Finite Group Databasebeta

← #29691127

Subgroups — #29691127

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839837C211yesmaximal, characteristic, complemented
2C2×#16839729C211yesmaximal, characteristic, complemented
3#21449032C211yesmaximal, characteristic
4#21446615C211yesmaximal, characteristic, complemented
5#21446611C211yesmaximal, characteristic, complemented
6#21446429C211yesmaximal, characteristic, complemented
7#21446428C211yesmaximal, characteristic, complemented
8#21446428C211yesmaximal, characteristic, complemented
9#21446422C211yesmaximal, characteristic, complemented
10#21446113C211yesmaximal, characteristic, complemented
11#21446113C211yesmaximal, characteristic, complemented
12#21446109C211yesmaximal, characteristic, complemented
13#21445996C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C61×#1780C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22#16839837—24no—
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26#16839729—24no—
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839681C411yescharacteristic
38#16839676C411yescharacteristic
39#16839676C411yescharacteristic
40#16839676C411yescharacteristic
41#16839673C411yescharacteristic
42#16839670C411yescharacteristic
43#16839670C411yescharacteristic
44#16839670C411yescharacteristic
45C4×C22⋊Dic61C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×#11758194—41no—
66C2×#11758194—41no—
67C2×#11758194D414yescomplemented
68C2×#11758189—22no—
69C2×#11758189—41no—
70C2×#11758189—41no—
71C22×#92418—22no—
72C22×#92418—41no—
73C22×#92418—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—41no—
81C4×C22⋊D61—41no—
82C4×C22⋊D61—41no—
83C4×C22⋊D61—41no—
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519706—22no—
103#14519706—41no—
104#14519706—41no—
105C22⋊#92418—22no—
106C22⋊#92418—22no—
107C22⋊#92418—22no—
108C22⋊#92418—22no—
109#14519689—22no—
110#14519689—41no—
111#14519689—41no—
112#14519687—41no—
113C8×Dic61—22no—
114C8×Dic61—41no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—41no—
124C2×#41×C61—41no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C22×Q8×C61C2×C411yescharacteristic
128C22×D4×C61C2×C411yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C22×D4×C61C2×C411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—41no—
141C22⋊C8×C61—41no—
142C22⋊C8×C61—41no—
143C22⋊C8×C61—41no—
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148#41×C61—44no—
149#41×C61—44no—
150#41×C61—44no—
151#41×C61—44no—
152C2×Q8×C61—22no—
153C2×Q8×C61—41no—
154C2×Q8×C61—41no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61—41no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
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×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—21no—
179C22×C4×C61—21no—
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61#4112yes—
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—41no—
190C2×C22⋊D61—41no—
191C2×C22⋊D61—41no—
192C2×C22⋊D61—41no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61—41no—
195C22×Dic61C22×C411yescharacteristic
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—41no—
226C22⋊Dic61—41no—
227C22⋊Dic61—41no—
228C22⋊Dic61—41no—
229#11758198—22no—
230#11758198—41no—
231#11758198—41no—
232#11758196—22no—
233#11758196—41no—
234#11758196—41no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241#11758194—44no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—44no—
253C2×#92418C2×D412yes—
254C2×#92418C2×D412yes—
255#11758189—44no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61C4×D412yes—
277C23×C61C23×C411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285Q8×C61—44no—
286D4×C61—44no—
287D4×C61—44no—
288D4×C61—44no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61C4×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C22⋊D61—44no—
317C22⋊D61—44no—
318C22⋊D61—44no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61#13112yes—
339C2×Dic61#13112yes—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C8×C61—41no—
345C8×C61—41no—
346C8×C61—41no—
347C8×C61—41no—
348#92418—22no—
349#92418—22no—
350#92418—41no—
351#92418—41no—
352#22039—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61C2×C4×D411yescharacteristic
375C22×C61#51811yescharacteristic
376C22×C61#51811yescharacteristic
377C22×C61C2×#13111yescharacteristic
378C22×C61C2×#13111yescharacteristic
379C22×C61#56811yescharacteristic
380C22×C61#56811yescharacteristic
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C4×C61—22no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61#53411yescharacteristic
392C4×C61#53511yescharacteristic
393C4×C61#53811yescharacteristic
394C4×C61#53811yescharacteristic
395Dic61—22no—
396Dic61—22no—
397Dic61—41no—
398Dic61—41no—
399Dic61—41no—
400Dic61—41no—
401Dic61—41no—
402C2×#436—611no—
403C2×#408—611no—
404#2388—611no—
405#1955—611no—
406#1954—611no—
407#1924—611no—
408#1923—611no—
409#1923—611no—
410#1923—611no—
411#1870—611no—
412#1870—611no—
413#1869—611no—
414#1850—611no—
415#1780D6111yescharacteristic, complemented
416#1753—611no—
417C2×C61—42no—
418C2×C61—81no—
419C2×C61—81no—
420C2×C61#232111yescharacteristic
421C2×C61#293311yescharacteristic
422C2×C61#293511yescharacteristic
423C2×C61#297611yescharacteristic
424C2×C61#297811yescharacteristic
425C2×C61#297911yescharacteristic
426C2×C61#298111yescharacteristic
427D61—81no—
428C22×#41C2×D6111yescharacteristic
429C22×M16—611no—
430C22×M16—611no—
431C23×C8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435#436—1224no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8—611no—
439#408—1224no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8C2×D6111yescharacteristic
448C2×C22⋊C8C2×D6111yescharacteristic
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×C22⋊C8C2×D6111yescharacteristic
451C2×C22⋊C8C2×D6111yescharacteristic
452C2×C22⋊C8C2×D6111yescharacteristic
453C2×#97—611no—
454C2×C4×C8—611no—
455C2×C4×C8—611no—
456#395—611no—
457#394—611no—
458#394—611no—
459#394—611no—
460#393—611no—
461#392—611no—
462#392—611no—
463#392—611no—
464C4×C22⋊C4—611no—
465C4×C22⋊C4—611no—
466C4×C22⋊C4—611no—
467#336—611no—
468#336—611no—
469#336—611no—
470#336—611no—
471#336—611no—
472#336—611no—
473C61#2203911yescharacteristic, complemented, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C4×D6111yescharacteristic
481C22×D4—611no—
482C22×D4—611no—
483C22×D4—611no—
484C22×D4C4×D6111yescharacteristic
485C22×D4C4×D6111yescharacteristic
486C22×D4C4×D6111yescharacteristic
487C23×C4—611no—
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C2×M16—614no—
492C2×M16—1222no—
493C2×M16—2441no—
494C2×M16—2441no—
495C2×M16—2441no—
496C2×M16—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—1222no—
502C22×C8—2441no—
503C22×C8—2441no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6111yescharacteristic
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513C4×D4—2441no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—611no—
532C4⋊C8—1222no—
533C4⋊C8—2441no—
534C4⋊C8—2441no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C22⋊C8—41no—
540C22⋊C8—41no—
541C22⋊C8—1222no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546C22⋊C8—2441no—
547C22⋊C8—2441no—
548#97—2441no—
549C4×C8—1222no—
550C4×C8—2441no—
551#95—611no—
552#95—611no—
553#95—611no—
554#95—611no—
555#95—611no—
556#95—611no—
557C24—611no—
558C24C2×C4×D6111yescharacteristic
559C24C2×C4×D6111yescharacteristic
560C24C2×C4×D6111yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—2441no—
581C2×D4—2441no—
582C2×D4—2441no—
583C2×D4—2441no—
584C2×D4—2441no—
585C2×D4—2441no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4C2×C4×D6111yescharacteristic
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4D4×D6112yes—
619C22×C4#1175822412yes—
620C22×C4C23×D6111yescharacteristic
621M16—2444no—
622M16—2444no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—612no—
636C2×C8—612no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—2444no—
648C4⋊C4—1222no—
649C4⋊C4—2441no—
650C4⋊C4—2441no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—2441no—
658C22⋊C4—2441no—
659C22⋊C4—2441no—
660C22⋊C4—2441no—
661C22⋊C4—2441no—
662C22⋊C4—2441no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C42—1221no—
668C42—1221no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23#1451973712yes—
697C23C22×C4×D6111yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—2444no—
703D4—2444no—
704D4—2444no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4#1451973712yes—
751C2×C4C2×D4×D6111yescharacteristic
752C2×C4C2×#1175822411yescharacteristic
753C2×C4#1451982211yescharacteristic
754C2×C4#1451982211yescharacteristic
755C2×C4#1451982211yescharacteristic
756C2×C4#1451982211yescharacteristic
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—1222no—
762C8—1222no—
763C8—2441no—
764C8—2441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C2×#1451973711yescharacteristic
794C22#1684023511yescharacteristic
795C22#1684023511yescharacteristic
796C22#131×D6111yescharacteristic
797C22#131×D6111yescharacteristic
798C22#1684052711yescharacteristic
799C22#1684052711yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—1222no—
804C4—1222no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C4—2441no—
809C4—2441no—
810C4#1684032211yescharacteristic
811C4#1684032711yescharacteristic
812C4#1684034711yescharacteristic
813C4#1684034711yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—4881no—
818C2#2144847411yescharacteristic
819C2#2145454911yescharacteristic
820C2#2145455911yescharacteristic
821C2#2145486211yescharacteristic
822C2#2145487711yescharacteristic
823C2#2145488311yescharacteristic
824C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1780C2
prime radical#21449032C2
cosocleC22×C4×C61C24
hypercenter#1780D61
hypocenterC61#22039
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#16839837C2semidirect
2. C2×#16839729C2semidirect
4. #21446615C2semidirect
5. #21446611C2semidirect
6. #21446429C2semidirect
7. #21446428C2semidirect
8. #21446428C2semidirect
9. #21446422C2semidirect
10. #21446113C2semidirect
11. #21446113C2semidirect
12. #21446109C2semidirect
13. #21445996C2semidirect
14. #21445605C2semidirect
15. C61×#1780C2semidirect
67. C2×#11758194D4semidirect
415. #1780D61semidirect
473. C61#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#168398372
C2×#168397292
#214490322
#214466152
#214466112
#214464292
#214464282
#214464222
#214461132
#214461092
#214459962
#214456052
C61×#17802
#2203961