Finite Group Databasebeta

← #29696546

Subgroups — #29696546

Order 15616.

1292 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2C2×#16839891C211yesmaximal, characteristic, complemented
3C2×#16839890C211yesmaximal, characteristic, complemented
4#21446760C211yesmaximal, characteristic, complemented
5#21446757C211yesmaximal, characteristic, complemented
6#21446757C211yesmaximal, characteristic, complemented
7#21446753C211yesmaximal, characteristic, complemented
8#21446753C211yesmaximal, characteristic, complemented
9#21445798C211yesmaximal, characteristic
10#21445798C211yesmaximal, characteristic
11#21445796C211yesmaximal, characteristic
12#21445582C211yesmaximal, characteristic
13#21445580C211yesmaximal, characteristic
14#21445576C211yesmaximal, characteristic
15C61×#1985C211yesmaximal, characteristic, complemented
16C22×Q8×D61C411yescharacteristic
17C2×Q8×Dic61C411yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519742C411yescharacteristic
22C2×#14519742C411yescharacteristic
23C2×#14519742C411yescharacteristic
24C4×Q8×D61—24no—
25C4×Q8×D61—24no—
26C2×C4⋊C4×D61C411yescharacteristic
27C2×C4⋊C4×D61C411yescharacteristic
28C2×C4⋊C4×D61C411yescharacteristic
29C2×C42×D61C2211yescharacteristic
30C2×C42×D61C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32#16839891—24no—
33#16839890—24no—
34C2×C4⋊#92418C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519706C2211yescharacteristic
38C2×#14519706C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519688C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×Dic122C2×C411yescharacteristic
65C22×Dic122C2×C411yescharacteristic
66C2×Q8×D61—24no—
67C2×Q8×D61—24no—
68C2×Q8×D61—24no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80Q8×Dic61—24no—
81C4×Dic122—22no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122D414yes—
86C4×Dic122D414yes—
87#14519742—24no—
88#14519742—24no—
89#14519742—24no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C4⋊C4×D61—24no—
100C4⋊C4×D61—24no—
101C4⋊C4×D61—24no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—22no—
112C42×D61—22no—
113C42×D61—22no—
114C42×D61—22no—
115C42×D61—22no—
116C42×D61—22no—
117C4⋊#92418—22no—
118#14519706—22no—
119#14519706—22no—
120#14519706—22no—
121#14519706—22no—
122#14519689—22no—
123#14519689—22no—
124#14519689—22no—
125#14519689Q814yescomplemented
126#14519688—22no—
127#14519687—22no—
128#14519687—22no—
129C8×Dic61—22no—
130C8×Dic61—22no—
131C22×Q8×C61C2×C411yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C4×Q8×C61—22no—
137C4×Q8×C61—22no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C411yescharacteristic
141C2×C42×C61C2311yescharacteristic
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C4⋊C8×C61—22no—
145#97×C61—22no—
146C23×D61C22×C411yescharacteristic
147C2×Q8×C61—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164Q8×D61—232no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—41no—
184C2×C4×D61—41no—
185C2×C4×D61—41no—
186C2×C4×D61M1614yes—
187C2×C4×D61C2×Q812yes—
188C2×C4×D61#4112yes—
189C2×Dic122—22no—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—22no—
193C2×Dic122—22no—
194C2×Dic122—22no—
195C2×Dic122—22no—
196C2×Dic122C22⋊C414yes—
197C2×Dic122M1614yes—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
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×C61C2×Q812yescomplemented
210C4⋊C4×C61—22no—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—22no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61C2×D412yes—
218C42×C61C2×D412yes—
219C4⋊Dic61—22no—
220C4⋊Dic61—22no—
221C4⋊Dic61C22⋊C414yes—
222#11758196—22no—
223#11758196—22no—
224#11758196—22no—
225#11758196—22no—
226#11758196C22⋊C414yes—
227#11758196C22⋊C414yes—
228C4×Dic61—22no—
229C4×Dic61—22no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—22no—
233C4×Dic61—22no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C4×Dic61C2×D412yes—
237C4×Dic61C2×D412yes—
238C4×Dic61C2×D412yes—
239C4×Dic61C2×D412yes—
240C2×#92418—21no—
241C2×#92418—21no—
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×#92418C2×Q812yescomplemented
252C23×C61C23×C411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61C4×Q812yes—
258C22×D61C2×M1612yes—
259C22×D61#13112yes—
260Q8×C61—28no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61C2×C22⋊C412yes—
276C2×C4×C61C2×C22⋊C412yes—
277C2×C4×C61C2×M1612yes—
278C2×C4×C61C2×M1612yes—
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C22×Q811yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C612−1+411yescharacteristic
284C2×C4×C612−1+411yescharacteristic
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61C2×C22⋊C412yes—
299C2×Dic61C2×C22⋊C412yes—
300C2×Dic61C2×C22⋊C412yes—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61C4×Q812yes—
303C2×Dic61C2×M1612yes—
304C2×Dic61C2×M1612yes—
305C2×Dic61C2×M1612yes—
306C4×D61—28no—
307C4×D61—28no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—28no—
313C4×D61—44no—
314C4×D61—44no—
315C4×D61—44no—
316Dic122—28no—
317Dic122—28no—
318Dic122—28no—
319C8×C61—22no—
320C8×C61—41no—
321C8×C61—41no—
322C8×C61—41no—
323#92418—22no—
324#92418—41no—
325#92418—41no—
326#92418—41no—
327#22510—611nomaximal, Sylow
328C22×C61C22×C22⋊C411yescharacteristic
329C22×C61C2×C4×Q811yescharacteristic
330C22×C61#51911yescharacteristic
331C22×C61C22×M1611yescharacteristic
332C22×C61C22×M1611yescharacteristic
333C22×C61C2×#13111yescharacteristic
334C22×C61#56811yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61#44614yescomplemented
342C4×C61—22no—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—22no—
346C4×C61—41no—
347C4×C61—41no—
348C4×C61#54811yescharacteristic
349C4×C61#54811yescharacteristic
350C4×C61D4×Q811yescharacteristic
351C4×C61D4×Q811yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—41no—
358Dic61#40714yes—
359C22×C4×Q8—611no—
360C2×#446—611no—
361C2×#446—611no—
362#1985—611no—
363#1985—611no—
364#1985—611no—
365#1985D6111yescharacteristic, complemented
366#1984—611no—
367#1984—611no—
368#1797—611no—
369#1797—611no—
370#1797—611no—
371#1749—611no—
372#1749—611no—
373C4×C22⋊C8—611no—
374C2×C61Q8×C22⋊C411yescharacteristic
375C2×C61C2×#40711yescharacteristic
376C2×C61#288011yescharacteristic
377C2×C61C2×#44611yescharacteristic
378C2×C61Q8×M1611yescharacteristic
379C2×C61#298311yescharacteristic
380C2×C61#298411yescharacteristic
381D61—24no—
382C23×Q8—611no—
383C2×C4×Q8—611no—
384C2×C4×Q8—611no—
385C2×C4×Q8—611no—
386C2×C4×Q8—611no—
387C2×C4×Q8—611no—
388C2×C4×Q8—611no—
389C2×C4×Q8—611no—
390C2×C4×Q8—1224no—
391C2×C4×Q8—1224no—
392C2×C4×Q8C2×D6111yescharacteristic
393C22×C4⋊C4—611no—
394C22×C4⋊C4—611no—
395C22×C4⋊C4—611no—
396C22×C42—611no—
397C22×C42—611no—
398C22×C42—611no—
399#446—1224no—
400#446—1224no—
401C2×C4⋊C8—611no—
402C2×C4⋊C8—611no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8C2×D6111yescharacteristic
407C2×C22⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×#97—611no—
412C2×#97—611no—
413C2×#97—611no—
414C2×#97C2×D6111yescharacteristic
415C2×C4×C8—611no—
416C2×C4×C8—611no—
417#336—611no—
418#336—611no—
419#336—611no—
420#336—611no—
421#336—611no—
422#336—611no—
423#336—611no—
424#336—611no—
425#336C2×D6111yescharacteristic
426#336C2×D6111yescharacteristic
427#336C2×D6111yescharacteristic
428#336C2×D6111yescharacteristic
429C61#2251011yescharacteristic, complemented, Sylow
430C22×Q8—611no—
431C22×Q8—611no—
432C22×Q8—611no—
433C22×Q8—1224no—
434C22×Q8—1224no—
435C22×Q8—1224no—
436C22×Q8C4×D6111yescharacteristic
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C22×C8—611no—
445C22×C8—611no—
446C22×C8—611no—
447C22×C8—611no—
448C22×C8C22×D6111yescharacteristic
449C22×C8C22×D6111yescharacteristic
450C22×C8C22×D6111yescharacteristic
451C22×C8C22×D6111yescharacteristic
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—614no—
455C4×Q8—614no—
456C4×Q8—1222no—
457C4×Q8—1222no—
458C4×Q8—1222no—
459C4×Q8—1222no—
460C4×Q8—1224no—
461C4×Q8—1224no—
462C4×Q8—1224no—
463C4×Q8—1224no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1224no—
474C2×C4⋊C4—1224no—
475C2×C4⋊C4—1224no—
476C2×C4⋊C4C4×D6111yescharacteristic
477C2×C4⋊C4C4×D6111yescharacteristic
478C2×C4⋊C4C4×D6111yescharacteristic
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1222no—
489C2×C42—1222no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42—1222no—
493C2×C42—1222no—
494C2×C42C22×D6111yescharacteristic
495C2×C42C22×D6111yescharacteristic
496C2×C42C22×D6111yescharacteristic
497C4⋊C8—22no—
498C4⋊C8—1222no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C22⋊C8—614no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507#97—22no—
508#97—1222no—
509#97—1222no—
510#97—1222no—
511C4×C8—1222no—
512C4×C8—1222no—
513C24—611no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—614no—
518C2×Q8—614no—
519C2×Q8—1222no—
520C2×Q8—1222no—
521C2×Q8—1222no—
522C2×Q8—1222no—
523C2×Q8—1222no—
524C2×Q8—1222no—
525C2×Q8—12232no—
526C2×Q8—1222no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—612no—
534C22×C4—612no—
535C22×C4—614no—
536C22×C4—611no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—2441no—
556C22×C4—2441no—
557C22×C4—2441no—
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4C2×C4×D6111yescharacteristic
563C22×C4C2×C4×D6111yescharacteristic
564C22×C4C23×D6111yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—612no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8Q8×D6112yescomplemented
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—614no—
593C4⋊C4—614no—
594C4⋊C4—614no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—612no—
606C42—612no—
607C42—612no—
608C42—612no—
609C42—1222no—
610C42—1222no—
611C42—1222no—
612C42—1222no—
613C42—1221no—
614C42—1221no—
615C42—1222no—
616C42—1222no—
617C42D4×D6112yes—
618C42D4×D6112yes—
619C23—612no—
620C23—612no—
621C23—612no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23C22×C4×D6111yescharacteristic
627Q8—28no—
628Q8—1228no—
629Q8—1228no—
630Q8—1228no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—612no—
646C2×C4—612no—
647C2×C4—612no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—1228no—
654C2×C4—1228no—
655C2×C4—1228no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—2444no—
674C2×C4—2444no—
675C2×C4—2444no—
676C2×C4C22⋊C4×D6112yes—
677C2×C4C22⋊C4×D6112yes—
678C2×C4M16×D6112yes—
679C2×C4M16×D6112yes—
680C2×C4C2×D4×D6111yescharacteristic
681C2×C4C2×D4×D6111yescharacteristic
682C2×C4C2×Q8×D6111yescharacteristic
683C2×C4#41×D6111yescharacteristic
684C2×C4#1451982411yescharacteristic
685C2×C4#1451982511yescharacteristic
686C8—22no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—1222no—
691C8—2441no—
692C8—2441no—
693C8—2441no—
694C22—614no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—1222no—
700C22—1222no—
701C22C2×C22⋊C4×D6111yescharacteristic
702C22C4×Q8×D6111yescharacteristic
703C22#1684023811yescharacteristic
704C22C2×M16×D6111yescharacteristic
705C22C2×M16×D6111yescharacteristic
706C22#131×D6111yescharacteristic
707C22#1684052711yescharacteristic
708C4—22no—
709C4—22no—
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—614no—
715C4—1222no—
716C4—1222no—
717C4—1222no—
718C4—1222no—
719C4—1222no—
720C4—2441no—
721C4#1684042011yescharacteristic
722C4#1684042211yescharacteristic
723C4#1684042511yescharacteristic
724C4#1684042711yescharacteristic
725C2—1224no—
726C2#2144865311yescharacteristic
727C2#407×D6111yescharacteristic
728C2#2145426711yescharacteristic
729C2#446×D6111yescharacteristic
730C2#2145477111yescharacteristic
731C2#2145490111yescharacteristic
732C2#2145490511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1985C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1985D61
hypocenterC61#22510
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#16839891C2semidirect
3. C2×#16839890C2semidirect
4. #21446760C2semidirect
5. #21446757C2semidirect
6. #21446757C2semidirect
7. #21446753C2semidirect
8. #21446753C2semidirect
15. C61×#1985C2semidirect
125. #14519689Q8semidirect
209. C2×C8×C61C2×Q8semidirect
251. C2×#92418C2×Q8semidirect
341. C2×D61#446semidirect
365. #1985D61semidirect
429. C61#22510semidirect
588. C2×C8Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
C2×#168398912
C2×#168398902
#214467602
#214467572
#214467532
#214457982
#214457962
#214455822
#214455802
#214455762
C61×#19852
#2251061