Finite Group Databasebeta

← #30610287

Subgroups — #30610287

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462407C212yesmaximal, complemented
2#21461098C212yesmaximal, complemented
3#21461087C212yesmaximal, complemented
4#21461086C212yesmaximal, complemented
5#21461077C211yesmaximal, characteristic, complemented
6#21461069C211yesmaximal, characteristic, complemented
7#21461068C211yesmaximal, characteristic, complemented
8#21461057C211yesmaximal, characteristic, complemented
9C2×#16840608C211yesmaximal, characteristic, complemented
10D61⋊#324C211yesmaximal, characteristic, complemented
11C2×#16840410C211yesmaximal, characteristic
12C2×#14519864—22no—
13#16840736—22no—
14#16840735—22no—
15#16840735—22no—
16#16840733C2212yes—
17#16840732C2212yes—
18#16840732C2212yes—
19D61⋊(C22⋊C8)C2212yes—
20C2×C22⋊#92420C2212yes—
21C2×C22⋊#92420C2212yes—
22#16840608C2211yescharacteristic
23#16840608C2211yescharacteristic
24#16840608C2211yescharacteristic
25#16840608C2212yes—
26#16840608C2211yescharacteristic
27#16840608C2212yes—
28#16840607C2212yes—
29#16840607C2212yes—
30#16840606C2212yes—
31#16840606C2212yes—
32C22×#11758222C411yescharacteristic
33C22×#11758224C2211yescharacteristic
34#16840410—22no—
35#16840410—22no—
36#16840410—22no—
37#16840410—22no—
38C2×#14519776C411yescharacteristic
39C2×#14519762C2211yescharacteristic
40C2×#14519761C2211yescharacteristic
41C2×#14519759C411yescharacteristic
42C2×#14519755C411yescharacteristic
43C2×#14519754C2211yescharacteristic
44C2×#14519750C411yescharacteristic
45C2×#14519749C411yescharacteristic
46C2×#14519737C411yescharacteristic
47C2×#14519737C2211yescharacteristic
48C22×#11758196C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×#123×C61C411yescharacteristic
51#14519864—48no—
52C2×#11758213—22no—
53C2×#11758217—22no—
54C2×#11758217—22no—
55C2×D61⋊C8—22no—
56C22×#92420—22no—
57C22×#92420—22no—
58#14519834—22no—
59#14519834—22no—
60C22⋊#92420—22no—
61C22⋊#92420—22no—
62C22⋊#92420—22no—
63C22⋊#92420—22no—
64C22⋊#92420C2312yes—
65C22⋊#92420C2312yes—
66C22⋊#92420C2312yes—
67C22⋊#92420C2312yes—
68C2×#11758222—21no—
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—21no—
72C2×#11758222—44no—
73C2×#11758224—44no—
74C2×#11758224D412yes—
75C2×#11758224D412yes—
76C2×#11758224D412yes—
77C2×#11758224D412yes—
78C22×Dic122C2×C411yescharacteristic
79C22×Dic122C2×C411yescharacteristic
80C22×D244C2×C411yescharacteristic
81C22×C22⋊D61C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C22×C22⋊D61C2×C411yescharacteristic
85C23×Dic61C2×C411yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C22×C4×D61C2×C411yescharacteristic
89C22×C4×D61C2×C411yescharacteristic
90C22×C4×D61C2×C411yescharacteristic
91C22×C4×D61C2311yescharacteristic
92#14519776—22no—
93#14519776—22no—
94#14519762—22no—
95#14519762—22no—
96#14519761—22no—
97#14519761—22no—
98#14519759—22no—
99#14519759—22no—
100#14519755—22no—
101#14519755—22no—
102#14519754—22no—
103#14519754—22no—
104#14519750—22no—
105#14519750—22no—
106#14519749—22no—
107#14519749—22no—
108#14519737—21no—
109#14519737—21no—
110#14519737—21no—
111#14519737—21no—
112#14519737—22no—
113#14519737—22no—
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×C4⋊Dic61C2311yescharacteristic
116C2×#11758196—22no—
117C2×#11758196—22no—
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2311yescharacteristic
123C2×#11758196C2311yescharacteristic
124C4⋊C4×D61—22no—
125C4⋊C4×D61—22no—
126C2×C22⋊Dic61C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2311yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C22×D4×C61C2×C411yescharacteristic
133C23×C4×C61C2×C411yescharacteristic
134#123×C61—22no—
135#123×C61—22no—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C24×C61C22×C411yescharacteristic
142C24×C61C22×C411yescharacteristic
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C2×D4×C61—42no—
146C2×D4×C61C22⋊C412yes—
147C2×D4×C61C22⋊C412yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—42no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C2×C22⋊D61—24no—
157C2×C22⋊D61—21no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61C22⋊C411yescharacteristic
165C2×C22⋊D61C22⋊C411yescharacteristic
166C2×C22⋊D61C22⋊C411yescharacteristic
167C2×C22⋊D61C22⋊C412yes—
168C2×C22⋊D61C22⋊C412yes—
169C2×C22⋊D61C22⋊C411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—42no—
174C22×Dic61—41no—
175C22×Dic61—42no—
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C2×D412yes—
182C22×Dic61C2×D412yes—
183C22×Dic61C2×D412yes—
184C22×Dic61C2×D412yes—
185C22×Dic61C2411yescharacteristic
186#11758224—28no—
187#11758224—44no—
188#11758224—44no—
189#11758224—44no—
190#11758222—44no—
191#11758222—44no—
192#11758222—44no—
193#11758222—44no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—42no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—22no—
204C2×C4×D61—42no—
205C2×C4×D61—41no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—42no—
213C2×Dic122—42no—
214C2×Dic122C22⋊C412yes—
215C2×Dic122C22⋊C412yes—
216#11758217—44no—
217#11758217—44no—
218C2×#92420—22no—
219C2×#92420—22no—
220C2×#92420—22no—
221C2×#92420—22no—
222C2×#92420—44no—
223C2×#92420—44no—
224#11758213—44no—
225D61⋊C8—44no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—22no—
232C22⋊Dic61—22no—
233#11758198—21no—
234#11758198—21no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238C4⋊Dic61—22no—
239C4⋊Dic61—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196—21no—
244#11758196—21no—
245#11758196—22no—
246#11758196—22no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61C2×C22⋊C412yes—
258C23×C61C2×C22⋊C411yescharacteristic
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C23×C411yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61C2×C22⋊C411yescharacteristic
271C22×D61C2×C22⋊C411yescharacteristic
272D4×C61—24no—
273D4×C61—42no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—41no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61C2×C22⋊C412yes—
287C22⋊D61—22no—
288C22⋊D61—22no—
289C22⋊D61—24no—
290C22⋊D61—22no—
291C22⋊D61—42no—
292C22⋊D61—44no—
293C22⋊D61—42no—
294C22⋊D61—42no—
295C22⋊D61#9914yes—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—24no—
299C2×Dic61—24no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—41no—
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61#13112yescomplemented
316C2×Dic61C22×D412yes—
317D244—42no—
318D244—42no—
319C4×D61—24no—
320C4×D61—42no—
321C4×D61—42no—
322C4×D61—42no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—42no—
326C4×D61—42no—
327Dic122—24no—
328Dic122—42no—
329Dic122—42no—
330Dic122—42no—
331#92420—42no—
332#92420—42no—
333#92420—42no—
334#92420—42no—
335#17416—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—22no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61C2×#9912yes—
351C22×C61C22×C22⋊C411yescharacteristic
352C22×C61C2×#13111yescharacteristic
353C22×C61#56811yescharacteristic
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61C2×#9912yes—
367C4×C61—22no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61—41no—
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—21no—
376Dic61—41no—
377Dic61—41no—
378Dic61C2×#9912yes—
379C2×#547—611no—
380#2880—612no—
381#1472—612no—
382#1468—612no—
383#1468—612no—
384#1465—611no—
385#1463—611no—
386#1463—611no—
387#1459—611no—
388C2×#324—611no—
389C2×#324—611no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—22no—
393C2×C61—41no—
394C2×C61—42no—
395C2×C61#288011yescharacteristic
396C2×C61C22×#9911yescharacteristic
397C2×C61#288911yescharacteristic
398D61—22no—
399D61—41no—
400D61—81no—
401C22×#41—611no—
402C22×#41—611no—
403C2×#131—1222no—
404#547—1222no—
405#547—1222no—
406#547—1222no—
407#547—1222no—
408C2×C4⋊Q8—611no—
409C2×#123—611no—
410C2×#123—611no—
411C2×#123—611no—
412C2×#123#692311yescharacteristic
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×#121—611no—
416C2×#121—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421#408—1222no—
422#408—1222no—
423#408—1222no—
424#407—612no—
425#407—612no—
426#407—612no—
427C2×C22⋊C8—612no—
428C2×C22⋊C8—612no—
429C2×C22⋊C8—612no—
430#324—612no—
431#324—612no—
432#324—611no—
433#324—611no—
434#324—611no—
435#324—612no—
436#324—611no—
437#324—612no—
438#323—612no—
439#323—612no—
440C61#1741611yescharacteristic, complemented, Sylow
441C2×#41—612no—
442C2×#41—612no—
443C2×#41—612no—
444C2×#41—612no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—1221no—
448C2×#41—1221no—
449C2×#41—2444no—
450C2×#41—2444no—
451C22×Q8—611no—
452C22×Q8—611no—
453C22×D4—611no—
454C22×D4—611no—
455C22×D4—611no—
456C22×D4—611no—
457C22×D4—611no—
458C22×D4C2×#692311yescharacteristic
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4C2×#692311yescharacteristic
467#131—2448no—
468C2×M16—1222no—
469C2×M16—1222no—
470C2×M16—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C4⋊Q8—1222no—
475C4⋊Q8—1222no—
476#123—22no—
477#123—22no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#121—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1221no—
495C4×D4—1221no—
496C4×D4—1221no—
497C4×D4—1221no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4C2×#692311yescharacteristic
511C2×C4⋊C4C2×#692311yescharacteristic
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4C2×#692311yescharacteristic
518C2×C22⋊C4C2×#692311yescharacteristic
519C2×C22⋊C4C2×#692311yescharacteristic
520C2×C42—611no—
521C22⋊C8—612no—
522C22⋊C8—612no—
523C22⋊C8—612no—
524C22⋊C8—612no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527C22⋊C8—1222no—
528C22⋊C8—1222no—
529C22⋊C8—1222no—
530C22⋊C8—1222no—
531C24—611no—
532C24—611no—
533C24C22×#692311yescharacteristic
534C24C22×#692311yescharacteristic
535#41—1228no—
536#41—2444no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540#41—2444no—
541#41—2444no—
542#41—2444no—
543C2×Q8—612no—
544C2×Q8—612no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—2442no—
548C2×Q8—2442no—
549C2×D4—42no—
550C2×D4—611no—
551C2×D4—611no—
552C2×D4—611no—
553C2×D4—611no—
554C2×D4—612no—
555C2×D4—612no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1222no—
559C2×D4—1224no—
560C2×D4—1222no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—2442no—
564C2×D4—2441no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4C22⋊#692312yes—
568C2×D4C22⋊#692312yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1222no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2441no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2441no—
601C22×C4C22×#692311yescharacteristic
602C22×C4C22×#692311yescharacteristic
603C22×C4C22×#692311yescharacteristic
604C22×C4C22×#692311yescharacteristic
605C22×C4C22×#692311yescharacteristic
606M16—2444no—
607M16—2444no—
608M16—2444no—
609C2×C8—1222no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C2×C8—2444no—
614C2×C8—2444no—
615C2×C8—2444no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1222no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1222no—
626C4⋊C4—1222no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1221no—
634C22⋊C4—1221no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C42—1221no—
638C42—1221no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—611no—
648C23—611no—
649C23—1222no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23C2×C22⋊#692312yes—
659C23C2×C22⋊#692311yescharacteristic
660C23C2×C22⋊#692311yescharacteristic
661C23C23×#692311yescharacteristic
662Q8—1224no—
663Q8—2442no—
664Q8—2442no—
665Q8—2442no—
666D4—24no—
667D4—42no—
668D4—614no—
669D4—1222no—
670D4—1222no—
671D4—1224no—
672D4—1222no—
673D4—2442no—
674D4—2442no—
675D4—2442no—
676D4—2444no—
677D4—2442no—
678D4—2442no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—611no—
692C2×C4—611no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—1224no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2441no—
720C2×C4C2×C22⋊#692312yes—
721C8—2442no—
722C8—2442no—
723C8—2442no—
724C8—2442no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—21no—
732C22—22no—
733C22—21no—
734C22—22no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—612no—
740C22—1221no—
741C22—1221no—
742C22—1221no—
743C22—1221no—
744C22—1221no—
745C22—4881no—
746C22—4881no—
747C22—2442no—
748C22—2442no—
749C22—2441no—
750C22—2441no—
751C22—2441no—
752C22D61⋊#9912yes—
753C22C22×C22⋊#692311yescharacteristic
754C22D61⋊#13111yescharacteristic
755C22#1684084111yescharacteristic
756C4—22no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—612no—
762C4—1222no—
763C4—1222no—
764C4—1221no—
765C4—1222no—
766C4—2441no—
767C4—2441no—
768C2—21no—
769C2—21no—
770C2—22no—
771C2—41no—
772C2—42no—
773C2—1222no—
774C2—4881no—
775C2—2441no—
776C2#2146240911yescharacteristic
777C2C2×D61⋊#9911yescharacteristic
778C2#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#17416
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462407C2semidirect
2. #21461098C2semidirect
3. #21461087C2semidirect
4. #21461086C2semidirect
5. #21461077C2semidirect
6. #21461069C2semidirect
7. #21461068C2semidirect
8. #21461057C2semidirect
9. C2×#16840608C2semidirect
10. D61⋊#324C2semidirect
315. C2×Dic61#131semidirect
440. C61#17416semidirect

Maximal subgroups

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

subgroupindex
#214624072
#214610982
#214610872
#214610862
#214610772
#214610692
#214610682
#214610572
C2×#168406082
D61⋊#3242
C2×#168404102
#1741661