Finite Group Databasebeta

← #29713976

Subgroups — #29713976

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840483C211yesmaximal, characteristic
2C2×#16840045C211yesmaximal, characteristic, complemented
3C2×Q16×Dic61C211yesmaximal, characteristic, complemented
4#21450738C211yesmaximal, characteristic
5#21447014C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21446826C211yesmaximal, characteristic, complemented
8#21446778C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic
10#21446132C211yesmaximal, characteristic, complemented
11#21446128C211yesmaximal, characteristic, complemented
12#21446021C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14#21445822C211yesmaximal, characteristic, complemented
15C61×#2001C211yesmaximal, characteristic, complemented
16#16840483—24no—
17#16840483—24no—
18C2×#14519776C2211yescharacteristic
19C2×#14519772—21no—
20C2×#14519770—21no—
21C2×#14519763—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×#14519742—21no—
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16840045—24no—
31Q16×Dic61—24no—
32C2×#14519711C2211yescharacteristic
33C2×#14519709C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44#16839685—21no—
45#16839684—21no—
46#16839662—21no—
47#16839657—21no—
48#16839631C2211yescharacteristic
49#16839622C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×C22⋊D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519776—22no—
69#14519776D414yes—
70#14519772—28no—
71#14519770—28no—
72#14519763—28no—
73#14519753—22no—
74#14519753—22no—
75#14519753—22no—
76#14519753—41no—
77Q8×Dic61—22no—
78Q8×Dic61—22no—
79Q8×Dic61—22no—
80Q8×Dic61D414yes—
81#14519742—28no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84#14519736—22no—
85#14519736—22no—
86#14519735—22no—
87#14519735—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61D411yescharacteristic
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198D411yescharacteristic
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519711—22no—
114#14519709—22no—
115#14519708—22no—
116#14519706—22no—
117#14519701—22no—
118#14519701—22no—
119#14519701—22no—
120#14519701—41no—
121C22⋊#92418—41no—
122#14519689—22no—
123#14519689—41no—
124C8×Dic61—22no—
125#14519684—21no—
126#14519684—21no—
127C22×Q8×C61C2311yescharacteristic
128C22×Q8×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C2×Q16×C61—22no—
131C2×Q16×C61—22no—
132C2×Q16×C61—22no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61—41no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145#103×C61—22no—
146#103×C61—41no—
147C22⋊C8×C61—22no—
148C24×C61C2×D411yescharacteristic
149C23×D61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C2×D412yes—
161C2×Q8×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×Dic122—24no—
191C2×Dic122—42no—
192C2×Dic122—42no—
193Q16×C61—28no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61#4112yes—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61C2×D412yes—
206C22⋊C4×C61—24no—
207C22⋊C4×C61—42no—
208C22⋊Dic61—24no—
209C22⋊Dic61—22no—
210C22⋊Dic61—81no—
211#11758198—24no—
212#11758198—24no—
213#11758198—22no—
214#11758198—42no—
215#11758198—81no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—24no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—42no—
224C4⋊Dic61C2×D412yes—
225C4⋊Dic61C2×D412yes—
226#11758196—24no—
227#11758196—24no—
228#11758196—22no—
229#11758196—42no—
230#11758196—42no—
231#11758196—81no—
232C4×Dic61—24no—
233C4×Dic61—24no—
234C4×Dic61—24no—
235C4×Dic61—42no—
236C4×Dic61C2×D412yes—
237C4×Dic61C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61C22×D411yescharacteristic
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—41no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C22⋊D61—44no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61#12012yes—
311C2×Dic61#12012yes—
312C2×Dic61#13512yes—
313C2×Dic61#13712yes—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318Dic122—48no—
319C8×C61—22no—
320C8×C61—41no—
321#92418—41no—
322#92418—41no—
323#24123—611nomaximal, Sylow
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61C2×#12011yescharacteristic
332C22×C61#54611yescharacteristic
333C22×C61#54711yescharacteristic
334C22×C61C2×#13511yescharacteristic
335C22×C61C2×#13711yescharacteristic
336C22×C61#57711yescharacteristic
337C22×C61#57811yescharacteristic
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C4×C61—41no—
346C4×C61—42no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—81no—
350C4×C61#52511yescharacteristic
351C4×C61#53711yescharacteristic
352C4×C61#54811yescharacteristic
353C4×C61#55011yescharacteristic
354Dic61—22no—
355Dic61—41no—
356Dic61—42no—
357Dic61—42no—
358Dic61—81no—
359Dic61—81no—
360Dic61#45214yes—
361C2×#556—611no—
362C2×#475—611no—
363C2×C4×Q16—611no—
364#2538—611no—
365#2035—611no—
366#2035—611no—
367#2001—611no—
368#2001D6111yescharacteristic, complemented
369#1990—611no—
370#1954—611no—
371#1873—611no—
372#1873—611no—
373#1854—611no—
374#1854—611no—
375#1803—611no—
376C2×C61—81no—
377C2×C61#240711yescharacteristic
378C2×C61C2×#45211yescharacteristic
379C2×C61#301311yescharacteristic
380C2×C61#330411yescharacteristic
381C2×C61#332811yescharacteristic
382C2×C61#334211yescharacteristic
383C2×C61#335611yescharacteristic
384D61—81no—
385C22×Q16C2×D6111yescharacteristic
386#556—1224no—
387#556—1224no—
388C2×C4⋊Q8—611no—
389C2×#126—1221no—
390C2×#126—1221no—
391C2×#124—1221no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8C2×D6111yescharacteristic
395C2×C22⋊Q8C2×D6111yescharacteristic
396C2×C4×Q8—611no—
397C2×C4×Q8—611no—
398C2×C4×Q8—1221no—
399C2×C4×D4—611no—
400C2×#117—611no—
401C2×#117—611no—
402#475—1224no—
403C4×Q16—1224no—
404C2×#107—611no—
405C2×#106—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103C2×D6111yescharacteristic
413C2×#103C2×D6111yescharacteristic
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×C4×C8—611no—
419#396—1221no—
420#396—1221no—
421#390—1221no—
422#389—1221no—
423#384—611no—
424#380—611no—
425#380—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340C2×D6111yescharacteristic
432C61#2412311yescharacteristic, complemented, Sylow
433C22×Q8—1221no—
434C22×Q8C22×D6111yescharacteristic
435C22×Q8C22×D6111yescharacteristic
436C22×D4—611no—
437C23×C4—611no—
438C23×C4C22×D6111yescharacteristic
439C2×Q16—22no—
440C2×Q16—22no—
441C2×Q16—22no—
442C22×C8—611no—
443C22×C8—611no—
444C22×C8C22×D6111yescharacteristic
445C22×C8C22×D6111yescharacteristic
446C4⋊Q8—614no—
447C4⋊Q8—1222no—
448#126—1228no—
449#126—1228no—
450#124—1228no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—41no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C22⋊Q8—2441no—
459C4×Q8—614no—
460C4×Q8—1222no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×Q8—1228no—
464C4×D4—1222no—
465C4×D4—1222no—
466#117—1222no—
467#117—1222no—
468#117—1222no—
469#117—1222no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501#107—1222no—
502#106—1222no—
503#106—1222no—
504C4⋊C8—1222no—
505#103—22no—
506#103—41no—
507#103—1222no—
508#103—1222no—
509#103—1222no—
510#103—2441no—
511C22⋊C8—22no—
512C22⋊C8—1222no—
513C22⋊C8—2441no—
514C22⋊C8—2441no—
515C4×C8—1222no—
516#95—1221no—
517#95—1221no—
518C24—611no—
519C24D4×D6111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—1224no—
531C2×Q8—2442no—
532C2×Q8—2442no—
533C2×Q8D4×D6112yes—
534C2×Q8#1175822412yes—
535C2×D4—1222no—
536C2×D4—1222no—
537C2×D4—1222no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4D4×D6111yescharacteristic
562C22×C4C23×D6111yescharacteristic
563Q16—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8#1175822412yes—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—612no—
582C4⋊C4—612no—
583C4⋊C4—1222no—
584C4⋊C4—1224no—
585C4⋊C4—1224no—
586C4⋊C4—1224no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—4881no—
594C4⋊C4—2442no—
595C4⋊C4—2442no—
596C4⋊C4—2442no—
597C4⋊C4D4×D6112yes—
598C22⋊C4—24no—
599C22⋊C4—42no—
600C22⋊C4—1222no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—1222no—
604C22⋊C4—1224no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—2442no—
608C42—612no—
609C42—612no—
610C42—1224no—
611C42—1224no—
612C42—1224no—
613C42—2442no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23C2×D4×D6111yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—2448no—
638D4—2444no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1222no—
665C2×C4—1221no—
666C2×C4—1222no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4C2×D4×D6111yescharacteristic
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4C2×#1175822411yescharacteristic
686C2×C4C2×#1175822411yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982411yescharacteristic
689C8—22no—
690C8—41no—
691C8—2441no—
692C8—2441no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22—2441no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22#120×D6111yescharacteristic
708C22#1684039911yescharacteristic
709C22#1684041211yescharacteristic
710C22#135×D6111yescharacteristic
711C22#137×D6111yescharacteristic
712C22#1684057111yescharacteristic
713C22#1684057511yescharacteristic
714C4—42no—
715C4—41no—
716C4—42no—
717C4—42no—
718C4—81no—
719C4—614no—
720C4—1222no—
721C4—4881no—
722C4—4881no—
723C4—2442no—
724C4—2442no—
725C4—2441no—
726C4#1684026811yescharacteristic
727C4#1684033911yescharacteristic
728C4#1684041811yescharacteristic
729C4#1684043211yescharacteristic
730C2—81no—
731C2—4881no—
732C2#2144915711yescharacteristic
733C2#452×D6111yescharacteristic
734C2#2145513511yescharacteristic
735C2#2145775111yescharacteristic
736C2#2145809511yescharacteristic
737C2#2145824611yescharacteristic
738C2#2145842911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2001C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2001D61
hypocenterC61#24123
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#16840045C2semidirect
3. C2×Q16×Dic61C2semidirect
5. #21447014C2semidirect
6. #21447012C2semidirect
7. #21446826C2semidirect
8. #21446778C2semidirect
10. #21446132C2semidirect
11. #21446128C2semidirect
12. #21446021C2semidirect
13. #21446020C2semidirect
14. #21445822C2semidirect
15. C61×#2001C2semidirect
368. #2001D61semidirect
432. C61#24123semidirect

Maximal subgroups

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

subgroupindex
C2×#168404832
C2×#168400452
C2×Q16×Dic612
#214507382
#214470142
#214470122
#214468262
#214467782
#214466112
#214461322
#214461282
#214460212
#214460202
#214458222
C61×#20012
#2412361