Finite Group Databasebeta

← C2×#21449516 #29847841

Subgroups — C2×#21449516 #29847841

Order 15616.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519776C211yesmaximal, characteristic, complemented
2C22×#14519757C211yesmaximal, characteristic
3C22×#14519755C211yesmaximal, characteristic
4C22×C4⋊C4×D61C211yesmaximal, characteristic
5#21449516C2116yesmaximal, direct product factor
6C2×#16839694C211yesmaximal, characteristic, complemented
7C2×#16839683C211yesmaximal, characteristic, complemented
8C2×#16839682C211yesmaximal, characteristic, complemented
9C2×#16839659C211yesmaximal, characteristic, complemented
10C2×#16839657C211yesmaximal, characteristic, complemented
11C2×#16839636C211yesmaximal, characteristic
12C2×#16839633C211yesmaximal, characteristic
13C2×#16839631C211yesmaximal, characteristic, complemented
14C2×#16839621C211yesmaximal, characteristic
15C2×#16839609C211yesmaximal, characteristic
16C2×C61×#398C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519776—28no—
23C2×#14519776C2218yescomplemented
24C2×#14519757—28no—
25C2×#14519757C2218yes—
26C2×#14519755—28no—
27C2×#14519755C2218yes—
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C22×#11758196C2211yescharacteristic
38C22×#11758196C2211yescharacteristic
39C22×#11758196C2211yescharacteristic
40C2×C4⋊C4×D61—28no—
41C2×C4⋊C4×D61C2218yes—
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45C22×#11758198C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47C22×C4×Dic61C2211yescharacteristic
48#16839694C2218yescomplemented
49#16839683C2218yescomplemented
50#16839682C2218yescomplemented
51#16839659C2218yescomplemented
52#16839657C2218yescomplemented
53#16839636C2218yes—
54#16839633C2218yes—
55#16839631C2218yescomplemented
56#16839621C2218yes—
57#16839609C2218yes—
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C61×#398C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C24×D61C2311yescharacteristic
72C22×Dic122—24no—
73C22×Dic122—24no—
74C22×Dic122—24no—
75C22×Dic122—24no—
76C22×Dic122—42no—
77C22×Dic122—42no—
78C22×Dic122C2314yes—
79C22×Dic122C2314yes—
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61—42no—
94C22×C4×D61—42no—
95C22×C4×D61Q818yescomplemented
96C22×C4×D61C2314yes—
97C22×C4×D61C2314yes—
98C22×C4×D61C2314yes—
99#14519776—232no—
100#14519757—232no—
101#14519755—232no—
102C2×C4⋊Dic61—24no—
103C2×C4⋊Dic61—24no—
104C2×C4⋊Dic61—24no—
105C2×C4⋊Dic61—24no—
106C2×C4⋊Dic61C2314yes—
107C2×C4⋊Dic61C2314yes—
108C2×C4⋊Dic61C2314yes—
109C2×C4⋊Dic61C2314yes—
110C2×#11758196—24no—
111C2×#11758196—24no—
112C2×#11758196—24no—
113C2×#11758196—24no—
114C2×#11758196—24no—
115C2×#11758196—42no—
116C2×#11758196—42no—
117C2×#11758196D418yes—
118C2×#11758196C2314yes—
119C2×#11758196C2314yes—
120C2×#11758196C2314yes—
121C2×#11758196C2314yes—
122C2×#11758196C2314yes—
123C2×#11758196C2314yes—
124C2×#11758196C2314yes—
125C2×#11758196C2314yes—
126C4⋊C4×D61—232no—
127C2×#11758198—24no—
128C2×#11758198—24no—
129C2×#11758198D418yes—
130C2×#11758198Q818yescomplemented
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×C4×Dic61—24no—
136C2×C4×Dic61—24no—
137C2×C4×Dic61C2314yes—
138C2×C4×Dic61C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143#14519684C2314yes—
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61—24no—
152C2×C4⋊C4×C61—24no—
153C2×C4⋊C4×C61—24no—
154C2×C4⋊C4×C61—24no—
155C2×C4⋊C4×C61C2314yes—
156C2×C4⋊C4×C61C2314yes—
157C2×C4⋊C4×C61C2314yes—
158C2×C4⋊C4×C61C2314yes—
159#95×C61C2314yes—
160#95×C61C2314yes—
161#95×C61C2314yes—
162C24×C61C2411yescharacteristic
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61C2×D414yes—
168C23×D61C2×Q814yes—
169C23×D61C2×Q814yes—
170C23×D61C2412yes—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C2×D414yes—
189C22×C4×C61C2×D414yes—
190C22×C4×C61C2×Q814yes—
191C22×C4×C61C2×Q814yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61C2×D414yes—
215C22×Dic61C2×D414yes—
216C22×Dic61C2×D414yes—
217C22×Dic61C2×Q814yes—
218C22×Dic61C2×Q814yes—
219C22×Dic61#4114yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×C4×D61—232no—
228C2×C4×D61—28no—
229C2×C4×D61—28no—
230C2×C4×D61—28no—
231C2×C4×D61—28no—
232C2×C4×D61—28no—
233C2×C4×D61—28no—
234C2×C4×D61—44no—
235C2×C4×D61—44no—
236C2×C4×D61—416no—
237C2×C4×D61—416no—
238C2×C4×D61C2×Q8116yescomplemented
239C2×Dic122—28no—
240C2×Dic122—28no—
241C2×Dic122—28no—
242C2×Dic122—28no—
243C2×Dic122—44no—
244C2×Dic122—44no—
245C2×Dic122—416no—
246C2×Dic122—416no—
247C4⋊C4×C61—28no—
248C4⋊C4×C61—28no—
249C4⋊C4×C61—28no—
250C4⋊C4×C61—28no—
251#11758198—28no—
252#11758198—28no—
253#11758198C2×D4116yes—
254#11758198C2×Q8116yescomplemented
255C4⋊Dic61—28no—
256C4⋊Dic61—28no—
257C4⋊Dic61—28no—
258C4⋊Dic61—28no—
259#11758196—28no—
260#11758196—28no—
261#11758196—28no—
262#11758196—28no—
263#11758196—28no—
264#11758196—44no—
265#11758196—44no—
266#11758196C2×D4116yes—
267C4×Dic61—28no—
268C4×Dic61—28no—
269C23×C61C22×D412yes—
270C23×C61C22×D412yes—
271C23×C61C22×Q812yes—
272C23×C61C22×Q812yes—
273C23×C61C2×#4112yes—
274C23×C61H(5,𝔽2)12yes—
275C23×C612−1+412yes—
276C23×C61C2511yescharacteristic
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—28no—
281C22×D61—28no—
282C22×D61—28no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61C4⋊Q8116yescomplemented
288C22×D61C22×D414yes—
289C22×D61C22×Q814yes—
290C22×D61C22×Q814yes—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—28no—
294C2×C4×C61—28no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61C22×D414yes—
316C2×C4×C61C22×D414yes—
317C2×C4×C61C22×Q814yes—
318C2×C4×C61C22×Q814yes—
319C2×Dic61—28no—
320C2×Dic61—28no—
321C2×Dic61—28no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61C22⋊Q8116yescomplemented
341C2×Dic61C22×D414yes—
342C2×Dic61C22×D414yes—
343C2×Dic61C22×D414yes—
344C2×Dic61C22×Q814yes—
345C2×Dic61C22×Q814yes—
346C2×Dic61C2×#4114yes—
347C4×D61—232no—
348C4×D61—416no—
349C4×D61—416no—
350Dic122—416no—
351Dic122—416no—
352C2×#2440—611nomaximal, Sylow
353C22×C61C2×C22⋊Q814yes—
354C22×C61C2×C4⋊Q814yes—
355C22×C61#54414yes—
356C22×C61D4214yes—
357C22×C61#54714yes—
358C22×C61D4×Q814yes—
359C22×C61#55414yes—
360C22×C61C23×D411yescharacteristic
361C22×C61C23×D411yescharacteristic
362C22×C61C23×Q811yescharacteristic
363C22×C61C23×Q811yescharacteristic
364C22×C61C22×#4111yescharacteristic
365C22×C61C2×H(5,𝔽2)11yescharacteristic
366C22×C61C2×2−1+411yescharacteristic
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—232no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61C2×C4⋊Q818yescomplemented
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61—42no—
382Dic61—24no—
383Dic61—24no—
384Dic61—24no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388Dic61C2×C22⋊Q818yescomplemented
389C22×C4⋊Q8—611no—
390C22×C22⋊Q8—611no—
391C22×C22⋊Q8—611no—
392C23×C4⋊C4—611no—
393#2440—6116no—
394C2×#398—611no—
395C2×#398D6111yescharacteristic, complemented
396C2×#395—611no—
397C2×#395—611no—
398C2×#389—611no—
399C2×#389—611no—
400C2×#385—611no—
401C2×#385—611no—
402C2×#384—611no—
403C2×#380—611no—
404C2×C4×C22⋊C4—611no—
405C2×C61#244018yescomplemented
406C2×C61C22×C22⋊Q811yescharacteristic
407C2×C61C22×C4⋊Q811yescharacteristic
408C2×C61C2×#54411yescharacteristic
409C2×C61C2×D4211yescharacteristic
410C2×C61C2×#54711yescharacteristic
411C2×C61C2×D4×Q811yescharacteristic
412C2×C61C2×#55411yescharacteristic
413D61—28no—
414C23×Q8—611no—
415C23×Q8—611no—
416C24×C4—611no—
417C24×C4—611no—
418C24×C4—611no—
419C2×C4⋊Q8—618no—
420C2×C4⋊Q8—1228no—
421C2×C22⋊Q8—618no—
422C2×C22⋊Q8—618no—
423C2×C22⋊Q8—1228no—
424C2×C22⋊Q8—1228no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4—611no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4—611no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4—618no—
438C22×C4⋊C4—1228no—
439C22×C4⋊C4C2×D6111yescharacteristic
440C22×C4⋊C4C2×D6111yescharacteristic
441C22×C4⋊C4C2×D6111yescharacteristic
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C42—611no—
448C22×C42—611no—
449#398—618no—
450#398C2×D6118yescomplemented
451#395—618no—
452#395—618no—
453#389—618no—
454#389—618no—
455#385—618no—
456#385—618no—
457#384—618no—
458#380—618no—
459C4×C22⋊C4—618no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95C2×D6111yescharacteristic
466C2×#95C2×D6111yescharacteristic
467C2×#95C2×D6111yescharacteristic
468C61C2×#244011yescharacteristic, complemented, Sylow
469C25—611no—
470C22×Q8—614no—
471C22×Q8—614no—
472C22×Q8—1224no—
473C22×Q8—1224no—
474C22×Q8—1224no—
475C22×Q8—1224no—
476C22×Q8—2442no—
477C22×Q8—2442no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—618no—
483C23×C4—614no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—614no—
488C23×C4—614no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4—1224no—
492C23×C4—1224no—
493C23×C4—1224no—
494C23×C4—1224no—
495C23×C4—2442no—
496C23×C4—2442no—
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C4⋊Q8—12232no—
505C22⋊Q8—12232no—
506C22⋊Q8—12232no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—618no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—12232no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—1224no—
527C2×C4⋊C4—1224no—
528C2×C4⋊C4—1224no—
529C2×C4⋊C4—1224no—
530C2×C4⋊C4—1224no—
531C2×C4⋊C4—1224no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—2442no—
535C2×C4⋊C4—2442no—
536C2×C4⋊C4C22×D6114yes—
537C2×C4⋊C4C22×D6114yes—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—618no—
541C2×C22⋊C4—618no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4—1224no—
548C2×C42—614no—
549C2×C42—614no—
550C2×C42—1224no—
551C2×C42—1224no—
552#95—614no—
553#95—614no—
554#95—614no—
555#95—614no—
556#95—614no—
557#95C22×D6114yes—
558#95C22×D6114yes—
559#95C22×D6114yes—
560C24—614no—
561C24—614no—
562C24—614no—
563C24—612no—
564C24—1222no—
565C24—1222no—
566C24—1222no—
567C24—1222no—
568C24C23×D6111yescharacteristic
569C2×Q8—1228no—
570C2×Q8—1228no—
571C2×Q8—1228no—
572C2×Q8—1228no—
573C2×Q8—2444no—
574C2×Q8—2444no—
575C2×Q8—24416no—
576C2×Q8—24416no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—614no—
595C22×C4—614no—
596C22×C4—614no—
597C22×C4—612no—
598C22×C4—614no—
599C22×C4—614no—
600C22×C4—614no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—6116no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—1228no—
609C22×C4—12232no—
610C22×C4—1228no—
611C22×C4—1228no—
612C22×C4—1228no—
613C22×C4—1228no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1228no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4—24416no—
633C22×C4—24416no—
634C22×C4D4×D6114yes—
635C22×C4D4×D6114yes—
636C22×C4Q8×D6114yes—
637C22×C4Q8×D6114yes—
638C22×C4C23×D6112yes—
639C22×C4C23×D6112yes—
640C22×C4C23×D6112yes—
641C22×C4C23×D6112yes—
642C22×C4C23×D6112yes—
643C22×C4C23×D6112yes—
644C22×C4C23×D6112yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—6116no—
650C4⋊C4—1228no—
651C4⋊C4—1228no—
652C4⋊C4—1228no—
653C4⋊C4—1228no—
654C4⋊C4—1228no—
655C4⋊C4—1228no—
656C4⋊C4—1228no—
657C4⋊C4—1228no—
658C4⋊C4—1228no—
659C4⋊C4—2444no—
660C4⋊C4—2444no—
661C22⋊C4—6116no—
662C22⋊C4—6116no—
663C22⋊C4—1228no—
664C22⋊C4—1228no—
665C42—1228no—
666C42—1228no—
667C23—6116no—
668C23—614no—
669C23—614no—
670C23—614no—
671C23—1228no—
672C23—1228no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1228no—
678C23—1228no—
679C23—1228no—
680C23—1228no—
681C23C2×D4×D6112yes—
682C23C2×D4×D6112yes—
683C23C2×Q8×D6112yes—
684C23C2×Q8×D6112yes—
685C23#41×D6112yes—
686C23#1451982312yes—
687C23#1451982412yes—
688C23C24×D6111yescharacteristic
689Q8—24416no—
690Q8—24416no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—6116no—
716C2×C4—614no—
717C2×C4—614no—
718C2×C4—614no—
719C2×C4—614no—
720C2×C4—614no—
721C2×C4—614no—
722C2×C4—12232no—
723C2×C4—1228no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1228no—
731C2×C4—1228no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—24416no—
742C2×C4—24416no—
743C2×C4—2444no—
744C2×C4—2444no—
745C2×C4—2444no—
746C2×C4C2×D4×D6114yes—
747C2×C4C2×D4×D6114yes—
748C2×C4C2×Q8×D6114yes—
749C2×C4C2×Q8×D6114yes—
750C22—618no—
751C22—1224no—
752C22—12232no—
753C22—1224no—
754C22—1224no—
755C22—1224no—
756C22—1224no—
757C22—1224no—
758C22C22⋊Q8×D6114yes—
759C22C4⋊Q8×D6114yes—
760C22#1684039214yes—
761C22#1684039614yes—
762C22#1684041014yes—
763C22#1684042514yes—
764C22#1684046814yes—
765C22C22×D4×D6111yescharacteristic
766C22C22×D4×D6111yescharacteristic
767C22C22×Q8×D6111yescharacteristic
768C22C22×Q8×D6111yescharacteristic
769C22C2×#41×D6111yescharacteristic
770C22C2×#1451982311yescharacteristic
771C22C2×#1451982411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—618no—
780C4—1224no—
781C4—1224no—
782C4—1224no—
783C4—2442no—
784C4—2442no—
785C4—2442no—
786C2—1228no—
787C2#2144951618yesdirect product factor
788C2C2×C22⋊Q8×D6111yescharacteristic
789C2C2×C4⋊Q8×D6111yescharacteristic
790C2C2×#1684039211yescharacteristic
791C2C2×#1684039611yescharacteristic
792C2C2×#1684041011yescharacteristic
793C2C2×#1684042511yescharacteristic
794C2C2×#1684046811yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#398C2
socleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#398D61
hypocenterC61C2×#2440
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14519776C2semidirect
5. #21449516C2direct (N × H)
6. C2×#16839694C2semidirect
7. C2×#16839683C2semidirect
8. C2×#16839682C2semidirect
9. C2×#16839659C2semidirect
10. C2×#16839657C2semidirect
13. C2×#16839631C2semidirect
16. C2×C61×#398C2semidirect
23. C2×#14519776C22semidirect
48. #16839694C22semidirect
49. #16839683C22semidirect
50. #16839682C22semidirect
51. #16839659C22semidirect
52. #16839657C22semidirect
55. #16839631C22semidirect
67. C61×#398C22semidirect
95. C22×C4×D61Q8semidirect
130. C2×#11758198Q8semidirect
238. C2×C4×D61C2×Q8semidirect
254. #11758198C2×Q8semidirect
287. C22×D61C4⋊Q8semidirect
340. C2×Dic61C22⋊Q8semidirect
374. C2×D61C2×C4⋊Q8semidirect
388. Dic61C2×C22⋊Q8semidirect
395. C2×#398D61semidirect
405. C2×C61#2440semidirect
450. #398C2×D61semidirect
468. C61C2×#2440semidirect
787. C2#21449516direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197762
C22×#145197572
C22×#145197552
C22×C4⋊C4×D612
#214495162
C2×#168396942
C2×#168396832
C2×#168396822
C2×#168396592
C2×#168396572
C2×#168396362
C2×#168396332
C2×#168396312
C2×#168396212
C2×#168396092
C2×C61×#3982
C2×#244061