Finite Group Databasebeta

← #29697056

Subgroups — #29697056

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839820C211yesmaximal, characteristic, complemented
2C2×#16839727C211yesmaximal, characteristic
3#21448309C211yesmaximal, characteristic
4#21446433C211yesmaximal, characteristic, complemented
5#21446432C211yesmaximal, characteristic, complemented
6#21446432C211yesmaximal, characteristic, complemented
7#21446426C211yesmaximal, characteristic, complemented
8#21446003C211yesmaximal, characteristic, complemented
9#21445998C211yesmaximal, characteristic, complemented
10#21445888C211yesmaximal, characteristic, complemented
11#21445799C211yesmaximal, characteristic, complemented
12#21445730C211yesmaximal, characteristic
13#21445604C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C61×#1749C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839820—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25#16839727—24no—
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839668C411yescharacteristic
37#16839668C411yescharacteristic
38#16839664C411yescharacteristic
39#16839664C411yescharacteristic
40#16839641C411yescharacteristic
41#16839641C411yescharacteristic
42#16839641C411yescharacteristic
43#16839641C411yescharacteristic
44C4×#11758198C2211yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—41no—
83#14519736—22no—
84#14519736—22no—
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C4⋊#92418—41no—
100C4⋊#92418—41no—
101#14519706—22no—
102#14519706—22no—
103C22⋊#92418—22no—
104C22⋊#92418—22no—
105#14519689—22no—
106#14519689—22no—
107#14519689—22no—
108#14519689—22no—
109#14519689—41no—
110#14519689—41no—
111#14519687—22no—
112C8×Dic61—22no—
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C23×C4×C61C2×C411yescharacteristic
122C23×C4×C61C2×C411yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C42×C61—41no—
129C2×C42×C61—41no—
130C2×C42×C61C2×C411yescharacteristic
131C2×C42×C61C2×C411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C22⋊C8×C61—22no—
135C22⋊C8×C61D414yes—
136#97×C61—41no—
137#97×C61—41no—
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—41no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61—41no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D412yes—
157C22×C4×C61#4112yes—
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
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174#11758222—44no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—41no—
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×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61#4112yes—
189C2×C4×D61#4112yes—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—41no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61C2×D412yes—
204C2×C8×C61C2×D412yes—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—41no—
210C42×C61—41no—
211C22⋊Dic61—22no—
212C22⋊Dic61—22no—
213#11758198—22no—
214#11758198—22no—
215#11758198—41no—
216#11758198—41no—
217#11758198—41no—
218#11758198—41no—
219#11758198—41no—
220#11758198—41no—
221C4⋊Dic61—22no—
222C4⋊Dic61—22no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—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×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239#11758189—44no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61C4×D412yes—
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×D61—21no—
262C22×D61#11712yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
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—21no—
279C2×C4×C61—21no—
280C2×C4×C61—44no—
281C2×C4×C61—44no—
282C2×C4×C61C4×D412yes—
283C2×C4×C61#13112yes—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C22⋊D61—44no—
291C22⋊D61—44no—
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×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61#11712yes—
310D244—44no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319Dic122—44no—
320C8×C61—22no—
321C8×C61—22no—
322C8×C61—41no—
323C8×C61—41no—
324#92418—41no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#22561—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61C2×#11711yescharacteristic
337C22×C61C2×C4×D411yescharacteristic
338C22×C61#51811yescharacteristic
339C22×C61C2×#13111yescharacteristic
340C22×C61#56811yescharacteristic
341C22×C61#56811yescharacteristic
342C22×C61#56811yescharacteristic
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—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61#54611yescharacteristic
363C4×C61#54611yescharacteristic
364C4×C61#55111yescharacteristic
365C4×C61#55111yescharacteristic
366Dic61—22no—
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372C2×#433—611no—
373C2×#408—611no—
374#2297—611no—
375#1924—611no—
376#1924—611no—
377#1924—611no—
378#1923—611no—
379#1851—611no—
380#1850—611no—
381#1818—611no—
382#1797—611no—
383#1780—611no—
384#1753—611no—
385#1752—611no—
386#1749D6111yescharacteristic, complemented
387C2×C61—42no—
388C2×C61#234211yescharacteristic
389C2×C61#292311yescharacteristic
390C2×C61#292511yescharacteristic
391C2×C61#293211yescharacteristic
392C2×C61#293511yescharacteristic
393C2×C61#297611yescharacteristic
394C2×C61#297811yescharacteristic
395D61—42no—
396D61—81no—
397C22×#41—611no—
398C22×M16—611no—
399C23×C8—611no—
400C2×#117—611no—
401C22×C42C2×D6111yescharacteristic
402#433—1224no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407#408—1224no—
408C2×C22⋊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
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×#97C2×D6111yescharacteristic
420C2×#97C2×D6111yescharacteristic
421C2×C4×C8—611no—
422#391—611no—
423#391—611no—
424#390—611no—
425#390—611no—
426#386—611no—
427#386—611no—
428#386—611no—
429#386—611no—
430C4×C22⋊C4—611no—
431C4×C22⋊C4—611no—
432C4×C22⋊C4—611no—
433C4×C22⋊C4—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336C2×D6111yescharacteristic
441#336C2×D6111yescharacteristic
442C61#2256111yescharacteristic, complemented, Sylow
443C2×#41—1222no—
444C2×#41—1222no—
445C2×#41—1222no—
446C2×#41—1222no—
447C2×#41—2441no—
448C2×#41—2441no—
449C22×Q8—611no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4C4×D6111yescharacteristic
456C23×C4C4×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—2441no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—1222no—
466C22×C8—1222no—
467C22×C8—2441no—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472#117—1222no—
473#117—1222no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C42—41no—
487C2×C42—41no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42C4×D6111yescharacteristic
491C2×C42C4×D6111yescharacteristic
492C2×C42C22×D6111yescharacteristic
493C2×C42C22×D6111yescharacteristic
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496C4⋊C8—2441no—
497C4⋊C8—2441no—
498C22⋊C8—22no—
499C22⋊C8—1222no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—2441no—
506C22⋊C8—2441no—
507C22⋊C8D24414yes—
508#97—41no—
509#97—41no—
510#97—1222no—
511C4×C8—1222no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95—611no—
519#95—611no—
520C24—611no—
521C24—611no—
522C24C2×C4×D6111yescharacteristic
523#41—2444no—
524#41—2444no—
525#41—2444no—
526#41—2444no—
527C2×Q8—1222no—
528C2×Q8—1222no—
529C2×Q8—2441no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—1222no—
533C2×D4—1222no—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—2441no—
537C2×D4—2441no—
538C2×D4—2441no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—611no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×C4×D6111yescharacteristic
569C22×C4C2×C4×D6111yescharacteristic
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4C2×D24412yes—
573C22×C4#1175822212yes—
574C22×C4C23×D6111yescharacteristic
575M16—2444no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—2444no—
599C2×C8C2×D24412yes—
600C2×C8C2×D24412yes—
601C4⋊C4—1222no—
602C4⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—2441no—
608C22⋊C4—2441no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—41no—
618C42—41no—
619C42—1221no—
620C42—1221no—
621C42—1221no—
622C42—1221no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—612no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23C4×D24412yes—
644C23C22×C4×D6111yescharacteristic
645Q8—2444no—
646D4—2444no—
647D4—2444no—
648D4—2444no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—612no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4C4×D24412yes—
695C2×C4#1451978512yes—
696C2×C4C22×D24411yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C2×C4C2×#1175822211yescharacteristic
700C2×C4#1451982211yescharacteristic
701C2×C4#1451982211yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—2441no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—1222no—
718C22—1222no—
719C22—1222no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22—2441no—
726C22—2441no—
727C22—2441no—
728C22—2441no—
729C22—2441no—
730C22—2441no—
731C22#117×D6111yescharacteristic
732C22C2×C4×D24411yescharacteristic
733C22#1684023511yescharacteristic
734C22C2×#1451978511yescharacteristic
735C22#1684052811yescharacteristic
736C22#1684052811yescharacteristic
737C22#1684052811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—1222no—
744C4—2441no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C4#1684040711yescharacteristic
750C4#1684040711yescharacteristic
751C4#1684044111yescharacteristic
752C4#1684044111yescharacteristic
753C2—42no—
754C2—4881no—
755C2—2442no—
756C2#2144867111yescharacteristic
757C2#2145446511yescharacteristic
758C2#2145448611yescharacteristic
759C2#2145453811yescharacteristic
760C2#2145456511yescharacteristic
761C2#2145486911yescharacteristic
762C2#2145487911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1749C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1749D61
hypocenterC61#22561
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#16839820C2semidirect
4. #21446433C2semidirect
5. #21446432C2semidirect
6. #21446432C2semidirect
7. #21446426C2semidirect
8. #21446003C2semidirect
9. #21445998C2semidirect
10. #21445888C2semidirect
11. #21445799C2semidirect
13. #21445604C2semidirect
14. #21445596C2semidirect
15. C61×#1749C2semidirect
386. #1749D61semidirect
442. C61#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#168398202
C2×#168397272
#214483092
#214464332
#214464322
#214464262
#214460032
#214459982
#214458882
#214457992
#214457302
#214456042
#214455962
C61×#17492
#2256161