Finite Group Databasebeta

← #29840422

Subgroups — #29840422

Order 15616.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C2×#16840239C211yesmaximal, characteristic, complemented
3C2×#16840235C211yesmaximal, characteristic
4#21448893C212yesmaximal, complemented
5#21448891C212yesmaximal, complemented
6#21448887C212yesmaximal, complemented
7#21448885C212yesmaximal, complemented
8#21448671C211yesmaximal, characteristic, complemented
9#21448670C211yesmaximal, characteristic, complemented
10#21448669C211yesmaximal, characteristic, complemented
11#21448668C211yesmaximal, characteristic, complemented
12#21448665C211yesmaximal, characteristic, complemented
13#21448664C211yesmaximal, characteristic, complemented
14#21448661C211yesmaximal, characteristic, complemented
15#21448528C212yesmaximal, complemented
16#21448525C212yesmaximal, complemented
17#21448404C211yesmaximal, characteristic, complemented
18#21448400C211yesmaximal, characteristic
19#21448360C212yesmaximal, complemented
20C4×#14519763C212yesmaximal, complemented
21#21448221C211yesmaximal, characteristic, complemented
22C4×#14519733C211yesmaximal, characteristic, complemented
23C61×#2342C211yesmaximal, characteristic, complemented
24C23×Dic122C2211yescharacteristic
25C23×C22⋊D61C2211yescharacteristic
26C2×#14519763C4116yescomplemented
27C2×#14519763C2211yescharacteristic
28C2×#14519763C2211yescharacteristic
29C2×#14519763C2211yescharacteristic
30C2×#14519763C2211yescharacteristic
31C2×#14519763C2211yescharacteristic
32C2×#14519763C2211yescharacteristic
33C2×#14519763C2211yescharacteristic
34C2×#14519763C2211yescharacteristic
35#16840239—28no—
36#16840235—28no—
37C2×C4×Dic122C2212yescomplemented
38C2×C4×Dic122C2212yescomplemented
39C2×#14519742C2212yescomplemented
40C2×#14519742C2212yescomplemented
41C2×C4×C22⋊D61C2212yes—
42C2×C4×C22⋊D61C2212yes—
43C2×#14519737C2212yes—
44C2×#14519737C2212yes—
45C2×#14519736C2211yescharacteristic
46C2×#14519733C2211yescharacteristic
47C2×#14519733C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49C2×#14519733C2211yescharacteristic
50C2×#14519733C2211yescharacteristic
51C2×#14519733C2211yescharacteristic
52C22×C22⋊Dic61C2211yescharacteristic
53C22×C22⋊Dic61C2211yescharacteristic
54C22×#11758198C2211yescharacteristic
55C22×#11758198C2211yescharacteristic
56C2×C22⋊C4×D61C2211yescharacteristic
57C2×C22⋊C4×D61C2211yescharacteristic
58C22×C4×Dic61C2211yescharacteristic
59#16839666C2212yescomplemented
60#16839666C2212yescomplemented
61#16839666C2212yescomplemented
62#16839666C2212yescomplemented
63#16839662C2212yes—
64#16839662C2212yes—
65#16839662C2212yes—
66#16839662C2212yes—
67#16839656C2212yescomplemented
68#16839656C2212yescomplemented
69#16839655C2212yescomplemented
70#16839655C2212yescomplemented
71#16839654C2212yescomplemented
72#16839654C2212yescomplemented
73#16839653C2212yescomplemented
74#16839653C2212yescomplemented
75#16839652C2212yescomplemented
76#16839652C2212yescomplemented
77#16839651C2212yescomplemented
78#16839651C2212yescomplemented
79#16839650C2212yescomplemented
80#16839650C2212yescomplemented
81#16839637C2212yescomplemented
82#16839636C2212yescomplemented
83#16839636C2212yescomplemented
84#16839635C2212yescomplemented
85#16839634C2212yescomplemented
86#16839633C2212yescomplemented
87#16839633C2212yescomplemented
88#16839631C2212yescomplemented
89#16839626C2212yescomplemented
90#16839625C2211yescharacteristic
91#16839623C2211yescharacteristic
92#16839623C2211yescharacteristic
93#16839622C2211yescharacteristic
94#16839620C2211yescharacteristic
95#16839620C2211yescharacteristic
96#16839618C2211yescharacteristic
97#16839617C2211yescharacteristic
98#16839617C2211yescharacteristic
99C4⋊C4×Dic61C2212yescomplemented
100C4×#11758196C2212yescomplemented
101#16839613C2212yescomplemented
102#16839613C2212yescomplemented
103C22⋊C4×Dic61C2211yescharacteristic
104C22⋊C4×Dic61C2211yescharacteristic
105C22⋊C4×Dic61C2212yescomplemented
106C22⋊C4×Dic61C2212yescomplemented
107C4×#11758198C2212yescomplemented
108C4×#11758198C2212yescomplemented
109C4×C22⋊Dic61C2211yescharacteristic
110C4×C22⋊Dic61C2212yescomplemented
111#16839609C2212yescomplemented
112#16839609C2212yescomplemented
113#16839607C2212yescomplemented
114C42×Dic61C2212yescomplemented
115C2×#117×C61C2211yescharacteristic
116C22×C22⋊C4×C61C2211yescharacteristic
117C22×C22⋊C4×C61C2211yescharacteristic
118C61×#388C2212yescomplemented
119C61×#388C2212yescomplemented
120C61×#385C2212yescomplemented
121C61×#381C2211yescharacteristic
122C61×#380C2211yescharacteristic
123C61×#379C2211yescharacteristic
124C4×C22⋊C4×C61C2211yescharacteristic
125C4×C22⋊C4×C61C2212yescomplemented
126C24×D61C2311yescharacteristic
127C22×Dic122—24no—
128C22×Dic122—24no—
129C22×Dic122C2×C418yescomplemented
130C22×Dic122C2311yescharacteristic
131C22×Dic122C2311yescharacteristic
132C22×Dic122C2311yescharacteristic
133C22×Dic122C2311yescharacteristic
134C22×C22⋊D61—24no—
135C22×C22⋊D61—24no—
136C22×C22⋊D61C2×C418yes—
137C22×C22⋊D61C2311yescharacteristic
138C22×C22⋊D61C2311yescharacteristic
139C22×C22⋊D61C2311yescharacteristic
140C22×C22⋊D61C2311yescharacteristic
141C23×Dic61C2311yescharacteristic
142C23×Dic61C2312yes—
143C23×Dic61C2311yescharacteristic
144C23×Dic61C2311yescharacteristic
145C22×C4×D61C2312yes—
146C22×C4×D61C2312yes—
147#14519763C2×C418yescomplemented
148#14519763C2×C418yescomplemented
149#14519763C2×C418yescomplemented
150#14519763C2×C418yescomplemented
151#14519763C2×C418yescomplemented
152#14519763C2×C418yescomplemented
153#14519763C2×C418yescomplemented
154#14519763C2×C418yescomplemented
155C4×Dic122—28no—
156C4×Dic122—28no—
157#14519742—28no—
158#14519742—28no—
159C4×C22⋊D61—28no—
160C4×C22⋊D61—28no—
161#14519737—28no—
162#14519737—28no—
163#14519736—24no—
164#14519733—24no—
165#14519733—24no—
166#14519733—24no—
167#14519733—24no—
168#14519733—24no—
169#14519733D418yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2312yes—
172C2×#11758196C2312yes—
173C2×#11758196C2312yes—
174C2×#11758196C2312yes—
175C2×#11758196C2312yes—
176C2×#11758196C2312yes—
177C2×#11758196C2312yes—
178C2×#11758196C2312yes—
179C2×#11758196C2312yes—
180C2×C22⋊Dic61—24no—
181C2×C22⋊Dic61C2×C418yescomplemented
182C2×C22⋊Dic61C2311yescharacteristic
183C2×C22⋊Dic61C2312yes—
184C2×C22⋊Dic61C2311yescharacteristic
185C2×C22⋊Dic61C2311yescharacteristic
186C2×C22⋊Dic61C2312yes—
187C2×C22⋊Dic61C2312yes—
188C2×C22⋊Dic61C2311yescharacteristic
189C2×C22⋊Dic61C2311yescharacteristic
190C2×C22⋊Dic61C2311yescharacteristic
191C2×C22⋊Dic61C2311yescharacteristic
192C2×C22⋊Dic61C2311yescharacteristic
193C2×#11758198C2×C418yescomplemented
194C2×#11758198C2×C418yescomplemented
195C2×#11758198C2312yes—
196C2×#11758198C2312yes—
197C2×#11758198C2312yes—
198C2×#11758198C2312yes—
199C2×#11758198C2312yes—
200C2×#11758198C2312yes—
201C2×#11758198C2311yescharacteristic
202C2×#11758198C2311yescharacteristic
203C2×#11758198C2311yescharacteristic
204C2×#11758198C2311yescharacteristic
205C2×#11758198C2311yescharacteristic
206C2×#11758198C2311yescharacteristic
207C2×#11758198C2311yescharacteristic
208C2×#11758198C2311yescharacteristic
209C22⋊C4×D61—24no—
210C22⋊C4×D61—24no—
211C2×C4×Dic61C2×C418yescomplemented
212C2×C4×Dic61C2312yes—
213C2×C4×Dic61C2312yes—
214C2×C4×Dic61C2312yes—
215C2×C4×Dic61C2312yes—
216C2×C4×Dic61C2312yes—
217C2×C4×Dic61C2312yes—
218C2×C4×Dic61C2312yes—
219C2×C4×Dic61C2312yes—
220C2×C4×Dic61C2312yes—
221C2×C4×Dic61C2311yescharacteristic
222C2×C4×Dic61C2311yescharacteristic
223C2×C4×Dic61C2311yescharacteristic
224C2×C4×Dic61C2311yescharacteristic
225C2×C4×Dic61C2312yes—
226#14519684C2312yes—
227#14519684C2312yes—
228#14519684C2312yes—
229#14519684C2312yes—
230#14519684C2312yes—
231#14519684C2312yes—
232#14519684C2312yes—
233#14519684C2312yes—
234#14519684C2312yes—
235#14519684C2312yes—
236#14519684C2312yes—
237#14519684C2312yes—
238C25×C61C2311yescharacteristic
239C23×C4×C61C2311yescharacteristic
240C23×C4×C61C2312yes—
241C23×C4×C61C2311yescharacteristic
242#117×C61—24no—
243C2×C4⋊C4×C61C2312yes—
244C2×C4⋊C4×C61C2312yes—
245C2×C22⋊C4×C61—24no—
246C2×C22⋊C4×C61C2×C418yescomplemented
247C2×C22⋊C4×C61C2311yescharacteristic
248C2×C22⋊C4×C61C2311yescharacteristic
249C2×C22⋊C4×C61C2311yescharacteristic
250C2×C22⋊C4×C61C2312yes—
251C2×C22⋊C4×C61C2312yes—
252C2×C22⋊C4×C61C2312yes—
253C2×C22⋊C4×C61C2311yescharacteristic
254C2×C22⋊C4×C61C2311yescharacteristic
255C2×C22⋊C4×C61C2311yescharacteristic
256C2×C22⋊C4×C61C2311yescharacteristic
257C2×C22⋊C4×C61C2311yescharacteristic
258C2×C42×C61C2312yes—
259C2×C42×C61C2312yes—
260#95×C61C2312yes—
261#95×C61C2312yes—
262#95×C61C2312yes—
263#95×C61C2312yes—
264C24×C61—22no—
265C24×C61—22no—
266C24×C61—42no—
267C24×C61—42no—
268C24×C61C22×C414yes—
269C24×C61C2411yescharacteristic
270C24×C61C2411yescharacteristic
271C24×C61C2411yescharacteristic
272C23×D61—22no—
273C23×D61—22no—
274C23×D61—42no—
275C23×D61—42no—
276C23×D61C22×C414yes—
277C23×D61C2411yescharacteristic
278C23×D61C2411yescharacteristic
279C22×C4×C61—22no—
280C22×C4×C61—22no—
281C22×C4×C61—24no—
282C22×C4×C61—42no—
283C22×C4×C61—42no—
284C22×C4×C61—42no—
285C22×C4×C61C22×C414yes—
286C22×C4×C61C22×C414yes—
287C22×C4×C61C2412yes—
288C22×C4×C61C2412yes—
289C22×C4×C61C2412yes—
290C22×C4×C61C2411yescharacteristic
291C22×C4×C61C2411yescharacteristic
292C22×C4×C61C2411yescharacteristic
293C22×C4×C61C2411yescharacteristic
294C22×C4×C61C2412yes—
295C2×C22⋊D61—232no—
296C2×C22⋊D61—22no—
297C2×C22⋊D61—22no—
298C2×C22⋊D61—22no—
299C2×C22⋊D61—22no—
300C2×C22⋊D61—22no—
301C2×C22⋊D61—22no—
302C2×C22⋊D61—22no—
303C2×C22⋊D61—22no—
304C2×C22⋊D61C22×C414yes—
305C2×C22⋊D61C22×C414yes—
306C2×C22⋊D61C22×C414yes—
307C2×C22⋊D61C22×C414yes—
308C22×Dic61—22no—
309C22×Dic61—22no—
310C22×Dic61—24no—
311C22×Dic61—42no—
312C22×Dic61—42no—
313C22×Dic61—42no—
314C22×Dic61C22×C414yes—
315C22×Dic61C22×C414yes—
316C22×Dic61C22×C414yes—
317C22×Dic61C2×D414yes—
318C22×Dic61#4114yes—
319C22×Dic61C2412yes—
320C22×Dic61C2412yes—
321C22×Dic61C2412yes—
322C22×Dic61C2411yescharacteristic
323C22×Dic61C2411yescharacteristic
324C22×Dic61C2411yescharacteristic
325C22×Dic61C2411yescharacteristic
326C22×Dic61C2412yes—
327C22×Dic61C2411yescharacteristic
328C22×Dic61C2411yescharacteristic
329C2×C4×D61—24no—
330C2×C4×D61—24no—
331C2×C4×D61—42no—
332C2×C4×D61—42no—
333C2×C4×D61—42no—
334C2×C4×D61—42no—
335C2×Dic122—232no—
336C2×Dic122—22no—
337C2×Dic122—22no—
338C2×Dic122—22no—
339C2×Dic122—22no—
340C2×Dic122—22no—
341C2×Dic122—22no—
342C2×Dic122—22no—
343C2×Dic122—22no—
344C2×Dic122C22×C414yes—
345C2×Dic122C22×C414yes—
346C2×Dic122C22×C414yes—
347C2×Dic122C22×C414yes—
348C4⋊C4×C61—24no—
349C4⋊C4×C61—42no—
350C22⋊C4×C61—22no—
351C22⋊C4×C61—22no—
352C22⋊C4×C61—22no—
353C22⋊C4×C61—24no—
354C22⋊C4×C61—42no—
355C22⋊C4×C61—42no—
356C22⋊C4×C61C22×C414yes—
357C22⋊C4×C61C22×C414yes—
358C22⋊C4×C61C22×C414yes—
359C22⋊C4×C61C22×C414yes—
360C22⋊C4×C61C2×D414yes—
361C42×C61—24no—
362C42×C61—42no—
363C22⋊Dic61—22no—
364C22⋊Dic61—22no—
365C22⋊Dic61—22no—
366C22⋊Dic61—24no—
367C22⋊Dic61—42no—
368C22⋊Dic61—42no—
369C22⋊Dic61C22×C414yes—
370C22⋊Dic61C22×C414yes—
371C22⋊Dic61C22×C414yes—
372C22⋊Dic61C22×C414yes—
373C22⋊Dic61C2×D414yes—
374#11758198—24no—
375#11758198—24no—
376#11758198—42no—
377#11758198—42no—
378#11758198—42no—
379#11758198—42no—
380#11758198C22×C414yes—
381#11758198C22×C414yes—
382#11758198C22×C414yes—
383#11758198C22×C414yes—
384#11758198C22×C414yes—
385#11758198C22×C414yes—
386#11758198C22×C414yes—
387#11758198C22×C414yes—
388C4⋊Dic61—24no—
389C4⋊Dic61—42no—
390#11758196—24no—
391#11758196—24no—
392#11758196—24no—
393#11758196—24no—
394#11758196—24no—
395#11758196—42no—
396#11758196—42no—
397#11758196C2×D418yes—
398C4×Dic61—24no—
399C4×Dic61—24no—
400C4×Dic61—24no—
401C4×Dic61—24no—
402C4×Dic61—24no—
403C4×Dic61—24no—
404C4×Dic61—42no—
405C4×Dic61—42no—
406C4×Dic61—42no—
407C4×Dic61C22×C414yes—
408C4×Dic61C22×C414yes—
409C4×Dic61C22×C414yes—
410C4×Dic61C22×C414yes—
411C4×Dic61C2×D418yes—
412C23×C61—22no—
413C23×C61—22no—
414C23×C61—21no—
415C23×C61—21no—
416C23×C61—21no—
417C23×C61—21no—
418C23×C61—22no—
419C23×C61—22no—
420C23×C61—22no—
421C23×C61—22no—
422C23×C61—28no—
423C23×C61—44no—
424C23×C61—44no—
425C23×C61—84no—
426C23×C61—84no—
427C23×C61C23×C412yes—
428C23×C61C23×C412yes—
429C23×C61C23×C412yes—
430C23×C61C22×D412yes—
431C23×C61C2×#4112yes—
432C23×C61C2511yescharacteristic
433C22×D61—21no—
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—22no—
438C22×D61—22no—
439C22×D61—22no—
440C22×D61—22no—
441C22×D61—28no—
442C22×D61—44no—
443C22×D61—44no—
444C22×D61—84no—
445C22×D61—84no—
446C22×D61C23×C412yes—
447C22×D61C23×C412yes—
448C2×C4×C61—28no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—21no—
452C2×C4×C61—21no—
453C2×C4×C61—22no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—22no—
457C2×C4×C61—22no—
458C2×C4×C61—22no—
459C2×C4×C61—22no—
460C2×C4×C61—22no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—44no—
467C2×C4×C61—84no—
468C2×C4×C61C23×C412yes—
469C2×C4×C61C23×C412yes—
470C2×C4×C61C23×C412yes—
471C2×C4×C61C23×C412yes—
472C2×C4×C61C22×D414yes—
473C22⋊D61—28no—
474C22⋊D61—28no—
475C22⋊D61—28no—
476C22⋊D61—28no—
477C2×Dic61—28no—
478C2×Dic61—21no—
479C2×Dic61—21no—
480C2×Dic61—21no—
481C2×Dic61—21no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—22no—
491C2×Dic61—22no—
492C2×Dic61—22no—
493C2×Dic61—22no—
494C2×Dic61—22no—
495C2×Dic61—44no—
496C2×Dic61—84no—
497C2×Dic61C4×D4116yes—
498C2×Dic61C23×C412yes—
499C2×Dic61C23×C412yes—
500C2×Dic61C23×C412yes—
501C2×Dic61C23×C412yes—
502C2×Dic61C23×C412yes—
503C2×Dic61C23×C412yes—
504C2×Dic61C22×D414yes—
505C2×Dic61C22×D412yes—
506C2×Dic61C22×D412yes—
507C2×Dic61C2×#4112yes—
508C2×Dic61C2×#4112yes—
509C4×D61—84no—
510C4×D61—84no—
511Dic122—28no—
512Dic122—28no—
513Dic122—28no—
514Dic122—28no—
515#34211—611nomaximal, Sylow
516C22×C61—22no—
517C22×C61—22no—
518C22×C61—24no—
519C22×C61—24no—
520C22×C61—22no—
521C22×C61—22no—
522C22×C61—22no—
523C22×C61—22no—
524C22×C61—22no—
525C22×C61—22no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61—42no—
530C22×C61—88no—
531C22×C61C2×C4×D414yes—
532C22×C61C24×C411yescharacteristic
533C22×C61C23×D411yescharacteristic
534C22×C61C22×#4111yescharacteristic
535C22×C61#58512yes—
536C22×C61#58512yes—
537C2×D61—22no—
538C2×D61—22no—
539C2×D61—22no—
540C2×D61—22no—
541C2×D61—22no—
542C2×D61—22no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—88no—
548C4×C61—22no—
549C4×C61—22no—
550C4×C61—22no—
551C4×C61—22no—
552C4×C61—24no—
553C4×C61—42no—
554C4×C61—42no—
555C4×C61—42no—
556Dic61—22no—
557Dic61—22no—
558Dic61—22no—
559Dic61—22no—
560Dic61—24no—
561Dic61—42no—
562Dic61—42no—
563Dic61—42no—
564Dic61C2×C4×D414yes—
565Dic61C2×C4×D414yes—
566C22×#124—611no—
567C2×#519—611no—
568C2×#518—611no—
569#2367—612no—
570#2367—612no—
571#2367—612no—
572#2367—612no—
573#2342—611no—
574#2342—611no—
575#2342—611no—
576#2342—611no—
577#2342—611no—
578#2342—611no—
579#2342—611no—
580#2342D6111yescharacteristic, complemented
581#2326—612no—
582#2326—612no—
583#2310—611no—
584#2309—611no—
585C4×#124—612no—
586C4×#124—612no—
587#2285—611no—
588C4×#117—611no—
589C2×C61—24no—
590C2×C61—42no—
591C2×C61—42no—
592C2×C61C22×C4×D411yescharacteristic
593C2×C61#342811yescharacteristic
594C2×C61#342811yescharacteristic
595C2×C61#350012yes—
596C2×C61#351012yes—
597D61—42no—
598D61—42no—
599C23×Q8—611no—
600C23×D4—611no—
601C2×#124—6116no—
602C2×#124—611no—
603C2×#124—611no—
604C2×#124—611no—
605C2×#124—611no—
606C2×#124—611no—
607C2×#124—611no—
608C2×#124—611no—
609C2×#124—611no—
610#519—1228no—
611#518—1228no—
612C2×C4×Q8—612no—
613C2×C4×Q8—612no—
614C2×C4×Q8—612no—
615C2×C4×Q8—612no—
616C2×C4×D4—612no—
617C2×C4×D4—612no—
618C2×C4×D4—612no—
619C2×C4×D4—612no—
620C2×#117—611no—
621C2×#117—611no—
622C2×#117—611no—
623C2×#117—611no—
624C2×#117—611no—
625C2×#117—611no—
626C2×#117—611no—
627C2×#117C2×D6111yescharacteristic
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4C2×D6111yescharacteristic
635C22×C22⋊C4C2×D6111yescharacteristic
636C22×C42—611no—
637#391—612no—
638#391—612no—
639#391—612no—
640#391—612no—
641#390—612no—
642#390—612no—
643#390—612no—
644#390—612no—
645#388—612no—
646#388—612no—
647#388—612no—
648#388—612no—
649#388—612no—
650#388—612no—
651#388—612no—
652#388—612no—
653#388—612no—
654#388—612no—
655#388—612no—
656#388—612no—
657#388—612no—
658#388—612no—
659#388C2×D6112yescomplemented
660#388C2×D6112yescomplemented
661#385—612no—
662#385—612no—
663#385—612no—
664#385—612no—
665#385—612no—
666#385—612no—
667#385—612no—
668#385C2×D6112yescomplemented
669#384—612no—
670#382—612no—
671#381—611no—
672#381—611no—
673#381—611no—
674#381C2×D6111yescharacteristic
675#380—611no—
676#380—611no—
677#380—611no—
678#380C2×D6111yescharacteristic
679#379—611no—
680#379—611no—
681#379—611no—
682#379C2×D6111yescharacteristic
683C4×C4⋊C4—612no—
684C4×C4⋊C4—612no—
685C4×C4⋊C4—612no—
686C4×C4⋊C4—612no—
687C4×C22⋊C4—611no—
688C4×C22⋊C4—612no—
689C4×C22⋊C4—611no—
690C4×C22⋊C4—611no—
691C4×C22⋊C4—612no—
692C4×C22⋊C4—612no—
693C4×C22⋊C4—612no—
694C4×C22⋊C4—612no—
695C4×C22⋊C4—612no—
696C4×C22⋊C4—612no—
697C4×C22⋊C4C2×D6111yescharacteristic
698C4×C22⋊C4C2×D6112yescomplemented
699#376—612no—
700C43—612no—
701C61#3421111yescharacteristic, complemented, Sylow
702C25—611no—
703C25C22×D6111yescharacteristic
704C22×Q8—618no—
705C22×Q8—611no—
706C22×Q8—611no—
707C22×Q8—611no—
708C22×Q8—611no—
709C22×Q8—1224no—
710C22×Q8—1224no—
711C22×D4—618no—
712C22×D4—611no—
713C22×D4—611no—
714C22×D4—611no—
715C22×D4—611no—
716C22×D4—1224no—
717C22×D4—1224no—
718C23×C4—611no—
719C23×C4—611no—
720C23×C4—611no—
721C23×C4—612no—
722C23×C4—612no—
723C23×C4—612no—
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6112yes—
726C23×C4C22×D6111yescharacteristic
727#124—618no—
728#124—618no—
729#124—618no—
730#124—618no—
731#124—618no—
732#124—618no—
733#124—618no—
734#124—618no—
735C4×Q8—1228no—
736C4×Q8—1228no—
737C4×Q8—1228no—
738C4×Q8—1228no—
739C4×D4—1228no—
740C4×D4—1228no—
741C4×D4—1228no—
742C4×D4—1228no—
743#117—24no—
744#117—618no—
745#117—1224no—
746#117—1224no—
747#117—1224no—
748#117—1224no—
749#117—1224no—
750#117—1224no—
751C2×C4⋊C4—612no—
752C2×C4⋊C4—612no—
753C2×C4⋊C4—612no—
754C2×C4⋊C4—612no—
755C2×C4⋊C4—612no—
756C2×C4⋊C4—612no—
757C2×C4⋊C4—612no—
758C2×C4⋊C4—612no—
759C2×C4⋊C4—612no—
760C2×C4⋊C4—612no—
761C2×C4⋊C4C22×D6112yes—
762C2×C4⋊C4C22×D6112yes—
763C2×C22⋊C4—24no—
764C2×C22⋊C4—618no—
765C2×C22⋊C4—611no—
766C2×C22⋊C4—611no—
767C2×C22⋊C4—611no—
768C2×C22⋊C4—611no—
769C2×C22⋊C4—611no—
770C2×C22⋊C4—618no—
771C2×C22⋊C4—618no—
772C2×C22⋊C4—611no—
773C2×C22⋊C4—611no—
774C2×C22⋊C4—611no—
775C2×C22⋊C4—611no—
776C2×C22⋊C4—611no—
777C2×C22⋊C4—611no—
778C2×C22⋊C4—611no—
779C2×C22⋊C4—611no—
780C2×C22⋊C4—611no—
781C2×C22⋊C4—612no—
782C2×C22⋊C4—611no—
783C2×C22⋊C4—611no—
784C2×C22⋊C4—612no—
785C2×C22⋊C4—612no—
786C2×C22⋊C4—612no—
787C2×C22⋊C4—612no—
788C2×C22⋊C4—612no—
789C2×C22⋊C4—612no—
790C2×C22⋊C4—612no—
791C2×C22⋊C4—612no—
792C2×C22⋊C4—1224no—
793C2×C22⋊C4—1224no—
794C2×C22⋊C4—1224no—
795C2×C22⋊C4C4×D6118yescomplemented
796C2×C22⋊C4C22×D6111yescharacteristic
797C2×C22⋊C4C22×D6112yes—
798C2×C22⋊C4C22×D6111yescharacteristic
799C2×C22⋊C4C22×D6111yescharacteristic
800C2×C22⋊C4C22×D6112yes—
801C2×C22⋊C4C22×D6112yes—
802C2×C22⋊C4C22×D6111yescharacteristic
803C2×C22⋊C4C22×D6111yescharacteristic
804C2×C22⋊C4C22×D6111yescharacteristic
805C2×C22⋊C4C22×D6111yescharacteristic
806C2×C22⋊C4C22×D6111yescharacteristic
807C2×C42—618no—
808C2×C42—612no—
809C2×C42—611no—
810C2×C42—611no—
811C2×C42—611no—
812C2×C42—611no—
813C2×C42—612no—
814C2×C42—612no—
815C2×C42—612no—
816C2×C42—612no—
817C2×C42—612no—
818C2×C42—612no—
819C2×C42—612no—
820C2×C42—612no—
821C2×C42—612no—
822C2×C42C22×D6112yes—
823C2×C42C22×D6112yes—
824#95—612no—
825#95—612no—
826#95—612no—
827#95—612no—
828#95—612no—
829#95—612no—
830#95—612no—
831#95—612no—
832#95—612no—
833#95—612no—
834#95—612no—
835#95—612no—
836#95C22×D6112yes—
837#95C22×D6112yes—
838#95C22×D6112yes—
839#95C22×D6112yes—
840C24—22no—
841C24—22no—
842C24—42no—
843C24—42no—
844C24—611no—
845C24—611no—
846C24—614no—
847C24—1222no—
848C24—1222no—
849C24—2442no—
850C24—2442no—
851C24C2×C4×D6114yes—
852C24C23×D6111yescharacteristic
853C24C23×D6111yescharacteristic
854C24C23×D6111yescharacteristic
855C2×Q8—614no—
856C2×Q8—614no—
857C2×Q8—614no—
858C2×Q8—614no—
859C2×Q8—1222no—
860C2×Q8—1222no—
861C2×Q8—1222no—
862C2×Q8—1222no—
863C2×Q8—12232no—
864C2×Q8—1222no—
865C2×Q8—1222no—
866C2×Q8—1222no—
867C2×Q8—1222no—
868C2×D4—614no—
869C2×D4—614no—
870C2×D4—614no—
871C2×D4—614no—
872C2×D4—1222no—
873C2×D4—1222no—
874C2×D4—1222no—
875C2×D4—1222no—
876C2×D4—12232no—
877C2×D4—1222no—
878C2×D4—1222no—
879C2×D4—1222no—
880C2×D4—1222no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—614no—
888C22×C4—614no—
889C22×C4—614no—
890C22×C4—611no—
891C22×C4—611no—
892C22×C4—614no—
893C22×C4—611no—
894C22×C4—611no—
895C22×C4—611no—
896C22×C4—611no—
897C22×C4—612no—
898C22×C4—614no—
899C22×C4—612no—
900C22×C4—612no—
901C22×C4—612no—
902C22×C4—1224no—
903C22×C4—1224no—
904C22×C4—1222no—
905C22×C4—1222no—
906C22×C4—1224no—
907C22×C4—2442no—
908C22×C4—2442no—
909C22×C4—2442no—
910C22×C4—2442no—
911C22×C4—2442no—
912C22×C4—2442no—
913C22×C4—2442no—
914C22×C4C2×C4×D6114yes—
915C22×C4C2×C4×D6114yes—
916C22×C4C23×D6112yes—
917C22×C4C23×D6112yes—
918C22×C4C23×D6112yes—
919C22×C4C23×D6111yescharacteristic
920C22×C4C23×D6111yescharacteristic
921C22×C4C23×D6111yescharacteristic
922C22×C4C23×D6111yescharacteristic
923C22×C4C23×D6112yes—
924C4⋊C4—24no—
925C4⋊C4—42no—
926C4⋊C4—618no—
927C4⋊C4—1224no—
928C4⋊C4—1224no—
929C4⋊C4—1224no—
930C4⋊C4—1224no—
931C4⋊C4—1224no—
932C4⋊C4—1224no—
933C4⋊C4—2442no—
934C4⋊C4—2442no—
935C4⋊C4—2442no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—24no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—614no—
943C22⋊C4—614no—
944C22⋊C4—614no—
945C22⋊C4—614no—
946C22⋊C4—614no—
947C22⋊C4—614no—
948C22⋊C4—614no—
949C22⋊C4—614no—
950C22⋊C4—614no—
951C22⋊C4—614no—
952C22⋊C4—614no—
953C22⋊C4—614no—
954C22⋊C4—614no—
955C22⋊C4—1224no—
956C22⋊C4—1224no—
957C22⋊C4—1222no—
958C22⋊C4—1222no—
959C22⋊C4—1222no—
960C22⋊C4—1224no—
961C22⋊C4—2442no—
962C22⋊C4—2442no—
963C22⋊C4—2442no—
964C22⋊C4—2442no—
965C22⋊C4—2442no—
966C22⋊C4—2442no—
967C22⋊C4C2×C4×D6114yes—
968C22⋊C4C2×C4×D6114yes—
969C22⋊C4C2×C4×D6114yes—
970C22⋊C4C2×C4×D6114yes—
971C22⋊C4D4×D6114yes—
972C42—24no—
973C42—42no—
974C42—614no—
975C42—614no—
976C42—614no—
977C42—614no—
978C42—618no—
979C42—1224no—
980C42—1224no—
981C42—1224no—
982C42—1224no—
983C42—1224no—
984C42—1224no—
985C42—2442no—
986C42—2442no—
987C42—2442no—
988C23—22no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—28no—
999C23—44no—
1000C23—44no—
1001C23—84no—
1002C23—84no—
1003C23—612no—
1004C23—612no—
1005C23—1228no—
1006C23—1221no—
1007C23—1221no—
1008C23—1221no—
1009C23—1221no—
1010C23—1222no—
1011C23—1222no—
1012C23—1222no—
1013C23—1222no—
1014C23—4884no—
1015C23—4884no—
1016C23—2444no—
1017C23—2444no—
1018C23C22×C4×D6112yes—
1019C23C22×C4×D6112yes—
1020C23C22×C4×D6112yes—
1021C23C2×D4×D6112yes—
1022C23#41×D6112yes—
1023C23C24×D6111yescharacteristic
1024Q8—1228no—
1025Q8—1228no—
1026Q8—1228no—
1027Q8—1228no—
1028D4—1228no—
1029D4—1228no—
1030D4—1228no—
1031D4—1228no—
1032C2×C4—28no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—44no—
1051C2×C4—84no—
1052C2×C4—6116no—
1053C2×C4—612no—
1054C2×C4—612no—
1055C2×C4—612no—
1056C2×C4—612no—
1057C2×C4—612no—
1058C2×C4—612no—
1059C2×C4—612no—
1060C2×C4—612no—
1061C2×C4—612no—
1062C2×C4—612no—
1063C2×C4—614no—
1064C2×C4—1228no—
1065C2×C4—1221no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—4884no—
1083C2×C4—4884no—
1084C2×C4—4884no—
1085C2×C4—2444no—
1086C2×C4C22×C4×D6112yes—
1087C2×C4C22×C4×D6112yes—
1088C2×C4C22×C4×D6112yes—
1089C2×C4C22×C4×D6112yes—
1090C2×C4C2×D4×D6114yes—
1091C22—22no—
1092C22—22no—
1093C22—24no—
1094C22—24no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—88no—
1106C22—1222no—
1107C22—1222no—
1108C22—1222no—
1109C22—1222no—
1110C22—1222no—
1111C22—1222no—
1112C22—4888no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22C4×D4×D6114yes—
1118C22C23×C4×D6111yescharacteristic
1119C22C22×D4×D6111yescharacteristic
1120C22C2×#41×D6111yescharacteristic
1121C22#1684059712yes—
1122C22#1684059812yes—
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—614no—
1132C4—614no—
1133C4—1222no—
1134C4—1222no—
1135C4—1222no—
1136C4—1222no—
1137C4—1224no—
1138C4—2442no—
1139C4—2442no—
1140C4—2442no—
1141C2—24no—
1142C2—42no—
1143C2—42no—
1144C2—2442no—
1145C2—2442no—
1146C2C2×C4×D4×D6111yescharacteristic
1147C2#2145901711yescharacteristic
1148C2#2145902011yescharacteristic
1149C2#2145960512yes—
1150C2#2145970712yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2342C2
socle, cosocleC23×C61C25
prime radicalC23×C22⋊D61C22
hypercenter#2342D61
hypocenterC61#34211
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. C2×#16840239C2semidirect
4. #21448893C2semidirect
5. #21448891C2semidirect
6. #21448887C2semidirect
7. #21448885C2semidirect
8. #21448671C2semidirect
9. #21448670C2semidirect
10. #21448669C2semidirect
11. #21448668C2semidirect
12. #21448665C2semidirect
13. #21448664C2semidirect
14. #21448661C2semidirect
15. #21448528C2semidirect
16. #21448525C2semidirect
17. #21448404C2semidirect
19. #21448360C2semidirect
20. C4×#14519763C2semidirect
21. #21448221C2semidirect
22. C4×#14519733C2semidirect
23. C61×#2342C2semidirect
26. C2×#14519763C4semidirect
37. C2×C4×Dic122C22semidirect
38. C2×C4×Dic122C22semidirect
39. C2×#14519742C22semidirect
40. C2×#14519742C22semidirect
59. #16839666C22semidirect
60. #16839666C22semidirect
61. #16839666C22semidirect
62. #16839666C22semidirect
67. #16839656C22semidirect
68. #16839656C22semidirect
69. #16839655C22semidirect
70. #16839655C22semidirect
71. #16839654C22semidirect
72. #16839654C22semidirect
73. #16839653C22semidirect
74. #16839653C22semidirect
75. #16839652C22semidirect
76. #16839652C22semidirect
77. #16839651C22semidirect
78. #16839651C22semidirect
79. #16839650C22semidirect
80. #16839650C22semidirect
81. #16839637C22semidirect
82. #16839636C22semidirect
83. #16839636C22semidirect
84. #16839635C22semidirect
85. #16839634C22semidirect
86. #16839633C22semidirect
87. #16839633C22semidirect
88. #16839631C22semidirect
89. #16839626C22semidirect
99. C4⋊C4×Dic61C22semidirect
100. C4×#11758196C22semidirect
101. #16839613C22semidirect
102. #16839613C22semidirect
105. C22⋊C4×Dic61C22semidirect
106. C22⋊C4×Dic61C22semidirect
107. C4×#11758198C22semidirect
108. C4×#11758198C22semidirect
110. C4×C22⋊Dic61C22semidirect
111. #16839609C22semidirect
112. #16839609C22semidirect
113. #16839607C22semidirect
114. C42×Dic61C22semidirect
118. C61×#388C22semidirect
119. C61×#388C22semidirect
120. C61×#385C22semidirect
125. C4×C22⋊C4×C61C22semidirect
129. C22×Dic122C2×C4semidirect
147. #14519763C2×C4semidirect
148. #14519763C2×C4semidirect
149. #14519763C2×C4semidirect
150. #14519763C2×C4semidirect
151. #14519763C2×C4semidirect
152. #14519763C2×C4semidirect
153. #14519763C2×C4semidirect
154. #14519763C2×C4semidirect
181. C2×C22⋊Dic61C2×C4semidirect
193. C2×#11758198C2×C4semidirect
194. C2×#11758198C2×C4semidirect
211. C2×C4×Dic61C2×C4semidirect
246. C2×C22⋊C4×C61C2×C4semidirect
580. #2342D61semidirect
659. #388C2×D61semidirect
660. #388C2×D61semidirect
668. #385C2×D61semidirect
698. C4×C22⋊C4C2×D61semidirect
701. C61#34211semidirect
795. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197632
C2×#168402392
C2×#168402352
#214488932
#214488912
#214488872
#214488852
#214486712
#214486702
#214486692
#214486682
#214486652
#214486642
#214486612
#214485282
#214485252
#214484042
#214484002
#214483602
C4×#145197632
#214482212
C4×#145197332
C61×#23422
#3421161