Finite Group Databasebeta

← #30610966

Subgroups — #30610966

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21461219C212yesmaximal, complemented
4#21461216C212yesmaximal, complemented
5#21461206C214yesmaximal, complemented
6#21461197C214yesmaximal, complemented
7C2×#16840275C211yesmaximal, characteristic
8C22×#11758213—21no—
9C22×C22⋊#6923—21no—
10C22×C4×#6923—21no—
11#16840733—21no—
12#16840733—21no—
13#16840733C2212yes—
14#16840733C2212yescomplemented
15C2×#14519834C2212yescomplemented
16C2×C22⋊#92420—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yescomplemented
21C2×(C2×#6923)⋊C4C2212yescomplemented
22#16840616C2218yescomplemented
23#16840614C2218yescomplemented
24C22×#11758226C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26#16840275—21no—
27#16840275—21no—
28#16840275—21no—
29#16840275—21no—
30#16840275C412yescomplemented
31#16840275C412yescomplemented
32#16840275C2212yes—
33#16840275C2212yes—
34C2×#14519762—21no—
35C2×#14519753C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519751C411yescharacteristic, complemented
38C2×#14519747—21no—
39C2×#14519739—21no—
40C2×#14519737—21no—
41C2×#14519735C411yescharacteristic, complemented
42C2×C22⋊Q8×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758213—22no—
45C2×#11758213—22no—
46C2×#11758213—44no—
47C22×#92420—22no—
48C2×C22⋊#6923—28no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923—22no—
52C2×C4×#6923—22no—
53C2×C4×#6923—44no—
54#14519834—22no—
55#14519834C2314yes—
56C22⋊#92420—22no—
57C22⋊#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4C2314yes—
60C24×D61D411yescharacteristic
61C2×#11758226—21no—
62C2×#11758226—21no—
63C2×#11758226—44no—
64C2×#11758226C2×C412yes—
65C2×#11758226C2×C412yescomplemented
66C22×D244—21no—
67C22×D244—21no—
68C22×D244C2×C411yescharacteristic, complemented
69C22×C22⋊D61—21no—
70C23×Dic61D411yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—44no—
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85#14519762—22no—
86#14519762—22no—
87#14519762—22no—
88#14519762—22no—
89#14519753—21no—
90#14519753—21no—
91#14519753C2×C412yescomplemented
92#14519753C2312yes—
93#14519752—21no—
94#14519752—21no—
95#14519752C2×C412yescomplemented
96#14519752C2312yes—
97#14519751—21no—
98#14519751—21no—
99#14519751C2×C412yes—
100#14519751C2×C412yescomplemented
101#14519747—22no—
102#14519747—22no—
103#14519747—22no—
104#14519747—22no—
105#14519739—22no—
106#14519739—22no—
107#14519739—22no—
108#14519739—22no—
109#14519737—22no—
110#14519737—22no—
111#14519737—22no—
112#14519737—22no—
113#14519735—21no—
114#14519735—21no—
115#14519735C2×C412yes—
116#14519735C2×C412yescomplemented
117C2×C4⋊Dic61C2×C411yescharacteristic, complemented
118C2×#11758196—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×C4×Dic61—21no—
124C22×Q8×C61C2×C411yescharacteristic, complemented
125C23×C4×C61C2×C411yescharacteristic
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61C2×C412yes—
129C22⋊Q8×C61C2×C412yescomplemented
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
132C2×C22⋊C4×C61—21no—
133C24×C61C22⋊C411yescharacteristic
134C23×D61—24no—
135C23×D61—21no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C22⋊C411yescharacteristic
139C23×D61C22⋊C411yescharacteristic
140C23×D61C22⋊C411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×#6923—28no—
145C22×#6923—24no—
146C22×#6923—44no—
147C22×#6923—44no—
148C2×Q8×C61—21no—
149C2×Q8×C61—42no—
150C2×Q8×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—42no—
154C22×C4×C61C22⋊C411yescharacteristic
155C22×C4×C61C22⋊C411yescharacteristic
156C22×C4×C61C22⋊C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—44no—
163C22×Dic61—21no—
164C22×Dic61—42no—
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171#11758226—44no—
172#11758226—44no—
173#11758226—44no—
174#11758226—44no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—21no—
180C2×D244—44no—
181C2×D244—44no—
182C2×D244—42no—
183C2×D244C22×C412yes—
184C2×C4×D61—24no—
185C2×C4×D61—24no—
186C2×C4×D61—24no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—44no—
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2411yescharacteristic
215C22⋊#6923—28no—
216C22⋊#6923—28no—
217C2×#92420—24no—
218C2×#92420—44no—
219C4×#6923—44no—
220C4×#6923—44no—
221#11758213—44no—
222#11758213—44no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61C22×C412yes—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237C4⋊Dic61—21no—
238C4⋊Dic61C22×C412yes—
239#11758196—22no—
240#11758196—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61#10414yes—
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C2×C22⋊C411yescharacteristic
248C23×C61C2×C22⋊C411yescharacteristic
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—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—416no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61C2×C22⋊C411yescharacteristic
273C22×D61C2×C22⋊C411yescharacteristic
274C22×D61C2×C22⋊C411yescharacteristic
275C22×D61C22×D411yescharacteristic
276C2×#6923—28no—
277C2×#6923—44no—
278C2×#6923—416no—
279C2×#6923—44no—
280Q8×C61—42no—
281Q8×C61—42no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C23×C411yescharacteristic
296C22⋊D61—44no—
297C22⋊D61—44no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—42no—
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61C2×C22⋊C411yescharacteristic
308C2×Dic61C2×C22⋊C411yescharacteristic
309C2×Dic61C22×D411yescharacteristic
310D244—42no—
311D244—44no—
312D244—44no—
313D244—44no—
314D244—44no—
315D244—42no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—44no—
332C4×D61—44no—
333C4×D61#9914yes—
334#92420—44no—
335#17542—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—44no—
343C22×C61C2×#10412yes—
344C22×C61C2×#10412yes—
345C22×C61C2×#10412yes—
346C22×C61C22×C22⋊C411yescharacteristic
347C2×D61—28no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—84no—
367C2×D61C2×#9912yes—
368C2×D61#57512yes—
369#6923—48no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61C2×#9912yes—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—42no—
380Dic61C2×#9912yes—
381C2×#525—611no—
382C2×#407—611no—
383C2×C4×C22⋊C4—611no—
384#1508—612no—
385#1507—612no—
386#1504—614no—
387#1501—614no—
388C2×C61—22no—
389C2×C61—22no—
390C2×C61—22no—
391C2×C61C22×#9911yescharacteristic
392C2×C61#289611yescharacteristic
393C2×C61C22×#10411yescharacteristic
394D61—22no—
395D61—22no—
396D61—41no—
397D61—41no—
398D61—82no—
399C22×#41—611no—
400C24×C4—611no—
401C22×M16—1221no—
402#525—612no—
403#525—612no—
404#525—612no—
405#525—612no—
406#525—1221no—
407#525—1221no—
408#525—1221no—
409#525—1221no—
410C2×#123—1221no—
411C2×C22⋊Q8—611no—
412C2×C22⋊Q8#692311yescharacteristic, complemented
413C2×#121—611no—
414C2×#121—611no—
415C2×#120—1221no—
416C2×C4×D4—1221no—
417C2×C4×D4—1221no—
418C2×#117—611no—
419C22×C22⋊C4—1221no—
420C22×C42—1221no—
421#407—612no—
422#407—612no—
423#407—1221no—
424#407—1221no—
425C2×C22⋊C8—612no—
426C2×C22⋊C8—1221no—
427C4×C22⋊C4—612no—
428C4×C22⋊C4—612no—
429C4×C22⋊C4—1221no—
430C4×C22⋊C4—1221no—
431C2×#95—612no—
432#328—618no—
433#327—618no—
434C61#1754211yescharacteristic, complemented, Sylow
435C25—611no—
436C2×#41—612no—
437C2×#41—612no—
438C2×#41—1221no—
439C2×#41—1221no—
440C2×#41—2444no—
441C22×Q8C2×#692311yescharacteristic, complemented
442C22×D4—611no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4—1221no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—1221no—
460C23×C4—1222no—
461C23×C4—2444no—
462C23×C4C2×#692311yescharacteristic
463C2×M16—1222no—
464C2×M16—1222no—
465C2×M16—2444no—
466C22×C8—1222no—
467#123—1222no—
468#123—1222no—
469#123—1222no—
470#123—1222no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—612no—
474C22⋊Q8—612no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8C2×#692312yes—
478C22⋊Q8C2×#692312yescomplemented
479#121—612no—
480#121—612no—
481#121—612no—
482#121—612no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#120—1222no—
488#120—1222no—
489#120—1222no—
490#120—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499#117—612no—
500#117—612no—
501#117—1221no—
502#117—1221no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C2×#692311yescharacteristic, complemented
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1222no—
513C2×C22⋊C4—1228no—
514C2×C22⋊C4—1221no—
515C2×C42—1221no—
516C2×C42—1222no—
517C2×C42—1222no—
518C2×C42—2444no—
519C22⋊C8—614no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523#95—614no—
524#95—1222no—
525C24—611no—
526C24—611no—
527C24—611no—
528C24—611no—
529C24—611no—
530C24—611no—
531C24—1224no—
532C24—1221no—
533C24—2442no—
534C24—2442no—
535C24C22⋊#692311yescharacteristic
536#41—2444no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540C2×Q8—21no—
541C2×Q8—42no—
542C2×Q8C22×#692312yes—
543C2×D4—612no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1221no—
551C2×D4—2442no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4—2444no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1224no—
586C22×C4—1228no—
587C22×C4—1221no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2444no—
598C22×C4—2442no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4C22⋊#692311yescharacteristic
602C22×C4C22⋊#692311yescharacteristic
603C22×C4C22⋊#692311yescharacteristic
604C22×C4C22×#692311yescharacteristic
605C22×C4C22×#692311yescharacteristic
606C22×C4C22×#692311yescharacteristic
607M16—2444no—
608M16—2444no—
609C2×C8—1224no—
610C2×C8—2444no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—612no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1221no—
618C4⋊C4C22×#692312yes—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1228no—
628C22⋊C4—1228no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C42—1222no—
632C42—1222no—
633C42—2444no—
634C42—2444no—
635C23—41no—
636C23—41no—
637C23—611no—
638C23—611no—
639C23—611no—
640C23—611no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2442no—
661C23—2442no—
662C23—24416no—
663C23—2442no—
664C23#1451984214yes—
665C23C2×C22⋊#692311yescharacteristic
666C23C2×C22⋊#692311yescharacteristic
667C23C2×C22⋊#692311yescharacteristic
668Q8—42no—
669Q8—42no—
670D4—2442no—
671D4—2444no—
672D4—2444no—
673D4—2444no—
674D4—2444no—
675D4—2444no—
676D4—2444no—
677D4—2442no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—611no—
689C2×C4—614no—
690C2×C4—611no—
691C2×C4—611no—
692C2×C4—611no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1228no—
706C2×C4—1222no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2444no—
714C2×C4—2444no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2444no—
719C2×C4—2444no—
720C2×C4—24416no—
721C2×C4—2442no—
722C2×C4C2×C22⋊#692311yescharacteristic
723C2×C4C2×C22⋊#692311yescharacteristic
724C2×C4C2×C22⋊#692311yescharacteristic
725C2×C4C23×#692311yescharacteristic
726C8—2444no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—44no—
734C22—612no—
735C22—612no—
736C22—1228no—
737C22—1221no—
738C22—1221no—
739C22—1221no—
740C22—1221no—
741C22—1221no—
742C22—1221no—
743C22—1221no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—4884no—
748C22—2444no—
749C22—2444no—
750C22—2444no—
751C22—2444no—
752C22—2444no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22C2×#1451984212yes—
757C22C2×#1451984212yes—
758C22C2×#1451984212yes—
759C22C22×C22⋊#692311yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—42no—
764C4—42no—
765C4—612no—
766C4—1221no—
767C4—1221no—
768C4—1221no—
769C4—2448no—
770C4—2442no—
771C4D61⋊#9912yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—1222no—
776C2—1222no—
777C2—4882no—
778C2—2441no—
779C2—2441no—
780C2C2×D61⋊#9911yescharacteristic
781C2#2146243911yescharacteristic
782C2C22×#1451984211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC2×C4×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840733C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21461219C2semidirect
4. #21461216C2semidirect
5. #21461206C2semidirect
6. #21461197C2semidirect
14. #16840733C22semidirect
15. C2×#14519834C22semidirect
20. C4×C22⋊#6923C22semidirect
21. C2×(C2×#6923)⋊C4C22semidirect
22. #16840616C22semidirect
23. #16840614C22semidirect
24. C22×#11758226C4semidirect
30. #16840275C4semidirect
31. #16840275C4semidirect
37. C2×#14519751C4semidirect
41. C2×#14519735C4semidirect
42. C2×C22⋊Q8×C61C4semidirect
65. C2×#11758226C2×C4semidirect
68. C22×D244C2×C4semidirect
91. #14519753C2×C4semidirect
95. #14519752C2×C4semidirect
100. #14519751C2×C4semidirect
116. #14519735C2×C4semidirect
117. C2×C4⋊Dic61C2×C4semidirect
124. C22×Q8×C61C2×C4semidirect
129. C22⋊Q8×C61C2×C4semidirect
131. C2×C4⋊C4×C61C2×C4semidirect
412. C2×C22⋊Q8#6923semidirect
434. C61#17542semidirect
441. C22×Q8C2×#6923semidirect
478. C22⋊Q8C2×#6923semidirect
506. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
C2×C4×C22⋊#69232
#214612192
#214612162
#214612062
#214611972
C2×#168402752
#1754261