Finite Group Databasebeta

← #30615603

Subgroups — #30615603

Order 15616.

1934 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic
2C2×#16840755C212yesmaximal, complemented
3D61⋊#407C211yesmaximal, characteristic
4#21461805C214yesmaximal, complemented
5#21461804C214yesmaximal, complemented
6#21461506C212yesmaximal, complemented
7C2×C22⋊Q8×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519856—28no—
10C2×#14519856—21no—
11C2×#14519856—21no—
12C2×#14519856C2212yes—
13C2×#14519856C2212yes—
14C22×C4⋊#6923C2212yes—
15C22×C22⋊#6923—21no—
16C22×C4×#6923—21no—
17#16840755—28no—
18C2×#14519840C2218yescomplemented
19#16840734—21no—
20#16840733—21no—
21#16840733—21no—
22#16840732—21no—
23D61⋊(C22⋊C8)C2212yes—
24D61⋊(C22⋊C8)C2212yes—
25#16840635C2218yescomplemented
26C22×Q8×D61C2211yescharacteristic
27C23×C4×D61C2211yescharacteristic
28C2×#14519757C411yescharacteristic, complemented
29C2×#14519756C411yescharacteristic, complemented
30C2×#14519755—21no—
31C2×#14519754—21no—
32C2×#14519753C411yescharacteristic, complemented
33C22⋊Q8×D61—21no—
34C22⋊Q8×D61—21no—
35C22⋊Q8×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61C412yescomplemented
38C22⋊Q8×D61C412yescomplemented
39C22⋊Q8×D61C2212yes—
40C22⋊Q8×D61C2212yes—
41C2×C4⋊C4×D61—21no—
42C2×C4⋊C4×D61C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44C2×C22⋊Q8×C61C411yescharacteristic, complemented
45C23×#6923—22no—
46C2×#11758213—22no—
47D61⋊M16—24no—
48D61⋊M16—24no—
49C2×#11758217—22no—
50C2×D61⋊C8C2314yes—
51#14519856—28no—
52#14519856—28no—
53#14519856—24no—
54#14519856—28no—
55#14519856D418yes—
56C2×C4⋊#6923—22no—
57C2×C4⋊#6923—28no—
58C2×C4⋊#6923C2314yes—
59C2×C22⋊#6923—28no—
60C2×C22⋊#6923—22no—
61C2×C22⋊#6923—22no—
62C2×C4×#6923—28no—
63C2×C4×#6923—22no—
64C2×C4×#6923—22no—
65#14519840—216no—
66#14519834—22no—
67#14519834—22no—
68C22⋊#92420—22no—
69C22⋊#92420—22no—
70C24×D61D411yescharacteristic
71C22×Dic122—21no—
72C22×Dic122C2×C411yescharacteristic, complemented
73C2×Q8×D61—21no—
74C2×Q8×D61—21no—
75C2×Q8×D61—24no—
76C2×Q8×D61—24no—
77C2×Q8×D61C2×C412yescomplemented
78C2×Q8×D61C2312yes—
79C23×Dic61D411yescharacteristic
80C22×C4×D61—24no—
81C22×C4×D61—24no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96#14519757—21no—
97#14519757—21no—
98#14519757C2×C412yes—
99#14519757C2×C412yescomplemented
100#14519756—21no—
101#14519756—21no—
102#14519756C2×C412yes—
103#14519756C2×C412yescomplemented
104#14519755—22no—
105#14519755—22no—
106#14519755—22no—
107#14519755—22no—
108#14519754—22no—
109#14519754—22no—
110#14519754—22no—
111#14519754—22no—
112#14519753—21no—
113#14519753—21no—
114#14519753C2×C412yes—
115#14519753C2×C412yescomplemented
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61C2×C411yescharacteristic, complemented
118C2×#11758196—21no—
119C2×#11758196—21no—
120C2×#11758196—21no—
121C4⋊C4×D61—22no—
122C4⋊C4×D61—22no—
123C4⋊C4×D61—22no—
124C4⋊C4×D61—22no—
125C4⋊C4×D61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61C2×C412yescomplemented
128C4⋊C4×D61C2312yes—
129C2×C22⋊Dic61—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C22⋊C4×D61—22no—
133C22⋊C4×D61—22no—
134C22⋊C4×D61—22no—
135C22⋊C4×D61—22no—
136C22×Q8×C61C2×C411yescharacteristic, complemented
137C23×C4×C61C2×C411yescharacteristic
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61C2×C412yes—
141C22⋊Q8×C61C2×C412yescomplemented
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
144C2×C22⋊C4×C61—21no—
145C24×C61C22⋊C411yescharacteristic
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C22×#6923—28no—
157C22×#6923—24no—
158C22×#6923—44no—
159C22×#6923—44no—
160C2×Q8×C61—21no—
161C2×Q8×C61—24no—
162C2×Q8×C61C22×C412yes—
163C22×C4×C61—24no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×Dic61—24no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181Q8×D61—28no—
182Q8×D61—24no—
183Q8×D61—24no—
184Q8×D61—42no—
185Q8×D61—44no—
186Q8×D61—42no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—24no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—44no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22×C411yescharacteristic
217C2×C4×D61C22×C411yescharacteristic
218C2×C4×D61C22×C411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D414yes—
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61#4114yes—
227C2×C4×D61C2411yescharacteristic
228C2×Dic122—24no—
229C2×Dic122—21no—
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—44no—
233C2×Dic122C22×C412yes—
234C22⋊#6923—28no—
235C22⋊#6923—28no—
236#11758217—44no—
237C2×#92420—24no—
238C4⋊#6923—28no—
239C4⋊#6923—24no—
240C4⋊#6923C2×D418yes—
241C4×#6923—28no—
242C4×#6923—28no—
243#11758213—44no—
244D61⋊C8—24no—
245D61⋊C8—24no—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C22×C412yes—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊Dic61—22no—
253C22⋊Dic61—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258C4⋊Dic61—21no—
259C4⋊Dic61—22no—
260C4⋊Dic61—22no—
261C4⋊Dic61C22×C412yes—
262#11758196—22no—
263#11758196—22no—
264#11758196—22no—
265#11758196—22no—
266#11758196—22no—
267#11758196—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—41no—
271C23×C61C2×C22⋊C411yescharacteristic
272C23×C61C2×C22⋊C411yescharacteristic
273C23×C61C2×C22⋊C411yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—48no—
293C22×D61—48no—
294C22×D61C2×C22⋊C411yescharacteristic
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C2×C22⋊C411yescharacteristic
297C22×D61#12012yes—
298C22×D61#12312yes—
299C22×D61#13714yes—
300C22×D61C22×D411yescharacteristic
301C2×#6923—28no—
302C2×#6923—416no—
303C2×#6923—44no—
304C2×#6923—44no—
305Q8×C61—24no—
306Q8×C61—42no—
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—42no—
315C2×C4×C61—42no—
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C4×D414yes—
320C2×C4×C61C23×C411yescharacteristic
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61#12114yes—
334C2×Dic61C22×D411yescharacteristic
335C4×D61—21no—
336C4×D61—21no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—44no—
350C4×D61—42no—
351C4×D61—42no—
352C4×D61—44no—
353C4×D61—44no—
354C4×D61C4×D414yes—
355C4×D61#12012yes—
356C4×D61#12114yes—
357C4×D61#12312yes—
358C4×D61C22×D412yes—
359C4×D61C2×#4112yes—
360Dic122—24no—
361Dic122—42no—
362Dic122—44no—
363Dic122—44no—
364#92420—44no—
365#20911—611nomaximal, Sylow
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—44no—
374C22×C61#38612yes—
375C22×C61#41912yescomplemented
376C22×C61C22×C22⋊C411yescharacteristic
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61#38612yes—
394C2×D61#41912yescomplemented
395C2×D61C2×#12011yescharacteristic
396C2×D61C2×#12311yescharacteristic
397C2×D61C2×#13712yes—
398C2×D61#57512yes—
399#6923—48no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61#38612yes—
405C4×C61C2×C4×D412yes—
406Dic61—21no—
407Dic61—21no—
408Dic61—42no—
409Dic61—42no—
410Dic61#38612yes—
411Dic61C2×#12112yes—
412C22×C22⋊Q8—611no—
413C22×#117—611no—
414C2×#419—612no—
415C2×#407—611no—
416#1873—614no—
417#1872—614no—
418#1736—612no—
419C2×C61—22no—
420C2×C61—22no—
421C2×C61—41no—
422C2×C61C2×#38611yescharacteristic
423C2×C61C2×#41911yescharacteristic
424C2×C61#289611yescharacteristic
425D61—22no—
426D61—22no—
427D61—41no—
428D61#300712yes—
429D61#309512yes—
430C23×Q8—611no—
431C24×C4—611no—
432C22×M16—612no—
433C2×C22⋊Q8—611no—
434C2×C22⋊Q8—611no—
435C2×C22⋊Q8—612no—
436C2×C22⋊Q8—612no—
437C2×C22⋊Q8—612no—
438C2×C22⋊Q8—612no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—1221no—
441C2×C22⋊Q8—1221no—
442C2×C22⋊Q8—1221no—
443C2×C22⋊Q8—1221no—
444C2×C22⋊Q8—1221no—
445C2×C22⋊Q8—1221no—
446C2×C22⋊Q8#692311yescharacteristic, complemented
447C2×#117—612no—
448C2×#117—612no—
449C2×#117—1228no—
450C2×#117—1221no—
451C2×#117—1221no—
452C22×C4⋊C4—611no—
453C22×C4⋊C4—612no—
454C22×C4⋊C4—1221no—
455C22×C22⋊C4—1221no—
456C22×C22⋊C4—1221no—
457C22×C42—1221no—
458#419—1228no—
459C2×#103—618no—
460#407—1221no—
461#407—1221no—
462#407—1221no—
463#407—1221no—
464C2×C22⋊C8—612no—
465C2×C22⋊C8—612no—
466#340—618no—
467C61#2091111yescharacteristic, complemented, Sylow
468C25—611no—
469C22×Q8—612no—
470C22×Q8—612no—
471C22×Q8—611no—
472C22×Q8—1221no—
473C22×Q8—1221no—
474C22×Q8—1221no—
475C22×Q8—1224no—
476C22×Q8—1224no—
477C22×Q8C2×#692311yescharacteristic, complemented
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—1224no—
492C23×C4—1224no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1222no—
496C23×C4C2×#692311yescharacteristic
497C2×M16—1222no—
498C2×M16—1224no—
499C2×M16—1224no—
500C2×M16—1222no—
501C22×C8—614no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—612no—
505C22⋊Q8—612no—
506C22⋊Q8—612no—
507C22⋊Q8—612no—
508C22⋊Q8—612no—
509C22⋊Q8—612no—
510C22⋊Q8—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8—1222no—
515C22⋊Q8—1222no—
516C22⋊Q8—1222no—
517C22⋊Q8—1222no—
518C22⋊Q8—1221no—
519C22⋊Q8—1221no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8C2×#692312yes—
525C22⋊Q8C2×#692312yescomplemented
526#117—618no—
527#117—1228no—
528#117—1224no—
529#117—1228no—
530#117—1228no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—614no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—612no—
535C2×C4⋊C4—612no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1222no—
542C2×C4⋊C4—1228no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1222no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4C2×#692311yescharacteristic, complemented
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1222no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1222no—
557C2×C22⋊C4—1222no—
558C2×C22⋊C4—1228no—
559C2×C22⋊C4—1221no—
560C2×C42—1222no—
561C2×C42—1222no—
562C2×C42—1228no—
563#103—12216no—
564C22⋊C8—1222no—
565C22⋊C8—1222no—
566C22⋊C8—1222no—
567C22⋊C8—1222no—
568C24—611no—
569C24—611no—
570C24—611no—
571C24—611no—
572C24—611no—
573C24—611no—
574C24—1222no—
575C24—1222no—
576C24—1224no—
577C24—2442no—
578C24C22⋊#692311yescharacteristic
579C2×Q8—21no—
580C2×Q8—24no—
581C2×Q8—612no—
582C2×Q8—1222no—
583C2×Q8—1222no—
584C2×Q8—1224no—
585C2×Q8—1228no—
586C2×Q8—1224no—
587C2×Q8—1221no—
588C2×Q8—1224no—
589C2×Q8—2444no—
590C2×Q8—2442no—
591C2×Q8—2444no—
592C2×Q8—2442no—
593C2×Q8C22×#692312yes—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—614no—
601C22×C4—614no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1224no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1224no—
631C22×C4—1224no—
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—1224no—
641C22×C4—1224no—
642C22×C4—1224no—
643C22×C4—1228no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2444no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4C22⋊#692311yescharacteristic
652C22×C4C22⋊#692311yescharacteristic
653C22×C4C22⋊#692311yescharacteristic
654C22×C4C22×#692311yescharacteristic
655C22×C4C22×#692311yescharacteristic
656C22×C4C22×#692311yescharacteristic
657M16—2444no—
658M16—2444no—
659C2×C8—1224no—
660C2×C8—1224no—
661C2×C8—1224no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—618no—
666C4⋊C4—612no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1224no—
674C4⋊C4—1228no—
675C4⋊C4—1221no—
676C4⋊C4—1222no—
677C4⋊C4—1222no—
678C4⋊C4C22×#692312yes—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1228no—
686C22⋊C4—1228no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C42—1228no—
690C42—1228no—
691C23—22no—
692C23—22no—
693C23—41no—
694C23—611no—
695C23—612no—
696C23—612no—
697C23—614no—
698C23—611no—
699C23—611no—
700C23—611no—
701C23—1221no—
702C23—1221no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1221no—
707C23—1222no—
708C23—1221no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—1222no—
716C23—2441no—
717C23—2441no—
718C23—2441no—
719C23—2448no—
720C23—2448no—
721C23C2×C22⋊#692311yescharacteristic
722C23C2×C22⋊#692311yescharacteristic
723C23C2×C22⋊#692311yescharacteristic
724Q8—24no—
725Q8—42no—
726Q8—1224no—
727Q8—2444no—
728Q8—2444no—
729Q8—2442no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—614no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—612no—
743C2×C4—614no—
744C2×C4—612no—
745C2×C4—614no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
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—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1228no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—2444no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2444no—
776C2×C4—2444no—
777C2×C4—2442no—
778C2×C4—2444no—
779C2×C4—2444no—
780C2×C4—24416no—
781C2×C4—2442no—
782C2×C4C2×C22⋊#692311yescharacteristic
783C2×C4C2×C22⋊#692311yescharacteristic
784C2×C4C2×C22⋊#692311yescharacteristic
785C2×C4D4×#692314yes—
786C2×C4C23×#692311yescharacteristic
787C8—2444no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—612no—
797C22—612no—
798C22—611no—
799C22—611no—
800C22—612no—
801C22—612no—
802C22—1224no—
803C22—1224no—
804C22—1224no—
805C22—1224no—
806C22—1221no—
807C22—1221no—
808C22—1221no—
809C22—1221no—
810C22—1221no—
811C22—1221no—
812C22—1221no—
813C22—2444no—
814C22—2444no—
815C22—2442no—
816C22—2442no—
817C22—2444no—
818C22#1684071012yes—
819C22#1684075512yescomplemented
820C22C22×C22⋊#692311yescharacteristic
821C4—21no—
822C4—21no—
823C4—42no—
824C4—42no—
825C4—612no—
826C4—612no—
827C4—1221no—
828C4—1221no—
829C4—2448no—
830C4—2442no—
831C4—2442no—
832C4#1684071012yes—
833C4C2×D4×#692312yes—
834C2—22no—
835C2—22no—
836C2—41no—
837C2—612no—
838C2—612no—
839C2—1222no—
840C2—1222no—
841C2—2441no—
842C2C2×#1684071011yescharacteristic
843C2C2×#1684075511yescharacteristic
844C2#2146243911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC2×C4×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#20911
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16840755C2semidirect
4. #21461805C2semidirect
5. #21461804C2semidirect
6. #21461506C2semidirect
18. C2×#14519840C22semidirect
25. #16840635C22semidirect
28. C2×#14519757C4semidirect
29. C2×#14519756C4semidirect
32. C2×#14519753C4semidirect
37. C22⋊Q8×D61C4semidirect
38. C22⋊Q8×D61C4semidirect
44. C2×C22⋊Q8×C61C4semidirect
72. C22×Dic122C2×C4semidirect
77. C2×Q8×D61C2×C4semidirect
99. #14519757C2×C4semidirect
103. #14519756C2×C4semidirect
115. #14519753C2×C4semidirect
117. C2×C4⋊Dic61C2×C4semidirect
127. C4⋊C4×D61C2×C4semidirect
136. C22×Q8×C61C2×C4semidirect
141. C22⋊Q8×C61C2×C4semidirect
143. C2×C4⋊C4×C61C2×C4semidirect
375. C22×C61#419semidirect
394. C2×D61#419semidirect
446. C2×C22⋊Q8#6923semidirect
467. C61#20911semidirect
477. C22×Q8C2×#6923semidirect
525. C22⋊Q8C2×#6923semidirect
548. C2×C4⋊C4C2×#6923semidirect
819. C22#16840755semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407552
D61⋊#4072
#214618052
#214618042
#214615062
C2×C22⋊Q8×D612
#2091161