Finite Group Databasebeta

← C2×#21449520 #29847842

Subgroups — C2×#21449520 #29847842

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×#14519756C211yesmaximal, characteristic
3C22×#14519754C211yesmaximal, characteristic
4C23×#11758196C211yesmaximal, characteristic
5#21449520C2116yesmaximal, direct product factor
6C2×#16839696C211yesmaximal, characteristic, complemented
7C2×#16839695C211yesmaximal, characteristic, complemented
8C2×#16839683C211yesmaximal, characteristic, complemented
9C2×#16839682C211yesmaximal, characteristic, complemented
10C2×#16839659C211yesmaximal, characteristic, complemented
11C2×#16839659C211yesmaximal, characteristic, complemented
12C2×#16839637C211yesmaximal, characteristic
13C2×#16839631C211yesmaximal, characteristic, complemented
14C2×#16839620C211yesmaximal, characteristic
15C2×C22⋊C4×Dic61C211yesmaximal, characteristic
16C2×C61×#385C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C24×Dic61C2211yescharacteristic
21C2×#14519776—28no—
22C2×#14519776C2218yescomplemented
23C2×#14519756—28no—
24C2×#14519756C2218yes—
25C2×#14519754—28no—
26C2×#14519754C2218yes—
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×#11758196—28no—
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2218yes—
37C22×#11758196C2211yescharacteristic
38C22×#11758196C2211yescharacteristic
39C22×#11758196C2211yescharacteristic
40C22×#11758196C2211yescharacteristic
41C22×#11758196C2211yescharacteristic
42C22×#11758196C2211yescharacteristic
43C22×C22⋊Dic61C2211yescharacteristic
44C22×C22⋊Dic61C2211yescharacteristic
45C22×C4×Dic61C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47#16839696C2218yescomplemented
48#16839695C2218yescomplemented
49#16839683C2218yescomplemented
50#16839682C2218yescomplemented
51#16839659C2218yescomplemented
52#16839659C2218yescomplemented
53#16839637C2218yes—
54#16839631C2218yescomplemented
55#16839620C2218yes—
56C22⋊C4×Dic61C2218yes—
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C24×C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C61×#385C2218yes—
69C2×#95×C61C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122—24no—
74C22×Dic122—24no—
75C22×Dic122—42no—
76C22×Dic122—42no—
77C22×Dic122C2314yes—
78C22×Dic122C2314yes—
79C23×Dic61—24no—
80C23×Dic61—24no—
81C23×Dic61—24no—
82C23×Dic61—24no—
83C23×Dic61—42no—
84C23×Dic61Q818yescomplemented
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2314yes—
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2314yes—
94C23×Dic61C2311yescharacteristic
95#14519776—232no—
96#14519756—232no—
97#14519754—232no—
98C2×C4⋊Dic61—24no—
99C2×C4⋊Dic61—24no—
100C2×C4⋊Dic61—24no—
101C2×C4⋊Dic61—42no—
102C2×C4⋊Dic61C2314yes—
103C2×C4⋊Dic61C2314yes—
104C2×C4⋊Dic61C2314yes—
105C2×C4⋊Dic61C2314yes—
106C2×#11758196—24no—
107C2×#11758196—24no—
108C2×#11758196—24no—
109C2×#11758196—24no—
110C2×#11758196—24no—
111C2×#11758196—24no—
112C2×#11758196—24no—
113C2×#11758196—24no—
114C2×#11758196—24no—
115C2×#11758196—232no—
116C2×#11758196D418yes—
117C2×#11758196C2314yes—
118C2×#11758196C2314yes—
119C2×#11758196C2314yes—
120C2×#11758196C2314yes—
121C2×#11758196C2314yes—
122C2×#11758196C2314yes—
123C2×#11758196C2314yes—
124C2×#11758196C2314yes—
125C2×#11758196C2314yes—
126C2×#11758196C2314yes—
127C2×C22⋊Dic61—24no—
128C2×C22⋊Dic61D418yes—
129C2×C22⋊Dic61C2314yes—
130C2×C22⋊Dic61C2314yes—
131C2×C4×Dic61—24no—
132C2×C4×Dic61—24no—
133C2×C4×Dic61C2314yes—
134C2×C4×Dic61C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141C25×C61C2311yescharacteristic
142C23×C4×C61—24no—
143C23×C4×C61—24no—
144C23×C4×C61—42no—
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2314yes—
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61—24no—
153C2×C4⋊C4×C61—42no—
154C2×C4⋊C4×C61C2314yes—
155C2×C4⋊C4×C61C2314yes—
156C2×C22⋊C4×C61—24no—
157C2×C22⋊C4×C61Q818yescomplemented
158C2×C22⋊C4×C61C2314yes—
159C2×C22⋊C4×C61C2314yes—
160#95×C61C2314yes—
161#95×C61C2314yes—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61C2×D414yes—
167C24×C61C2×Q814yes—
168C24×C61C2×Q814yes—
169C24×C61C2412yes—
170C24×C61C2411yescharacteristic
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—28no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—28no—
188C22×C4×C61—44no—
189C22×C4×C61—416no—
190C22×C4×C61C2×D414yes—
191C22×C4×C61C2×Q814yes—
192C22×C4×C61C2×Q814yes—
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—232no—
208C22×Dic61—28no—
209C22×Dic61—28no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—28no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—28no—
221C22×Dic61—44no—
222C22×Dic61—416no—
223C22×Dic61C2×D414yes—
224C22×Dic61C2×D414yes—
225C22×Dic61C2×D414yes—
226C22×Dic61C2×D414yes—
227C22×Dic61C2×Q814yes—
228C22×Dic61C2×Q814yes—
229C22×Dic61C2×Q8116yescomplemented
230C22×Dic61#4114yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
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—44no—
249C22⋊C4×C61—28no—
250C22⋊C4×C61C2×Q8116yescomplemented
251C22⋊Dic61—28no—
252C22⋊Dic61C2×D4116yes—
253C4⋊Dic61—28no—
254C4⋊Dic61—28no—
255C4⋊Dic61—28no—
256C4⋊Dic61—44no—
257#11758196—28no—
258#11758196—28no—
259#11758196—28no—
260#11758196—28no—
261#11758196—28no—
262#11758196—28no—
263#11758196—28no—
264#11758196—28no—
265#11758196—28no—
266#11758196C2×D4116yes—
267C4×Dic61—28no—
268C4×Dic61—28no—
269C23×C61—28no—
270C23×C61—28no—
271C23×C61—28no—
272C23×C61—28no—
273C23×C61—28no—
274C23×C61—28no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61C4⋊Q8116yescomplemented
280C23×C61C22×D414yes—
281C23×C61C22×D412yes—
282C23×C61C22×D412yes—
283C23×C61C22×Q814yes—
284C23×C61C22×Q814yes—
285C23×C61C22×Q812yes—
286C23×C61C22×Q812yes—
287C23×C61C2×#4112yes—
288C23×C61H(5,𝔽2)12yes—
289C23×C612−1+412yes—
290C23×C61C2511yescharacteristic
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—28no—
294C2×C4×C61—22no—
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—416no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61—44no—
313C2×C4×C61C22×D414yes—
314C2×C4×C61C22×Q814yes—
315C2×C4×C61C22×Q814yes—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—28no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—232no—
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—22no—
338C2×Dic61—416no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61C22⋊Q8116yescomplemented
343C2×Dic61C22×D414yes—
344C2×Dic61C22×D414yes—
345C2×Dic61C22×D414yes—
346C2×Dic61C22×D414yes—
347C2×Dic61C22×Q814yes—
348C2×Dic61C22×Q814yes—
349C2×Dic61C2×#4114yes—
350Dic122—416no—
351Dic122—416no—
352C2×#2440—611nomaximal, Sylow
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61—232no—
357C22×C61—24no—
358C22×C61—24no—
359C22×C61—24no—
360C22×C61C2×C22⋊Q814yes—
361C22×C61C2×C4⋊Q814yes—
362C22×C61C2×C4⋊Q818yescomplemented
363C22×C61#54414yes—
364C22×C61D4214yes—
365C22×C61#54714yes—
366C22×C61D4×Q814yes—
367C22×C61#55414yes—
368C22×C61C23×D411yescharacteristic
369C22×C61C23×D411yescharacteristic
370C22×C61C23×Q811yescharacteristic
371C22×C61C23×Q811yescharacteristic
372C22×C61C22×#4111yescharacteristic
373C22×C61C2×H(5,𝔽2)11yescharacteristic
374C22×C61C2×2−1+411yescharacteristic
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—42no—
381Dic61—24no—
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×#398—611no—
396C2×#395—611no—
397C2×#395—611no—
398C2×#389—611no—
399C2×#389—611no—
400C2×#385—611no—
401C2×#385D6111yescharacteristic
402C2×#384—611no—
403C2×#380—611no—
404C2×C4×C22⋊C4—611no—
405C2×C61—28no—
406C2×C61#244018yescomplemented
407C2×C61C22×C22⋊Q811yescharacteristic
408C2×C61C22×C4⋊Q811yescharacteristic
409C2×C61C2×#54411yescharacteristic
410C2×C61C2×D4211yescharacteristic
411C2×C61C2×#54711yescharacteristic
412C2×C61C2×D4×Q811yescharacteristic
413C2×C61C2×#55411yescharacteristic
414C23×Q8—611no—
415C23×Q8—611no—
416C24×C4—611no—
417C24×C4—611no—
418C24×C4C2×D6111yescharacteristic
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—618no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4—611no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4—611no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—1228no—
441C22×C4⋊C4C2×D6111yescharacteristic
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4C2×D6111yescharacteristic
446C22×C22⋊C4C2×D6111yescharacteristic
447C22×C42—611no—
448C22×C42—611no—
449#398—618no—
450#398—618no—
451#395—618no—
452#395—618no—
453#389—618no—
454#389—618no—
455#385—618no—
456#385C2×D6118yes—
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×#95—611no—
466C2×#95C2×D6111yescharacteristic
467C2×#95C2×D6111yescharacteristic
468C61C2×#244011yescharacteristic, complemented, Sylow
469C25C22×D6111yescharacteristic
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—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—611no—
482C23×C4—618no—
483C23×C4—614no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—614no—
492C23×C4—1224no—
493C23×C4—1224no—
494C23×C4—1224no—
495C23×C4—1224no—
496C23×C4—2442no—
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6114yes—
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—42no—
509C2×C4⋊C4—618no—
510C2×C4⋊C4—614no—
511C2×C4⋊C4—614no—
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—1224no—
535C2×C4⋊C4—1224no—
536C2×C4⋊C4—1224no—
537C2×C4⋊C4—2442no—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—618no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—1224no—
545C2×C22⋊C4Dic12218yescomplemented
546C2×C22⋊C4C22×D6114yes—
547C2×C22⋊C4C22×D6114yes—
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#95—614no—
558#95C22×D6114yes—
559#95C22×D6114yes—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24C2×Dic12214yes—
565C24D4×D6114yes—
566C24Q8×D6114yes—
567C24C23×D6112yes—
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—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—614no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—612no—
600C22×C4—614no—
601C22×C4—614no—
602C22×C4—614no—
603C22×C4—614no—
604C22×C4—6116no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—1228no—
613C22×C4—12232no—
614C22×C4—1228no—
615C22×C4—1228no—
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—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—2444no—
635C22×C4—24416no—
636C22×C4C2×Dic12214yes—
637C22×C4C2×Dic12214yes—
638C22×C4D4×D6114yes—
639C22×C4C23×D6112yes—
640C22×C4C23×D6112yes—
641C22×C4C23×D6112yes—
642C22×C4C23×D6112yes—
643C22×C4C23×D6112yes—
644C22×C4C23×D6112yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—6116no—
648C4⋊C4—1228no—
649C4⋊C4—1228no—
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—1228no—
660C4⋊C4—2444no—
661C22⋊C4—28no—
662C22⋊C4—6116no—
663C22⋊C4—1228no—
664C22⋊C4C2×Dic122116yescomplemented
665C42—1228no—
666C42—1228no—
667C23—28no—
668C23—28no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—28no—
676C23—28no—
677C23#14519776116yescomplemented
678C23C2×D4×D6114yes—
679C23C2×D4×D6112yes—
680C23C2×D4×D6112yes—
681C23C2×Q8×D6114yes—
682C23C2×Q8×D6112yes—
683C23C22×Dic12214yes—
684C23C22×Dic12212yes—
685C23#41×D6112yes—
686C23#1451982212yes—
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—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—6116no—
714C2×C4—614no—
715C2×C4—614no—
716C2×C4—614no—
717C2×C4—614no—
718C2×C4—614no—
719C2×C4—614no—
720C2×C4—614no—
721C2×C4—12232no—
722C2×C4—1228no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1228no—
732C2×C4—1228no—
733C2×C4—1228no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—24416no—
744C2×C4—2444no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4C2×D4×D6114yes—
748C2×C4C22×Dic12214yes—
749C2×C4C22×Dic12214yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D6114yes—
758C22C2×#1451977614yes—
759C22C2×#1451977618yescomplemented
760C22#1684039114yes—
761C22#1684039414yes—
762C22#1684041014yes—
763C22D4×Dic12214yes—
764C22#1684047114yes—
765C22C22×D4×D6111yescharacteristic
766C22C22×D4×D6111yescharacteristic
767C22C22×Q8×D6111yescharacteristic
768C22C23×Dic12211yescharacteristic
769C22C2×#41×D6111yescharacteristic
770C22C2×#1451982211yescharacteristic
771C22C2×#1451982411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—618no—
779C4—1224no—
780C4—1224no—
781C4—1224no—
782C4—1224no—
783C4—2442no—
784C4—2442no—
785C4—2442no—
786C2—28no—
787C2#2144952018yesdirect product factor
788C2C2×C22⋊Q8×D6111yescharacteristic
789C2C22×#1451977611yescharacteristic
790C2C2×#1684039111yescharacteristic
791C2C2×#1684039411yescharacteristic
792C2C2×#1684041011yescharacteristic
793C2C2×D4×Dic12211yescharacteristic
794C2C2×#1684047111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61C2×#2440
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14519776C2semidirect
5. #21449520C2direct (N × H)
6. C2×#16839696C2semidirect
7. C2×#16839695C2semidirect
8. C2×#16839683C2semidirect
9. C2×#16839682C2semidirect
10. C2×#16839659C2semidirect
11. C2×#16839659C2semidirect
13. C2×#16839631C2semidirect
22. C2×#14519776C22semidirect
47. #16839696C22semidirect
48. #16839695C22semidirect
49. #16839683C22semidirect
50. #16839682C22semidirect
51. #16839659C22semidirect
52. #16839659C22semidirect
54. #16839631C22semidirect
84. C23×Dic61Q8semidirect
157. C2×C22⋊C4×C61Q8semidirect
229. C22×Dic61C2×Q8semidirect
250. C22⋊C4×C61C2×Q8semidirect
279. C23×C61C4⋊Q8semidirect
342. C2×Dic61C22⋊Q8semidirect
362. C22×C61C2×C4⋊Q8semidirect
388. Dic61C2×C22⋊Q8semidirect
406. C2×C61#2440semidirect
468. C61C2×#2440semidirect
545. C2×C22⋊C4Dic122semidirect
664. C22⋊C4C2×Dic122semidirect
677. C23#14519776semidirect
759. C22C2×#14519776semidirect
787. C2#21449520direct (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×#145197562
C22×#145197542
C23×#117581962
#214495202
C2×#168396962
C2×#168396952
C2×#168396832
C2×#168396822
C2×#168396592
C2×#168396372
C2×#168396312
C2×#168396202
C2×C22⋊C4×Dic612
C2×C61×#3852
C2×#244061