Finite Group Databasebeta

← C2×#21448809 #29839514

Subgroups — C2×#21448809 #29839514

Order 15616.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519761C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic
3C22×#14519733C211yesmaximal, characteristic, complemented
4#21448809C2116yesmaximal, direct product factor
5C2×#16839658C211yesmaximal, characteristic, complemented
6C2×#16839652C211yesmaximal, characteristic, complemented
7C2×#16839651C211yesmaximal, characteristic, complemented
8C2×#16839645C211yesmaximal, characteristic, complemented
9C2×#16839645C211yesmaximal, characteristic, complemented
10C2×#16839639C211yesmaximal, characteristic
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C2×#16839609C211yesmaximal, characteristic, complemented
15C22×#14519684C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519761C4116yescomplemented
22C2×#14519761C2218yes—
23C2×C4×C22⋊D61—28no—
24C2×C4×C22⋊D61C2218yes—
25C2×#14519733—28no—
26C2×#14519733C2218yescomplemented
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839658C2218yescomplemented
44#16839652C2218yescomplemented
45#16839651C2218yescomplemented
46#16839645C2218yescomplemented
47#16839645C2218yescomplemented
48#16839639C2218yes—
49#16839633C2218yescomplemented
50C4⋊C4×Dic61C2218yescomplemented
51C22⋊C4×Dic61C2218yescomplemented
52#16839609C2218yescomplemented
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2218yescomplemented
62C24×C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C61×#385C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C22×C22⋊D61—24no—
72C22×C22⋊D61—24no—
73C22×C22⋊D61C2×C418yes—
74C22×C22⋊D61C2314yes—
75C23×Dic61—24no—
76C23×Dic61—24no—
77C23×Dic61—24no—
78C23×Dic61—24no—
79C23×Dic61—42no—
80C23×Dic61C2×C418yescomplemented
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2314yes—
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2314yes—
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—42no—
93C22×C4×D61C2314yes—
94#14519761C2×C4164yescomplemented
95C4×C22⋊D61—232no—
96#14519733—232no—
97C2×C4⋊Dic61C2×C418yescomplemented
98C2×C4⋊Dic61C2×C418yescomplemented
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2314yes—
101C2×#11758196—24no—
102C2×#11758196—24no—
103C2×#11758196—24no—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×C22⋊Dic61D418yes—
108C2×C22⋊Dic61C2314yes—
109C2×#11758198—24no—
110C2×#11758198—24no—
111C2×#11758198—42no—
112C2×#11758198C2×C418yescomplemented
113C2×#11758198C2×C418yescomplemented
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61—24no—
123C2×C4×Dic61—42no—
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137C25×C61C2311yescharacteristic
138C23×C4×C61—24no—
139C23×C4×C61—24no—
140C23×C4×C61—42no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2314yes—
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61—24no—
149C2×C4⋊C4×C61—42no—
150C2×C4⋊C4×C61C2314yes—
151C2×C4⋊C4×C61C2314yes—
152C2×C22⋊C4×C61—24no—
153C2×C22⋊C4×C61C2×C418yescomplemented
154C2×C22⋊C4×C61C2314yes—
155C2×C22⋊C4×C61C2314yes—
156#95×C61C2314yes—
157#95×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61C22×C414yes—
163C24×C61C2×D414yes—
164C24×C61#4114yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61C22×C414yes—
174C23×D61C2412yes—
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—28no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—28no—
192C22×C4×C61—44no—
193C22×C4×C61—416no—
194C22×C4×C61C22×C414yes—
195C22×C4×C61C22×C414yes—
196C22×C4×C61#4114yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C2×C22⋊D61—232no—
204C2×C22⋊D61—28no—
205C2×C22⋊D61—28no—
206C2×C22⋊D61C22×C4116yes—
207C22×Dic61—232no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—28no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—28no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—28no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—28no—
227C22×Dic61—44no—
228C22×Dic61—416no—
229C22×Dic61C22×C414yes—
230C22×Dic61C22×C414yes—
231C22×Dic61C22×C414yes—
232C22×Dic61C22×C4116yescomplemented
233C22×Dic61C2×D414yes—
234C22×Dic61C2×D414yes—
235C22×Dic61#4114yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C2×C4×D61—28no—
244C2×C4×D61—28no—
245C2×C4×D61—44no—
246C2×C4×D61—416no—
247C4⋊C4×C61—28no—
248C4⋊C4×C61—44no—
249C22⋊C4×C61—28no—
250C22⋊C4×C61C22×C4116yescomplemented
251C22⋊Dic61C2×D4116yes—
252#11758198—28no—
253#11758198—28no—
254#11758198—44no—
255#11758198C22×C4116yescomplemented
256#11758198C22×C4116yescomplemented
257C4⋊Dic61C22×C4116yescomplemented
258C4⋊Dic61C22×C4116yescomplemented
259#11758196—28no—
260#11758196—28no—
261#11758196—28no—
262C4×Dic61—28no—
263C4×Dic61—28no—
264C4×Dic61—28no—
265C4×Dic61—28no—
266C4×Dic61—44no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—28no—
270C23×C61—28no—
271C23×C61—28no—
272C23×C61—28no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61C4×D4116yes—
278C23×C61C23×C414yes—
279C23×C61C23×C412yes—
280C23×C61C22×D414yes—
281C23×C61C22×D412yes—
282C23×C61C2×#4114yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61C2×#4112yes—
286C23×C61H(5,𝔽2)12yes—
287C23×C612−1+412yes—
288C23×C61C2511yescharacteristic
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—28no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61C23×C414yes—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—28no—
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—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—416no—
322C2×C4×C61—44no—
323C2×C4×C61—44no—
324C2×C4×C61—44no—
325C2×C4×C61C23×C414yes—
326C2×C4×C61C23×C414yes—
327C2×C4×C61C2×#4114yes—
328C22⋊D61—232no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—232no—
332C2×Dic61—28no—
333C2×Dic61—28no—
334C2×Dic61—28no—
335C2×Dic61—28no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—416no—
352C2×Dic61—44no—
353C2×Dic61C23×C414yes—
354C2×Dic61C23×C414yes—
355C2×Dic61C23×C414yes—
356C2×Dic61C22×D414yes—
357C2×Dic61C22×D414yes—
358C2×Dic61C2×#4114yes—
359C4×D61—416no—
360C2×#2359—611nomaximal, Sylow
361C22×C61—232no—
362C22×C61—24no—
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61—24no—
367C22×C61—24no—
368C22×C61C2×C4×D418yes—
369C22×C61C2×C4×D414yes—
370C22×C61C4×#4114yes—
371C22×C61#52014yes—
372C22×C61#54614yes—
373C22×C61#54714yes—
374C22×C61#55114yes—
375C22×C61#55214yes—
376C22×C61C24×C411yescharacteristic
377C22×C61C23×D411yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4111yescharacteristic
380C22×C61C22×#4111yescharacteristic
381C22×C61C2×H(5,𝔽2)11yescharacteristic
382C22×C61C2×2−1+411yescharacteristic
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—416no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—42no—
397Dic61—24no—
398Dic61—24no—
399Dic61—24no—
400Dic61—24no—
401Dic61—24no—
402Dic61—24no—
403Dic61—42no—
404C22×#123—611no—
405C22×C4×D4—611no—
406C22×#117—611no—
407#2359—6116no—
408C2×#389—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#387—611no—
412C2×#387—611no—
413C2×#386—611no—
414C2×#385—611no—
415C2×#385D6111yescharacteristic, complemented
416C2×C4×C4⋊C4—611no—
417C2×C4×C22⋊C4—611no—
418C2×C4×C22⋊C4—611no—
419C22×#95—611no—
420C2×C61—28no—
421C2×C61#235918yescomplemented
422C2×C61C22×C4×D411yescharacteristic
423C2×C61C2×C4×#4111yescharacteristic
424C2×C61C2×#52011yescharacteristic
425C2×C61C2×#54611yescharacteristic
426C2×C61C2×#54711yescharacteristic
427C2×C61C2×#55111yescharacteristic
428C2×C61C2×#55211yescharacteristic
429D61—44no—
430C23×D4—611no—
431C24×C4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C24×C4C2×D6111yescharacteristic
435C2×#123—6116no—
436C2×#123—618no—
437C2×C4×D4—618no—
438C2×C4×D4—1228no—
439C2×#117—618no—
440C2×#117—1228no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C4⋊C4C2×D6111yescharacteristic
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4C2×D6111yescharacteristic
455C22×C22⋊C4C2×D6111yescharacteristic
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—611no—
459C22×C42—611no—
460C22×C42—611no—
461#389—618no—
462#388—618no—
463#388—618no—
464#387—618no—
465#387—618no—
466#386—618no—
467#385—618no—
468#385C2×D6118yescomplemented
469C4×C4⋊C4—618no—
470C4×C22⋊C4—618no—
471C4×C22⋊C4—618no—
472C2×#95—618no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95—611no—
480C2×#95—611no—
481C2×#95C2×D6111yescharacteristic
482C2×#95C2×D6111yescharacteristic
483C61C2×#235911yescharacteristic, complemented, Sylow
484C25—611no—
485C25C22×D6111yescharacteristic
486C22×D4—618no—
487C22×D4—614no—
488C22×D4—1224no—
489C22×D4—1224no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—42no—
493C23×C4—618no—
494C23×C4—614no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—614no—
503C23×C4—614no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4—1224no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—2442no—
511C23×C4—2442no—
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6114yes—
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6111yescharacteristic
519#123—6164no—
520C4×D4—12232no—
521#117—12232no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—42no—
524C2×C4⋊C4—618no—
525C2×C4⋊C4—618no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—1224no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4C22×D6114yes—
535C2×C4⋊C4C22×D6114yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—618no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—618no—
540C2×C22⋊C4—618no—
541C2×C22⋊C4—614no—
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×C22⋊C4—2442no—
549C2×C22⋊C4C4×D6118yescomplemented
550C2×C22⋊C4C22×D6114yes—
551C2×C22⋊C4C22×D6114yes—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—614no—
556C2×C42—614no—
557C2×C42—1224no—
558C2×C42—1224no—
559C2×C42—1224no—
560C2×C42—1224no—
561C2×C42—2442no—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95C22×D6114yes—
571#95C22×D6114yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—614no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24C2×C4×D6114yes—
585C24D4×D6114yes—
586C24#1175822614yes—
587C24C23×D6112yes—
588C24C23×D6111yescharacteristic
589C2×D4—6116no—
590C2×D4—1228no—
591C2×D4—1228no—
592C2×D4—12232no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—6116no—
616C22×C4—614no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—1228no—
627C22×C4—1228no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1228no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1228no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—12232no—
643C22×C4—1222no—
644C22×C4—1228no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1228no—
648C22×C4—2444no—
649C22×C4—24416no—
650C22×C4—2444no—
651C22×C4—24416no—
652C22×C4C2×C4×D6114yes—
653C22×C4C2×C4×D6114yes—
654C22×C4#1175822414yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—6116no—
664C4⋊C4—6116no—
665C4⋊C4—1228no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C22⋊C4—28no—
669C22⋊C4—6116no—
670C22⋊C4—6116no—
671C22⋊C4—6116no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—2444no—
675C22⋊C4C2×C4×D61116yescomplemented
676C42—1228no—
677C42—1228no—
678C42—1228no—
679C42—1228no—
680C42—2444no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—614no—
692C23—1228no—
693C23—1228no—
694C23—1228no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—2444no—
702C23—2444no—
703C23—2444no—
704C23—2444no—
705C23#14519739116yes—
706C23C22×C4×D6114yes—
707C23C22×C4×D6112yes—
708C23C2×D4×D6114yes—
709C23C2×D4×D6112yes—
710C23#41×D6112yes—
711C23C2×#1175822412yes—
712C23C2×#1175822614yes—
713C23C2×#1175822612yes—
714C23#1451982212yes—
715C23#1451982412yes—
716C23C24×D6111yescharacteristic
717D4—12232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—614no—
745C2×C4—614no—
746C2×C4—12232no—
747C2×C4—1228no—
748C2×C4—1228no—
749C2×C4—1228no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1228no—
763C2×C4—1228no—
764C2×C4—1228no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—24416no—
769C2×C4—24416no—
770C2×C4—2444no—
771C2×C4C22×C4×D6114yes—
772C2×C4C22×C4×D6114yes—
773C2×C4C2×#1175822414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—2442no—
785C22—2442no—
786C22—24416no—
787C22—2442no—
788C22—2442no—
789C22C2×#1451973918yes—
790C22C2×#1451973914yes—
791C22C4×#1175822414yes—
792C22#1684024114yes—
793C22#1684039914yes—
794C22#1684041014yes—
795C22#1684043914yes—
796C22#1684045414yes—
797C22C23×C4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C22×#1175822411yescharacteristic
801C22C22×#1175822611yescharacteristic
802C22C2×#1451982211yescharacteristic
803C22C2×#1451982411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—1224no—
811C4—1224no—
812C4—1224no—
813C4—1224no—
814C4—1224no—
815C4—1224no—
816C4—2442no—
817C2—28no—
818C2—2444no—
819C2#2144880918yesdirect product factor
820C2C22×#1451973911yescharacteristic
821C2C2×C4×#1175822411yescharacteristic
822C2C2×#1684024111yescharacteristic
823C2C2×#1684039911yescharacteristic
824C2C2×#1684041011yescharacteristic
825C2C2×#1684043911yescharacteristic
826C2C2×#1684045411yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#385D61
hypocenterC61C2×#2359
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×#14519733C2semidirect
4. #21448809C2direct (N × H)
5. C2×#16839658C2semidirect
6. C2×#16839652C2semidirect
7. C2×#16839651C2semidirect
8. C2×#16839645C2semidirect
9. C2×#16839645C2semidirect
11. C2×#16839633C2semidirect
12. C2×C4⋊C4×Dic61C2semidirect
13. C2×C22⋊C4×Dic61C2semidirect
14. C2×#16839609C2semidirect
15. C22×#14519684C2semidirect
16. C2×C61×#385C2semidirect
21. C2×#14519761C4semidirect
26. C2×#14519733C22semidirect
43. #16839658C22semidirect
44. #16839652C22semidirect
45. #16839651C22semidirect
46. #16839645C22semidirect
47. #16839645C22semidirect
49. #16839633C22semidirect
50. C4⋊C4×Dic61C22semidirect
51. C22⋊C4×Dic61C22semidirect
52. #16839609C22semidirect
61. C2×#14519684C22semidirect
67. C61×#385C22semidirect
80. C23×Dic61C2×C4semidirect
94. #14519761C2×C4semidirect
97. C2×C4⋊Dic61C2×C4semidirect
98. C2×C4⋊Dic61C2×C4semidirect
112. C2×#11758198C2×C4semidirect
113. C2×#11758198C2×C4semidirect
153. C2×C22⋊C4×C61C2×C4semidirect
232. C22×Dic61C22×C4semidirect
250. C22⋊C4×C61C22×C4semidirect
255. #11758198C22×C4semidirect
256. #11758198C22×C4semidirect
257. C4⋊Dic61C22×C4semidirect
258. C4⋊Dic61C22×C4semidirect
415. C2×#385D61semidirect
421. C2×C61#2359semidirect
468. #385C2×D61semidirect
483. C61C2×#2359semidirect
549. C2×C22⋊C4C4×D61semidirect
675. C22⋊C4C2×C4×D61semidirect
819. C2#21448809direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197612
C22×C4×C22⋊D612
C22×#145197332
#214488092
C2×#168396582
C2×#168396522
C2×#168396512
C2×#168396452
C2×#168396392
C2×#168396332
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
C2×#168396092
C22×#145196842
C2×C61×#3852
C2×#235961