Finite Group Databasebeta

← #30616739

Subgroups — #30616739

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21462008C212yesmaximal, complemented
4#21461958C212yesmaximal, complemented
5#21461840C214yesmaximal, complemented
6C4×#14519835C214yesmaximal, complemented
7C2×#16840269C211yesmaximal, characteristic
8C2×#14519856—21no—
9C22×C22⋊#6923C2212yes—
10C22×C4×#6923—21no—
11C2×#14519835C2218yes—
12#16840705—21no—
13#16840704—21no—
14#16840704C2212yes—
15#16840703C2212yes—
16C4×C22⋊#6923—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yes—
21C4×C22⋊#6923C2212yes—
22C2×(C2×#6923)⋊C4—21no—
23#16840640C2218yes—
24C23×C4×D61C2211yescharacteristic
25#16840269—21no—
26#16840269—21no—
27#16840269—21no—
28#16840269—21no—
29#16840269—21no—
30#16840269—21no—
31#16840269—21no—
32#16840269—21no—
33C2×#14519758C412yescomplemented
34C2×#14519753C411yescharacteristic, complemented
35C2×#14519753C2211yescharacteristic
36C2×#14519748C411yescharacteristic, complemented
37C2×#14519748C2211yescharacteristic
38C2×#14519745C2212yes—
39C2×C4×C22⋊D61C412yescomplemented
40C2×C4×C22⋊D61C2212yes—
41C2×#14519736C411yescharacteristic, complemented
42C22×#41×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44#14519856—44no—
45C2×C4⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C22⋊#6923—28no—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923C2314yes—
51C2×C22⋊#6923C2314yes—
52C2×C4×#6923—22no—
53C2×C4×#6923—22no—
54C2×C4×#6923—22no—
55C2×C4×#6923—44no—
56#14519835—216no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60(C2×#6923)⋊C4—22no—
61C24×D61C2311yescharacteristic
62C22×C22⋊D61C2×C412yes—
63C22×C22⋊D61C2312yes—
64C23×Dic61C2×C411yescharacteristic
65C22×C4×D61—44no—
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78#14519758—22no—
79#14519758—22no—
80#14519758—22no—
81#14519758—22no—
82#14519753—21no—
83#14519753—21no—
84#14519753—21no—
85#14519753—21no—
86#14519753—21no—
87#14519753—21no—
88#14519753—21no—
89#14519753—21no—
90#14519748—21no—
91#14519748—21no—
92#14519748—21no—
93#14519748—21no—
94#14519748—21no—
95#14519748—21no—
96#14519748—21no—
97#14519748—21no—
98#14519745—22no—
99#14519745—22no—
100#14519745—22no—
101#14519745—22no—
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104C4×C22⋊D61—22no—
105C4×C22⋊D61—22no—
106C4×C22⋊D61—22no—
107C4×C22⋊D61—22no—
108C4×C22⋊D61—22no—
109C4×C22⋊D61—22no—
110#14519736—21no—
111#14519736—21no—
112#14519736—21no—
113#14519736—21no—
114C2×C4⋊Dic61C2×C411yescharacteristic, complemented
115C2×C4⋊Dic61C2×C411yescharacteristic, complemented
116C2×#11758196C2×C412yescomplemented
117C2×#11758196C2×C412yescomplemented
118C2×C22⋊Dic61C2×C412yes—
119C2×C22⋊Dic61C2×C412yescomplemented
120C2×C22⋊Dic61C2×C412yescomplemented
121C2×#11758198C2×C412yes—
122C2×#11758198C2312yes—
123C2×C4×Dic61C2×C412yescomplemented
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—44no—
129C22×Q8×C61C2×C411yescharacteristic, complemented
130C22×D4×C61C2×C412yes—
131C22×D4×C61C2×C411yescharacteristic, complemented
132C23×C4×C61C2×C411yescharacteristic
133C23×C4×C61C2×C412yescomplemented
134C24×C61C22×C411yescharacteristic
135C24×C61C22×C412yes—
136C23×D61—24no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61C22×C411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C23×D61C2411yescharacteristic
145C22×#6923—28no—
146C22×#6923—24no—
147C22×#6923—24no—
148C22×#6923—44no—
149C22×#6923—44no—
150#41×C61—44no—
151#41×C61—44no—
152#41×C61—44no—
153#41×C61—44no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—42no—
162C2×D4×C61—44no—
163C22×C4×C61—24no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—44no—
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22⋊C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C412yes—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—28no—
179C2×C22⋊D61—44no—
180C22×Dic61—42no—
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C22⋊C411yescharacteristic
184C22×Dic61C22⋊C411yescharacteristic
185C22×Dic61C22×C412yes—
186C22×Dic61C22×C412yes—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C2×C4×D61—24no—
190C2×C4×D61—24no—
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—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
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×D61C22⋊C411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C22⋊#6923—28no—
218C22⋊#6923—24no—
219C22⋊#6923—28no—
220C22⋊#6923—44no—
221C22⋊#6923—44no—
222C22⋊#6923#4118yescomplemented
223C4⋊#6923—44no—
224C4×#6923—44no—
225C4×#6923—44no—
226C4×#6923—44no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241#11758196—22no—
242#11758196—22no—
243#11758196—22no—
244#11758196—22no—
245C4×Dic61—22no—
246C4×Dic61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—24no—
251C23×C61—41no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61C2×C22⋊C411yescharacteristic
255C23×C61C2×C22⋊C411yescharacteristic
256C23×C61C23×C411yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—416no—
275C22×D61C2×C22⋊C411yescharacteristic
276C22×D61C2×C22⋊C411yescharacteristic
277C22×D61C22×D411yescharacteristic
278C22×D61C22×D411yescharacteristic
279C22×D61C2×#4114yes—
280C2×#6923—28no—
281C2×#6923—44no—
282C2×#6923—416no—
283C2×#6923—44no—
284C2×#6923—44no—
285C2×#6923—44no—
286C2×#6923—44no—
287Q8×C61—42no—
288Q8×C61—42no—
289D4×C61—42no—
290D4×C61—44no—
291D4×C61—44no—
292D4×C61—42no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—44no—
300C2×C4×C61—44no—
301C2×C4×C61—42no—
302C2×C4×C61#9914yescomplemented
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C22⋊D61—44no—
308C22⋊D61—44no—
309C22⋊D61—44no—
310C22⋊D61—44no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—24no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—42no—
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341#21420—611nomaximal, Sylow
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—44no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—84no—
354C22×C61C2×#9912yes—
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C4×#4112yes—
357C2×D61—28no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61#41012yes—
373C2×D61#52512yes—
374C2×D61#53212yes—
375#6923—48no—
376#6923—84no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—42no—
380C4×C61C2×#9912yes—
381C4×C61C2×#9912yes—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—21no—
386Dic61—42no—
387Dic61—42no—
388C2×#525—611no—
389#2280—611no—
390C2×C4×C22⋊C4—611no—
391#1996—612no—
392#1964—612no—
393#1898—614no—
394C4×#99—614no—
395C2×C61—22no—
396C2×C61—22no—
397C2×C61—41no—
398C2×C61—82no—
399C2×C61#229711yescharacteristic
400C2×C61C22×#9911yescharacteristic
401C2×C61C2×#41011yescharacteristic
402D61—22no—
403D61—22no—
404D61—22no—
405D61—41no—
406C22×#41#692311yescharacteristic, complemented
407C24×C4—611no—
408#525—1221no—
409#525—1221no—
410#525—1221no—
411#525—1221no—
412#525—1221no—
413#525—1221no—
414#525—1221no—
415#525—1221no—
416C2×#123—612no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×#121—611no—
420C2×#121—611no—
421C2×#120—612no—
422C2×C4×D4—612no—
423C2×C4×D4—612no—
424C2×#117—611no—
425C2×#117—1221no—
426C22×C22⋊C4—612no—
427C22×C42—1221no—
428C2×#99—618no—
429#381—1221no—
430#380—612no—
431#380—1221no—
432#379—612no—
433C4×C22⋊C4—612no—
434C4×C22⋊C4—612no—
435C4×C22⋊C4—612no—
436C4×C22⋊C4—1221no—
437C4×C22⋊C4—1221no—
438C4×C22⋊C4—1221no—
439C2×#95—1221no—
440#342—618no—
441C61#2142011yescharacteristic, complemented, Sylow
442C25—611no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—44no—
448C22×Q8C2×#692311yescharacteristic, complemented
449C22×D4—612no—
450C22×D4—612no—
451C22×D4C2×#692312yes—
452C22×D4C2×#692311yescharacteristic, complemented
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1222no—
467C23×C4—2444no—
468C23×C4C2×#692311yescharacteristic
469C23×C4C2×#692312yescomplemented
470#123—1222no—
471#123—1222no—
472#123—1222no—
473#123—1222no—
474C22⋊Q8—1221no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479C22⋊Q8—1221no—
480C22⋊Q8—1221no—
481C22⋊Q8—1221no—
482#121—1221no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#121—1221no—
488#121—1221no—
489#121—1221no—
490#120—1222no—
491#120—1222no—
492#120—1222no—
493#120—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—1221no—
503#117—1221no—
504#117—1221no—
505#117—1221no—
506#117—2444no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—1222no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4—612no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—1228no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4—1222no—
523C2×C42—612no—
524C2×C42—1222no—
525C2×C42—1222no—
526C2×C42—1222no—
527C2×C42—2444no—
528#99—12216no—
529#95—1222no—
530#95—1222no—
531#95—1222no—
532#95—1222no—
533C24—611no—
534C24—611no—
535C24—611no—
536C24—611no—
537C24—611no—
538C24—611no—
539C24—1224no—
540C24—2442no—
541C24—2442no—
542C24C22×#692311yescharacteristic
543C24C22×#692312yes—
544#41—44no—
545#41—44no—
546#41—44no—
547#41—44no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4—1228no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—2444no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—44no—
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—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—1224no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1228no—
595C22×C4—1224no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2444no—
608C22×C4—2444no—
609C22×C4C22⋊#692311yescharacteristic
610C22×C4C22⋊#692311yescharacteristic
611C22×C4C22⋊#692311yescharacteristic
612C22×C4C22⋊#692311yescharacteristic
613C22×C4C22×#692311yescharacteristic
614C22×C4C22×#692311yescharacteristic
615C22×C4C22×#692312yes—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—2444no—
625C22⋊C4—618no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1222no—
634C22⋊C4—1224no—
635C22⋊C4—1228no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1228no—
639C22⋊C4—2444no—
640C22⋊C4—2444no—
641C42—1222no—
642C42—1222no—
643C42—2444no—
644C42—2444no—
645C42—2444no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—611no—
654C23—611no—
655C23—611no—
656C23—614no—
657C23—611no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—24416no—
676C23C2×C22⋊#692311yescharacteristic
677C23C2×C22⋊#692311yescharacteristic
678C23C23×#692311yescharacteristic
679Q8—42no—
680Q8—42no—
681D4—42no—
682D4—44no—
683D4—44no—
684D4—42no—
685D4—2444no—
686D4—2444no—
687D4—2444no—
688D4—2444no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—611no—
699C2×C4—611no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1228no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1224no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4—2444no—
731C2×C4—2444no—
732C2×C4—24416no—
733C2×C4—2444no—
734C2×C4—2442no—
735C2×C4#1451983514yescomplemented
736C2×C4C2×C22⋊#692311yescharacteristic
737C2×C4C2×C22⋊#692311yescharacteristic
738C2×C4C2×C22⋊#692311yescharacteristic
739C2×C4C2×C22⋊#692311yescharacteristic
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—44no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—84no—
752C22—612no—
753C22—612no—
754C22—612no—
755C22—1228no—
756C22—1221no—
757C22—1221no—
758C22—1221no—
759C22—1221no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—1221no—
764C22—1221no—
765C22—2444no—
766C22—2444no—
767C22—2444no—
768C22—2444no—
769C22—2444no—
770C22C2×#1451983512yes—
771C22C22×C22⋊#692311yescharacteristic
772C22#41×#692312yes—
773C4—21no—
774C4—21no—
775C4—42no—
776C4—1221no—
777C4—1221no—
778C4—1221no—
779C4—1221no—
780C4—4884no—
781C4—2448no—
782C4—2442no—
783C4—2442no—
784C4C2×#1451983512yes—
785C4C2×#1451983512yes—
786C2—22no—
787C2—22no—
788C2—41no—
789C2—82no—
790C2—1222no—
791C2—1222no—
792C2—1222no—
793C2—2441no—
794C2#2146228011yescharacteristic
795C2C22×#1451983511yescharacteristic
796C2D61⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840269C2
cosocleC23×D61C24
hypercenterC22×#41#6923
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #21462263C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21462008C2semidirect
4. #21461958C2semidirect
5. #21461840C2semidirect
6. C4×#14519835C2semidirect
33. C2×#14519758C4semidirect
34. C2×#14519753C4semidirect
36. C2×#14519748C4semidirect
39. C2×C4×C22⋊D61C4semidirect
41. C2×#14519736C4semidirect
42. C22×#41×C61C4semidirect
114. C2×C4⋊Dic61C2×C4semidirect
115. C2×C4⋊Dic61C2×C4semidirect
116. C2×#11758196C2×C4semidirect
117. C2×#11758196C2×C4semidirect
119. C2×C22⋊Dic61C2×C4semidirect
120. C2×C22⋊Dic61C2×C4semidirect
123. C2×C4×Dic61C2×C4semidirect
129. C22×Q8×C61C2×C4semidirect
131. C22×D4×C61C2×C4semidirect
133. C23×C4×C61C2×C4semidirect
222. C22⋊#6923#41semidirect
302. C2×C4×C61#99semidirect
406. C22×#41#6923semidirect
441. C61#21420semidirect
448. C22×Q8C2×#6923semidirect
452. C22×D4C2×#6923semidirect
469. C23×C4C2×#6923semidirect
735. C2×C4#14519835semidirect

Maximal subgroups

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

subgroupindex
#214622632
C2×C4×C22⋊#69232
#214620082
#214619582
#214618402
C4×#145198352
C2×#168402692
#2142061