Finite Group Databasebeta

← #30616741

Subgroups — #30616741

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#21462009C212yesmaximal, complemented
4#21461959C212yesmaximal, complemented
5#21461841C214yesmaximal, complemented
6C4×#14519836C214yesmaximal, complemented
7C2×#16840274C211yesmaximal, characteristic
8C2×#14519856—21no—
9C22×C22⋊#6923C2212yes—
10C22×C4×#6923—21no—
11C2×#14519836C2218yes—
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—
24C22×#11758222C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26#16840274—21no—
27#16840274—21no—
28#16840274—21no—
29#16840274—21no—
30#16840274—21no—
31#16840274—21no—
32#16840274—21no—
33#16840274—21no—
34C2×#14519761C412yescomplemented
35C2×#14519757C411yescharacteristic, complemented
36C2×#14519757C2211yescharacteristic
37C2×#14519752C411yescharacteristic, complemented
38C2×#14519752C2211yescharacteristic
39C2×#14519747C2212yes—
40C2×C4×D244C412yescomplemented
41C2×C4×D244C2212yes—
42C2×#117×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#14519836—216no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60(C2×#6923)⋊C4—22no—
61C24×D61C2311yescharacteristic
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222—21no—
65C2×#11758222—21no—
66C2×#11758222—44no—
67C22×Dic122C2×C411yescharacteristic, complemented
68C22×D244C2×C412yes—
69C22×D244C2×C411yescharacteristic, complemented
70C22×D244C2312yes—
71C22×C22⋊D61C2×C412yes—
72C23×Dic61C2×C411yescharacteristic
73C22×C4×D61—44no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C412yescomplemented
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87#14519761—22no—
88#14519761—22no—
89#14519761—22no—
90#14519761—22no—
91#14519757—21no—
92#14519757—21no—
93#14519757—21no—
94#14519757—21no—
95#14519757—21no—
96#14519757—21no—
97#14519757—21no—
98#14519757—21no—
99#14519752—21no—
100#14519752—21no—
101#14519752—21no—
102#14519752—21no—
103#14519752—21no—
104#14519752—21no—
105#14519752—21no—
106#14519752—21no—
107#14519747—22no—
108#14519747—22no—
109#14519747—22no—
110#14519747—22no—
111C4×D244—22no—
112C4×D244—22no—
113C4×D244—22no—
114C4×D244—22no—
115C4×D244—22no—
116C4×D244—22no—
117C4×D244—22no—
118C4×D244—22no—
119C2×C4⋊Dic61C2×C412yescomplemented
120C2×C4⋊Dic61C2×C412yescomplemented
121C2×#11758198C2×C412yes—
122C2×#11758198C2×C412yescomplemented
123C2×#11758198C2×C412yescomplemented
124C2×#11758198C2312yes—
125C23×C4×C61C2×C411yescharacteristic
126#117×C61—21no—
127#117×C61—21no—
128#117×C61—21no—
129#117×C61—21no—
130C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
131C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
132C2×C22⋊C4×C61C2×C412yes—
133C2×C42×C61C2×C412yescomplemented
134C24×C61C22×C411yescharacteristic
135C23×D61—24no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C22×C411yescharacteristic
139C23×D61C22×C412yes—
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—
150C22×C4×C61—24no—
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22⋊C411yescharacteristic
153C22×C4×C61C22⋊C411yescharacteristic
154C22×C4×C61C22⋊C411yescharacteristic
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C412yes—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—44no—
162C22×Dic61—42no—
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22×C412yes—
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170#11758222—44no—
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—28no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—42no—
182C2×D244—44no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
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—44no—
198C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
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×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—42no—
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—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C42×C61—22no—
234C42×C61—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246C4⋊Dic61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—41no—
250C23×C61C2×C22⋊C411yescharacteristic
251C23×C61C2×C22⋊C411yescharacteristic
252C23×C61C23×C411yescharacteristic
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—22no—
263C22×D61—22no—
264C22×D61—24no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—416no—
273C22×D61—42no—
274C22×D61—42no—
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—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—42no—
296C2×C4×C61#9914yescomplemented
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C22⋊D61—44no—
302C22⋊D61—44no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—42no—
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315D244—42no—
316D244—44no—
317D244—44no—
318D244—44no—
319D244—44no—
320D244—42no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—44no—
338C4×D61—44no—
339Dic122—42no—
340Dic122—42no—
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×C61C2×#9912yes—
351C22×C61C22×C22⋊C411yescharacteristic
352C22×C61C4×#4112yes—
353C2×D61—28no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—84no—
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×C61—42no—
381C4×C61C2×#9912yes—
382C4×C61C2×#9912yes—
383Dic61—21no—
384Dic61—21no—
385Dic61—21no—
386Dic61—21no—
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#229711yescharacteristic
399C2×C61C22×#9911yescharacteristic
400C2×C61C2×#41011yescharacteristic
401D61—22no—
402D61—22no—
403D61—22no—
404D61—41no—
405D61—82no—
406C22×#41—611no—
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—1221no—
425C2×#117#692311yescharacteristic, complemented
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—1221no—
444C2×#41—1221no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—2444no—
448C22×Q8—611no—
449C22×D4—612no—
450C22×D4—612no—
451C22×D4—612no—
452C22×D4—611no—
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—612no—
467C23×C4—1222no—
468C23×C4—2444no—
469C23×C4C2×#692311yescharacteristic
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—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—2444no—
507C2×C4⋊C4—612no—
508C2×C4⋊C4—612no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4C2×#692311yescharacteristic, complemented
511C2×C4⋊C4C2×#692311yescharacteristic, complemented
512C2×C22⋊C4—614no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4—612no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—1228no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4C2×#692312yes—
523C2×C42—1222no—
524C2×C42—1222no—
525C2×C42—1222no—
526C2×C42—2444no—
527C2×C42C2×#692312yescomplemented
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—612no—
540C24—1224no—
541C24—2442no—
542C24—2442no—
543C24C22×#692311yescharacteristic
544#41—2444no—
545#41—2444no—
546#41—2444no—
547#41—2444no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—2442no—
551C2×D4—1228no—
552C2×D4—1222no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—2442no—
561C2×D4—2444no—
562C2×D4—2444no—
563C22×C4—24no—
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—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—612no—
587C22×C4—1224no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1228no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1224no—
594C22×C4—2442no—
595C22×C4—2442no—
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—2444no—
605C22×C4—2442no—
606C22×C4—2444no—
607C22×C4—2444no—
608C22×C4C22⋊#692311yescharacteristic
609C22×C4C22⋊#692311yescharacteristic
610C22×C4C22⋊#692311yescharacteristic
611C22×C4C22⋊#692311yescharacteristic
612C22×C4C22×#692312yes—
613C22×C4C22×#692311yescharacteristic
614C22×C4C22×#692311yescharacteristic
615C22×C4C22×#692312yes—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1222no—
623C4⋊C4—1222no—
624C4⋊C4—2444no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—618no—
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—1224no—
637C22⋊C4—1228no—
638C22⋊C4—1228no—
639C22⋊C4—2444no—
640C22⋊C4—2444no—
641C42—22no—
642C42—22no—
643C42—2444no—
644C42—2444no—
645C42—2444no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—611no—
650C23—611no—
651C23—611no—
652C23—614no—
653C23—611no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1224no—
665C23—1222no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2442no—
674C23—2442no—
675C23—24416no—
676C23C2×C22⋊#692311yescharacteristic
677C23C2×C22⋊#692311yescharacteristic
678C23C23×#692311yescharacteristic
679Q8—2442no—
680Q8—2442no—
681D4—2442no—
682D4—2444no—
683D4—2444no—
684D4—2444no—
685D4—2444no—
686D4—2444no—
687D4—2444no—
688D4—2442no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
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—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2444no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2444no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4—2444no—
731C2×C4—24416no—
732C2×C4—2444no—
733C2×C4—2444no—
734C2×C4—2442no—
735C2×C4#1451983614yescomplemented
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—612no—
749C22—612no—
750C22—612no—
751C22—1228no—
752C22—1221no—
753C22—1221no—
754C22—1221no—
755C22—1221no—
756C22—1221no—
757C22—1221no—
758C22—1221no—
759C22—1221no—
760C22—1221no—
761C22—4884no—
762C22—2444no—
763C22—2444no—
764C22—2444no—
765C22—2444no—
766C22—2444no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22C2×#1451983612yes—
771C22C22×C22⋊#692311yescharacteristic
772C22#41×#692312yes—
773C4—21no—
774C4—21no—
775C4—42no—
776C4—42no—
777C4—1221no—
778C4—1221no—
779C4—1221no—
780C4—1221no—
781C4—4884no—
782C4—2448no—
783C4—2442no—
784C4C2×#1451983612yes—
785C4C2×#1451983612yes—
786C2—22no—
787C2—22no—
788C2—41no—
789C2—1222no—
790C2—1222no—
791C2—1222no—
792C2—4882no—
793C2—2441no—
794C2#2146228011yescharacteristic
795C2C22×#1451983611yescharacteristic
796C2D61⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840274C2
cosocleC23×D61C24
hypercenterC2×#117#6923
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462263C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21462009C2semidirect
4. #21461959C2semidirect
5. #21461841C2semidirect
6. C4×#14519836C2semidirect
24. C22×#11758222C4semidirect
34. C2×#14519761C4semidirect
35. C2×#14519757C4semidirect
37. C2×#14519752C4semidirect
40. C2×C4×D244C4semidirect
42. C2×#117×C61C4semidirect
67. C22×Dic122C2×C4semidirect
69. C22×D244C2×C4semidirect
76. C22×C4×D61C2×C4semidirect
119. C2×C4⋊Dic61C2×C4semidirect
120. C2×C4⋊Dic61C2×C4semidirect
122. C2×#11758198C2×C4semidirect
123. C2×#11758198C2×C4semidirect
130. C2×C4⋊C4×C61C2×C4semidirect
131. C2×C4⋊C4×C61C2×C4semidirect
133. C2×C42×C61C2×C4semidirect
222. C22⋊#6923#41semidirect
296. C2×C4×C61#99semidirect
425. C2×#117#6923semidirect
441. C61#21420semidirect
510. C2×C4⋊C4C2×#6923semidirect
511. C2×C4⋊C4C2×#6923semidirect
527. C2×C42C2×#6923semidirect
735. C2×C4#14519836semidirect

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
#214620092
#214619592
#214618412
C4×#145198362
C2×#168402742
#2142061