Finite Group Databasebeta

← #30620332

Subgroups — #30620332

Order 15616.

1322 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462557C212yesmaximal, complemented
2#21462012C212yesmaximal, complemented
3#21461845C212yesmaximal, complemented
4#21461844C212yesmaximal, complemented
5#21461719C211yesmaximal, characteristic, complemented
6#21461718C211yesmaximal, characteristic, complemented
7#21461684C211yesmaximal, characteristic, complemented
8#21461569C211yesmaximal, characteristic, complemented
9#21461522C211yesmaximal, characteristic, complemented
10C2×#16840642C211yesmaximal, characteristic, complemented
11C2×#16840410C211yesmaximal, characteristic
12C2×D61⋊M16C2212yes—
13C22×#11758217C2212yes—
14#16840795—22no—
15#16840794—22no—
16#16840791—22no—
17#16840789—22no—
18#16840765C2212yes—
19C2×#14519837C2212yes—
20C2×#14519837C2212yes—
21#16840734C2212yes—
22#16840732C2212yes—
23C4×#11758217C2212yes—
24#16840642C2211yescharacteristic
25#16840642C2212yes—
26#16840642C2211yescharacteristic
27#16840642C2212yes—
28#16840642C2211yescharacteristic
29#16840642C2211yescharacteristic
30#16840642C2212yes—
31#16840642C2212yes—
32C22×#11758222C411yescharacteristic
33C22×#11758224C411yescharacteristic
34#16840410—22no—
35#16840410—22no—
36#16840410—22no—
37#16840410—22no—
38C2×#14519776C2211yescharacteristic
39C2×#14519762C411yescharacteristic
40C2×#14519761C411yescharacteristic
41C2×#14519759C411yescharacteristic
42C2×#14519755C411yescharacteristic
43C2×#14519754C411yescharacteristic
44C2×#14519750C2211yescharacteristic
45C2×#14519749C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519737C2211yescharacteristic
48C22×#11758196C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×#123×C61C411yescharacteristic
51C2×#11758213—22no—
52D61⋊M16—24no—
53D61⋊M16—42no—
54C2×#11758217—22no—
55C2×#11758217—24no—
56C2×#11758217—42no—
57C2×#11758217C2312yes—
58C2×#11758217C2312yes—
59C2×#11758217C2312yes—
60C2×#11758217C2312yes—
61C2×D61⋊C8—22no—
62C22×#92420—22no—
63#14519844—22no—
64C4⋊#92420—22no—
65#14519837—24no—
66#14519837—42no—
67#14519834—22no—
68#14519834—22no—
69C22⋊#92420—22no—
70C22⋊#92420—22no—
71#14519832—22no—
72C4×#92420—22no—
73C2×#11758222—21no—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—44no—
78C2×#11758224—21no—
79C2×#11758224—21no—
80C2×#11758224—21no—
81C2×#11758224—21no—
82C2×#11758224—44no—
83C22×Dic122C2×C411yescharacteristic
84C22×Dic122C2×C411yescharacteristic
85C22×D244C2×C411yescharacteristic
86C22×C22⋊D61C2×C411yescharacteristic
87C22×C22⋊D61C2×C411yescharacteristic
88C22×C22⋊D61C2×C411yescharacteristic
89C22×C22⋊D61C2311yescharacteristic
90C23×Dic61C2×C411yescharacteristic
91C23×Dic61C2×C411yescharacteristic
92C23×Dic61C2311yescharacteristic
93C22×C4×D61C2×C411yescharacteristic
94C22×C4×D61C2×C411yescharacteristic
95C22×C4×D61C2×C411yescharacteristic
96C22×C4×D61C2311yescharacteristic
97#14519776—22no—
98#14519776—22no—
99#14519762—22no—
100#14519762—22no—
101#14519761—22no—
102#14519761—22no—
103#14519759—22no—
104#14519759—22no—
105#14519755—22no—
106#14519755—22no—
107#14519754—22no—
108#14519754—22no—
109#14519750—22no—
110#14519750—22no—
111#14519749—22no—
112#14519749—22no—
113#14519737—22no—
114#14519737—22no—
115#14519737D412yes—
116#14519737D412yes—
117#14519737D412yes—
118#14519737D412yes—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×#11758196—22no—
122C2×#11758196—22no—
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2311yescharacteristic
127C2×#11758196C2311yescharacteristic
128C2×#11758196C2311yescharacteristic
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C22×D4×C61C2×C411yescharacteristic
138C23×C4×C61C2×C411yescharacteristic
139#123×C61—22no—
140#123×C61—22no—
141C2×C4⋊C4×C61C2×C411yescharacteristic
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2×C411yescharacteristic
145C2×C22⋊C4×C61C2×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C24×C61C22×C411yescharacteristic
148C23×D61C22×C411yescharacteristic
149C23×D61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—42no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—42no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—21no—
165C2×C22⋊D61—21no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—21no—
169C2×C22⋊D61—21no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61C22⋊C411yescharacteristic
173C2×C22⋊D61C22⋊C411yescharacteristic
174C2×C22⋊D61C22⋊C411yescharacteristic
175C2×C22⋊D61C22⋊C411yescharacteristic
176C22×Dic61—22no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C2×D412yes—
191C22×Dic61C2×D412yes—
192C22×Dic61C2411yescharacteristic
193#11758224—44no—
194#11758224—44no—
195#11758224—44no—
196#11758224—44no—
197#11758222—44no—
198#11758222—44no—
199#11758222—44no—
200#11758222—44no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—42no—
204C2×C4×D61—22no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2×D412yes—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—42no—
223C2×Dic122—42no—
224#11758217—22no—
225#11758217—22no—
226#11758217—22no—
227#11758217—22no—
228#11758217—22no—
229#11758217—22no—
230#11758217—22no—
231#11758217—44no—
232#11758217#4114yescomplemented
233C2×#92420—22no—
234C2×#92420—22no—
235C2×#92420—22no—
236C2×#92420—22no—
237C2×#92420—44no—
238#11758213—44no—
239D61⋊C8—44no—
240C4⋊C4×C61—22no—
241C4⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61C22⋊C412yes—
245C22⋊C4×C61C22⋊C412yes—
246C22⋊Dic61—22no—
247#11758198—22no—
248#11758198—22no—
249#11758198—22no—
250#11758198C22⋊C412yes—
251#11758198C22⋊C412yes—
252C4⋊Dic61—22no—
253C4⋊Dic61—22no—
254#11758196—22no—
255#11758196—22no—
256#11758196—22no—
257#11758196—22no—
258#11758196—22no—
259#11758196C22⋊C412yes—
260#11758196C22⋊C412yes—
261C4×Dic61C2×D412yes—
262C4×Dic61C2×D412yes—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—22no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61C2×C22⋊C411yescharacteristic
273C23×C61C2×C22⋊C411yescharacteristic
274C23×C61C23×C411yescharacteristic
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—22no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61C2×C22⋊C411yescharacteristic
285C22×D61C2×C22⋊C411yescharacteristic
286D4×C61—42no—
287D4×C61—42no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61C2×C22⋊C412yes—
300C2×C4×C61C2×C22⋊C412yes—
301C22⋊D61—22no—
302C22⋊D61—22no—
303C22⋊D61—22no—
304C22⋊D61—42no—
305C22⋊D61—42no—
306C22⋊D61—42no—
307C22⋊D61—42no—
308C22⋊D61—42no—
309C22⋊D61—42no—
310C22⋊D61#10014yescomplemented
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C412yes—
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C22×D412yes—
332C2×Dic61C2×#4112yes—
333C2×Dic61H(5,𝔽2)11yescharacteristic
334C2×Dic612−1+411yescharacteristic
335D244—42no—
336D244—42no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347Dic122—42no—
348Dic122—42no—
349Dic122—42no—
350Dic122—42no—
351#92420—24no—
352#92420—42no—
353#92420—42no—
354#92420—42no—
355#22479—611nomaximal, Sylow
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61C2×#10012yes—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61C4×#4111yescharacteristic
373C22×C61#52011yescharacteristic
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61C2×#10012yes—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392Dic61—22no—
393Dic61—21no—
394Dic61—41no—
395Dic61—41no—
396Dic61—41no—
397Dic61C2×#10012yes—
398Dic61#54612yes—
399Dic61#54712yes—
400C2×#547—611no—
401D4×M16—612no—
402#1997—612no—
403#1900—612no—
404#1900—612no—
405#1821—611no—
406#1821—611no—
407#1800—611no—
408C4×#100—611no—
409C2×#343—611no—
410C2×#343—611no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—22no—
414C2×C61—41no—
415C2×C61—81no—
416C2×C61#233911yescharacteristic
417C2×C61C22×#10011yescharacteristic
418C2×C61#288911yescharacteristic
419D61—22no—
420D61—41no—
421D61—81no—
422C22×#41—611no—
423C22×#41—611no—
424C22×M16—612no—
425C22×M16—612no—
426#547—1222no—
427#547—1222no—
428#547—1222no—
429#547—1222no—
430C2×C4⋊Q8—611no—
431C2×#123—611no—
432C2×#123—611no—
433C2×#123—611no—
434C2×#123#692311yescharacteristic
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8—611no—
437C2×#121—611no—
438C2×#121—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443#436—1222no—
444#435—1222no—
445#435—1222no—
446C8×D4—1222no—
447#423—612no—
448C2×#100—612no—
449C2×#100—612no—
450#407—612no—
451#407—612no—
452C4×M16—612no—
453#343—611no—
454#343—611no—
455#343—611no—
456#343—612no—
457#343—612no—
458#343—612no—
459#343—612no—
460#343—611no—
461C61#2247911yescharacteristic, complemented, Sylow
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—2444no—
471C2×#41—2444no—
472C22×Q8—611no—
473C22×Q8—611no—
474C22×D4—611no—
475C22×D4—611no—
476C22×D4—611no—
477C22×D4—611no—
478C22×D4—611no—
479C22×D4C2×#692311yescharacteristic
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4C2×#692311yescharacteristic
488C2×M16—612no—
489C2×M16—612no—
490C2×M16—612no—
491C2×M16—612no—
492C2×M16—1222no—
493C2×M16—1222no—
494C2×M16—1224no—
495C2×M16—1224no—
496C2×M16—2442no—
497C2×M16—2442no—
498C22×C8—1222no—
499C22×C8—1222no—
500C4⋊Q8—1222no—
501C4⋊Q8—1222no—
502#123—22no—
503#123—22no—
504#123—1222no—
505#123—1222no—
506#123—1222no—
507#123—1222no—
508#123—1222no—
509#123—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514#121—1222no—
515#121—1222no—
516#121—1222no—
517#121—1222no—
518C4×D4—612no—
519C4×D4—612no—
520C4×D4—612no—
521C4×D4—612no—
522C4×D4—1222no—
523C4×D4—1222no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—1222no—
533C2×C4⋊C4—1222no—
534C2×C4⋊C4—1222no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4C2×#692311yescharacteristic
537C2×C4⋊C4C2×#692311yescharacteristic
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4C2×#692311yescharacteristic
544C2×C22⋊C4C2×#692311yescharacteristic
545C2×C22⋊C4C2×#692311yescharacteristic
546C2×C42—611no—
547C4⋊C8—1222no—
548C4⋊C8—1222no—
549#100—1224no—
550#100—2442no—
551C22⋊C8—1222no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555#97—1222no—
556C4×C8—1222no—
557C24—611no—
558C24—611no—
559C24C22×#692311yescharacteristic
560C24C22×#692311yescharacteristic
561#41—2444no—
562#41—2444no—
563#41—2444no—
564#41—2444no—
565#41—2444no—
566#41—2444no—
567#41—2444no—
568#41—2444no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—2442no—
574C2×Q8—2442no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—611no—
579C2×D4—611no—
580C2×D4—611no—
581C2×D4—611no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1222no—
587C2×D4—1221no—
588C2×D4—1224no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—2442no—
594C2×D4—2442no—
595C2×D4—2442no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—611no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1222no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4C22×#692311yescharacteristic
631C22×C4C22×#692311yescharacteristic
632C22×C4C22×#692311yescharacteristic
633C22×C4C22×#692311yescharacteristic
634C22×C4C22×#692311yescharacteristic
635M16—614no—
636M16—1222no—
637M16—1222no—
638M16—1222no—
639M16—1222no—
640M16—1222no—
641M16—1222no—
642M16—1222no—
643M16—2444no—
644M16—2444no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—2444no—
650C2×C8—2444no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1222no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—612no—
665C22⋊C4—612no—
666C22⋊C4—1222no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4C22⋊#692312yes—
671C22⋊C4C22⋊#692312yes—
672C42—612no—
673C42—612no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—611no—
684C23—611no—
685C23—1222no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23C2×C22⋊#692311yescharacteristic
695C23C2×C22⋊#692311yescharacteristic
696C23C23×#692311yescharacteristic
697Q8—2442no—
698Q8—2442no—
699Q8—2442no—
700Q8—2442no—
701D4—42no—
702D4—42no—
703D4—614no—
704D4—1222no—
705D4—1222no—
706D4—1222no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2442no—
713D4—2442no—
714D4—2442no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—611no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—612no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4C2×C22⋊#692312yes—
761C2×C4C2×C22⋊#692312yes—
762C8—1224no—
763C8—2442no—
764C8—2442no—
765C8—2442no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—81no—
779C22—81no—
780C22—612no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1221no—
786C22—4881no—
787C22—4881no—
788C22—2442no—
789C22—2442no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22D61⋊#10012yes—
794C22C22×C22⋊#692311yescharacteristic
795C22#41×#692311yescharacteristic
796C22#1684083111yescharacteristic
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—612no—
803C4—612no—
804C4—612no—
805C4—1222no—
806C4—1221no—
807C4—2441no—
808C4—2441no—
809C4—2441no—
810C2—21no—
811C2—21no—
812C2—22no—
813C2—41no—
814C2—81no—
815C2—1222no—
816C2—4881no—
817C2—2441no—
818C2#2146232211yescharacteristic
819C2C2×D61⋊#10011yescharacteristic
820C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840410C2
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#22479
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462557C2semidirect
2. #21462012C2semidirect
3. #21461845C2semidirect
4. #21461844C2semidirect
5. #21461719C2semidirect
6. #21461718C2semidirect
7. #21461684C2semidirect
8. #21461569C2semidirect
9. #21461522C2semidirect
10. C2×#16840642C2semidirect
232. #11758217#41semidirect
310. C22⋊D61#100semidirect
461. C61#22479semidirect

Maximal subgroups

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

subgroupindex
#214625572
#214620122
#214618452
#214618442
#214617192
#214617182
#214616842
#214615692
#214615222
C2×#168406422
C2×#168404102
#2247961