Finite Group Databasebeta

← #29691125

Subgroups — #29691125

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×#16839730C211yesmaximal, characteristic, complemented
2#21449034C211yesmaximal, characteristic
3#21446615C211yesmaximal, characteristic, complemented
4#21446611C211yesmaximal, characteristic, complemented
5#21446431C211yesmaximal, characteristic, complemented
6#21446425C211yesmaximal, characteristic, complemented
7#21446425C211yesmaximal, characteristic, complemented
8#21446424C211yesmaximal, characteristic, complemented
9#21446116C211yesmaximal, characteristic, complemented
10#21446116C211yesmaximal, characteristic, complemented
11#21446112C211yesmaximal, characteristic, complemented
12#21445996C211yesmaximal, characteristic, complemented
13#21445730C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#436C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22#16839730—24no—
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839682C411yescharacteristic
37#16839679C411yescharacteristic
38#16839677C411yescharacteristic
39#16839677C411yescharacteristic
40#16839674C411yescharacteristic
41#16839671C411yescharacteristic
42#16839670C411yescharacteristic
43#16839670C411yescharacteristic
44C4×#11758198C2211yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×M16×C61C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#436—24no—
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C22×C22⋊D61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×#92418—22no—
76C22×#92418—41no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C4×C22⋊D61—41no—
83C4×C22⋊D61—41no—
84C4×C22⋊D61—41no—
85C4×C22⋊D61—41no—
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519706—41no—
101#14519706—41no—
102C22⋊#92418—22no—
103C22⋊#92418—41no—
104C22⋊#92418—41no—
105#14519689—22no—
106#14519689—22no—
107#14519689—22no—
108#14519689—22no—
109#14519689—41no—
110#14519689—41no—
111#14519689—41no—
112#14519689—41no—
113#14519687—41no—
114C8×Dic61—41no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C22×D4×C61C2×C411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×M16×C61—22no—
125C2×M16×C61—41no—
126C2×M16×C61—41no—
127C2×M16×C61—41no—
128C2×M16×C61—41no—
129C2×M16×C61D414yescomplemented
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C4×D4×C61—22no—
135C4×D4×C61—22no—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61—22no—
141C22⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143C4×C8×C61—22no—
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—41no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D412yes—
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61—41no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—41no—
177C2×C22⋊D61—41no—
178C2×C22⋊D61—41no—
179C2×C22⋊D61—41no—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186#11758222—44no—
187#11758222—44no—
188#11758222—44no—
189#11758222—44no—
190C2×D244—22no—
191C2×D244—41no—
192C2×D244—41no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×Dic122—22no—
206C2×Dic122—41no—
207C2×Dic122—41no—
208M16×C61—44no—
209M16×C61—44no—
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—
220C2×C8×C61C2×D412yes—
221C2×C8×C61C2×D412yes—
222C4⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C42×C61—21no—
226C42×C61—21no—
227C22⋊Dic61—22no—
228C22⋊Dic61—41no—
229C22⋊Dic61—41no—
230C22⋊Dic61—41no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—41no—
235#11758198—41no—
236#11758198—41no—
237#11758196—41no—
238#11758196—41no—
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—
255C2×#92418—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×C61C4×D412yes—
270C23×C61C23×C411yescharacteristic
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285D4×C61—44no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61C4×D412yes—
305C2×C4×C61#13112yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C22⋊D61—44no—
313C22⋊D61—44no—
314C22⋊D61—44no—
315C22⋊D61—44no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
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#13112yes—
334D244—44no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343Dic122—44no—
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×C61C2×C4×D411yescharacteristic
368C22×C61#51811yescharacteristic
369C22×C61#51811yescharacteristic
370C22×C61C2×#13111yescharacteristic
371C22×C61C2×#13111yescharacteristic
372C22×C61#56811yescharacteristic
373C22×C61#56811yescharacteristic
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
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—22no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61#53411yescharacteristic
393C4×C61#53511yescharacteristic
394C4×C61#53811yescharacteristic
395C4×C61#53811yescharacteristic
396Dic61—22no—
397Dic61—41no—
398Dic61—41no—
399Dic61—41no—
400Dic61—41no—
401Dic61—41no—
402C2×#436D6111yescharacteristic, complemented
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#1780—611no—
416#1753—611no—
417C2×C61—42no—
418C2×C61—81no—
419C2×C61#232111yescharacteristic
420C2×C61#293311yescharacteristic
421C2×C61#293511yescharacteristic
422C2×C61#297611yescharacteristic
423C2×C61#297811yescharacteristic
424C2×C61#297911yescharacteristic
425C2×C61#298111yescharacteristic
426D61—81no—
427D61—81no—
428C22×#41—611no—
429C22×M16C2×D6111yescharacteristic
430C22×M16C2×D6111yescharacteristic
431C23×C8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4C2×D6111yescharacteristic
435#436—24no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8C2×D6111yescharacteristic
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⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8C2×D6111yescharacteristic
452C2×C22⋊C8C2×D6111yescharacteristic
453C2×#97—611no—
454C2×C4×C8—611no—
455C2×C4×C8C2×D6111yescharacteristic
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—1222no—
475C2×#41—1222no—
476C2×#41—2441no—
477C2×#41—2441no—
478C2×#41—2441no—
479C2×#41—2441no—
480C22×Q8—611no—
481C22×D4—611no—
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4C4×D6111yescharacteristic
487C23×C4—611no—
488C23×C4—611no—
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16C22⋊D6114yescomplemented
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—22no—
509C4×D4—22no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513C4×D4—2441no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4C4×D6111yescharacteristic
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⋊C4C4×D6111yescharacteristic
528C2×C22⋊C4C4×D6111yescharacteristic
529C2×C42—611no—
530C2×C42—611no—
531C2×C42C22×D6111yescharacteristic
532C4⋊C8—22no—
533C4⋊C8—2441no—
534C4⋊C8—2441no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
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—22no—
550C4×C8—2441no—
551#95—611no—
552#95—611no—
553#95—611no—
554#95—611no—
555#95—611no—
556#95—611no—
557C24—611no—
558C24—611no—
559C24C2×C4×D6111yescharacteristic
560C24C2×C4×D6111yescharacteristic
561#41—2444no—
562#41—2444no—
563#41—2444no—
564#41—2444no—
565C2×Q8—1222no—
566C2×Q8—2441no—
567C2×Q8—2441no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—41no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C2×D4—2441no—
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—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4C2×C4×D6111yescharacteristic
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—44no—
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—1221no—
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—2444no—
646C2×C8C2×C22⋊D6112yes—
647C2×C8C2×C22⋊D6112yes—
648C4⋊C4—22no—
649C4⋊C4—2441no—
650C4⋊C4—2441no—
651C22⋊C4—22no—
652C22⋊C4—22no—
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—21no—
664C42—21no—
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—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23C4×C22⋊D6112yes—
697C23C22×C4×D6111yescharacteristic
698Q8—2444no—
699D4—44no—
700D4—2444no—
701D4—2444no—
702D4—2444no—
703D4—2444no—
704D4—2444no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—612no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
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—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4C4×C22⋊D6112yes—
750C2×C4#1451978512yes—
751C2×C4C22×C22⋊D6111yescharacteristic
752C2×C4C2×#1175822211yescharacteristic
753C2×C4#1451982211yescharacteristic
754C2×C4#1451982211yescharacteristic
755C2×C4#1451982311yescharacteristic
756C2×C4#1451982311yescharacteristic
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—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C2×C4×C22⋊D6111yescharacteristic
794C22#1684023411yescharacteristic
795C22#1684023411yescharacteristic
796C22#131×D6111yescharacteristic
797C22C2×#1451978511yescharacteristic
798C22#1684052711yescharacteristic
799C22#1684052811yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—1222no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C4—2441no—
809C4—2441no—
810C4#1684032111yescharacteristic
811C4#1684032611yescharacteristic
812C4#1684034511yescharacteristic
813C4#1684034511yescharacteristic
814C2—42no—
815C2—81no—
816C2—4881no—
817C2—4881no—
818C2#2144847311yescharacteristic
819C2#2145454411yescharacteristic
820C2#2145456111yescharacteristic
821C2#2145486311yescharacteristic
822C2#2145487611yescharacteristic
823C2#2145488411yescharacteristic
824C2#2145489611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#436C2
prime radical#21449034C2
cosocleC22×C4×C61C24
hypercenterC2×#436D61
hypocenterC61#22039
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#16839730C2semidirect
3. #21446615C2semidirect
4. #21446611C2semidirect
5. #21446431C2semidirect
6. #21446425C2semidirect
7. #21446425C2semidirect
8. #21446424C2semidirect
9. #21446116C2semidirect
10. #21446116C2semidirect
11. #21446112C2semidirect
12. #21445996C2semidirect
13. #21445730C2semidirect
14. #21445600C2semidirect
15. C2×C61×#436C2semidirect
129. C2×M16×C61D4semidirect
402. C2×#436D61semidirect
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×#168397302
#214490342
#214466152
#214466112
#214464312
#214464252
#214464242
#214461162
#214461122
#214459962
#214457302
#214456002
C2×C61×#4362
#2203961