C22semidirect
64. D4⋊#92418C22semidirect
65. D4⋊#92418C22semidirect
66. #16839489C22semidirect
67. #16839489C22semidirect
69. C61×#432C22semidirect
70. C4×M16×C61C22semidirect
71. C61×D4⋊C8C22semidirect
72. C61×D4⋊C8C22semidirect
73. C61×D4⋊C8C22semidirect
74. C61×D4⋊C8C22semidirect
245. #11758224M16semidirect
250. D4×D61M16semidirect
485. #1490D61semidirect
537. #432C2×D61semidirect
546. C4×M16C2×D61semidirect
560. D4⋊C8C2×D61semidirect
561. D4⋊C8C2×D61semidirect
562. D4⋊C8C2×D61semidirect
563. D4⋊C8C2×D61semidirect
564. C61#17453semidirect

Maximal subgroups

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

subgroupindex
C4×#145198222
#214549382
#214547812
#214442602
#214442592
#214442552
#214442512
#214442502
#214442442
#214442422
#214442082
#214442032
#214441982
D4⋊C8×D612
C61×#14902
#1745361