Finite Group Databasebeta

← C2×#21448486 #29838739

Subgroups — C2×#21448486 #29838739

Order 15616.

3718 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×#14519759C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic
3C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21448486C2116yesmaximal, direct product factor
5C2×#16839659C211yesmaximal, characteristic, complemented
6C2×#16839658C211yesmaximal, characteristic, complemented
7C2×#16839655C211yesmaximal, characteristic, complemented
8C2×#16839650C211yesmaximal, characteristic, complemented
9C2×#16839647C211yesmaximal, characteristic, complemented
10C2×#16839643C211yesmaximal, characteristic, complemented
11C2×#16839638C211yesmaximal, characteristic
12C2×#16839635C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic, complemented
14C2×#16839624C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519759C4116yescomplemented
22C2×#14519759C2218yes—
23C2×C4×C22⋊D61—28no—
24C2×C4×C22⋊D61C2218yes—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C2×C4⋊C4×D61—28no—
33C2×C4⋊C4×D61C2218yescomplemented
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839659C2218yescomplemented
44#16839658C2218yescomplemented
45#16839655C2218yescomplemented
46#16839650C2218yescomplemented
47#16839647C2218yescomplemented
48#16839643C2218yescomplemented
49#16839638C2218yes—
50#16839635C2218yescomplemented
51#16839633C2218yescomplemented
52#16839624C2218yescomplemented
53#16839609C2218yescomplemented
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
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×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61—24no—
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61—42no—
88C22×C4×D61—42no—
89C22×C4×D61C2×C418yescomplemented
90C22×C4×D61D418yes—
91C22×C4×D61C2314yes—
92C22×C4×D61C2314yes—
93C22×C4×D61C2314yes—
94#14519759C2×C4164yescomplemented
95C4×C22⋊D61—232no—
96C2×C4⋊Dic61—24no—
97C2×C4⋊Dic61C2×C418yescomplemented
98C2×C4⋊Dic61C2314yes—
99C2×C4⋊Dic61C2314yes—
100C2×#11758196—24no—
101C2×#11758196—24no—
102C2×#11758196—24no—
103C2×#11758196—42no—
104C2×#11758196C2×C418yescomplemented
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C4⋊C4×D61—232no—
111C2×C22⋊Dic61—24no—
112C2×C22⋊Dic61—42no—
113C2×C22⋊Dic61C2×C418yescomplemented
114C2×C22⋊Dic61C2314yes—
115C2×C22⋊Dic61C2314yes—
116C2×C22⋊Dic61C2314yes—
117C2×#11758198—24no—
118C2×#11758198—24no—
119C2×#11758198C2×C418yescomplemented
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×C4×Dic61—24no—
124C2×C4×Dic61—42no—
125C2×C4×Dic61—42no—
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—42no—
140C23×C4×C61—42no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2314yes—
148C2×C4⋊C4×C61—24no—
149C2×C4⋊C4×C61—42no—
150C2×C4⋊C4×C61C2314yes—
151C2×C4⋊C4×C61C2314yes—
152C2×C22⋊C4×C61—42no—
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×C61—22no—
163C24×C61—22no—
164C24×C61C22×C414yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61C22×C414yes—
172C23×D61C2×D414yes—
173C23×D61#4114yes—
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—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—28no—
191C22×C4×C61—44no—
192C22×C4×C61—44no—
193C22×C4×C61—416no—
194C22×C4×C61C22×C414yes—
195C22×C4×C61C22×C414yes—
196C22×C4×C61C2×D414yes—
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—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61C22×C414yes—
225C22×Dic61C22×C414yes—
226C22×Dic61C22×C414yes—
227C22×Dic61C2×D414yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—232no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—28no—
239C2×C4×D61—416no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61—416no—
245C2×C4×D61C22×C4116yescomplemented
246C2×C4×D61C2×D4116yes—
247C4⋊C4×C61—28no—
248C4⋊C4×C61—44no—
249C22⋊C4×C61—44no—
250C22⋊C4×C61C22×C4116yescomplemented
251C22⋊Dic61—28no—
252C22⋊Dic61—44no—
253C22⋊Dic61C22×C4116yescomplemented
254#11758198—28no—
255#11758198—28no—
256#11758198C22×C4116yescomplemented
257C4⋊Dic61—28no—
258C4⋊Dic61C22×C4116yescomplemented
259#11758196—28no—
260#11758196—28no—
261#11758196—28no—
262#11758196—44no—
263#11758196C22×C4116yescomplemented
264C4×Dic61—28no—
265C4×Dic61—44no—
266C4×Dic61—44no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—28no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61—44no—
280C23×C61C23×C414yes—
281C23×C61C23×C412yes—
282C23×C61C22×D412yes—
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C612−1+412yes—
287C23×C612−1+412yes—
288C23×C61C2511yescharacteristic
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—28no—
292C22×D61—28no—
293C22×D61—28no—
294C22×D61—28no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61C4×D4116yes—
300C22×D61C23×C414yes—
301C22×D61C22×D414yes—
302C22×D61C2×#4114yes—
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×C61C22×D414yes—
328C22⋊D61—232no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—28no—
332C2×Dic61—28no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
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—44no—
351C2×Dic61—44no—
352C2×Dic61—44no—
353C2×Dic61C23×C414yes—
354C2×Dic61C23×C414yes—
355C2×Dic61C23×C414yes—
356C2×Dic61C22×D414yes—
357C4×D61—232no—
358C4×D61—416no—
359C4×D61—416no—
360C2×#2322—611nomaximal, Sylow
361C22×C61—24no—
362C22×C61—24no—
363C22×C61—24no—
364C22×C61—416no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61C2×C4×D414yes—
370C22×C61#52014yes—
371C22×C61#52014yes—
372C22×C61#53414yes—
373C22×C61#53614yes—
374C22×C61#53914yes—
375C22×C61#53914yes—
376C22×C61C24×C411yescharacteristic
377C22×C61C23×D411yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×H(5,𝔽2)11yescharacteristic
381C22×C61C2×2−1+411yescharacteristic
382C22×C61C2×2−1+411yescharacteristic
383C2×D61—232no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—24no—
390C2×D61C2×C4×D418yes—
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—42no—
402Dic61—42no—
403Dic61—42no—
404C22×#123—611no—
405C22×C4×D4—611no—
406C23×C4⋊C4—611no—
407#2322—6116no—
408C2×#389—611no—
409C2×#389—611no—
410C2×#388—611no—
411C2×#388—611no—
412C2×#387—611no—
413C2×#387—611no—
414C2×#386—611no—
415C2×#385—611no—
416C2×#385—611no—
417C2×#385D6111yescharacteristic, complemented
418C2×#381—611no—
419C2×C4×C22⋊C4—611no—
420C2×C61—44no—
421C2×C61#232218yescomplemented
422C2×C61C22×C4×D411yescharacteristic
423C2×C61C2×#52011yescharacteristic
424C2×C61C2×#52011yescharacteristic
425C2×C61C2×#53411yescharacteristic
426C2×C61C2×#53611yescharacteristic
427C2×C61C2×#53911yescharacteristic
428C2×C61C2×#53911yescharacteristic
429D61—28no—
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—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4—618no—
447C22×C4⋊C4—1228no—
448C22×C4⋊C4C2×D6111yescharacteristic
449C22×C4⋊C4C2×D6111yescharacteristic
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C22⋊C4C2×D6111yescharacteristic
457C22×C22⋊C4C2×D6111yescharacteristic
458C22×C42—611no—
459C22×C42—611no—
460C22×C42—611no—
461#389—618no—
462#389—618no—
463#388—618no—
464#388—618no—
465#387—618no—
466#387—618no—
467#386—618no—
468#385—618no—
469#385—618no—
470#385C2×D6118yescomplemented
471#381—618no—
472C4×C22⋊C4—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×#232211yescharacteristic, complemented, Sylow
484C25—611no—
485C25C22×D6111yescharacteristic
486C22×D4—618no—
487C22×D4—614no—
488C22×D4—1224no—
489C22×D4—1224no—
490C23×C4—24no—
491C23×C4—42no—
492C23×C4—42no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—618no—
498C23×C4—614no—
499C23×C4—618no—
500C23×C4—614no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—614no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4—1224no—
508C23×C4—2442no—
509C23×C4—2442no—
510C23×C4—2442no—
511C23×C4—2442no—
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6114yes—
519#123—6164no—
520C4×D4—12232no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—618no—
524C2×C4⋊C4—618no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—12232no—
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—42no—
541C2×C22⋊C4—618no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—618no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—1224no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4C4×D6118yescomplemented
554C2×C22⋊C4C22×D6114yes—
555C2×C22⋊C4C22×D6114yes—
556C2×C42—614no—
557C2×C42—614no—
558C2×C42—614no—
559C2×C42—1224no—
560C2×C42—2442no—
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—22no—
577C24—22no—
578C24—614no—
579C24—614no—
580C24—614no—
581C24—612no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24C2×C4×D6114yes—
587C24C23×D6112yes—
588C24C23×D6111yescharacteristic
589C2×D4—6116no—
590C2×D4—1228no—
591C2×D4—12232no—
592C2×D4—1228no—
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—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—614no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—6116no—
621C22×C4—6116no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—1228no—
626C22×C4—12232no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—24416no—
647C22×C4—2444no—
648C22×C4—2444no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—24416no—
652C22×C4C2×C4×D6114yes—
653C22×C4C2×C4×D6114yes—
654C22×C4D4×D6114yes—
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—
668C4⋊C4—1228no—
669C4⋊C4—2444no—
670C22⋊C4—44no—
671C22⋊C4—6116no—
672C22⋊C4—6116no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—1228no—
676C22⋊C4—2444no—
677C22⋊C4C2×C4×D61116yescomplemented
678C42—1228no—
679C42—2444no—
680C42—2444no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—6116no—
695C23—614no—
696C23—614no—
697C23—614no—
698C23—1228no—
699C23—1228no—
700C23—1228no—
701C23—1228no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1228no—
707C23—1228no—
708C23C22×C4×D6114yes—
709C23C22×C4×D6112yes—
710C23C2×D4×D6112yes—
711C23#41×D6112yes—
712C23#1451982212yes—
713C23#1451982212yes—
714C23#1451982412yes—
715C23#1451982512yes—
716C23C24×D6111yescharacteristic
717D4—12232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
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—12232no—
745C2×C4—1228no—
746C2×C4—1228no—
747C2×C4—1228no—
748C2×C4—1228no—
749C2×C4—1222no—
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—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—24416no—
767C2×C4—24416no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4C22×C4×D6114yes—
772C2×C4C22×C4×D6114yes—
773C2×C4C2×D4×D6114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—618no—
783C22—12232no—
784C22—1224no—
785C22—1224no—
786C22—1224no—
787C22—1224no—
788C22—1224no—
789C22—1224no—
790C22C4×D4×D6114yes—
791C22#1684024114yes—
792C22#1684024314yes—
793C22#1684032214yes—
794C22#1684033514yes—
795C22#1684035514yes—
796C22#1684035814yes—
797C22C23×C4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C2×#1451982211yescharacteristic
801C22C2×#1451982211yescharacteristic
802C22C2×#1451982411yescharacteristic
803C22C2×#1451982511yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—1224no—
811C4—1224no—
812C4—1224no—
813C4—1224no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—44no—
818C2—1228no—
819C2#2144848618yesdirect product factor
820C2C2×C4×D4×D6111yescharacteristic
821C2C2×#1684024111yescharacteristic
822C2C2×#1684024311yescharacteristic
823C2C2×#1684032211yescharacteristic
824C2C2×#1684033511yescharacteristic
825C2C2×#1684035511yescharacteristic
826C2C2×#1684035811yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#385D61
hypocenterC61C2×#2322
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D61C2semidirect
4. #21448486C2direct (N × H)
5. C2×#16839659C2semidirect
6. C2×#16839658C2semidirect
7. C2×#16839655C2semidirect
8. C2×#16839650C2semidirect
9. C2×#16839647C2semidirect
10. C2×#16839643C2semidirect
12. C2×#16839635C2semidirect
13. C2×#16839633C2semidirect
14. C2×#16839624C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#385C2semidirect
21. C2×#14519759C4semidirect
33. C2×C4⋊C4×D61C22semidirect
43. #16839659C22semidirect
44. #16839658C22semidirect
45. #16839655C22semidirect
46. #16839650C22semidirect
47. #16839647C22semidirect
48. #16839643C22semidirect
50. #16839635C22semidirect
51. #16839633C22semidirect
52. #16839624C22semidirect
53. #16839609C22semidirect
67. C61×#385C22semidirect
89. C22×C4×D61C2×C4semidirect
94. #14519759C2×C4semidirect
97. C2×C4⋊Dic61C2×C4semidirect
104. C2×#11758196C2×C4semidirect
113. C2×C22⋊Dic61C2×C4semidirect
119. C2×#11758198C2×C4semidirect
153. C2×C22⋊C4×C61C2×C4semidirect
245. C2×C4×D61C22×C4semidirect
250. C22⋊C4×C61C22×C4semidirect
253. C22⋊Dic61C22×C4semidirect
256. #11758198C22×C4semidirect
258. C4⋊Dic61C22×C4semidirect
263. #11758196C22×C4semidirect
417. C2×#385D61semidirect
421. C2×C61#2322semidirect
470. #385C2×D61semidirect
483. C61C2×#2322semidirect
553. C2×C22⋊C4C4×D61semidirect
677. C22⋊C4C2×C4×D61semidirect
819. C2#21448486direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197592
C22×C4×C22⋊D612
C22×C4⋊C4×D612
#214484862
C2×#168396592
C2×#168396582
C2×#168396552
C2×#168396502
C2×#168396472
C2×#168396432
C2×#168396382
C2×#168396352
C2×#168396332
C2×#168396242
C2×#168396092
C2×C61×#3852
C2×#232261