Finite Group Databasebeta

← #29691131

Subgroups — #29691131

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×#16839838C211yesmaximal, characteristic, complemented
2#21449032C211yesmaximal, characteristic
3#21446615C211yesmaximal, characteristic, complemented
4#21446611C211yesmaximal, characteristic, complemented
5#21446435C211yesmaximal, characteristic, complemented
6#21446428C211yesmaximal, characteristic, complemented
7#21446422C211yesmaximal, characteristic, complemented
8#21446422C211yesmaximal, characteristic, complemented
9#21446113C211yesmaximal, characteristic, complemented
10#21446113C211yesmaximal, characteristic, complemented
11#21446111C211yesmaximal, characteristic, complemented
12#21445997C211yesmaximal, characteristic, complemented
13#21445731C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#408C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20#16839838—24no—
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839681C411yescharacteristic
37#16839676C411yescharacteristic
38#16839676C411yescharacteristic
39#16839676C411yescharacteristic
40#16839673C411yescharacteristic
41#16839670C411yescharacteristic
42#16839670C411yescharacteristic
43#16839670C411yescharacteristic
44C4×C22⋊Dic61C2211yescharacteristic
45C4×C22⋊Dic61C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C61×#408—24no—
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×#11758189—22no—
66C2×#11758189—41no—
67C2×#11758189—41no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—41no—
75C4×C22⋊D61—41no—
76C4×C22⋊D61—41no—
77C4×C22⋊D61—41no—
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519706—22no—
97#14519706—41no—
98#14519706—41no—
99C22⋊#92418—22no—
100C22⋊#92418—22no—
101C22⋊#92418—41no—
102C22⋊#92418—41no—
103C22⋊#92418—41no—
104C22⋊#92418—41no—
105#14519689—22no—
106#14519689—41no—
107#14519689—41no—
108#14519687—41no—
109C8×Dic61—22no—
110C8×Dic61—41no—
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—41no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C22×Q8×C61C2×C411yescharacteristic
124C22×D4×C61C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C2×M16×C61—41no—
131C2×M16×C61—41no—
132C2×M16×C61D414yescomplemented
133C22×C8×C61—22no—
134C22×C8×C61—41no—
135C22×C8×C61—41no—
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22⋊C8×C61—22no—
141C22⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143C22⋊C8×C61—22no—
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—
208M16×C61—44no—
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—44no—
220C2×C8×C61C2×D412yes—
221C2×C8×C61C2×D412yes—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—41no—
228C22⋊Dic61—41no—
229C22⋊Dic61—41no—
230C22⋊Dic61—41no—
231#11758198—22no—
232#11758198—41no—
233#11758198—41no—
234#11758196—22no—
235#11758196—41no—
236#11758196—41no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—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—21no—
253C2×#92418—21no—
254C2×#92418—21no—
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—22no—
345C8×C61—22no—
346C8×C61—41no—
347C8×C61—41no—
348#92418—41no—
349#92418—41no—
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×#408D6111yescharacteristic, complemented
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#1780—611no—
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×M16C2×D6111yescharacteristic
431C23×C8C2×D6111yescharacteristic
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—24no—
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⋊C8—611no—
448C2×C22⋊C8—611no—
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—41no—
492C2×M16—41no—
493C2×M16—1222no—
494C2×M16—2441no—
495C2×M16—2441no—
496C2×M16C22⋊D6114yescomplemented
497C22×C8—22no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
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—22no—
538C22⋊C8—22no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
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×C4#1175822212yes—
619C22×C4C2×C22⋊D6112yes—
620C22×C4C23×D6111yescharacteristic
621M16—44no—
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—44no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
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×C8C2×C22⋊D6112yes—
647C2×C8C2×C22⋊D6112yes—
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—
696C23C4×C22⋊D6112yes—
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×C4C4×C22⋊D6112yes—
751C2×C4C22×C22⋊D6111yescharacteristic
752C2×C4C2×#1175822211yescharacteristic
753C2×C4#1451982211yescharacteristic
754C2×C4#1451982211yescharacteristic
755C2×C4#1451982211yescharacteristic
756C2×C4#1451982211yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—2441no—
762C8—2441no—
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×C4×C22⋊D6111yescharacteristic
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#1684032111yescharacteristic
811C4#1684032911yescharacteristic
812C4#1684035011yescharacteristic
813C4#1684035011yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—4881no—
818C2#2144847711yescharacteristic
819C2#2145454111yescharacteristic
820C2#2145456111yescharacteristic
821C2#2145486211yescharacteristic
822C2#2145487711yescharacteristic
823C2#2145488311yescharacteristic
824C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#408C2
prime radical#21449032C2
cosocleC22×C4×C61C24
hypercenterC2×#408D61
hypocenterC61#22039
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#16839838C2semidirect
3. #21446615C2semidirect
4. #21446611C2semidirect
5. #21446435C2semidirect
6. #21446428C2semidirect
7. #21446422C2semidirect
8. #21446422C2semidirect
9. #21446113C2semidirect
10. #21446113C2semidirect
11. #21446111C2semidirect
12. #21445997C2semidirect
13. #21445731C2semidirect
14. #21445600C2semidirect
15. C2×C61×#408C2semidirect
132. C2×M16×C61D4semidirect
403. C2×#408D61semidirect
473. C61#22039semidirect
496. C2×M16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398382
#214490322
#214466152
#214466112
#214464352
#214464282
#214464222
#214461132
#214461112
#214459972
#214457312
#214456002
C2×C61×#4082
#2203961