Finite Group Databasebeta

← #389×Dic61 #29601209

Subgroups — #389×Dic61 #29601209

Order 15616.

1918 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839661C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic
3C2×C4⋊C4×Dic61C212yesmaximal
4C2×C4⋊C4×Dic61C211yesmaximal, characteristic
5C2×C42×Dic61C211yesmaximal, characteristic
6#21444053C212yesmaximal
7#21444051C212yesmaximal
8#21444049C211yesmaximal, characteristic
9#21444048C211yesmaximal, characteristic
10#95×Dic61C212yesmaximal
11C2×C61×#389C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2212yes—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4×Dic61C2212yes—
16C22×C4×Dic61C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16839661C418yescomplemented
24C4⋊C4×Dic61—28no—
25C4⋊C4×Dic61—24no—
26C4⋊C4×Dic61C418yescomplemented
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C42×Dic61—24no—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2212yes—
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C61×#389C418yescomplemented
40C2×#95×C61C2212yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2311yescharacteristic
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61—24no—
52C2×C4⋊Dic61—24no—
53C2×C4⋊Dic61C2×C414yes—
54C2×C4⋊Dic61C2×C414yes—
55C2×C4⋊Dic61C2×C418yes—
56C2×C4×Dic61—22no—
57C2×C4×Dic61—22no—
58C2×C4×Dic61—22no—
59C2×C4×Dic61—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61—24no—
65C2×C4×Dic61—22no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—24no—
68C2×C4×Dic61—22no—
69C2×C4×Dic61—22no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—24no—
72C2×C4×Dic61—24no—
73C2×C4×Dic61C2×C418yes—
74C2×C4×Dic61C2×C414yes—
75C2×C4×Dic61C2×C414yes—
76C2×C4×Dic61D414yes—
77C2×C4×Dic61D414yes—
78C2×C4×Dic61Q814yes—
79C2×C4×Dic61Q814yes—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684C2×C418yes—
86#14519684C2×C418yes—
87C23×C4×C61C2312yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61—24no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—24no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61C2×C414yes—
97C2×C4⋊C4×C61C2×C414yes—
98C2×C4⋊C4×C61C2×C414yes—
99C2×C4⋊C4×C61C2×C418yes—
100C2×C4⋊C4×C61C2×C414yes—
101C2×C42×C61—22no—
102C2×C42×C61—22no—
103C2×C42×C61C2×C414yes—
104#95×C61C2×C418yes—
105C24×C61C2411yescharacteristic
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61C22×C414yes—
125C22×C4×C61C22×C414yes—
126C22×C4×C61C22×C414yes—
127C22×C4×C61C22×C414yes—
128C22×C4×C61C22×C412yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C412yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×Q812yes—
136C22×C4×C61C2×Q812yes—
137C22×C4×C61#4112yes—
138C22×C4×C61#4112yes—
139C22×C4×C61#4112yes—
140C22×C4×C61#4112yes—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61C22×C414yes—
166C22×Dic61C22×C414yes—
167C22×Dic61C22×C412yes—
168C22×Dic61C22×C412yes—
169C22×Dic61C22×C412yes—
170C22×Dic61C22×C412yes—
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173C22×Dic61C2×D412yes—
174C22×Dic61C2×D412yes—
175C22×Dic61C2×Q812yes—
176C22×Dic61C2×Q812yes—
177C22×Dic61C2×Q812yes—
178C22×Dic61C2×Q812yes—
179C22×Dic61#4112yes—
180C22×Dic61#4112yes—
181C22×Dic61#4112yes—
182C22×Dic61#4112yes—
183C4⋊C4×C61—216no—
184C4⋊C4×C61—28no—
185C4⋊C4×C61C42116yescomplemented
186C42×C61—28no—
187C4⋊Dic61—28no—
188C4⋊Dic61—28no—
189C4⋊Dic61—216no—
190C4×Dic61—28no—
191C4×Dic61—28no—
192C4×Dic61—28no—
193C4×Dic61—216no—
194C4×Dic61—28no—
195C4×Dic61—28no—
196C4×Dic61—48no—
197C4×Dic61C4⋊C4116yescomplemented
198C23×C61C23×C411yescharacteristic
199C23×C61C23×C411yescharacteristic
200C23×C61C23×C411yescharacteristic
201C23×C61C22×D411yescharacteristic
202C23×C61C22×D411yescharacteristic
203C23×C61C22×Q811yescharacteristic
204C23×C61C22×Q811yescharacteristic
205C23×C61C2×#4111yescharacteristic
206C23×C61C2×#4111yescharacteristic
207C23×C61C2×#4111yescharacteristic
208C23×C61C2×#4111yescharacteristic
209C23×C61C2×#4111yescharacteristic
210C23×C61C2×#4111yescharacteristic
211C23×C61C2×#4111yescharacteristic
212C23×C61C2×#4111yescharacteristic
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61C2×C4218yes—
239C2×C4×C61C2×C4214yes—
240C2×C4×C61C2×C4⋊C414yes—
241C2×C4×C61#11714yes—
242C2×C4×C61C4×D414yes—
243C2×C4×C61C4×D414yes—
244C2×C4×C61C4×D414yes—
245C2×C4×C61C4×Q814yes—
246C2×C4×C61C4×Q814yes—
247C2×C4×C61C4×Q814yes—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—24no—
271C2×Dic61—24no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61C2×C4⋊C414yes—
281C2×Dic61C2×C4⋊C414yes—
282C2×Dic61C4×D414yes—
283C2×Dic61C4×D414yes—
284C2×Dic61C4×Q814yes—
285C2×Dic61C4×Q814yes—
286C2×Dic61#12114yes—
287C2×Dic61C22⋊Q814yes—
288C2×Dic61#12514yes—
289C2×Dic61C4⋊Q814yes—
290C4×#389—611nomaximal, Sylow
291C22×C61C22×C4211yescharacteristic
292C22×C61C22×C4⋊C411yescharacteristic
293C22×C61C2×#11711yescharacteristic
294C22×C61C2×C4×D411yescharacteristic
295C22×C61C2×C4×D411yescharacteristic
296C22×C61C2×C4×D411yescharacteristic
297C22×C61C2×C4×D411yescharacteristic
298C22×C61C2×C4×D411yescharacteristic
299C22×C61C2×C4×Q811yescharacteristic
300C22×C61C2×C4×Q811yescharacteristic
301C22×C61C2×C4×Q811yescharacteristic
302C22×C61C2×C4×Q811yescharacteristic
303C22×C61C2×C4×Q811yescharacteristic
304C22×C61C4×#4111yescharacteristic
305C22×C61C4×#4111yescharacteristic
306C22×C61C4×#4111yescharacteristic
307C22×C61C4×#4111yescharacteristic
308C22×C61C4×#4111yescharacteristic
309C22×C61C4×#4111yescharacteristic
310C22×C61C2×#12111yescharacteristic
311C22×C61C2×C22⋊Q811yescharacteristic
312C22×C61#52511yescharacteristic
313C22×C61#52511yescharacteristic
314C22×C61C2×#12511yescharacteristic
315C22×C61#52911yescharacteristic
316C22×C61#52911yescharacteristic
317C22×C61#52911yescharacteristic
318C22×C61#52911yescharacteristic
319C22×C61C2×C4⋊Q811yescharacteristic
320C22×C61#53211yescharacteristic
321C22×C61#53211yescharacteristic
322C22×C61#53311yescharacteristic
323C22×C61#53311yescharacteristic
324C22×C61#53311yescharacteristic
325C22×C61#53311yescharacteristic
326C4×C61—28no—
327C4×C61—24no—
328C4×C61—24no—
329C4×C61—44no—
330C4×C61C4×C4⋊C418yescomplemented
331Dic61—24no—
332Dic61—24no—
333Dic61—24no—
334Dic61—44no—
335Dic61—44no—
336Dic61#38918yesdirect product factor
337C2×#389—611no—
338C2×#389D6111yescharacteristic
339C2×C4×C4⋊C4—611no—
340C2×C4×C4⋊C4—611no—
341C2×C4×C4⋊C4—612no—
342C2×C43—611no—
343#1436—612no—
344#1436—612no—
345C4⋊#95—611no—
346C4⋊#95—611no—
347C4×#95—612no—
348C2×C61C2×C4×C4⋊C411yescharacteristic
349C2×C61C42×D411yescharacteristic
350C2×C61C42×Q811yescharacteristic
351C2×C61C2×#38911yescharacteristic
352C2×C61#229311yescharacteristic
353C2×C61#229511yescharacteristic
354C2×C61#229611yescharacteristic
355C2×C61C4×#12111yescharacteristic
356C2×C61C4×#12111yescharacteristic
357C2×C61C4×C22⋊Q811yescharacteristic
358C2×C61C4×C22⋊Q811yescharacteristic
359C2×C61C4×#12511yescharacteristic
360C2×C61C4×#12511yescharacteristic
361C2×C61C4×C4⋊Q811yescharacteristic
362C2×C61C4×C4⋊Q811yescharacteristic
363C22×C4⋊C4—611no—
364C22×C4⋊C4—611no—
365C22×C4⋊C4—612no—
366C22×C4⋊C4C2×D6111yescharacteristic
367C22×C4⋊C4C2×D6112yes—
368C22×C4⋊C4C2×D6111yescharacteristic
369C22×C42—611no—
370C22×C42—611no—
371C22×C42—612no—
372C22×C42—611no—
373C22×C42—611no—
374C22×C42—612no—
375C22×C42—611no—
376C22×C42—611no—
377C22×C42C2×D6111yescharacteristic
378#389—618no—
379#389Dic6118yesdirect product factor
380C4×C4⋊C4—618no—
381C4×C4⋊C4—1224no—
382C4×C4⋊C4—1228no—
383C2×#95—612no—
384C2×#95—612no—
385C2×#95—612no—
386C2×#95—612no—
387C2×#95—612no—
388C2×#95—612no—
389C2×#95—612no—
390C2×#95C2×D6112yes—
391C43—1224no—
392C61C4×#38911yescharacteristic, complemented, Sylow
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—612no—
398C23×C4—612no—
399C23×C4C22×D6112yes—
400C23×C4C22×D6112yes—
401C23×C4C22×D6111yescharacteristic
402C23×C4C22×D6111yescharacteristic
403C23×C4C22×D6111yescharacteristic
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—614no—
409C2×C4⋊C4—618no—
410C2×C4⋊C4—614no—
411C2×C4⋊C4—1224no—
412C2×C4⋊C4—1224no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1222no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4C4×D6114yes—
418C2×C4⋊C4C4×D6114yes—
419C2×C4⋊C4C2×Dic6114yes—
420C2×C4⋊C4C2×Dic6118yes—
421C2×C4⋊C4C2×Dic6114yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—614no—
425C2×C42—614no—
426C2×C42—614no—
427C2×C42—618no—
428C2×C42—614no—
429C2×C42—614no—
430C2×C42—614no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1222no—
434C2×C42—1222no—
435C2×C42—1224no—
436C2×C42—1222no—
437C2×C42—1222no—
438C2×C42—1224no—
439C2×C42—1222no—
440C2×C42—1222no—
441C2×C42—1222no—
442C2×C42—1222no—
443C2×C42—1222no—
444C2×C42—1222no—
445C2×C42—1224no—
446C2×C42—1224no—
447C2×C42—1224no—
448C2×C42C2×Dic6114yes—
449#95—618no—
450#95—618no—
451#95—1224no—
452#95—1224no—
453#95—1224no—
454#95—1224no—
455#95—1224no—
456#95C2×Dic6118yes—
457C24C23×D6111yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—614no—
493C22×C4—614no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4C2×C4×D6114yes—
519C22×C4C2×C4×D6114yes—
520C22×C4C2×C4×D6112yes—
521C22×C4C2×C4×D6112yes—
522C22×C4D4×D6112yes—
523C22×C4D4×D6112yes—
524C22×C4#1175822412yes—
525C22×C4#1175822412yes—
526C22×C4Q8×D6112yes—
527C22×C4Q8×D6112yes—
528C22×C4#1175822612yes—
529C22×C4#1175822612yes—
530C22×C4C22×Dic6114yes—
531C22×C4C22×Dic6114yes—
532C22×C4C22×Dic6112yes—
533C22×C4C22×Dic6112yes—
534C22×C4C22×Dic6112yes—
535C4⋊C4—216no—
536C4⋊C4—28no—
537C4⋊C4—12216no—
538C4⋊C4—1228no—
539C4⋊C4—1228no—
540C4⋊C4C4×Dic61116yescomplemented
541C42—28no—
542C42—6116no—
543C42—12216no—
544C42—1228no—
545C42—1228no—
546C42—1228no—
547C42—1228no—
548C42—1228no—
549C42—2448no—
550C23C22×C4×D6111yescharacteristic
551C23C22×C4×D6111yescharacteristic
552C23C23×Dic6111yescharacteristic
553C23C2×D4×D6111yescharacteristic
554C23C2×D4×D6111yescharacteristic
555C23C2×Q8×D6111yescharacteristic
556C23C2×Q8×D6111yescharacteristic
557C23#41×D6111yescharacteristic
558C23#41×D6111yescharacteristic
559C23#41×D6111yescharacteristic
560C23#41×D6111yescharacteristic
561C23C2×#1175822411yescharacteristic
562C23C2×#1175822411yescharacteristic
563C23C2×#1175822611yescharacteristic
564C23C2×#1175822611yescharacteristic
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—614no—
591C2×C4—614no—
592C2×C4—614no—
593C2×C4—614no—
594C2×C4—614no—
595C2×C4—614no—
596C2×C4—614no—
597C2×C4—614no—
598C2×C4—614no—
599C2×C4—614no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1224no—
619C2×C4—1224no—
620C2×C4—1224no—
621C2×C4—1224no—
622C2×C4—1224no—
623C2×C4—1224no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4—2442no—
630C2×C4—2442no—
631C2×C4—2442no—
632C2×C4C2×C4×Dic6118yes—
633C2×C4C2×C4×Dic6114yes—
634C2×C4C4⋊C4×D6114yes—
635C2×C4#1451973514yes—
636C2×C4#1451973914yes—
637C2×C4D4×Dic6114yes—
638C2×C4D4×Dic6114yes—
639C2×C4#1451974214yes—
640C2×C4Q8×Dic6114yes—
641C2×C4Q8×Dic6114yes—
642C22C22×C4×Dic6111yescharacteristic
643C22C2×C4⋊C4×D6111yescharacteristic
644C22C2×#1451973511yescharacteristic
645C22C4×D4×D6111yescharacteristic
646C22C4×D4×D6111yescharacteristic
647C22C2×#1451973911yescharacteristic
648C22C2×D4×Dic6111yescharacteristic
649C22C2×D4×Dic6111yescharacteristic
650C22C4×Q8×D6111yescharacteristic
651C22C4×Q8×D6111yescharacteristic
652C22C2×#1451974211yescharacteristic
653C22C2×Q8×Dic6111yescharacteristic
654C22C2×Q8×Dic6111yescharacteristic
655C22C4×#1175822411yescharacteristic
656C22C4×#1175822411yescharacteristic
657C22C4×#1175822611yescharacteristic
658C22C4×#1175822611yescharacteristic
659C22#41×Dic6111yescharacteristic
660C22#41×Dic6111yescharacteristic
661C22#121×D6111yescharacteristic
662C22C22⋊Q8×D6111yescharacteristic
663C22#1684027211yescharacteristic
664C22#1684027511yescharacteristic
665C22#125×D6111yescharacteristic
666C22#1684029311yescharacteristic
667C22#1684029711yescharacteristic
668C22#1684029711yescharacteristic
669C22#1684029811yescharacteristic
670C22C4⋊Q8×D6111yescharacteristic
671C22#1684030711yescharacteristic
672C22#1684031311yescharacteristic
673C22#1684031411yescharacteristic
674C22#1684031711yescharacteristic
675C22#1684031711yescharacteristic
676C22#1684031811yescharacteristic
677C4—24no—
678C4—24no—
679C4—28no—
680C4—44no—
681C4—618no—
682C4—1224no—
683C4—1224no—
684C4—1224no—
685C4—2444no—
686C4—2444no—
687C4C4⋊C4×Dic6118yescomplemented
688C2C2×C4⋊C4×Dic6111yescharacteristic
689C2C4×D4×Dic6111yescharacteristic
690C2C4×Q8×Dic6111yescharacteristic
691C2#389×D6111yescharacteristic
692C2#2144827711yescharacteristic
693C2#2144829011yescharacteristic
694C2#2144830011yescharacteristic
695C2#2144832711yescharacteristic
696C2#121×Dic6111yescharacteristic
697C2#2144834911yescharacteristic
698C2C22⋊Q8×Dic6111yescharacteristic
699C2#2144837811yescharacteristic
700C2#125×Dic6111yescharacteristic
701C2#2144839011yescharacteristic
702C2C4⋊Q8×Dic6111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C61×#389C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×#389D61
hypocenterC61C4×#389
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
23. #16839661C4semidirect
26. C4⋊C4×Dic61C4semidirect
39. C61×#389C4semidirect
185. C4⋊C4×C61C42semidirect
197. C4×Dic61C4⋊C4semidirect
330. C4×C61C4×C4⋊C4semidirect
336. Dic61#389direct (N × H)
379. #389Dic61direct (N × H)
392. C61C4×#389semidirect
540. C4⋊C4C4×Dic61semidirect
687. C4C4⋊C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396612
C2×C4⋊C4×Dic612
C2×C42×Dic612
#214440532
#214440512
#214440492
#214440482
#95×Dic612
C2×C61×#3892
C4×#38961