Finite Group Databasebeta

← C2×#21448887 #29839617

Subgroups — C2×#21448887 #29839617

Order 15616.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D61C211yesmaximal, characteristic
4#21448887C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839662C211yesmaximal, characteristic
7C2×#16839655C211yesmaximal, characteristic, complemented
8C2×#16839654C211yesmaximal, characteristic, complemented
9C2×#16839652C211yesmaximal, characteristic, complemented
10C2×#16839650C211yesmaximal, characteristic, complemented
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839613C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519763C4116yescomplemented
21C2×#14519763C2218yes—
22C2×#14519742—28no—
23C2×#14519742C2218yescomplemented
24C2×C4×C22⋊D61—28no—
25C2×C4×C22⋊D61C2218yes—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
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
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45#16839666C2218yescomplemented
46#16839662C2218yes—
47#16839655C2218yescomplemented
48#16839654C2218yescomplemented
49#16839652C2218yescomplemented
50#16839650C2218yescomplemented
51#16839633C2218yescomplemented
52C4⋊C4×Dic61C2218yescomplemented
53#16839613C2218yescomplemented
54C4×C22⋊Dic61C2218yescomplemented
55#16839609C2218yescomplemented
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×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122C2×C418yescomplemented
74C22×Dic122C2314yes—
75C22×C22⋊D61—24no—
76C22×C22⋊D61—24no—
77C22×C22⋊D61C2×C418yes—
78C22×C22⋊D61C2314yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—42no—
89C22×C4×D61C2314yes—
90#14519763C2×C4164yescomplemented
91#14519742—232no—
92C4×C22⋊D61—232no—
93C2×C4⋊Dic61—24no—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196D418yes—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—24no—
103C2×C22⋊Dic61C2×C418yescomplemented
104C2×C22⋊Dic61C2314yes—
105C2×C22⋊Dic61C2314yes—
106C2×C22⋊Dic61C2314yes—
107C2×#11758198—24no—
108C2×#11758198—24no—
109C2×#11758198—42no—
110C2×#11758198C2×C418yescomplemented
111C2×#11758198C2×C418yescomplemented
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—42no—
122C2×C4×Dic61—42no—
123C2×C4×Dic61C2×C418yescomplemented
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
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×C61C2314yes—
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61—24no—
149C2×C4⋊C4×C61—24no—
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×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—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—28no—
190C22×C4×C61—28no—
191C22×C4×C61—44no—
192C22×C4×C61—416no—
193C22×C4×C61C22×C414yes—
194C22×C4×C61C22×C414yes—
195C22×C4×C61C2×D414yes—
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—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×Dic61C22×C414yes—
222C22×Dic61C22×C414yes—
223C22×Dic61C22×C414yes—
224C22×Dic61C2×D414yes—
225C22×Dic61C2×D414yes—
226C22×Dic61#4114yes—
227C22×Dic61#4114yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—28no—
236C2×C4×D61—28no—
237C2×C4×D61—44no—
238C2×C4×D61—416no—
239C2×Dic122—232no—
240C2×Dic122—28no—
241C2×Dic122—28no—
242C2×Dic122C22×C4116yescomplemented
243C4⋊C4×C61—28no—
244C4⋊C4×C61—28no—
245C22⋊C4×C61—44no—
246C22⋊C4×C61C22×C4116yescomplemented
247C22⋊Dic61—28no—
248C22⋊Dic61—28no—
249C22⋊Dic61C22×C4116yescomplemented
250#11758198—28no—
251#11758198—28no—
252#11758198—44no—
253#11758198C22×C4116yescomplemented
254#11758198C22×C4116yescomplemented
255C4⋊Dic61—28no—
256#11758196—28no—
257#11758196—28no—
258#11758196C2×D4116yes—
259C4×Dic61—28no—
260C4×Dic61—28no—
261C4×Dic61—28no—
262C4×Dic61—28no—
263C4×Dic61—44no—
264C4×Dic61—44no—
265C4×Dic61C22×C4116yescomplemented
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61C23×C414yes—
280C23×C61C23×C412yes—
281C23×C61C22×D412yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C612−1+412yes—
287C23×C61C2511yescharacteristic
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61C23×C414yes—
302C2×C4×C61—28no—
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—416no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61C23×C414yes—
324C2×C4×C61C23×C414yes—
325C2×C4×C61C22×D414yes—
326C2×C4×C61C2×#4114yes—
327C22⋊D61—232no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—28no—
332C2×Dic61—22no—
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—44no—
347C2×Dic61—44no—
348C2×Dic61C4×D4116yes—
349C2×Dic61C23×C414yes—
350C2×Dic61C23×C414yes—
351C2×Dic61C23×C414yes—
352C2×Dic61C22×D414yes—
353C2×Dic61C22×D414yes—
354C2×Dic61C2×#4114yes—
355C2×Dic61C2×#4114yes—
356C4×D61—416no—
357Dic122—232no—
358C2×#2367—611nomaximal, Sylow
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—416no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61C2×C4×D414yes—
368C22×C61C4×#4114yes—
369C22×C61#52014yes—
370C22×C61#54614yes—
371C22×C61#54814yes—
372C22×C61#55614yes—
373C22×C61#55914yes—
374C22×C61C24×C411yescharacteristic
375C22×C61C23×D411yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×2−1+411yescharacteristic
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—416no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—42no—
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—24no—
399Dic61—42no—
400Dic61—42no—
401Dic61C2×C4×D418yes—
402C22×#124—611no—
403C22×C4×Q8—611no—
404C22×C4×D4—611no—
405#2367—6116no—
406C2×#391—611no—
407C2×#390—611no—
408C2×#388—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#388—611no—
412C2×#385—611no—
413C2×#385D6111yescharacteristic, complemented
414C2×C4×C4⋊C4—611no—
415C2×C4×C4⋊C4—611no—
416C2×C4×C22⋊C4—611no—
417C2×C4×C22⋊C4—611no—
418C2×C61—44no—
419C2×C61#236718yescomplemented
420C2×C61C22×C4×D411yescharacteristic
421C2×C61C2×C4×#4111yescharacteristic
422C2×C61C2×#52011yescharacteristic
423C2×C61C2×#54611yescharacteristic
424C2×C61C2×#54811yescharacteristic
425C2×C61C2×#55611yescharacteristic
426C2×C61C2×#55911yescharacteristic
427D61—44no—
428C23×Q8—611no—
429C23×D4—611no—
430C24×C4—611no—
431C24×C4C2×D6111yescharacteristic
432C2×#124—6116no—
433C2×#124—618no—
434C2×C4×Q8—618no—
435C2×C4×Q8—1228no—
436C2×C4×D4—618no—
437C2×C4×D4—1228no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C4⋊C4C2×D6111yescharacteristic
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4C2×D6111yescharacteristic
453C22×C22⋊C4C2×D6111yescharacteristic
454C22×C42—611no—
455C22×C42—611no—
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—611no—
459C22×C42—611no—
460C22×C42—611no—
461#391—618no—
462#390—618no—
463#388—618no—
464#388—618no—
465#388—618no—
466#388—618no—
467#385—618no—
468#385C2×D6118yescomplemented
469C4×C4⋊C4—618no—
470C4×C4⋊C4—618no—
471C4×C22⋊C4—618no—
472C4×C22⋊C4—618no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95C2×D6111yescharacteristic
480C2×#95C2×D6111yescharacteristic
481C61C2×#236711yescharacteristic, complemented, Sylow
482C25—611no—
483C25C22×D6111yescharacteristic
484C22×Q8—618no—
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×D4—618no—
489C22×D4—614no—
490C22×D4—1224no—
491C22×D4—1224no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
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—1224no—
504C23×C4—1224no—
505C23×C4—2442no—
506C23×C4C22×D6111yescharacteristic
507C23×C4C22×D6111yescharacteristic
508C23×C4C22×D6114yes—
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513#124—6164no—
514C4×Q8—12232no—
515C4×D4—12232no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—618no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—1224no—
524C2×C4⋊C4—1224no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4C22×D6114yes—
527C2×C4⋊C4C22×D6114yes—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—618no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—618no—
532C2×C22⋊C4—618no—
533C2×C22⋊C4—614no—
534C2×C22⋊C4—614no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—614no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—614no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4—1224no—
542C2×C22⋊C4—1224no—
543C2×C22⋊C4—1224no—
544C2×C22⋊C4—2442no—
545C2×C22⋊C4C4×D6118yescomplemented
546C2×C22⋊C4C22×D6114yes—
547C2×C22⋊C4C22×D6114yes—
548C2×C42—618no—
549C2×C42—614no—
550C2×C42—614no—
551C2×C42—614no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—614no—
556C2×C42—1224no—
557C2×C42—1224no—
558C2×C42—1224no—
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#95C22×D6114yes—
569#95C22×D6114yes—
570C24—22no—
571C24—22no—
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—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—6116no—
588C2×Q8—1228no—
589C2×Q8—12232no—
590C2×Q8—1228no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—12232no—
594C2×D4—1228no—
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—22no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—44no—
612C22×C4—416no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—614no—
616C22×C4—612no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—614no—
620C22×C4—614no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—1228no—
628C22×C4—1222no—
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—1228no—
643C22×C4—2444no—
644C22×C4—24416no—
645C22×C4C2×C4×D6114yes—
646C22×C4C2×C4×D6114yes—
647C22×C4D4×D6114yes—
648C22×C4#1175822414yes—
649C22×C4C23×D6112yes—
650C22×C4C23×D6112yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—6116no—
658C4⋊C4—1228no—
659C4⋊C4—1228no—
660C4⋊C4—1228no—
661C22⋊C4—44no—
662C22⋊C4—6116no—
663C22⋊C4—6116no—
664C22⋊C4—6116no—
665C22⋊C4—1228no—
666C22⋊C4—1228no—
667C22⋊C4—1228no—
668C22⋊C4—1228no—
669C22⋊C4—2444no—
670C22⋊C4C2×C4×D61116yescomplemented
671C42—6116no—
672C42—1228no—
673C42—1228no—
674C42—1228no—
675C42—1228no—
676C42—2444no—
677C42—2444no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
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—
705C23C22×C4×D6114yes—
706C23C22×C4×D6112yes—
707C23C2×D4×D6112yes—
708C23#41×D6112yes—
709C23#41×D6112yes—
710C23C2×#1175822412yes—
711C23#1451982212yes—
712C23#1451982512yes—
713C23C24×D6111yescharacteristic
714Q8—12232no—
715D4—12232no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—6116no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—614no—
745C2×C4—1228no—
746C2×C4—1228no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1228no—
756C2×C4—1228no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—24416no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4C22×C4×D6114yes—
767C2×C4C22×C4×D6114yes—
768C2×C4C2×D4×D6114yes—
769C2×C4C2×#1175822414yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—24416no—
785C22—2442no—
786C22C4×D4×D6114yes—
787C22C4×#1175822414yes—
788C22#1684024314yes—
789C22#1684039914yes—
790C22#1684042214yes—
791C22#1684048314yes—
792C22#1684049614yes—
793C22C23×C4×D6111yescharacteristic
794C22C22×D4×D6111yescharacteristic
795C22C2×#41×D6111yescharacteristic
796C22C2×#41×D6111yescharacteristic
797C22C22×#1175822411yescharacteristic
798C22C2×#1451982211yescharacteristic
799C22C2×#1451982511yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—618no—
807C4—1224no—
808C4—1224no—
809C4—1224no—
810C4—1224no—
811C4—2442no—
812C4—2442no—
813C2—44no—
814C2—2444no—
815C2#2144888718yesdirect product factor
816C2C2×C4×D4×D6111yescharacteristic
817C2C2×C4×#1175822411yescharacteristic
818C2C2×#1684024311yescharacteristic
819C2C2×#1684039911yescharacteristic
820C2C2×#1684042211yescharacteristic
821C2C2×#1684048311yescharacteristic
822C2C2×#1684049611yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#385D61
hypocenterC61C2×#2367
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
4. #21448887C2direct (N × H)
5. C2×#16839666C2semidirect
7. C2×#16839655C2semidirect
8. C2×#16839654C2semidirect
9. C2×#16839652C2semidirect
10. C2×#16839650C2semidirect
11. C2×#16839633C2semidirect
12. C2×C4⋊C4×Dic61C2semidirect
13. C2×#16839613C2semidirect
14. C2×C4×C22⋊Dic61C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#385C2semidirect
20. C2×#14519763C4semidirect
23. C2×#14519742C22semidirect
45. #16839666C22semidirect
47. #16839655C22semidirect
48. #16839654C22semidirect
49. #16839652C22semidirect
50. #16839650C22semidirect
51. #16839633C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. #16839613C22semidirect
54. C4×C22⋊Dic61C22semidirect
55. #16839609C22semidirect
67. C61×#385C22semidirect
73. C22×Dic122C2×C4semidirect
90. #14519763C2×C4semidirect
103. C2×C22⋊Dic61C2×C4semidirect
110. C2×#11758198C2×C4semidirect
111. C2×#11758198C2×C4semidirect
123. C2×C4×Dic61C2×C4semidirect
153. C2×C22⋊C4×C61C2×C4semidirect
242. C2×Dic122C22×C4semidirect
246. C22⋊C4×C61C22×C4semidirect
249. C22⋊Dic61C22×C4semidirect
253. #11758198C22×C4semidirect
254. #11758198C22×C4semidirect
265. C4×Dic61C22×C4semidirect
413. C2×#385D61semidirect
419. C2×C61#2367semidirect
468. #385C2×D61semidirect
481. C61C2×#2367semidirect
545. C2×C22⋊C4C4×D61semidirect
670. C22⋊C4C2×C4×D61semidirect
815. C2#21448887direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×#145197422
C22×C4×C22⋊D612
#214488872
C2×#168396662
C2×#168396622
C2×#168396552
C2×#168396542
C2×#168396522
C2×#168396502
C2×#168396332
C2×C4⋊C4×Dic612
C2×#168396132
C2×C4×C22⋊Dic612
C2×#168396092
C2×C61×#3852
C2×#236761