Finite Group Databasebeta

← #29686180

Subgroups — #29686180

Order 15616.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839838C211yesmaximal, characteristic, complemented
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839831C211yesmaximal, characteristic, complemented
4C2×#16839716C211yesmaximal, characteristic, complemented
5#21449063C211yesmaximal, characteristic
6#21446611C211yesmaximal, characteristic, complemented
7#21446536C211yesmaximal, characteristic, complemented
8#21446434C211yesmaximal, characteristic, complemented
9#21446430C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic, complemented
12#21445802C211yesmaximal, characteristic, complemented
13#21445695C211yesmaximal, characteristic, complemented
14C8×#11758198C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×#14519734C2211yescharacteristic
23#16839838—24no—
24#16839835—24no—
25#16839831—24no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37#16839716—24no—
38C2×#14519688C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42#16839696C411yescharacteristic
43#16839691C411yescharacteristic
44#16839686C411yescharacteristic
45#16839685C411yescharacteristic
46#16839680C411yescharacteristic
47#16839677C411yescharacteristic
48#16839677C411yescharacteristic
49#16839671C411yescharacteristic
50C4×#11758196C2211yescharacteristic
51C4×#11758198C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C2×C4×C8×C61C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189D414yescomplemented
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C4×D244—22no—
82C4×D244—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87#14519734—22no—
88#14519734—22no—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C4⋊#92418—22no—
109#14519706—22no—
110#14519706—22no—
111#14519706—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114#14519689—22no—
115#14519689—22no—
116#14519689—22no—
117#14519689—22no—
118#14519689—22no—
119#14519688—22no—
120#14519687D414yescomplemented
121C8×Dic61—22no—
122C8×Dic61—22no—
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C22⋊C8×C61—22no—
140#97×C61—22no—
141C4×C8×C61—22no—
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—41no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61C2×D412yes—
185C2×C4×D61#4112yes—
186M16×C61—44no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61C2×D412yes—
196C2×C8×C61C2×D412yes—
197C2×C8×C61#4112yes—
198C2×C8×C61#4112yes—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—22no—
215C4⋊Dic61—22no—
216#11758196—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221#11758196—41no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61C2×D412yes—
225C4×Dic61#4112yes—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×D412yes—
237C2×#92418C2×D412yes—
238#11758189—28no—
239C8×D61—28no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61C4×D412yes—
262C22×D61#13112yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C22⋊D61—44no—
289C22⋊D61—44no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61C4×D412yes—
305C2×Dic61C4×D412yes—
306C2×Dic61C4×D412yes—
307C2×Dic61#13112yes—
308D244—44no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C8×C61—22no—
318C8×C61—41no—
319C8×C61—41no—
320C8×C61#12114yes—
321#92418—22no—
322#92418—22no—
323#92418—41no—
324#92418—41no—
325#21496—611nomaximal, Sylow
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C2×C4×D411yescharacteristic
334C22×C61C2×C4×D411yescharacteristic
335C22×C61C4×#4111yescharacteristic
336C22×C61C2×#13111yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61#56811yescharacteristic
339C22×C61#56811yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61C2×#12111yescharacteristic
360C4×C61#52511yescharacteristic
361C4×C61#52911yescharacteristic
362C4×C61#53211yescharacteristic
363Dic61—22no—
364Dic61—22no—
365Dic61—22no—
366Dic61—22no—
367Dic61—41no—
368Dic61—41no—
369C2×#436—611no—
370C2×#435—611no—
371C2×#435—611no—
372C2×#405—611no—
373#2392—611no—
374#1954—611no—
375#1939—611no—
376#1924—611no—
377#1924—611no—
378#1869—611no—
379#1869—611no—
380#1798—611no—
381#1771—611no—
382#1753D6111yescharacteristic, complemented
383C8×C22⋊C4—611no—
384C2×C61—81no—
385C2×C61C4×#12111yescharacteristic
386C2×C61#293311yescharacteristic
387C2×C61#293311yescharacteristic
388C2×C61#293311yescharacteristic
389C2×C61#293511yescharacteristic
390C2×C61#296611yescharacteristic
391C2×C61#296711yescharacteristic
392D61—42no—
393D61—42no—
394C22×M16—611no—
395C22×M16C2×D6111yescharacteristic
396C23×C8—611no—
397C23×C8—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×#117—611no—
402#436—1224no—
403#435—1224no—
404#435—1224no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8C2×D6111yescharacteristic
417#405—1224no—
418C2×#97—611no—
419C2×#97—611no—
420C2×#97C2×D6111yescharacteristic
421C2×C4×C8—611no—
422C2×C4×C8—611no—
423C2×C4×C8C2×D6111yescharacteristic
424#398—611no—
425#397—611no—
426#396—611no—
427#396—611no—
428#394—611no—
429#394—611no—
430#394—611no—
431#392—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—611no—
434C4×C22⋊C4C2×D6111yescharacteristic
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336C2×D6111yescharacteristic
440#336C2×D6111yescharacteristic
441C61#2149611yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4C22×D6111yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—614no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—1222no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—1222no—
475#117—1222no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4C4×D6111yescharacteristic
494C2×C22⋊C4C4×D6111yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42C22×D6111yescharacteristic
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C22⋊C8—22no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511#97—22no—
512#97—614no—
513#97—1222no—
514C4×C8—22no—
515C4×C8—1222no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95C4×D6111yescharacteristic
522#95C4×D6111yescharacteristic
523C24—611no—
524C24—611no—
525C24C2×C4×D6111yescharacteristic
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—1221no—
550C22×C4—1221no—
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×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4C2×C4×D6111yescharacteristic
563C22×C4C2×C4×D6111yescharacteristic
564C22×C4C23×D6111yescharacteristic
565M16—44no—
566M16—1228no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—612no—
576C2×C8—612no—
577C2×C8—1228no—
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—
588C2×C8—2444no—
589C2×C8#1175822212yes—
590C2×C8#1175822212yes—
591C2×C8D4×D6112yes—
592C2×C8D4×D6112yes—
593C4⋊C4—1222no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—612no—
617C42—612no—
618C42—1221no—
619C42—1221no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—612no—
628C23—612no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23C22×C4×D6111yescharacteristic
642D4—2444no—
643D4—2444no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×D4×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822211yescharacteristic
695C2×C4C2×#1175822211yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—1222no—
700C8—1222no—
701C8—2441no—
702C8—2441no—
703C8#1451975014yes—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C4×D4×D6111yescharacteristic
726C22C4×D4×D6111yescharacteristic
727C22C4×#1175822211yescharacteristic
728C22#131×D6111yescharacteristic
729C22#131×D6111yescharacteristic
730C22#1684052811yescharacteristic
731C22#1684052811yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—1222no—
738C4—1222no—
739C4—1222no—
740C4—1222no—
741C4—2441no—
742C4—2441no—
743C4C2×#1451975011yescharacteristic
744C4#1684027111yescharacteristic
745C4#1684029011yescharacteristic
746C4#1684030911yescharacteristic
747C2—81no—
748C2—2442no—
749C2—2442no—
750C2C4×#1451975011yescharacteristic
751C2#2145454211yescharacteristic
752C2#2145454811yescharacteristic
753C2#2145454811yescharacteristic
754C2#2145456011yescharacteristic
755C2#2145479011yescharacteristic
756C2#2145480411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1753C2
prime radical#16839671C4
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#21496
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#16839838C2semidirect
2. C2×#16839835C2semidirect
3. C2×#16839831C2semidirect
4. C2×#16839716C2semidirect
6. #21446611C2semidirect
7. #21446536C2semidirect
8. #21446434C2semidirect
9. #21446430C2semidirect
10. #21446110C2semidirect
11. #21446108C2semidirect
12. #21445802C2semidirect
13. #21445695C2semidirect
14. C8×#11758198C2semidirect
15. C61×#1753C2semidirect
70. C2×#11758189D4semidirect
120. #14519687D4semidirect
382. #1753D61semidirect
441. C61#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#168398382
C2×#168398352
C2×#168398312
C2×#168397162
#214490632
#214466112
#214465362
#214464342
#214464302
#214461102
#214461082
#214458022
#214456952
C8×#117581982
C61×#17532
#2149661