Finite Group Databasebeta

← #29696131

Subgroups — #29696131

Order 15616.

1168 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840294C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic, complemented
3#21446759C211yesmaximal, characteristic, complemented
4#21446758C211yesmaximal, characteristic, complemented
5#21446116C211yesmaximal, characteristic, complemented
6#21446114C211yesmaximal, characteristic, complemented
7#21446111C211yesmaximal, characteristic, complemented
8#21446109C211yesmaximal, characteristic, complemented
9#21445888C211yesmaximal, characteristic, complemented
10#21445888C211yesmaximal, characteristic, complemented
11#21445796C211yesmaximal, characteristic, complemented
12#21445582C211yesmaximal, characteristic, complemented
13#21445517C211yesmaximal, characteristic, complemented
14#21445515C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16840294—24no—
19#16840294—24no—
20C2×#14519770C411yescharacteristic
21C2×#14519770C411yescharacteristic
22C2×#14519768C411yescharacteristic
23C2×#14519764C411yescharacteristic
24C2×#14519759C411yescharacteristic
25C2×#14519759C411yescharacteristic
26C2×#14519757C411yescharacteristic
27C2×#14519748C411yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519736C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839834—24no—
35C2×C4⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43#16839516C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#435—24no—
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—41no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519770—24no—
80#14519770—24no—
81#14519768—24no—
82#14519764—24no—
83#14519759—24no—
84#14519759—24no—
85#14519757—24no—
86#14519748—24no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93#14519736—22no—
94#14519736—22no—
95#14519736—22no—
96#14519736—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C42×D61—22no—
120C42×D61—22no—
121C4⋊#92418—22no—
122C22⋊#92418—22no—
123C22⋊#92418—22no—
124#14519689—22no—
125#14519689—22no—
126#14519689—41no—
127#14519689—41no—
128#14519688—22no—
129C22×D4×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—22no—
133C2×M16×C61—22no—
134C2×M16×C61—41no—
135C22×C8×C61—22no—
136C22×C8×C61—22no—
137C22×C8×C61—41no—
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C4×D4×C61D414yes—
143C4×D4×C61D414yes—
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C22⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C4⋊C8×C61—22no—
149C22⋊C8×C61—22no—
150C22⋊C8×C61—22no—
151#97×C61—22no—
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61C22⋊C414yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—41no—
198C2×C4×D61—41no—
199C2×C4×D61—41no—
200C2×Dic122—22no—
201C2×Dic122—41no—
202C2×Dic122—41no—
203M16×C61—44no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—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—44no—
216C2×C8×C61#4112yes—
217C4⋊C4×C61C22⋊C414yes—
218C22⋊C4×C61C22⋊C414yes—
219C22⋊C4×C61C22⋊C414yes—
220C42×C61C2×D412yes—
221C42×C61C2×D412yes—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228#11758198—22no—
229#11758198—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61—22no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247#11758194—44no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—44no—
260C2×#92418#4112yes—
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×C61C2×C22⋊C412yes—
274C23×C61C2×C22⋊C412yes—
275C23×C61C23×C411yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61#13112yes—
283D4×C61—44no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61C2×C22⋊C412yes—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C2×C22⋊C412yes—
303C2×C4×C61C2×C22⋊C412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C22⋊D61—44no—
311C22⋊D61—44no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
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—
333C4×D61—44no—
334C4×D61—44no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339Dic122—44no—
340C8×C61—22no—
341C8×C61—41no—
342C8×C61—41no—
343C8×C61—41no—
344#92418—22no—
345#92418—41no—
346#92418—41no—
347#92418—41no—
348#22475—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61C22×C22⋊C411yescharacteristic
364C22×C61C4×#4111yescharacteristic
365C22×C61#52011yescharacteristic
366C22×C61C2×#13111yescharacteristic
367C22×C61#56811yescharacteristic
368C22×C61#56811yescharacteristic
369C22×C61#56811yescharacteristic
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61#54611yescharacteristic
382C4×C61#54611yescharacteristic
383C4×C61#54711yescharacteristic
384C4×C61#54711yescharacteristic
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
388Dic61—41no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392C2×#529—611no—
393C2×#435—611no—
394C2×#435D6111yescharacteristic, complemented
395#1985—611no—
396#1985—611no—
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1818—611no—
402#1818—611no—
403#1797—611no—
404#1749—611no—
405#1729—611no—
406#1729—611no—
407C2×C61—42no—
408C2×C61—42no—
409C2×C61#233911yescharacteristic
410C2×C61#287911yescharacteristic
411C2×C61#288011yescharacteristic
412C2×C61#296711yescharacteristic
413C2×C61#296811yescharacteristic
414C2×C61#299211yescharacteristic
415C2×C61#299511yescharacteristic
416D61—42no—
417C22×M16—611no—
418C22×M16C2×D6111yescharacteristic
419C23×C8—611no—
420C23×C8C2×D6111yescharacteristic
421#529—1224no—
422#529—1224no—
423C2×#126—611no—
424C2×#126—611no—
425C2×#125—611no—
426C2×#124—611no—
427C2×#123—611no—
428C2×#123—611no—
429C2×C22⋊Q8—611no—
430C2×#121—611no—
431C2×C4×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4C2×D6111yescharacteristic
435C2×#117—611no—
436C2×#117—611no—
437C22×C42—611no—
438#435—24no—
439#435—1224no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×#97—611no—
451C2×#97C2×D6111yescharacteristic
452#336—611no—
453#336—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336—611no—
461#336—611no—
462#336—611no—
463#336—611no—
464C61#2247511yescharacteristic, complemented, Sylow
465C22×Q8—611no—
466C22×D4—611no—
467C22×D4—611no—
468C22×D4C4×D6111yescharacteristic
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—41no—
477C2×M16—1222no—
478C2×M16—1222no—
479C2×M16—2441no—
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—41no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—1222no—
488C22×C8—1222no—
489C22×C8—2441no—
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494#126—1224no—
495#126—1224no—
496#125—1224no—
497#124—1224no—
498#123—1224no—
499#123—1224no—
500C22⋊Q8—1224no—
501#121—1224no—
502C4×Q8—1222no—
503C4×Q8—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4D24414yes—
509C4×D4C22⋊D6114yes—
510#117—1222no—
511#117—1222no—
512#117—1222no—
513#117—1222no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4C4×D6111yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4C4×D6111yescharacteristic
533C2×C22⋊C4C4×D6111yescharacteristic
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—1222no—
540C2×C42—1222no—
541C2×C42C22×D6111yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—1222no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—2441no—
551C22⋊C8—2441no—
552#97—22no—
553#97—1222no—
554C24—611no—
555C24C2×C4×D6111yescharacteristic
556C24C2×C4×D6111yescharacteristic
557C2×Q8—1222no—
558C2×Q8—2441no—
559C2×Q8—2441no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4#1175819814yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1222no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×D24412yes—
601C22×C4C2×D24412yes—
602C22×C4C2×C22⋊D6112yes—
603C22×C4C2×C22⋊D6112yes—
604C22×C4C23×D6111yescharacteristic
605M16—44no—
606M16—2444no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—44no—
619C2×C8—612no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—2444no—
632C2×C8#1175822412yes—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4#1175819814yes—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4#1175819814yes—
652C22⋊C4#1175819814yes—
653C42—1221no—
654C42—1221no—
655C42—1221no—
656C42—1221no—
657C42—1221no—
658C42—1221no—
659C42—1222no—
660C42—1222no—
661C42C2×D24412yes—
662C42C2×C22⋊D6112yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—612no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23C2×#1175819812yes—
683C23C2×#1175819812yes—
684C23C22×C4×D6111yescharacteristic
685Q8—2444no—
686D4—44no—
687D4—2444no—
688D4—2444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—2444no—
727C2×C4—2444no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4C2×#1175819812yes—
733C2×C4C2×#1175819812yes—
734C2×C4C2×#1175819812yes—
735C2×C4C2×#1175819812yes—
736C2×C4C22×C22⋊D6111yescharacteristic
737C2×C4C22×D24411yescharacteristic
738C2×C4#41×D6111yescharacteristic
739C2×C4C2×#1175822411yescharacteristic
740C2×C4#1451982211yescharacteristic
741C2×C4#1451982411yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—1222no—
747C8—2441no—
748C8—2441no—
749C8—2441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22C22×#1175819811yescharacteristic
772C22C4×#1175822411yescharacteristic
773C22#1684024111yescharacteristic
774C22#131×D6111yescharacteristic
775C22#1684052711yescharacteristic
776C22#1684052811yescharacteristic
777C22#1684052811yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—2441no—
783C4—2441no—
784C4—2441no—
785C4—2441no—
786C4—2441no—
787C4—2441no—
788C4—2441no—
789C4#1684040611yescharacteristic
790C4#1684040711yescharacteristic
791C4#1684041111yescharacteristic
792C4#1684041611yescharacteristic
793C2—42no—
794C2—42no—
795C2—2442no—
796C2#2144864411yescharacteristic
797C2#2145426311yescharacteristic
798C2#2145426611yescharacteristic
799C2#2145480111yescharacteristic
800C2#2145481011yescharacteristic
801C2#2145495411yescharacteristic
802C2#2145498511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#435C2
prime radicalC2×#14519748C4
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22475
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16839834C2semidirect
3. #21446759C2semidirect
4. #21446758C2semidirect
5. #21446116C2semidirect
6. #21446114C2semidirect
7. #21446111C2semidirect
8. #21446109C2semidirect
9. #21445888C2semidirect
10. #21445888C2semidirect
11. #21445796C2semidirect
12. #21445582C2semidirect
13. #21445517C2semidirect
14. #21445515C2semidirect
15. C2×C61×#435C2semidirect
394. C2×#435D61semidirect
464. C61#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#168402942
C2×#168398342
#214467592
#214467582
#214461162
#214461142
#214461112
#214461092
#214458882
#214457962
#214455822
#214455172
#214455152
C2×C61×#4352
#2247561