Finite Group Databasebeta

← #29733119

Subgroups — #29733119

Order 15616.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840092C211yesmaximal, characteristic, complemented
2C2×#16840018C211yesmaximal, characteristic, complemented
3#21449248C211yesmaximal, characteristic
4#21447149C211yesmaximal, characteristic, complemented
5#21447012C211yesmaximal, characteristic, complemented
6#21446957C211yesmaximal, characteristic, complemented
7#21446827C211yesmaximal, characteristic, complemented
8#21446160C211yesmaximal, characteristic, complemented
9#21446132C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic
12#21446087C211yesmaximal, characteristic, complemented
13#21446012C211yesmaximal, characteristic, complemented
14#21445538C211yesmaximal, characteristic, complemented
15C2×C61×#554C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16840092—24no—
22#16840018—24no—
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35#16839690—21no—
36#16839676—21no—
37#16839668C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839657—21no—
40#16839656—21no—
41#16839622C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#554—24no—
51C61×#554—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#125×C61—21no—
54C2×C22⋊Q8×C61—21no—
55C2×C22⋊Q8×C61—21no—
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61—21no—
60C2×C4×D4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202—41no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519756—22no—
75#14519756—22no—
76#14519756—22no—
77#14519756—41no—
78#14519736—22no—
79#14519736—41no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C4×Dic61—21no—
91#14519708—22no—
92#14519708—22no—
93#14519708—22no—
94#14519701—22no—
95#14519701—22no—
96#14519701—41no—
97#14519700—22no—
98#14519700—22no—
99#14519700—22no—
100C22⋊#92418—22no—
101C22⋊#92418—22no—
102C22⋊#92418—41no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×Q8×C61—21no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61D411yescharacteristic
110C23×C4×C61—21no—
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C4⋊Q8×C61—22no—
115C4⋊Q8×C61—22no—
116#125×C61—28no—
117C22⋊Q8×C61—28no—
118C22⋊Q8×C61—28no—
119C22⋊Q8×C61—22no—
120C22⋊Q8×C61—22no—
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61D414yes—
123C4×Q8×C61—22no—
124C4×Q8×C61—22no—
125C4×D4×C61—28no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C4⋊C4×C61D414yes—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61C2311yescharacteristic
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×Q8×C61—24no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—81no—
157C2×Q8×C61—81no—
158C2×Q8×C61C2×D412yes—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
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—24no—
171C22×C4×C61—24no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—81no—
179C22×C4×C61—81no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D412yes—
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C4⋊C4×C61—24no—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—24no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61C2×D412yes—
210C4⋊C4×C61C2×D412yes—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—24no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C42×C61—24no—
217C42×C61—21no—
218C42×C61—21no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223#11758202—44no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61#4112yes—
230#11758196—42no—
231#11758196—42no—
232#11758196—42no—
233C4×Dic61—42no—
234#11758194—44no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418#4112yes—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61#12012yes—
260C23×C61#13712yes—
261C23×C61C22×D411yescharacteristic
262Q8×C61—22no—
263Q8×C61—22no—
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—84no—
267D4×C61—28no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—84no—
299C2×C4×C61—84no—
300C2×C4×C61#12012yes—
301C2×C4×C61#13712yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C612−1+411yescharacteristic
308C2×Dic61—22no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#25561—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61C2×#12011yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61#54711yescharacteristic
346C22×C61C2×#13711yescharacteristic
347C22×C61C2×#13711yescharacteristic
348C22×C61#57711yescharacteristic
349C22×C61#57711yescharacteristic
350C4×C61—22no—
351C4×C61—22no—
352C4×C61—41no—
353C4×C61—42no—
354C4×C61—41no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61#53211yescharacteristic
359C4×C61#53711yescharacteristic
360C4×C61#54611yescharacteristic
361C4×C61#54711yescharacteristic
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366C2×#554D6111yescharacteristic
367C2×#483—611no—
368C2×#470—611no—
369#2415—611no—
370#2058—611no—
371#2035—611no—
372#2024—611no—
373#2001—611no—
374#1878—611no—
375#1873—611no—
376#1872—611no—
377#1870—611no—
378#1865—611no—
379#1853—611no—
380#1736—611no—
381C2×C61—42no—
382C2×C61—42no—
383C2×C61#243011yescharacteristic
384C2×C61#300411yescharacteristic
385C2×C61#300911yescharacteristic
386C2×C61#331611yescharacteristic
387C2×C61#333111yescharacteristic
388C2×C61#334411yescharacteristic
389C2×C61#335611yescharacteristic
390C22×Q16—611no—
391C22×M16—611no—
392#554—24no—
393#554—24no—
394C2×C4⋊Q8C2×D6111yescharacteristic
395C2×#125—21no—
396C2×C22⋊Q8—21no—
397C2×C22⋊Q8—21no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8C2×D6111yescharacteristic
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×C4×Q8C2×D6111yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4C2×D6111yescharacteristic
405C2×#117—611no—
406C22×C4⋊C4C2×D6111yescharacteristic
407C22×C4⋊C4C2×D6111yescharacteristic
408#483—1224no—
409#470—1224no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422#397—1221no—
423#394—1221no—
424#391—611no—
425#389—611no—
426#389—1221no—
427#388—1221no—
428#380—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#336—611no—
436#336—611no—
437C61#2556111yescharacteristic, complemented, Sylow
438C22×Q8—21no—
439C22×Q8—611no—
440C22×Q8C22×D6111yescharacteristic
441C22×D4C22⋊D6111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C2×Q16—1222no—
447C2×Q16—1222no—
448C2×Q16—2441no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—2441no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458#125—28no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467C22⋊Q8—2441no—
468C22⋊Q8C22⋊D6114yes—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×D4—28no—
472C4×D4—22no—
473C4×D4—22no—
474#117—1222no—
475#117—2441no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4C22⋊D6111yescharacteristic
492C2×C4⋊C4C22⋊D6114yes—
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22⋊D6111yescharacteristic
504C2×C42—21no—
505C2×C42—1221no—
506C2×C42C22×D6111yescharacteristic
507#106—1222no—
508#106—1222no—
509#106—1222no—
510#103—1222no—
511#103—1222no—
512#103—1222no—
513#103—1222no—
514#103—1222no—
515#103—2441no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—2441no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523C24C2×C22⋊D6111yescharacteristic
524C24C2×C22⋊D6111yescharacteristic
525C2×Q8—24no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—81no—
532C2×Q8—81no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8C2×C22⋊D6112yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6112yes—
571C22×C4C2×C22⋊D6112yes—
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574Q16—2444no—
575M16—2444no—
576C2×C8—612no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—612no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—2442no—
605C4⋊C4—2442no—
606C4⋊C4—2442no—
607C4⋊C4C2×C22⋊D6112yes—
608C4⋊C4C2×C22⋊D6112yes—
609C4⋊C4C2×C22⋊D6112yes—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C42—24no—
619C42—21no—
620C42—21no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#1451974612yes—
635C23#1451980812yes—
636C23C22×C22⋊D6111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—84no—
642Q8—2441no—
643Q8—2441no—
644Q8—2441no—
645Q8—2441no—
646D4—28no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—1222no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4#1451974612yes—
692C2×C4#1451980812yes—
693C2×C4C22×C22⋊D6111yescharacteristic
694C2×C4C22×C22⋊D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4#41×D6111yescharacteristic
697C2×C4#1451982311yescharacteristic
698C2×C4#1451982411yescharacteristic
699C8—1222no—
700C8—2441no—
701C8—2441no—
702C8—2441no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#1451974611yescharacteristic
718C22#1684040011yescharacteristic
719C22#1684041111yescharacteristic
720C22C2×#1451980811yescharacteristic
721C22C2×#1451980811yescharacteristic
722C22#1684057311yescharacteristic
723C22#1684057311yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—4881no—
733C4—4881no—
734C4—4881no—
735C4—2442no—
736C4#1684030811yescharacteristic
737C4#1684034011yescharacteristic
738C4#1684040011yescharacteristic
739C4#1684041111yescharacteristic
740C2—42no—
741C2—42no—
742C2#2144942311yescharacteristic
743C2#2145505311yescharacteristic
744C2#2145509611yescharacteristic
745C2#2145792411yescharacteristic
746C2#2145812911yescharacteristic
747C2#2145826811yescharacteristic
748C2#2145843411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterC2×#554D61
hypocenterC61#25561
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16840092C2semidirect
2. C2×#16840018C2semidirect
4. #21447149C2semidirect
5. #21447012C2semidirect
6. #21446957C2semidirect
7. #21446827C2semidirect
8. #21446160C2semidirect
9. #21446132C2semidirect
10. #21446126C2semidirect
12. #21446087C2semidirect
13. #21446012C2semidirect
14. #21445538C2semidirect
437. C61#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#168400922
C2×#168400182
#214492482
#214471492
#214470122
#214469572
#214468272
#214461602
#214461322
#214461262
#214461172
#214460872
#214460122
#214455382
C2×C61×#5542
#2556161