Finite Group Databasebeta

← #29696565

Subgroups — #29696565

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840466C211yesmaximal, characteristic
2#21448697C211yesmaximal, characteristic, complemented
3#21448691C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446802C211yesmaximal, characteristic, complemented
6#21446802C211yesmaximal, characteristic, complemented
7#21446802C211yesmaximal, characteristic, complemented
8#21446802C211yesmaximal, characteristic, complemented
9#21445806C211yesmaximal, characteristic
10#21445806C211yesmaximal, characteristic
11#21445804C211yesmaximal, characteristic
12C4×#14519691C211yesmaximal, characteristic
13#21445606C211yesmaximal, characteristic
14#21445606C211yesmaximal, characteristic
15C61×#1996C211yesmaximal, characteristic, complemented
16#16840466—21no—
17#16840466—21no—
18#16840466—21no—
19#16840466—21no—
20#16840466—21no—
21#16840466—21no—
22#16840466—21no—
23#16840466—21no—
24C2×#14519775C411yescharacteristic, complemented
25C2×#14519767C411yescharacteristic, complemented
26C2×#14519767C411yescharacteristic, complemented
27C2×#14519755C411yescharacteristic, complemented
28C2×#14519755C411yescharacteristic, complemented
29C2×#14519754C2211yescharacteristic
30C2×#14519754C2211yescharacteristic
31C2×#14519753C411yescharacteristic, complemented
32C2×#14519742C411yescharacteristic, complemented
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519737C2211yescharacteristic
35C2×#14519737C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C2×C4⋊C4×D61C411yescharacteristic, complemented
38C2×#14519691C2211yescharacteristic
39C2×#14519691C2211yescharacteristic
40C2×#14519691C2211yescharacteristic
41C2×#14519691C2211yescharacteristic
42#16839659—21no—
43#16839657—21no—
44#16839649—21no—
45#16839646—21no—
46#16839644—21no—
47#16839643—21no—
48#16839622C2211yescharacteristic
49#16839620C2211yescharacteristic
50#16839620C2211yescharacteristic
51#16839620C2211yescharacteristic
52#16839620C2211yescharacteristic
53C4×#11758196—21no—
54#16839613—21no—
55C22⋊C4×Dic61C2211yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59C4×C22⋊Dic61C2211yescharacteristic
60#16839529C2211yescharacteristic
61#16839529C2211yescharacteristic
62#16839529C2211yescharacteristic
63#16839529C2211yescharacteristic
64#16839528C2211yescharacteristic
65#16839528C2211yescharacteristic
66#16839528C2211yescharacteristic
67#16839528C2211yescharacteristic
68C2×C22⋊Q8×C61C2211yescharacteristic
69C61×#380C2211yescharacteristic
70C4×C22⋊C4×C61C2211yescharacteristic
71C61×#342C2211yescharacteristic
72C61×#342C2211yescharacteristic
73C61×#342C2211yescharacteristic
74C61×#342C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83#14519775—21no—
84#14519775—21no—
85#14519775—21no—
86#14519775—21no—
87#14519767—21no—
88#14519767—21no—
89#14519767—21no—
90#14519767—21no—
91#14519767—21no—
92#14519767—21no—
93#14519767—21no—
94#14519767—21no—
95#14519755—21no—
96#14519755—21no—
97#14519755—21no—
98#14519755—21no—
99#14519755—21no—
100#14519755—21no—
101#14519755—21no—
102#14519755—21no—
103#14519754—21no—
104#14519754—21no—
105#14519754—21no—
106#14519754—21no—
107#14519754—21no—
108#14519754—21no—
109#14519754—21no—
110#14519754—21no—
111#14519753—21no—
112#14519753—21no—
113#14519753—21no—
114#14519753—21no—
115#14519742—21no—
116#14519742—21no—
117#14519742—21no—
118#14519742—21no—
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2×C411yescharacteristic
133C2×C4⋊Dic61C2×C411yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196C2×C411yescharacteristic
139C2×#11758196C2×C411yescharacteristic
140C2×#11758196C2×C411yescharacteristic
141C2×#11758196C2×C411yescharacteristic
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
157C4⋊C4×D61—21no—
158C4⋊C4×D61—21no—
159C4⋊C4×D61—21no—
160C4⋊C4×D61—21no—
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#14519691—22no—
178#14519691—22no—
179#14519691—22no—
180#14519691Q814yescomplemented
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684—21no—
187#14519684—21no—
188#14519684—21no—
189#14519684—21no—
190#14519684—21no—
191C22×Q8×C61C2×C411yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61—21no—
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61C2×C411yescharacteristic
199C2×C4⋊C4×C61C2×C411yescharacteristic
200C2×C4⋊C4×C61C2×C411yescharacteristic
201C2×C22⋊C4×C61C2311yescharacteristic
202C2×C22⋊C4×C61C2311yescharacteristic
203C2×C22⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61C2311yescharacteristic
205C2×C22⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61C2311yescharacteristic
207C2×C42×C61—21no—
208#95×C61—21no—
209#95×C61—21no—
210C24×C61C2411yescharacteristic
211C23×D61C22×C411yescharacteristic
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—81no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61C2×Q812yes—
235C2×C22⋊D61#4112yes—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—42no—
241C22×Dic61—81no—
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C22×C411yescharacteristic
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253C22×Dic61C2×D411yescharacteristic
254C22×Dic61C2×D411yescharacteristic
255C22×Dic61C2×D411yescharacteristic
256C22×Dic61C2×D411yescharacteristic
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—42no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×Dic122—21no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—21no—
270C2×Dic122—42no—
271C2×Dic122—81no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—81no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61C2×Q812yes—
291C42×C61—81no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61C2×Q812yes—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—81no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—42no—
328#11758196—42no—
329#11758196—81no—
330#11758196—81no—
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335#11758196C22⋊C411yescharacteristic
336#11758196C22⋊C411yescharacteristic
337#11758196C22⋊C411yescharacteristic
338#11758196C22⋊C411yescharacteristic
339#11758196C22⋊C411yescharacteristic
340#11758196C22⋊C411yescharacteristic
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343#11758196C22⋊C411yescharacteristic
344#11758196C22⋊C411yescharacteristic
345#11758196C22⋊C411yescharacteristic
346#11758196C22⋊C411yescharacteristic
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61—42no—
354C4×Dic61—42no—
355C4×Dic61—81no—
356C4×Dic61—81no—
357C4×Dic61—81no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61C23×C411yescharacteristic
361C23×C61C22×D411yescharacteristic
362C23×C61C22×D411yescharacteristic
363C23×C61C22×Q811yescharacteristic
364C23×C61C2×#4111yescharacteristic
365C23×C612−1+411yescharacteristic
366C23×C612−1+411yescharacteristic
367C22×D61—21no—
368C22×D61—21no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61C4×Q812yes—
372Q8×C61—81no—
373Q8×C61—81no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—22no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C2×C22⋊C411yescharacteristic
402C2×C4×C61C2×C22⋊C411yescharacteristic
403C2×C4×C61C2×C22⋊C411yescharacteristic
404C22⋊D61—22no—
405C22⋊D61—22no—
406C22⋊D61—22no—
407C22⋊D61—22no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—21no—
414C2×Dic61—21no—
415C2×Dic61—22no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61C2×C22⋊C411yescharacteristic
439C2×Dic61C2×C22⋊C411yescharacteristic
440C2×Dic61C2×C22⋊C411yescharacteristic
441C2×Dic61C2×C22⋊C411yescharacteristic
442C2×Dic61C2×C22⋊C411yescharacteristic
443C2×Dic61C2×C22⋊C411yescharacteristic
444C2×Dic61C2×C22⋊C411yescharacteristic
445C2×Dic61C2×C22⋊C411yescharacteristic
446C2×Dic61C4×Q812yes—
447C4×D61—42no—
448C4×D61—42no—
449C4×D61—81no—
450C4×D61—81no—
451C4×D61—81no—
452C4×D61—81no—
453Dic122—42no—
454Dic122—42no—
455Dic122—81no—
456Dic122—81no—
457#22513—611nomaximal, Sylow
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—21no—
462C22×C61—21no—
463C22×C61—21no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61—41no—
467C22×C61—41no—
468C22×C61C22×C22⋊C411yescharacteristic
469C22×C61C2×C4×Q811yescharacteristic
470C22×C61#51911yescharacteristic
471C22×C61#54811yescharacteristic
472C22×C61#54811yescharacteristic
473C22×C61D4×Q811yescharacteristic
474C22×C61D4×Q811yescharacteristic
475C2×D61—22no—
476C2×D61—42no—
477C2×D61—41no—
478C2×D61—41no—
479C2×D61—42no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—42no—
485C4×C61—41no—
486C4×C61—41no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61—81no—
490C4×C61—81no—
491C4×C61—81no—
492Dic61—22no—
493Dic61—21no—
494Dic61—21no—
495Dic61—21no—
496Dic61—21no—
497Dic61—21no—
498Dic61—21no—
499Dic61—21no—
500Dic61—42no—
501Dic61—41no—
502Dic61—41no—
503Dic61—81no—
504Dic61—81no—
505Dic61—81no—
506Dic61#41012yes—
507C2×#554—611no—
508#2345—611no—
509#2345—611no—
510#1996—611no—
511#1996—611no—
512#1996—611no—
513#1996—611no—
514#1996—611no—
515#1996D6111yescharacteristic, complemented
516#1799—611no—
517#1799—611no—
518#1799—611no—
519C4×#99—611no—
520C4×#99—611no—
521C4×#99—611no—
522C2×C61—21no—
523C2×C61—21no—
524C2×C61—21no—
525C2×C61—21no—
526C2×C61—21no—
527C2×C61—21no—
528C2×C61Q8×C22⋊C411yescharacteristic
529C2×C61C2×#41011yescharacteristic
530C2×C61#288311yescharacteristic
531D61—42no—
532#554—1221no—
533#554—1221no—
534#554—1221no—
535#554—1221no—
536#554—1221no—
537#554—1221no—
538#554—1221no—
539#554—1221no—
540C2×C4⋊Q8—611no—
541C2×#125—611no—
542C2×#125—611no—
543C2×C22⋊Q8—611no—
544C2×C22⋊Q8—611no—
545C2×C22⋊Q8—611no—
546C2×C22⋊Q8—611no—
547C2×C22⋊Q8—611no—
548C2×C22⋊Q8C2×D6111yescharacteristic
549C2×C4×Q8—611no—
550C2×C4×D4—611no—
551C2×C4×D4—611no—
552C2×C4×D4—611no—
553C22×C4⋊C4—611no—
554C22×C4⋊C4—611no—
555C2×#99—611no—
556C2×#99—611no—
557C2×#99—611no—
558C2×#99—611no—
559#389—1221no—
560#389—1221no—
561#387—1221no—
562#387—1221no—
563#387—1221no—
564#387—1221no—
565#380—611no—
566#380—611no—
567#380—611no—
568#380—611no—
569#380—611no—
570#380C2×D6111yescharacteristic
571C4×C4⋊C4—1221no—
572C4×C4⋊C4—1221no—
573C4×C22⋊C4—611no—
574C4×C22⋊C4—611no—
575C4×C22⋊C4—611no—
576C4×C22⋊C4—611no—
577C4×C22⋊C4—611no—
578C4×C22⋊C4C2×D6111yescharacteristic
579#342—611no—
580#342—611no—
581#342—611no—
582#342—611no—
583#342—611no—
584#342—611no—
585#342—611no—
586#342—611no—
587#342C2×D6111yescharacteristic
588#342C2×D6111yescharacteristic
589#342C2×D6111yescharacteristic
590#342C2×D6111yescharacteristic
591C61#2251311yescharacteristic, complemented, Sylow
592C22×Q8—611no—
593C22×Q8—611no—
594C22×Q8C4×D6111yescharacteristic
595C22×D4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4C22×D6111yescharacteristic
602C4⋊Q8—1221no—
603C4⋊Q8—1221no—
604C4⋊Q8—1221no—
605C4⋊Q8—1221no—
606#125—1221no—
607#125—1221no—
608#125—1221no—
609#125—1221no—
610#125—1221no—
611#125—1221no—
612#125—1221no—
613#125—1221no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8—1221no—
633C22⋊Q8—1221no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8—1221no—
637C22⋊Q8—1221no—
638C4×Q8—1221no—
639C4×Q8—1221no—
640C4×Q8—1221no—
641C4×Q8—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—611no—
663C2×C4⋊C4—611no—
664C2×C4⋊C4—611no—
665C2×C4⋊C4—611no—
666C2×C4⋊C4—611no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—611no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—611no—
671C2×C4⋊C4—611no—
672C2×C4⋊C4—611no—
673C2×C4⋊C4—611no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C4⋊C4—1221no—
681C2×C4⋊C4—1221no—
682C2×C4⋊C4—1221no—
683C2×C4⋊C4—1221no—
684C2×C4⋊C4—1221no—
685C2×C4⋊C4C4×D6111yescharacteristic
686C2×C4⋊C4C4×D6111yescharacteristic
687C2×C4⋊C4C4×D6111yescharacteristic
688C2×C22⋊C4—611no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—611no—
691C2×C22⋊C4—611no—
692C2×C22⋊C4—611no—
693C2×C22⋊C4—611no—
694C2×C22⋊C4—611no—
695C2×C22⋊C4—611no—
696C2×C22⋊C4C22×D6111yescharacteristic
697C2×C22⋊C4C22×D6111yescharacteristic
698C2×C22⋊C4C22×D6111yescharacteristic
699C2×C22⋊C4C22×D6111yescharacteristic
700C2×C22⋊C4C22×D6111yescharacteristic
701C2×C22⋊C4C22×D6111yescharacteristic
702C2×C42—21no—
703C2×C42—611no—
704C2×C42—611no—
705C2×C42—611no—
706C2×C42—1221no—
707C2×C42—1221no—
708C2×C42—1221no—
709C2×C42—1221no—
710C2×C42—1221no—
711#99—614no—
712#99—1222no—
713#99—1222no—
714#99—1222no—
715#95—21no—
716#95—21no—
717#95—1221no—
718#95—1221no—
719#95—1221no—
720#95—1221no—
721#95—1221no—
722#95—1221no—
723#95—1221no—
724#95—1221no—
725#95—1221no—
726#95—1221no—
727C24—611no—
728C24C23×D6111yescharacteristic
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—81no—
732C2×Q8—1221no—
733C2×Q8—1221no—
734C2×Q8—1221no—
735C2×Q8—1221no—
736C2×Q8—4881no—
737C2×Q8—2442no—
738C2×D4—612no—
739C2×D4—612no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—81no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—2442no—
778C22×C4—2442no—
779C22×C4C2×C4×D6111yescharacteristic
780C22×C4C2×C4×D6111yescharacteristic
781C22×C4C2×C4×D6111yescharacteristic
782C22×C4C2×C4×D6111yescharacteristic
783C22×C4C2×C4×D6111yescharacteristic
784C22×C4C2×C4×D6111yescharacteristic
785C22×C4D4×D6111yescharacteristic
786C22×C4D4×D6111yescharacteristic
787C22×C4D4×D6111yescharacteristic
788C22×C4D4×D6111yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—81no—
796C4⋊C4—611no—
797C4⋊C4—611no—
798C4⋊C4—611no—
799C4⋊C4—611no—
800C4⋊C4—611no—
801C4⋊C4—611no—
802C4⋊C4—611no—
803C4⋊C4—611no—
804C4⋊C4—611no—
805C4⋊C4—611no—
806C4⋊C4—611no—
807C4⋊C4—611no—
808C4⋊C4—611no—
809C4⋊C4—611no—
810C4⋊C4—611no—
811C4⋊C4—611no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4—1221no—
819C4⋊C4—1221no—
820C4⋊C4—1221no—
821C4⋊C4—1221no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1221no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4—1221no—
829C4⋊C4—1221no—
830C4⋊C4—4881no—
831C4⋊C4—4881no—
832C4⋊C4—4881no—
833C4⋊C4—2442no—
834C4⋊C4—2442no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—612no—
847C22⋊C4—1221no—
848C22⋊C4—1221no—
849C22⋊C4—1221no—
850C22⋊C4—1221no—
851C22⋊C4—1221no—
852C22⋊C4—1221no—
853C22⋊C4—1221no—
854C22⋊C4—1221no—
855C22⋊C4—1221no—
856C22⋊C4—1221no—
857C22⋊C4—1221no—
858C22⋊C4—1221no—
859C22⋊C4—1221no—
860C22⋊C4—1221no—
861C22⋊C4—1221no—
862C22⋊C4Q8×D6112yes—
863C42—81no—
864C42—1221no—
865C42—1221no—
866C42—1221no—
867C42—1221no—
868C42—1221no—
869C42—1221no—
870C42—4881no—
871C42—4881no—
872C42—4881no—
873C42—2442no—
874C42—2442no—
875C23—41no—
876C23—41no—
877C23—612no—
878C23—1221no—
879C23—1221no—
880C23—2441no—
881C23—2441no—
882C23C22×C4×D6111yescharacteristic
883C23C2×D4×D6111yescharacteristic
884C23C2×D4×D6111yescharacteristic
885C23C2×Q8×D6111yescharacteristic
886C23#41×D6111yescharacteristic
887C23#1451982411yescharacteristic
888C23#1451982511yescharacteristic
889Q8—81no—
890Q8—81no—
891Q8—4881no—
892Q8—4881no—
893Q8—2442no—
894Q8—2442no—
895D4—1222no—
896D4—1222no—
897D4—1222no—
898D4—1222no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—22no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—611no—
926C2×C4—611no—
927C2×C4—611no—
928C2×C4—611no—
929C2×C4—611no—
930C2×C4—611no—
931C2×C4—611no—
932C2×C4—611no—
933C2×C4—612no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1221no—
938C2×C4—1221no—
939C2×C4—1221no—
940C2×C4—1221no—
941C2×C4—1222no—
942C2×C4—4881no—
943C2×C4—4881no—
944C2×C4—4881no—
945C2×C4—4881no—
946C2×C4—2442no—
947C2×C4—2442no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2441no—
958C2×C4—2441no—
959C2×C4—2441no—
960C2×C4—2441no—
961C2×C4—2441no—
962C2×C4—2441no—
963C2×C4—2441no—
964C2×C4—2441no—
965C2×C4—2441no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2441no—
969C2×C4—2441no—
970C2×C4C22⋊C4×D6111yescharacteristic
971C2×C4C22⋊C4×D6111yescharacteristic
972C2×C4C22⋊C4×D6111yescharacteristic
973C2×C4C22⋊C4×D6111yescharacteristic
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—1222no—
985C22—2442no—
986C22—2442no—
987C22—2441no—
988C22—2441no—
989C22C2×C22⋊C4×D6111yescharacteristic
990C22C4×Q8×D6111yescharacteristic
991C22#1684023811yescharacteristic
992C22#1684042011yescharacteristic
993C22#1684042211yescharacteristic
994C22#1684042511yescharacteristic
995C22#1684042711yescharacteristic
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—42no—
1001C4—41no—
1002C4—41no—
1003C4—41no—
1004C4—41no—
1005C4—81no—
1006C4—81no—
1007C4—81no—
1008C4—612no—
1009C4—1221no—
1010C4—1221no—
1011C4—1221no—
1012C4—1221no—
1013C4—1221no—
1014C4—1221no—
1015C4—1221no—
1016C4—1222no—
1017C4—4881no—
1018C4—4881no—
1019C4—4881no—
1020C4—2442no—
1021C4—2441no—
1022C4—2441no—
1023C2—21no—
1024C2—21no—
1025C2—21no—
1026C2—21no—
1027C2—21no—
1028C2—21no—
1029C2—2442no—
1030C2#2144865311yescharacteristic
1031C2#410×D6111yescharacteristic
1032C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C23
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#22513
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #21448697C2semidirect
3. #21448691C2semidirect
4. #21446805C2semidirect
5. #21446802C2semidirect
6. #21446802C2semidirect
7. #21446802C2semidirect
8. #21446802C2semidirect
15. C61×#1996C2semidirect
24. C2×#14519775C4semidirect
25. C2×#14519767C4semidirect
26. C2×#14519767C4semidirect
27. C2×#14519755C4semidirect
28. C2×#14519755C4semidirect
31. C2×#14519753C4semidirect
32. C2×#14519742C4semidirect
37. C2×C4⋊C4×D61C4semidirect
180. #14519691Q8semidirect
515. #1996D61semidirect
591. C61#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#168404662
#214486972
#214486912
#214468052
#214468022
#214458062
#214458042
C4×#145196912
#214456062
C61×#19962
#2251361