Finite Group Databasebeta

← #29685035

Subgroups — #29685035

Order 15616.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2C2×#16839822C211yesmaximal, characteristic, complemented
3C2×#16839719C211yesmaximal, characteristic, complemented
4#21446759C211yesmaximal, characteristic, complemented
5#21446754C211yesmaximal, characteristic, complemented
6#21446614C211yesmaximal, characteristic, complemented
7#21446113C211yesmaximal, characteristic, complemented
8#21446113C211yesmaximal, characteristic, complemented
9#21446108C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21445587C211yesmaximal, characteristic, complemented
12#21445587C211yesmaximal, characteristic, complemented
13#21445583C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic61C211yesmaximal, characteristic, complemented
15C61×#1955C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840292—24no—
19#16840292—24no—
20C2×#14519772C411yescharacteristic
21C2×#14519770C411yescharacteristic
22C2×#14519767C411yescharacteristic
23C2×#14519763C411yescharacteristic
24C2×#14519761C411yescharacteristic
25C2×#14519758C411yescharacteristic
26C2×#14519754C411yescharacteristic
27C2×#14519749C411yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519734C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839822—24no—
35C2×C4⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42#16839719—24no—
43C2×#14519687C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C23×Dic61C2×C411yescharacteristic
67C23×Dic61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—22no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61—22no—
79#14519772—24no—
80#14519770—24no—
81#14519767—24no—
82#14519763—24no—
83#14519761—24no—
84#14519758—24no—
85#14519754—24no—
86#14519749—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#14519734D414yes—
96#14519734D414yes—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×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×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61C2×C411yescharacteristic
117C2×C4×Dic61C2×C411yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121C4⋊#92418—22no—
122C22⋊#92418—22no—
123C22⋊#92418—22no—
124C22⋊#92418—22no—
125C22⋊#92418—22no—
126#14519689—22no—
127#14519689—22no—
128#14519687—22no—
129#14519687—22no—
130C4×#92418—22no—
131C8×Dic61—22no—
132C8×Dic61—22no—
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C4×D4×C61—22no—
141C4×D4×C61—22no—
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2×C411yescharacteristic
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C22⋊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—22no—
156C2×D4×C61—22no—
157C2×D4×C61—41no—
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×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
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×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—41no—
186C22×Dic61—41no—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61C2×D412yes—
199C2×C4×D61C2×D412yes—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—41no—
203C2×C8×C61—21no—
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#4112yes—
214C2×C8×C61#4112yes—
215C4⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C42×C61C2×D412yes—
219C42×C61C2×D412yes—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198C22⋊C414yes—
227#11758198C22⋊C414yes—
228C4⋊Dic61—22no—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196C22⋊C414yes—
236#11758196C22⋊C414yes—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61C2×D412yes—
244C4×Dic61C2×D412yes—
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#4112yes—
256C2×#92418#4112yes—
257#11758189—28no—
258C8×D61—28no—
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#13112yes—
273C23×C61C23×C411yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61C2×C22⋊C412yes—
281D4×C61—44no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
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—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61C2×C22⋊C412yes—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—44no—
309C22⋊D61—44no—
310C2×Dic61—21no—
311C2×Dic61—21no—
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—44no—
328C2×Dic61—44no—
329C2×Dic61C2×C22⋊C412yes—
330C2×Dic61C2×C22⋊C412yes—
331C2×Dic61C2×C22⋊C412yes—
332C2×Dic61#13112yes—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337Dic122—44no—
338C8×C61—22no—
339C8×C61—22no—
340C8×C61—41no—
341C8×C61—41no—
342#92418—22no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#21381—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61C22×C22⋊C411yescharacteristic
362C22×C61C4×#4111yescharacteristic
363C22×C61C4×#4111yescharacteristic
364C22×C61C2×#13111yescharacteristic
365C22×C61C2×#13111yescharacteristic
366C22×C61#56811yescharacteristic
367C22×C61#56811yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61#52511yescharacteristic
380C4×C61#52511yescharacteristic
381C4×C61#53211yescharacteristic
382C4×C61#53211yescharacteristic
383Dic61—22no—
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—41no—
388Dic61—41no—
389Dic61—41no—
390C2×#529—611no—
391C2×#433—611no—
392C2×#405—611no—
393#1985—611no—
394#1984—611no—
395#1955D6111yescharacteristic, complemented
396#1954—611no—
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1750—611no—
402#1750—611no—
403#1749—611no—
404C4×C22⋊C8—611no—
405C2×C61—42no—
406C2×C61—81no—
407C2×C61#229711yescharacteristic
408C2×C61#288011yescharacteristic
409C2×C61#288011yescharacteristic
410C2×C61#296611yescharacteristic
411C2×C61#296711yescharacteristic
412C2×C61#296811yescharacteristic
413C2×C61#296911yescharacteristic
414D61—42no—
415C22×M16—611no—
416C23×C8—611no—
417#529—1224no—
418#529—1224no—
419C2×#126—611no—
420C2×#126—611no—
421C2×#125—611no—
422C2×#124—611no—
423C2×#123—611no—
424C2×#123—611no—
425C2×C22⋊Q8—611no—
426C2×#121—611no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4C2×D6111yescharacteristic
431C2×#117—611no—
432C2×#117—611no—
433C22×C42—611no—
434#433—1224no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8C2×D6111yescharacteristic
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8C2×D6111yescharacteristic
444C2×C22⋊C8C2×D6111yescharacteristic
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×C22⋊C8C2×D6111yescharacteristic
447#405—1224no—
448C2×#97—611no—
449C2×#97—611no—
450C2×#97C2×D6111yescharacteristic
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453C2×C4×C8—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—
462C61#2138111yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×D4—611no—
465C22×D4—611no—
466C22×D4C4×D6111yescharacteristic
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—1222no—
480C22×C8—1222no—
481C22×C8—1222no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#126—1224no—
487#126—1224no—
488#125—1224no—
489#124—1224no—
490#123—1224no—
491#123—1224no—
492C22⋊Q8—1224no—
493#121—1224no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—614no—
503#117—614no—
504#117—1222no—
505#117—1222no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4C4×D6111yescharacteristic
516C2×C22⋊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⋊C4C4×D6111yescharacteristic
525C2×C22⋊C4C4×D6111yescharacteristic
526C2×C42—611no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—1222no—
532C2×C42—1222no—
533C2×C42C22×D6111yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—1222no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546#97—22no—
547#97—1222no—
548#97—1222no—
549C4×C8—1222no—
550C4×C8—1222no—
551C4×C8—1222no—
552C24—611no—
553C24C2×C4×D6111yescharacteristic
554C24C2×C4×D6111yescharacteristic
555C2×Q8—1222no—
556C2×Q8—1222no—
557C2×Q8—2441no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—41no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—2441no—
566C2×D4—2441no—
567C22×C4—21no—
568C22×C4—21no—
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—21no—
578C22×C4—21no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—2441no—
597C22×C4—2441no—
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603M16—1228no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1228no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8#1175822412yes—
628C2×C8#1175822412yes—
629C4⋊C4—22no—
630C4⋊C4—614no—
631C4⋊C4—614no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—614no—
642C22⋊C4—614no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C42—612no—
650C42—612no—
651C42—1222no—
652C42—1222no—
653C42—1221no—
654C42—1221no—
655C42—1221no—
656C42—1221no—
657C42D4×D6112yes—
658C42D4×D6112yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—612no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23#1451978512yes—
680C23C22×C4×D6111yescharacteristic
681Q8—2444no—
682D4—44no—
683D4—2444no—
684D4—2444no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
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—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4C22⋊C4×D6112yes—
731C2×C4C22⋊C4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4#41×D6111yescharacteristic
736C2×C4C2×#1175822411yescharacteristic
737C2×C4C2×#1175822411yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—1222no—
743C8—1222no—
744C8—2441no—
745C8—2441no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22C2×C22⋊C4×D6111yescharacteristic
768C22C4×#1175822411yescharacteristic
769C22C4×#1175822411yescharacteristic
770C22#131×D6111yescharacteristic
771C22C2×#1451978511yescharacteristic
772C22#1684052711yescharacteristic
773C22#1684052811yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—1222no—
779C4—1222no—
780C4—1222no—
781C4—1222no—
782C4—2441no—
783C4—2441no—
784C4—2441no—
785C4#1684027211yescharacteristic
786C4#1684027211yescharacteristic
787C4#1684031011yescharacteristic
788C4#1684031111yescharacteristic
789C2—42no—
790C2—81no—
791C2—2442no—
792C2#2144830611yescharacteristic
793C2#2145426711yescharacteristic
794C2#2145426911yescharacteristic
795C2#2145478911yescharacteristic
796C2#2145479811yescharacteristic
797C2#2145481411yescharacteristic
798C2#2145481611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1955C2
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1955D61
hypocenterC61#21381
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#16839822C2semidirect
3. C2×#16839719C2semidirect
4. #21446759C2semidirect
5. #21446754C2semidirect
6. #21446614C2semidirect
7. #21446113C2semidirect
8. #21446113C2semidirect
9. #21446108C2semidirect
10. #21446108C2semidirect
11. #21445587C2semidirect
12. #21445587C2semidirect
13. #21445583C2semidirect
14. C22⋊C8×Dic61C2semidirect
15. C61×#1955C2semidirect
395. #1955D61semidirect
462. C61#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
C2×#168398222
C2×#168397192
#214467592
#214467542
#214466142
#214461132
#214461082
#214455872
#214455832
C22⋊C8×Dic612
C61×#19552
#2138161