Finite Group Databasebeta

← #30616740

Subgroups — #30616740

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#21461958C212yesmaximal, complemented
5#21461840C214yesmaximal, complemented
6#21461566C214yesmaximal, complemented
7C2×#16840272C211yesmaximal, 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—
24C22×#11758224C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26#16840272—21no—
27#16840272—21no—
28#16840272—21no—
29#16840272—21no—
30#16840272—21no—
31#16840272—21no—
32#16840272—21no—
33#16840272—21no—
34C2×#14519759C412yescomplemented
35C2×#14519757C2211yescharacteristic
36C2×#14519756C411yescharacteristic, complemented
37C2×#14519748C2211yescharacteristic
38C2×#14519745C2212yes—
39C2×D4×Dic61C412yescomplemented
40C2×#14519737C2212yes—
41C2×#14519735C411yescharacteristic, complemented
42C2×#121×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
62C2×#11758224—21no—
63C2×#11758224—21no—
64C2×#11758224—21no—
65C2×#11758224—21no—
66C2×#11758224—44no—
67C22×Dic122C2×C411yescharacteristic, complemented
68C22×C22⋊D61C2×C412yes—
69C22×C22⋊D61C2312yes—
70C23×Dic61C2×C411yescharacteristic
71C23×Dic61C2×C412yescomplemented
72C22×C4×D61—44no—
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85#14519759—22no—
86#14519759—22no—
87#14519759—22no—
88#14519759—22no—
89#14519757—21no—
90#14519757—21no—
91#14519757—21no—
92#14519757—21no—
93#14519756—21no—
94#14519756—21no—
95#14519756—21no—
96#14519756—21no—
97#14519748—21no—
98#14519748—21no—
99#14519748—21no—
100#14519748—21no—
101#14519745—22no—
102#14519745—22no—
103#14519745—22no—
104#14519745—22no—
105D4×Dic61—22no—
106D4×Dic61—22no—
107D4×Dic61—22no—
108D4×Dic61—22no—
109#14519737—22no—
110#14519737—22no—
111#14519737—22no—
112#14519737—22no—
113#14519735—21no—
114#14519735—21no—
115#14519735—21no—
116#14519735—21no—
117C2×C4⋊Dic61C2×C411yescharacteristic, complemented
118C2×C4⋊Dic61C2×C412yescomplemented
119C2×#11758196C2×C412yescomplemented
120C2×C22⋊Dic61C2×C412yes—
121C2×C22⋊Dic61C2×C412yescomplemented
122C2×#11758198C2×C412yes—
123C2×#11758198C2312yes—
124C2×C4×Dic61C2×C412yescomplemented
125C22×D4×C61C2×C412yes—
126C22×D4×C61C2×C411yescharacteristic, complemented
127C23×C4×C61C2×C411yescharacteristic
128#121×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
133C2×C22⋊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—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—42no—
155C2×D4×C61—44no—
156C22×C4×C61—42no—
157C22×C4×C61C22⋊C411yescharacteristic
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C412yes—
163C22×C4×C61C22×C411yescharacteristic
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—28no—
169C2×C22⋊D61—44no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—42no—
173C22×Dic61—44no—
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C22×C412yes—
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C412yes—
181C22×Dic61C22×C411yescharacteristic
182#11758224—44no—
183#11758224—44no—
184#11758224—44no—
185#11758224—44no—
186C2×C4×D61—24no—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
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×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—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—22no—
242C4⋊Dic61—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—
287D4×C61—42no—
288D4×C61—44no—
289D4×C61—44no—
290D4×C61—42no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C22⋊D61—44no—
304C22⋊D61—44no—
305C22⋊D61—44no—
306C22⋊D61—44no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—44no—
317C2×Dic61—44no—
318C2×Dic61—42no—
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61#9914yescomplemented
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×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—84no—
354C22×C61#41012yes—
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×D61C2×#9912yes—
373C2×D61#52512yes—
374C2×D61#53212yes—
375#6923—48no—
376#6923—84no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—42no—
381C4×C61C2×#9912yes—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—42no—
386Dic61—42no—
387Dic61C2×#9912yes—
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—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#692311yescharacteristic, complemented
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—1221no—
444C2×#41—1221no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—2444no—
448C22×Q8—611no—
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—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—21no—
483#121—21no—
484#121—21no—
485#121—21no—
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—612no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—1222no—
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×#692312yescomplemented
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—2444no—
545#41—2444no—
546#41—2444no—
547#41—2444no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—2442no—
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—42no—
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—612no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1222no—
592C22×C4—1222no—
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—2444no—
607C22×C4—2444no—
608C22×C4—2444no—
609C22×C4C22⋊#692311yescharacteristic
610C22×C4C22⋊#692311yescharacteristic
611C22×C4C22⋊#692311yescharacteristic
612C22×C4C22⋊#692311yescharacteristic
613C22×C4C22×#692311yescharacteristic
614C22×C4C22×#692312yes—
615C22×C4C22×#692311yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
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—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—2442no—
680Q8—2442no—
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—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—611no—
698C2×C4—614no—
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—1222no—
713C2×C4—1222no—
714C2×C4—1228no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1224no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2444no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4—2444no—
731C2×C4—2444no—
732C2×C4—2444no—
733C2×C4—24416no—
734C2×C4—2444no—
735C2×C4—2442no—
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—
770C22#1684074212yes—
771C22C22×C22⋊#692311yescharacteristic
772C22#41×#692312yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—42no—
777C4—612no—
778C4—1221no—
779C4—1221no—
780C4—1221no—
781C4—4884no—
782C4—2448no—
783C4—2442no—
784C4—2442no—
785C4D61⋊#9912yes—
786C2—22no—
787C2—22no—
788C2—41no—
789C2—82no—
790C2—1222no—
791C2—1222no—
792C2—1222no—
793C2—2441no—
794C2#2146228011yescharacteristic
795C2C2×D61⋊#9911yescharacteristic
796C2C2×#1684074211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC23×D61C24
hypercenterC2×#121#6923
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462263C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21462009C2semidirect
4. #21461958C2semidirect
5. #21461840C2semidirect
6. #21461566C2semidirect
24. C22×#11758224C4semidirect
34. C2×#14519759C4semidirect
36. C2×#14519756C4semidirect
39. C2×D4×Dic61C4semidirect
41. C2×#14519735C4semidirect
42. C2×#121×C61C4semidirect
67. C22×Dic122C2×C4semidirect
71. C23×Dic61C2×C4semidirect
117. C2×C4⋊Dic61C2×C4semidirect
118. C2×C4⋊Dic61C2×C4semidirect
119. C2×#11758196C2×C4semidirect
121. C2×C22⋊Dic61C2×C4semidirect
124. C2×C4×Dic61C2×C4semidirect
126. C22×D4×C61C2×C4semidirect
132. C2×C4⋊C4×C61C2×C4semidirect
133. C2×C22⋊C4×C61C2×C4semidirect
222. C22⋊#6923#41semidirect
338. C4×D61#99semidirect
420. C2×#121#6923semidirect
441. C61#21420semidirect
452. C22×D4C2×#6923semidirect
511. C2×C4⋊C4C2×#6923semidirect
522. C2×C22⋊C4C2×#6923semidirect

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
#214619582
#214618402
#214615662
C2×#168402722
#2142061