Finite Group Databasebeta

← #29696765

Subgroups — #29696765

Order 15616.

1172 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840455C211yesmaximal, characteristic
2#21448697C211yesmaximal, characteristic, complemented
3#21448691C211yesmaximal, characteristic, complemented
4#21446656C211yesmaximal, characteristic, complemented
5#21446653C211yesmaximal, characteristic, complemented
6#21446653C211yesmaximal, characteristic, complemented
7#21446653C211yesmaximal, characteristic, complemented
8#21446653C211yesmaximal, characteristic, complemented
9#21445805C211yesmaximal, characteristic, complemented
10#21445805C211yesmaximal, characteristic, complemented
11#21445804C211yesmaximal, characteristic, complemented
12#99×Dic61C211yesmaximal, characteristic, complemented
13#99×Dic61C211yesmaximal, characteristic, complemented
14C4×#14519691C211yesmaximal, characteristic, complemented
15C61×#1964C211yesmaximal, characteristic, complemented
16#16840455—21no—
17#16840455—21no—
18#16840455—21no—
19#16840455—21no—
20#16840455—21no—
21#16840455—21no—
22#16840455—21no—
23#16840455—21no—
24C2×#14519772C411yescharacteristic, complemented
25C2×#14519770C411yescharacteristic, complemented
26C2×#14519767C411yescharacteristic, complemented
27C2×#14519759C411yescharacteristic, complemented
28C2×#14519758C411yescharacteristic, complemented
29C2×#14519749C411yescharacteristic, complemented
30C2×#14519749C2211yescharacteristic
31C2×#14519749C2211yescharacteristic
32C2×D4×Dic61C2211yescharacteristic
33C2×D4×Dic61C2211yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×#14519737C411yescharacteristic, complemented
36C2×#14519733C411yescharacteristic, complemented
37C22×#11758196C2211yescharacteristic
38C2×#14519692C2211yescharacteristic
39C2×#14519692C2211yescharacteristic
40C2×#14519692C2211yescharacteristic
41C2×#14519692C2211yescharacteristic
42C2×#14519691C2211yescharacteristic
43C2×#14519691C2211yescharacteristic
44C2×#14519691C2211yescharacteristic
45C2×#14519691C2211yescharacteristic
46#16839659—21no—
47#16839657—21no—
48#16839649—21no—
49#16839646—21no—
50#16839644—21no—
51#16839643—21no—
52#16839622C2211yescharacteristic
53#16839620C2211yescharacteristic
54#16839620C2211yescharacteristic
55#16839620C2211yescharacteristic
56#16839620C2211yescharacteristic
57C4×#11758196—21no—
58#16839613—21no—
59C22⋊C4×Dic61C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61C22⋊C4×Dic61C2211yescharacteristic
62C22⋊C4×Dic61C2211yescharacteristic
63C4×C22⋊Dic61C2211yescharacteristic
64#16839528C2211yescharacteristic
65#16839528C2211yescharacteristic
66#16839528C2211yescharacteristic
67#16839528C2211yescharacteristic
68C2×#121×C61C2211yescharacteristic
69C2×#99×C61C2211yescharacteristic
70C2×#99×C61C2211yescharacteristic
71C2×#99×C61C2211yescharacteristic
72C2×#99×C61C2211yescharacteristic
73C61×#380C2211yescharacteristic
74C4×C22⋊C4×C61C2211yescharacteristic
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C22×C22⋊D61C2311yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83#14519772—21no—
84#14519772—21no—
85#14519772—21no—
86#14519772—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519767—21no—
92#14519767—21no—
93#14519767—21no—
94#14519767—21no—
95#14519759—21no—
96#14519759—21no—
97#14519759—21no—
98#14519759—21no—
99#14519758—21no—
100#14519758—21no—
101#14519758—21no—
102#14519758—21no—
103#14519749—21no—
104#14519749—21no—
105#14519749—21no—
106#14519749—21no—
107#14519749—21no—
108#14519749—21no—
109#14519749—21no—
110#14519749—21no—
111#14519749—21no—
112#14519749—21no—
113#14519749—21no—
114#14519749—21no—
115D4×Dic61—21no—
116D4×Dic61—21no—
117D4×Dic61—21no—
118D4×Dic61—21no—
119D4×Dic61—21no—
120D4×Dic61—21no—
121D4×Dic61—21no—
122D4×Dic61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61C2×C411yescharacteristic
137C2×C4⋊Dic61C2×C411yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196D411yescharacteristic
150C2×#11758196D411yescharacteristic
151C2×#11758196D411yescharacteristic
152C2×#11758196D411yescharacteristic
153C2×#11758196D411yescharacteristic
154C2×#11758196D411yescharacteristic
155C2×#11758196D411yescharacteristic
156C2×#11758196D411yescharacteristic
157C2×C22⋊Dic61C2×C411yescharacteristic
158C2×C22⋊Dic61C2×C411yescharacteristic
159C2×C22⋊Dic61C2×C411yescharacteristic
160C2×C22⋊Dic61C2×C411yescharacteristic
161C2×C22⋊Dic61C2311yescharacteristic
162C2×C22⋊Dic61C2311yescharacteristic
163C2×C22⋊Dic61C2311yescharacteristic
164C2×C22⋊Dic61C2311yescharacteristic
165C2×C22⋊Dic61C2311yescharacteristic
166C2×#11758198C2×C411yescharacteristic
167C2×#11758198C2×C411yescharacteristic
168C2×#11758198C2×C411yescharacteristic
169C2×C4×Dic61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—21no—
174C2×C4×Dic61C2×C411yescharacteristic
175C2×C4×Dic61C2×C411yescharacteristic
176C2×C4×Dic61C2×C411yescharacteristic
177#14519692—22no—
178#14519692—22no—
179#14519692—41no—
180#14519692—41no—
181#14519691—22no—
182#14519691—22no—
183#14519691—41no—
184#14519691—41no—
185#14519684—21no—
186#14519684—21no—
187#14519684—21no—
188#14519684—21no—
189#14519684—21no—
190#14519684—21no—
191#14519684—21no—
192#14519684—21no—
193#14519684—21no—
194#14519684—21no—
195C22×D4×C61C2×C411yescharacteristic
196C22×D4×C61C2311yescharacteristic
197C22×D4×C61C2311yescharacteristic
198C23×C4×C61C2311yescharacteristic
199#121×C61—21no—
200#121×C61—21no—
201#121×C61—21no—
202#121×C61—21no—
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61C2×C411yescharacteristic
205C2×C22⋊C4×C61C2×C411yescharacteristic
206C2×C22⋊C4×C61C2×C411yescharacteristic
207C2×C22⋊C4×C61C2311yescharacteristic
208C2×C22⋊C4×C61C2311yescharacteristic
209C2×C22⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61C2311yescharacteristic
211C2×C42×C61—21no—
212#99×C61—22no—
213#99×C61—22no—
214#99×C61—41no—
215#99×C61—41no—
216#95×C61—21no—
217#95×C61—21no—
218C24×C61C22×C411yescharacteristic
219C24×C61C22×C411yescharacteristic
220C24×C61C2411yescharacteristic
221C23×D61C22×C411yescharacteristic
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—81no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—81no—
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C22×C411yescharacteristic
245C22×C4×C61C22×C411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C2×C22⋊D61—21no—
251C2×C22⋊D61—21no—
252C2×C22⋊D61—21no—
253C2×C22⋊D61—21no—
254C2×C22⋊D61—21no—
255C2×C22⋊D61—21no—
256C2×C22⋊D61—21no—
257C2×C22⋊D61—21no—
258C2×C22⋊D61—21no—
259C2×C22⋊D61—21no—
260C2×C22⋊D61—42no—
261C2×C22⋊D61—81no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—42no—
271C22×Dic61—42no—
272C22×Dic61—81no—
273C22×Dic61—81no—
274C22×Dic61C22×C411yescharacteristic
275C22×Dic61C22×C411yescharacteristic
276C22×Dic61C22×C411yescharacteristic
277C22×Dic61C22×C411yescharacteristic
278C22×Dic61C22×C411yescharacteristic
279C22×Dic61C22×C411yescharacteristic
280C22×Dic61C22×C411yescharacteristic
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284C22×Dic61C2×D411yescharacteristic
285C22×Dic61C2×D411yescharacteristic
286C22×Dic61C2×D411yescharacteristic
287C22×Dic61C2×D411yescharacteristic
288C22×Dic61C2×D411yescharacteristic
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—81no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—81no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61#4112yes—
307C42×C61—81no—
308C22⋊Dic61—21no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61—21no—
323C22⋊Dic61—21no—
324C22⋊Dic61—21no—
325C22⋊Dic61#4112yes—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332C4⋊Dic61—21no—
333C4⋊Dic61—21no—
334C4⋊Dic61—21no—
335C4⋊Dic61—21no—
336C4⋊Dic61—81no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—42no—
344#11758196—42no—
345#11758196—81no—
346#11758196—81no—
347#11758196C22⋊C411yescharacteristic
348#11758196C22⋊C411yescharacteristic
349#11758196C22⋊C411yescharacteristic
350#11758196C22⋊C411yescharacteristic
351#11758196C22⋊C411yescharacteristic
352#11758196C22⋊C411yescharacteristic
353#11758196C22⋊C411yescharacteristic
354#11758196C22⋊C411yescharacteristic
355#11758196C22⋊C411yescharacteristic
356#11758196C22⋊C411yescharacteristic
357#11758196C22⋊C411yescharacteristic
358#11758196C22⋊C411yescharacteristic
359#11758196C22⋊C411yescharacteristic
360#11758196C22⋊C411yescharacteristic
361#11758196C22⋊C411yescharacteristic
362#11758196C22⋊C411yescharacteristic
363C4×Dic61—21no—
364C4×Dic61—21no—
365C4×Dic61—21no—
366C4×Dic61—21no—
367C4×Dic61—21no—
368C4×Dic61—21no—
369C4×Dic61—42no—
370C4×Dic61—42no—
371C4×Dic61—81no—
372C4×Dic61—81no—
373C4×Dic61—81no—
374C23×C61—21no—
375C23×C61—21no—
376C23×C61—21no—
377C23×C61—21no—
378C23×C61—21no—
379C23×C61—21no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61C23×C411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C22×D411yescharacteristic
389C23×C61C2×#4111yescharacteristic
390C23×C61C2×#4111yescharacteristic
391C23×C61H(5,𝔽2)11yescharacteristic
392C23×C612−1+411yescharacteristic
393C22×D61—21no—
394C22×D61—21no—
395C22×D61—21no—
396C22×D61—41no—
397C22×D61—41no—
398D4×C61—41no—
399D4×C61—41no—
400D4×C61—41no—
401D4×C61—41no—
402D4×C61—41no—
403D4×C61—41no—
404D4×C61—41no—
405D4×C61—41no—
406D4×C61—81no—
407D4×C61—81no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—22no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61C2×C22⋊C411yescharacteristic
433C2×C4×C61C2×C22⋊C411yescharacteristic
434C2×C4×C61C2×C22⋊C411yescharacteristic
435C2×C4×C61C2×C22⋊C411yescharacteristic
436C22⋊D61—42no—
437C22⋊D61—41no—
438C22⋊D61—41no—
439C22⋊D61—41no—
440C22⋊D61—41no—
441C22⋊D61—42no—
442C22⋊D61—81no—
443C22⋊D61—81no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—21no—
448C2×Dic61—21no—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—21no—
452C2×Dic61—22no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—42no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—42no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—81no—
478C2×Dic61—81no—
479C2×Dic61C2×C22⋊C411yescharacteristic
480C2×Dic61C2×C22⋊C411yescharacteristic
481C2×Dic61C2×C22⋊C411yescharacteristic
482C2×Dic61C2×C22⋊C411yescharacteristic
483C2×Dic61C2×C22⋊C411yescharacteristic
484C2×Dic61C2×C22⋊C411yescharacteristic
485C2×Dic61C2×C22⋊C411yescharacteristic
486C2×Dic61C2×C22⋊C411yescharacteristic
487C4×D61—81no—
488C4×D61—81no—
489#22535—611nomaximal, Sylow
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—21no—
495C22×C61—21no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61—41no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—41no—
504C22×C61—41no—
505C22×C61—41no—
506C22×C61—81no—
507C22×C61—81no—
508C22×C61—81no—
509C22×C61—81no—
510C22×C61C22×C22⋊C411yescharacteristic
511C22×C61C4×#4111yescharacteristic
512C22×C61#52011yescharacteristic
513C22×C61#54811yescharacteristic
514C22×C61#54811yescharacteristic
515C22×C61#55011yescharacteristic
516C22×C61#55011yescharacteristic
517C2×D61—41no—
518C2×D61—41no—
519C2×D61—41no—
520C2×D61—81no—
521C2×D61—81no—
522C4×C61—21no—
523C4×C61—21no—
524C4×C61—21no—
525C4×C61—21no—
526C4×C61—42no—
527C4×C61—41no—
528C4×C61—41no—
529C4×C61—81no—
530C4×C61—81no—
531C4×C61—81no—
532Dic61—21no—
533Dic61—21no—
534Dic61—21no—
535Dic61—21no—
536Dic61—21no—
537Dic61—21no—
538Dic61—21no—
539Dic61—42no—
540Dic61—41no—
541Dic61—41no—
542Dic61—41no—
543Dic61—81no—
544Dic61—81no—
545Dic61—81no—
546Dic61#41012yes—
547C2×#553—611no—
548#2345—611no—
549#2345—611no—
550#1964—611no—
551#1964—611no—
552#1964—611no—
553#1964—611no—
554#1964—611no—
555#1964D6111yescharacteristic, complemented
556#1799—611no—
557#1799—611no—
558#1799—611no—
559C4×#99—611no—
560C4×#99—611no—
561C4×#99—611no—
562C2×C61—21no—
563C2×C61—21no—
564C2×C61—21no—
565C2×C61—21no—
566C2×C61—21no—
567C2×C61—21no—
568C2×C61—81no—
569C2×C61—81no—
570C2×C61#234111yescharacteristic
571C2×C61C2×#41011yescharacteristic
572C2×C61#288311yescharacteristic
573D61—81no—
574#553—1221no—
575#553—1221no—
576#553—1221no—
577#553—1221no—
578#553—1221no—
579#553—1221no—
580#553—1221no—
581#553—1221no—
582C2×#126—611no—
583C2×#126—611no—
584C2×#125—611no—
585C2×#123—611no—
586C2×#123—611no—
587C2×#121—611no—
588C2×#121—611no—
589C2×#121—611no—
590C2×#121C2×D6111yescharacteristic
591C2×C4×D4—611no—
592C2×C4×D4—611no—
593C2×C4×D4—611no—
594C2×C4×D4—611no—
595C2×#117—611no—
596C22×C4⋊C4—611no—
597C2×#99—611no—
598C2×#99—611no—
599C2×#99—611no—
600C2×#99—611no—
601C2×#99—611no—
602C2×#99—611no—
603C2×#99—611no—
604C2×#99—611no—
605C2×#99C2×D6111yescharacteristic
606C2×#99C2×D6111yescharacteristic
607C2×#99C2×D6111yescharacteristic
608C2×#99C2×D6111yescharacteristic
609#389—1221no—
610#389—1221no—
611#387—1221no—
612#387—1221no—
613#387—1221no—
614#387—1221no—
615#380—611no—
616#380—611no—
617#380—611no—
618#380—611no—
619#380—611no—
620#380C2×D6111yescharacteristic
621C4×C4⋊C4—1221no—
622C4×C4⋊C4—1221no—
623C4×C22⋊C4—611no—
624C4×C22⋊C4—611no—
625C4×C22⋊C4—611no—
626C4×C22⋊C4—611no—
627C4×C22⋊C4—611no—
628C4×C22⋊C4C2×D6111yescharacteristic
629#342—611no—
630#342—611no—
631#342—611no—
632#342—611no—
633C61#2253511yescharacteristic, complemented, Sylow
634C22×D4—611no—
635C22×D4—611no—
636C22×D4—611no—
637C22×D4C4×D6111yescharacteristic
638C22×D4C22×D6111yescharacteristic
639C22×D4C22×D6111yescharacteristic
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C23×C4—611no—
644C23×C4—611no—
645C23×C4C22×D6111yescharacteristic
646#126—1221no—
647#126—1221no—
648#126—1221no—
649#126—1221no—
650#126—1221no—
651#126—1221no—
652#126—1221no—
653#126—1221no—
654#125—1221no—
655#125—1221no—
656#125—1221no—
657#125—1221no—
658#123—1221no—
659#123—1221no—
660#123—1221no—
661#123—1221no—
662#123—1221no—
663#123—1221no—
664#123—1221no—
665#123—1221no—
666#121—21no—
667#121—21no—
668#121—21no—
669#121—21no—
670#121—1221no—
671#121—1221no—
672#121—1221no—
673#121—1221no—
674#121—1221no—
675#121—1221no—
676#121—1221no—
677#121—1221no—
678#121—1221no—
679#121—1221no—
680#121—1221no—
681#121—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690C4×D4—1221no—
691C4×D4—1221no—
692C4×D4—1221no—
693C4×D4—1221no—
694C4×D4—1221no—
695C4×D4—1221no—
696C4×D4—1221no—
697C4×D4—1221no—
698#117—1221no—
699#117—1221no—
700#117—1221no—
701#117—1221no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—611no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4—611no—
717C2×C4⋊C4—611no—
718C2×C4⋊C4—611no—
719C2×C4⋊C4—611no—
720C2×C4⋊C4—1221no—
721C2×C4⋊C4—1221no—
722C2×C4⋊C4—1221no—
723C2×C4⋊C4—1221no—
724C2×C4⋊C4—1221no—
725C2×C4⋊C4C4×D6111yescharacteristic
726C2×C22⋊C4—611no—
727C2×C22⋊C4—611no—
728C2×C22⋊C4—611no—
729C2×C22⋊C4—611no—
730C2×C22⋊C4—611no—
731C2×C22⋊C4—611no—
732C2×C22⋊C4—611no—
733C2×C22⋊C4—611no—
734C2×C22⋊C4—611no—
735C2×C22⋊C4—611no—
736C2×C22⋊C4—611no—
737C2×C22⋊C4—611no—
738C2×C22⋊C4C4×D6111yescharacteristic
739C2×C22⋊C4C4×D6111yescharacteristic
740C2×C22⋊C4C22×D6111yescharacteristic
741C2×C22⋊C4C22×D6111yescharacteristic
742C2×C22⋊C4C22×D6111yescharacteristic
743C2×C22⋊C4C22×D6111yescharacteristic
744C2×C42—21no—
745C2×C42—611no—
746C2×C42—611no—
747C2×C42—611no—
748C2×C42—1221no—
749C2×C42—1221no—
750C2×C42—1221no—
751C2×C42—1221no—
752C2×C42—1221no—
753#99—22no—
754#99—22no—
755#99—41no—
756#99—41no—
757#99—1222no—
758#99—1222no—
759#99—1222no—
760#99—1222no—
761#99—2441no—
762#99—2441no—
763#99—2441no—
764#99—2441no—
765#95—21no—
766#95—21no—
767#95—1221no—
768#95—1221no—
769#95—1221no—
770#95—1221no—
771#95—1221no—
772#95—1221no—
773#95—1221no—
774#95—1221no—
775#95—1221no—
776#95—1221no—
777C24—611no—
778C24C2×C4×D6111yescharacteristic
779C24C2×C4×D6111yescharacteristic
780C24C23×D6111yescharacteristic
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—81no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—1221no—
800C2×D4—1221no—
801C2×D4—1221no—
802C2×D4—1221no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1221no—
806C2×D4—4881no—
807C2×D4—2442no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—81no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—1221no—
829C22×C4—1221no—
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—4881no—
839C22×C4—4881no—
840C22×C4—4881no—
841C22×C4—2442no—
842C22×C4—2442no—
843C22×C4C2×C4×D6111yescharacteristic
844C22×C4C2×C4×D6111yescharacteristic
845C22×C4C2×C4×D6111yescharacteristic
846C22×C4C2×C4×D6111yescharacteristic
847C22×C4D4×D6111yescharacteristic
848C22×C4D4×D6111yescharacteristic
849C22×C4D4×D6111yescharacteristic
850C22×C4D4×D6111yescharacteristic
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—81no—
854C4⋊C4—611no—
855C4⋊C4—611no—
856C4⋊C4—611no—
857C4⋊C4—611no—
858C4⋊C4—611no—
859C4⋊C4—611no—
860C4⋊C4—611no—
861C4⋊C4—611no—
862C4⋊C4—611no—
863C4⋊C4—611no—
864C4⋊C4—611no—
865C4⋊C4—611no—
866C4⋊C4—611no—
867C4⋊C4—611no—
868C4⋊C4—611no—
869C4⋊C4—611no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—1221no—
874C4⋊C4—1221no—
875C4⋊C4—1221no—
876C4⋊C4—1221no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1221no—
880C4⋊C4—4881no—
881C4⋊C4—4881no—
882C4⋊C4—4881no—
883C4⋊C4—2442no—
884C4⋊C4—2442no—
885C22⋊C4—21no—
886C22⋊C4—21no—
887C22⋊C4—21no—
888C22⋊C4—21no—
889C22⋊C4—21no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—612no—
897C22⋊C4—1221no—
898C22⋊C4—1221no—
899C22⋊C4—1221no—
900C22⋊C4—1221no—
901C22⋊C4—1221no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—1221no—
905C22⋊C4—1221no—
906C22⋊C4—1221no—
907C22⋊C4—1221no—
908C22⋊C4—1221no—
909C22⋊C4—1221no—
910C22⋊C4—1221no—
911C22⋊C4—1221no—
912C22⋊C4—1221no—
913C22⋊C4—1221no—
914C22⋊C4—1221no—
915C22⋊C4—1221no—
916C22⋊C4—1221no—
917C22⋊C4—1221no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4#1175822412yes—
921C42—81no—
922C42—1221no—
923C42—1221no—
924C42—1221no—
925C42—1221no—
926C42—1221no—
927C42—1221no—
928C42—4881no—
929C42—4881no—
930C42—4881no—
931C42—2442no—
932C42—2442no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—1221no—
946C23—1221no—
947C23—1221no—
948C23—2441no—
949C23—2441no—
950C23C22×C4×D6111yescharacteristic
951C23C2×D4×D6111yescharacteristic
952C23C2×D4×D6111yescharacteristic
953C23#41×D6111yescharacteristic
954C23C2×#1175822411yescharacteristic
955C23#1451982211yescharacteristic
956C23#1451982411yescharacteristic
957D4—41no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—81no—
966D4—81no—
967D4—4881no—
968D4—4881no—
969D4—2442no—
970D4—2442no—
971D4—2441no—
972D4—2441no—
973D4—2441no—
974D4—2441no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—611no—
1000C2×C4—611no—
1001C2×C4—611no—
1002C2×C4—611no—
1003C2×C4—611no—
1004C2×C4—611no—
1005C2×C4—611no—
1006C2×C4—611no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1222no—
1016C2×C4—4881no—
1017C2×C4—4881no—
1018C2×C4—4881no—
1019C2×C4—4881no—
1020C2×C4—2442no—
1021C2×C4—2441no—
1022C2×C4—2441no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2442no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4C22⋊C4×D6111yescharacteristic
1045C2×C4C22⋊C4×D6111yescharacteristic
1046C2×C4C22⋊C4×D6111yescharacteristic
1047C2×C4C22⋊C4×D6111yescharacteristic
1048C22—21no—
1049C22—21no—
1050C22—21no—
1051C22—21no—
1052C22—21no—
1053C22—21no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—4881no—
1069C22—4881no—
1070C22—2441no—
1071C22—2441no—
1072C22—2441no—
1073C22C2×C22⋊C4×D6111yescharacteristic
1074C22C4×#1175822411yescharacteristic
1075C22#1684024111yescharacteristic
1076C22#1684041811yescharacteristic
1077C22#1684042011yescharacteristic
1078C22#1684043011yescharacteristic
1079C22#1684043211yescharacteristic
1080C4—21no—
1081C4—21no—
1082C4—21no—
1083C4—21no—
1084C4—42no—
1085C4—41no—
1086C4—41no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—612no—
1091C4—1221no—
1092C4—1221no—
1093C4—1221no—
1094C4—1221no—
1095C4—1221no—
1096C4—1221no—
1097C4—1221no—
1098C4—4881no—
1099C4—4881no—
1100C4—4881no—
1101C4—2442no—
1102C4—2441no—
1103C4—2441no—
1104C4—2441no—
1105C2—21no—
1106C2—21no—
1107C2—21no—
1108C2—21no—
1109C2—21no—
1110C2—21no—
1111C2—81no—
1112C2—81no—
1113C2—4881no—
1114C2#2144865811yescharacteristic
1115C2#410×D6111yescharacteristic
1116C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840455C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#22535
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448697C2semidirect
3. #21448691C2semidirect
4. #21446656C2semidirect
5. #21446653C2semidirect
6. #21446653C2semidirect
7. #21446653C2semidirect
8. #21446653C2semidirect
9. #21445805C2semidirect
10. #21445805C2semidirect
11. #21445804C2semidirect
12. #99×Dic61C2semidirect
13. #99×Dic61C2semidirect
14. C4×#14519691C2semidirect
15. C61×#1964C2semidirect
24. C2×#14519772C4semidirect
25. C2×#14519770C4semidirect
26. C2×#14519767C4semidirect
27. C2×#14519759C4semidirect
28. C2×#14519758C4semidirect
29. C2×#14519749C4semidirect
35. C2×#14519737C4semidirect
36. C2×#14519733C4semidirect
555. #1964D61semidirect
633. C61#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#168404552
#214486972
#214486912
#214466562
#214466532
#214458052
#214458042
#99×Dic612
C4×#145196912
C61×#19642
#2253561