Finite Group Databasebeta

← #30617878

Subgroups — #30617878

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21462010C214yesmaximal, complemented
4#21462009C212yesmaximal, complemented
5#21462008C212yesmaximal, complemented
6#21461715C214yesmaximal
7C2×C22⋊Q8×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9C2×#14519856—21no—
10#16840705—21no—
11#16840705—21no—
12#16840704—21no—
13#16840704—21no—
14#16840704C2212yes—
15#16840704C2212yes—
16#16840703C2212yes—
17#16840703C2212yes—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923—21no—
20C4×C22⋊#6923C2212yes—
21C4×C22⋊#6923C2212yes—
22#16840640C2218yes—
23#16840640C2218yes—
24C22×Q8×D61C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519756C411yescharacteristic, complemented
28C2×#14519755C2212yes—
29C2×#14519754C412yescomplemented
30C2×#14519753C2211yescharacteristic
31C22⋊Q8×D61—21no—
32C22⋊Q8×D61—21no—
33C22⋊Q8×D61—21no—
34C22⋊Q8×D61—21no—
35C22⋊Q8×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61—21no—
38C22⋊Q8×D61—21no—
39C2×C4⋊C4×D61C411yescharacteristic, complemented
40C2×C4⋊C4×D61C412yescomplemented
41C2×C22⋊C4×D61C2212yes—
42C2×C22⋊Q8×C61C411yescharacteristic, complemented
43#14519856—44no—
44#14519856—44no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—22no—
47C2×C22⋊#6923—22no—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C22⋊#6923C2314yes—
52C2×C22⋊#6923C2314yes—
53C2×C4×#6923—22no—
54C2×C4×#6923—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59C24×D61C2311yescharacteristic
60C22×Dic122C2×C412yes—
61C22×Dic122C2×C411yescharacteristic
62C2×Q8×D61—21no—
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—21no—
66C2×Q8×D61—44no—
67C23×Dic61C2×C411yescharacteristic
68C22×C4×D61—44no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2×C412yes—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83#14519757—21no—
84#14519757—21no—
85#14519757—21no—
86#14519757—21no—
87#14519756—21no—
88#14519756—21no—
89#14519756—21no—
90#14519756—21no—
91#14519755—22no—
92#14519755—22no—
93#14519755—22no—
94#14519755—22no—
95#14519754—22no—
96#14519754—22no—
97#14519754—22no—
98#14519754—22no—
99#14519753—21no—
100#14519753—21no—
101#14519753—21no—
102#14519753—21no—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×C4⋊Dic61C2×C412yes—
105C2×#11758196C2×C412yes—
106C2×#11758196C2×C412yes—
107C2×#11758196C2×C412yes—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—21no—
113C4⋊C4×D61—21no—
114C4⋊C4×D61—21no—
115C4⋊C4×D61—21no—
116C2×C22⋊Dic61C2×C412yes—
117C2×#11758198C2312yes—
118C2×#11758198C2312yes—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C22⋊C4×D61—22no—
123C22×Q8×C61C2×C411yescharacteristic
124C23×C4×C61C2×C411yescharacteristic
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C2×C4⋊C4×C61C2×C412yes—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2×C412yes—
132C24×C61C22×C411yescharacteristic
133C23×D61—24no—
134C23×D61—42no—
135C23×D61—42no—
136C23×D61C22×C411yescharacteristic
137C23×D61C2×D411yescharacteristic
138C23×D61C2×D411yescharacteristic
139C23×D61C2×D411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2411yescharacteristic
142C22×#6923—24no—
143C22×#6923—24no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—42no—
147C22×C4×C61—42no—
148C22×C4×C61C22⋊C411yescharacteristic
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22⋊C411yescharacteristic
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C411yescharacteristic
156C22×Dic61—42no—
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C412yes—
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C411yescharacteristic
165Q8×D61—44no—
166Q8×D61—44no—
167Q8×D61—44no—
168Q8×D61—44no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—44no—
186C2×C4×D61—44no—
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22⋊C411yescharacteristic
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C22⋊C411yescharacteristic
194C2×C4×D61C22⋊C411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×C4×D61C2×D411yescharacteristic
199C2×C4×D61C2×D411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122—44no—
208C2×Dic122—42no—
209C22⋊#6923—28no—
210C22⋊#6923—28no—
211C22⋊#6923—44no—
212C22⋊#6923—44no—
213C22⋊#6923—44no—
214C22⋊#6923—44no—
215C4⋊#6923—44no—
216C4⋊#6923—44no—
217C4×#6923—44no—
218C4×#6923—44no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241C23×C61—22no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61C2×C22⋊C411yescharacteristic
245C23×C61C2×C22⋊C411yescharacteristic
246C23×C61C23×C411yescharacteristic
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—416no—
265C22×D61C2×C22⋊C411yescharacteristic
266C22×D61C2×C22⋊C411yescharacteristic
267C22×D61C22×D411yescharacteristic
268C22×D61C22×D411yescharacteristic
269C22×D612−1+414yes—
270C2×#6923—44no—
271C2×#6923—44no—
272C2×#6923—44no—
273C2×#6923—44no—
274C2×#6923—44no—
275C2×#6923—44no—
276Q8×C61—42no—
277Q8×C61—42no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304C2×Dic61C2×C22⋊C411yescharacteristic
305C2×Dic61C2×C22⋊C411yescharacteristic
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—44no—
322C4×D61—44no—
323C4×D61—44no—
324C4×D61—44no—
325C4×D61#9914yes—
326Dic122—44no—
327Dic122—42no—
328Dic122—42no—
329Dic122—44no—
330#21825—611nomaximal, Sylow
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—44no—
340C22×C61C22×C22⋊C411yescharacteristic
341C22×C61#51912yes—
342C2×D61—28no—
343C2×D61—21no—
344C2×D61—21no—
345C2×D61—21no—
346C2×D61—21no—
347C2×D61—21no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—44no—
352C2×D61—44no—
353C2×D61—44no—
354C2×D61—44no—
355C2×D61—44no—
356C2×D61C2×#9912yes—
357C2×D61#41012yes—
358C2×D61#53612yes—
359C2×D61#53612yes—
360#6923—84no—
361#6923—84no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61C2×#9912yes—
368Dic61—21no—
369Dic61—21no—
370Dic61—21no—
371Dic61—42no—
372Dic61—42no—
373Dic61C2×#9912yes—
374C22×C22⋊Q8—611no—
375#2280—611no—
376#2280—611no—
377#1996—612no—
378#1996—612no—
379#1996—614no—
380#1819—614no—
381C2×C61—22no—
382C2×C61—41no—
383C2×C61—41no—
384C2×C61#231011yescharacteristic
385C2×C61C22×#9911yescharacteristic
386C2×C61C2×#41011yescharacteristic
387D61—22no—
388D61—22no—
389D61—22no—
390D61—22no—
391C23×Q8—611no—
392C24×C4—611no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8—611no—
395C2×C22⋊Q8—612no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8—612no—
398C2×C22⋊Q8—1221no—
399C2×C22⋊Q8—1221no—
400C2×C22⋊Q8—1221no—
401C2×C22⋊Q8—1221no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8—1221no—
404C2×C22⋊Q8—1221no—
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8#692311yescharacteristic, complemented
407C2×#117—1221no—
408C2×#117—1221no—
409C22×C4⋊C4—611no—
410C22×C4⋊C4—612no—
411C22×C22⋊C4—612no—
412#381—1221no—
413#381—1221no—
414#380—612no—
415#380—612no—
416#380—1221no—
417#380—1221no—
418#379—612no—
419#379—612no—
420C4×C22⋊C4—612no—
421C4×C22⋊C4—612no—
422C4×C22⋊C4—1221no—
423C4×C22⋊C4—1221no—
424#342—618no—
425#342—618no—
426C61#2182511yescharacteristic, complemented, Sylow
427C25—611no—
428C22×Q8—612no—
429C22×Q8—611no—
430C22×Q8—1221no—
431C22×Q8—1221no—
432C22×Q8—1221no—
433C22×Q8—1221no—
434C22×Q8—2444no—
435C22×Q8C2×#692311yescharacteristic
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—612no—
450C23×C4—612no—
451C23×C4—2444no—
452C23×C4C2×#692311yescharacteristic
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—1222no—
458C22⋊Q8—1222no—
459C22⋊Q8—1222no—
460C22⋊Q8—1222no—
461C22⋊Q8—1222no—
462C22⋊Q8—1222no—
463C22⋊Q8—1222no—
464C22⋊Q8—1222no—
465C22⋊Q8—1221no—
466C22⋊Q8—1221no—
467C22⋊Q8—1221no—
468C22⋊Q8—1221no—
469C22⋊Q8—1221no—
470C22⋊Q8—1221no—
471C22⋊Q8—1221no—
472C22⋊Q8—1221no—
473C22⋊Q8—1221no—
474C22⋊Q8—1221no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477#117—2444no—
478#117—2444no—
479C2×C4⋊C4—612no—
480C2×C4⋊C4—612no—
481C2×C4⋊C4—612no—
482C2×C4⋊C4—612no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1222no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4C2×#692311yescharacteristic
495C2×C4⋊C4C2×#692312yes—
496C2×C22⋊C4—612no—
497C2×C22⋊C4—612no—
498C2×C22⋊C4—612no—
499C2×C22⋊C4—614no—
500C2×C22⋊C4—614no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4—1222no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4—1222no—
507C2×C22⋊C4—1222no—
508C2×C22⋊C4—1222no—
509C2×C22⋊C4C2×#692312yes—
510C2×C42—1222no—
511C2×C42—1222no—
512#95—1222no—
513#95—1222no—
514#95—1222no—
515#95—1222no—
516C24—611no—
517C24—611no—
518C24—611no—
519C24—611no—
520C24—611no—
521C24—611no—
522C24—1224no—
523C24—2442no—
524C24—2442no—
525C24C22×#692311yescharacteristic
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—42no—
529C2×Q8—1222no—
530C2×Q8—1222no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—2442no—
534C2×Q8—2444no—
535C2×Q8—2444no—
536C2×Q8—2444no—
537C2×Q8—2444no—
538C2×Q8—2444no—
539C22×C4—42no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—1224no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1224no—
572C22×C4—1224no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2444no—
583C22×C4—2444no—
584C22×C4—2442no—
585C22×C4C22⋊#692311yescharacteristic
586C22×C4C22⋊#692311yescharacteristic
587C22×C4C22⋊#692311yescharacteristic
588C22×C4C22⋊#692311yescharacteristic
589C22×C4C22×#692311yescharacteristic
590C22×C4C22×#692312yes—
591C22×C4C22×#692312yes—
592C22×C4C22×#692311yescharacteristic
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1222no—
602C4⋊C4—1222no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—2444no—
608C4⋊C4—2444no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1228no—
618C22⋊C4—1228no—
619C22⋊C4—2444no—
620C22⋊C4—2444no—
621C22⋊C4—2444no—
622C22⋊C4—2444no—
623C42—2444no—
624C42—2444no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—611no—
629C23—611no—
630C23—611no—
631C23—611no—
632C23—614no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—24416no—
651C23C2×C22⋊#692311yescharacteristic
652C23C2×C22⋊#692311yescharacteristic
653C23C23×#692311yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—2442no—
657Q8—2444no—
658Q8—2444no—
659Q8—2442no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—611no—
671C2×C4—614no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2444no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4—2444no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2444no—
703C2×C4—2444no—
704C2×C4—2444no—
705C2×C4—2444no—
706C2×C4—2444no—
707C2×C4—2444no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4C2×C22⋊#692311yescharacteristic
711C2×C4C2×C22⋊#692311yescharacteristic
712C2×C4C2×C22⋊#692311yescharacteristic
713C2×C4C2×C22⋊#692311yescharacteristic
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—44no—
723C22—612no—
724C22—612no—
725C22—612no—
726C22—612no—
727C22—1228no—
728C22—1221no—
729C22—1221no—
730C22—1221no—
731C22—1221no—
732C22—1221no—
733C22—1221no—
734C22—1221no—
735C22—1221no—
736C22—2444no—
737C22—2444no—
738C22—2444no—
739C22—2444no—
740C22—2444no—
741C22C22×C22⋊#692311yescharacteristic
742C22#1684083012yes—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—42no—
747C4—42no—
748C4—612no—
749C4—1221no—
750C4—1221no—
751C4—1221no—
752C4—4884no—
753C4—4884no—
754C4—2442no—
755C4—2442no—
756C4D61⋊#9912yes—
757C2—22no—
758C2—41no—
759C2—41no—
760C2—1222no—
761C2—1222no—
762C2—1222no—
763C2—1222no—
764C2#2146229311yescharacteristic
765C2C2×D61⋊#9911yescharacteristic
766C2D61⋊#41011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#21825
LCSG ▷ C23×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
3. #21462010C2semidirect
4. #21462009C2semidirect
5. #21462008C2semidirect
24. C22×Q8×D61C4semidirect
27. C2×#14519756C4semidirect
29. C2×#14519754C4semidirect
39. C2×C4⋊C4×D61C4semidirect
40. C2×C4⋊C4×D61C4semidirect
42. C2×C22⋊Q8×C61C4semidirect
406. C2×C22⋊Q8#6923semidirect
426. C61#21825semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214620102
#214620092
#214620082
#214617152
C2×C22⋊Q8×D612
#2182561