Finite Group Databasebeta

← C2×#21448754 #29839347

Subgroups — C2×#21448754 #29839347

Order 15616.

3374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2#21448754C2116yesmaximal, direct product factor
3C2×#16839655C211yesmaximal, characteristic, complemented
4C2×#16839649C211yesmaximal, characteristic, complemented
5C2×#16839643C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic
7C2×#16839638C211yesmaximal, characteristic
8C2×#16839629C211yesmaximal, characteristic, complemented
9C2×#16839623C211yesmaximal, characteristic, complemented
10C2×#16839619C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
12C2×C4×#11758198C211yesmaximal, characteristic, complemented
13C2×#16839609C211yesmaximal, characteristic, complemented
14C2×#16839608C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519737C4116yescomplemented
23C2×#14519737C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839655C2218yescomplemented
36#16839649C2218yescomplemented
37#16839643C2218yescomplemented
38#16839638C2218yes—
39#16839638C2218yes—
40#16839629C2218yescomplemented
41#16839623C2218yescomplemented
42#16839619C2218yescomplemented
43C22⋊C4×Dic61C2218yescomplemented
44C4×#11758198C2218yescomplemented
45#16839609C2218yescomplemented
46#16839608C2218yescomplemented
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59#95×D61C2218yescomplemented
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#388C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C22×C22⋊D61—24no—
70C22×C22⋊D61—24no—
71C22×C22⋊D61C2×C418yes—
72C22×C22⋊D61C2314yes—
73C23×Dic61—42no—
74C23×Dic61—42no—
75C23×Dic61C2×C418yescomplemented
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2314yes—
84C22×C4×D61—24no—
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—42no—
89C22×C4×D61—42no—
90C22×C4×D61—42no—
91C22×C4×D61—42no—
92C22×C4×D61C2×C418yes—
93C22×C4×D61C2314yes—
94C22×C4×D61C2314yes—
95C22×C4×D61C2314yes—
96#14519737C2×C4164yescomplemented
97C2×C4⋊Dic61—42no—
98C2×C4⋊Dic61C2314yes—
99C2×#11758196C2×C418yescomplemented
100C2×#11758196C2314yes—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—42no—
103C2×C22⋊Dic61C2314yes—
104C2×C22⋊Dic61C2314yes—
105C2×#11758198—24no—
106C2×#11758198—24no—
107C2×#11758198C2×C418yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—42no—
113C2×C4×Dic61—42no—
114C2×C4×Dic61C2×C418yescomplemented
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C25×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2314yes—
140C2×C22⋊C4×C61—24no—
141C2×C22⋊C4×C61—42no—
142C2×C22⋊C4×C61C2×C418yescomplemented
143C2×C22⋊C4×C61C2314yes—
144C2×C22⋊C4×C61C2314yes—
145C2×C22⋊C4×C61C2314yes—
146C2×C42×C61—24no—
147C2×C42×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61C22×C414yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61C22×C414yes—
164C23×D61#4114yes—
165C23×D61#4114yes—
166C23×D61C2412yes—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
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×C61C22×C414yes—
183C22×C4×C61C22×C414yes—
184C22×C4×C61#4114yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C2×C22⋊D61—232no—
192C2×C22⋊D61—28no—
193C2×C22⋊D61—28no—
194C2×C22⋊D61C22×C4116yes—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
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—416no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61C22×C414yes—
216C22×Dic61C22×C414yes—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C4116yescomplemented
219C22×Dic61#4114yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×C4×D61—28no—
228C2×C4×D61—28no—
229C2×C4×D61—28no—
230C2×C4×D61—28no—
231C2×C4×D61—416no—
232C2×C4×D61—44no—
233C2×C4×D61—44no—
234C2×C4×D61—44no—
235C2×C4×D61—44no—
236C2×C4×D61—416no—
237C2×C4×D61—416no—
238C2×C4×D61C22×C4116yes—
239C4⋊C4×C61—44no—
240C22⋊C4×C61—28no—
241C22⋊C4×C61—44no—
242C22⋊C4×C61C22×C4116yescomplemented
243C42×C61—28no—
244C22⋊Dic61—28no—
245C22⋊Dic61—44no—
246#11758198—28no—
247#11758198—28no—
248#11758198C22×C4116yes—
249C4⋊Dic61—44no—
250#11758196C22×C4116yescomplemented
251C4×Dic61—28no—
252C4×Dic61—44no—
253C4×Dic61—44no—
254C4×Dic61C22×C4116yescomplemented
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61C23×C414yes—
269C23×C61C23×C412yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C23×C61C2×#4112yes—
274C23×C61H(5,𝔽2)12yes—
275C23×C61H(5,𝔽2)12yes—
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×D61#117116yes—
288C22×D61C23×C414yes—
289C22×D61C2×#4114yes—
290C22×D61C2×#4114yes—
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—44no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61C23×C414yes—
313C2×C4×C61C23×C414yes—
314C2×C4×C61C2×#4114yes—
315C22⋊D61—232no—
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—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—416no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61C23×C414yes—
342C2×Dic61C23×C414yes—
343C2×Dic61C23×C414yes—
344C2×Dic61C2×#4114yes—
345C4×D61—416no—
346C4×D61—416no—
347C4×D61—416no—
348C2×#2353—611nomaximal, Sylow
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61—416no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61C2×#11714yes—
358C22×C61C4×#4114yes—
359C22×C61#51814yes—
360C22×C61#55114yes—
361C22×C61#55114yes—
362C22×C61#55314yes—
363C22×C61#55314yes—
364C22×C61C24×C411yescharacteristic
365C22×C61C22×#4111yescharacteristic
366C22×C61C22×#4111yescharacteristic
367C22×C61C22×#4111yescharacteristic
368C22×C61C22×#4111yescharacteristic
369C22×C61C2×H(5,𝔽2)11yescharacteristic
370C22×C61C2×H(5,𝔽2)11yescharacteristic
371C2×D61—232no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61—24no—
375C2×D61—24no—
376C2×D61—24no—
377C2×D61—24no—
378C2×D61C2×#11718yes—
379C4×C61—24no—
380C4×C61—24no—
381C4×C61—24no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385Dic61—24no—
386Dic61—24no—
387Dic61—24no—
388Dic61—24no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392C22×C4×D4—611no—
393#2353—6116no—
394C2×#388—611no—
395C2×#388D6111yescharacteristic, complemented
396C2×#387—611no—
397C2×#387—611no—
398C2×#386—611no—
399C2×#386—611no—
400C2×#383—611no—
401C2×#381—611no—
402C2×#380—611no—
403C2×C4×C22⋊C4—611no—
404C2×C4×C22⋊C4—611no—
405C2×C4×C22⋊C4—611no—
406C2×#376—611no—
407C22×#95—611no—
408C2×C61—44no—
409C2×C61#235318yescomplemented
410C2×C61C22×#11711yescharacteristic
411C2×C61C2×C4×#4111yescharacteristic
412C2×C61C2×#51811yescharacteristic
413C2×C61C2×#55111yescharacteristic
414C2×C61C2×#55111yescharacteristic
415C2×C61C2×#55311yescharacteristic
416C2×C61C2×#55311yescharacteristic
417D61—28no—
418C23×D4—611no—
419C24×C4—611no—
420C24×C4—611no—
421C24×C4—611no—
422C24×C4—611no—
423C2×C4×D4—6116no—
424C2×C4×D4—618no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4C2×D6111yescharacteristic
428C22×C22⋊C4—611no—
429C22×C22⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—611no—
433C22×C22⋊C4C2×D6111yescharacteristic
434C22×C22⋊C4C2×D6111yescharacteristic
435C22×C22⋊C4C2×D6111yescharacteristic
436C22×C42—611no—
437C22×C42—611no—
438C22×C42—611no—
439C22×C42—611no—
440C22×C42C2×D6111yescharacteristic
441#388—618no—
442#388C2×D6118yescomplemented
443#387—618no—
444#387—618no—
445#386—618no—
446#386—618no—
447#383—618no—
448#381—618no—
449#380—618no—
450C4×C22⋊C4—618no—
451C4×C22⋊C4—618no—
452C4×C22⋊C4—618no—
453#376—618no—
454C2×#95—611no—
455C2×#95—611no—
456C2×#95—611no—
457C2×#95—611no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95—618no—
467C2×#95C2×D6111yescharacteristic
468C2×#95C2×D6111yescharacteristic
469C61C2×#235311yescharacteristic, complemented, Sylow
470C25—611no—
471C25C22×D6111yescharacteristic
472C22×D4—618no—
473C22×D4—614no—
474C22×D4—1224no—
475C22×D4—1224no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—618no—
481C23×C4—614no—
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—2442no—
494C23×C4—2442no—
495C23×C4—2442no—
496C23×C4—2442no—
497C23×C4—2442no—
498C23×C4—2442no—
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C23×C4C22×D6111yescharacteristic
505C4×D4—6164no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—618no—
508C2×C4⋊C4—614no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—2442no—
511C2×C4⋊C4C22×D6114yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—618no—
515C2×C22⋊C4—614no—
516C2×C22⋊C4—614no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—2442no—
524C2×C22⋊C4C4×D6118yescomplemented
525C2×C22⋊C4C22×D6114yes—
526C2×C22⋊C4C22×D6114yes—
527C2×C22⋊C4C22×D6114yes—
528C2×C42—24no—
529C2×C42—618no—
530C2×C42—614no—
531C2×C42—614no—
532C2×C42—614no—
533C2×C42—614no—
534C2×C42—1224no—
535C2×C42—2442no—
536C2×C42—2442no—
537C2×C42C22×D6114yes—
538#95—614no—
539#95—614no—
540#95—614no—
541#95—614no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95C22×D6114yes—
551#95C22×D6114yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—614no—
559C24—614no—
560C24—614no—
561C24—612no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—1222no—
566C24C2×C4×D6114yes—
567C24C23×D6112yes—
568C24C23×D6111yescharacteristic
569C2×D4—6116no—
570C2×D4—12232no—
571C2×D4—1228no—
572C2×D4—1228no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
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—614no—
589C22×C4—614no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—6116no—
597C22×C4—6116no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—1228no—
602C22×C4—1228no—
603C22×C4—1228no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1228no—
622C22×C4—24416no—
623C22×C4—2444no—
624C22×C4—2444no—
625C22×C4—2444no—
626C22×C4—2444no—
627C22×C4—24416no—
628C22×C4—24416no—
629C22×C4—24416no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4C2×C4×D6114yes—
633C22×C4C2×C4×D6114yes—
634C22×C4#1175822414yes—
635C22×C4C23×D6112yes—
636C22×C4C23×D6112yes—
637C22×C4C23×D6112yes—
638C22×C4C23×D6112yes—
639C22×C4C23×D6112yes—
640C22×C4C23×D6112yes—
641C4⋊C4—44no—
642C4⋊C4—6116no—
643C4⋊C4—2444no—
644C22⋊C4—28no—
645C22⋊C4—44no—
646C22⋊C4—6116no—
647C22⋊C4—1228no—
648C22⋊C4—1228no—
649C22⋊C4—1228no—
650C22⋊C4—2444no—
651C22⋊C4C2×C4×D61116yescomplemented
652C42—28no—
653C42—6116no—
654C42—1228no—
655C42—2444no—
656C42—2444no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—6116no—
671C23—614no—
672C23—614no—
673C23—614no—
674C23—1228no—
675C23—1228no—
676C23—1228no—
677C23—1228no—
678C23—1222no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1228no—
683C23—1228no—
684C23C22×C4×D6114yes—
685C23C22×C4×D6112yes—
686C23#41×D6112yes—
687C23#41×D6112yes—
688C23#41×D6112yes—
689C23C2×#1175822412yes—
690C23#1451982212yes—
691C23#1451982312yes—
692C23C24×D6111yescharacteristic
693D4—12232no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
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—614no—
716C2×C4—614no—
717C2×C4—614no—
718C2×C4—614no—
719C2×C4—1228no—
720C2×C4—1228no—
721C2×C4—1228no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1228no—
731C2×C4—1222no—
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—24416no—
741C2×C4—24416no—
742C2×C4—24416no—
743C2×C4—24416no—
744C2×C4—2444no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4C22×C4×D6114yes—
748C2×C4C22×C4×D6114yes—
749C2×C4C2×#1175822414yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—618no—
759C22—12232no—
760C22—1224no—
761C22—1224no—
762C22—1224no—
763C22—1224no—
764C22—1224no—
765C22—1224no—
766C22#117×D6114yes—
767C22C4×#1175822414yes—
768C22#1684023414yes—
769C22#1684043514yes—
770C22#1684044214yes—
771C22#1684045914yes—
772C22#1684046314yes—
773C22C23×C4×D6111yescharacteristic
774C22C2×#41×D6111yescharacteristic
775C22C2×#41×D6111yescharacteristic
776C22C2×#41×D6111yescharacteristic
777C22C22×#1175822411yescharacteristic
778C22C2×#1451982211yescharacteristic
779C22C2×#1451982311yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—1224no—
787C4—1224no—
788C4—1224no—
789C4—1224no—
790C4—2442no—
791C4—2442no—
792C4—2442no—
793C2—44no—
794C2—1228no—
795C2#2144875418yesdirect product factor
796C2C2×#117×D6111yescharacteristic
797C2C2×C4×#1175822411yescharacteristic
798C2C2×#1684023411yescharacteristic
799C2C2×#1684043511yescharacteristic
800C2C2×#1684044211yescharacteristic
801C2C2×#1684045911yescharacteristic
802C2C2×#1684046311yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2353
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21448754C2direct (N × H)
3. C2×#16839655C2semidirect
4. C2×#16839649C2semidirect
5. C2×#16839643C2semidirect
8. C2×#16839629C2semidirect
9. C2×#16839623C2semidirect
10. C2×#16839619C2semidirect
11. C2×C22⋊C4×Dic61C2semidirect
12. C2×C4×#11758198C2semidirect
13. C2×#16839609C2semidirect
14. C2×#16839608C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#388C2semidirect
22. C2×#14519737C4semidirect
35. #16839655C22semidirect
36. #16839649C22semidirect
37. #16839643C22semidirect
40. #16839629C22semidirect
41. #16839623C22semidirect
42. #16839619C22semidirect
43. C22⋊C4×Dic61C22semidirect
44. C4×#11758198C22semidirect
45. #16839609C22semidirect
46. #16839608C22semidirect
59. #95×D61C22semidirect
65. C61×#388C22semidirect
75. C23×Dic61C2×C4semidirect
96. #14519737C2×C4semidirect
99. C2×#11758196C2×C4semidirect
114. C2×C4×Dic61C2×C4semidirect
142. C2×C22⋊C4×C61C2×C4semidirect
218. C22×Dic61C22×C4semidirect
242. C22⋊C4×C61C22×C4semidirect
250. #11758196C22×C4semidirect
254. C4×Dic61C22×C4semidirect
395. C2×#388D61semidirect
409. C2×C61#2353semidirect
442. #388C2×D61semidirect
469. C61C2×#2353semidirect
524. C2×C22⋊C4C4×D61semidirect
651. C22⋊C4C2×C4×D61semidirect
795. C2#21448754direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
#214487542
C2×#168396552
C2×#168396492
C2×#168396432
C2×#168396382
C2×#168396292
C2×#168396232
C2×#168396192
C2×C22⋊C4×Dic612
C2×C4×#117581982
C2×#168396092
C2×#168396082
C2×#95×D612
C2×C61×#3882
C2×#235361