Finite Group Databasebeta

← #29677824

Subgroups — #29677824

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic
2C2×#16839765C211yesmaximal, characteristic
3C2×#102×D61C211yesmaximal, characteristic
4C2×#16839719C211yesmaximal, characteristic, complemented
5#21448173C211yesmaximal, characteristic, complemented
6#21445646C211yesmaximal, characteristic, complemented
7#21445645C211yesmaximal, characteristic, complemented
8#21445643C211yesmaximal, characteristic, complemented
9C4×#14519697C211yesmaximal, characteristic, complemented
10#102×Dic61C211yesmaximal, characteristic, complemented
11C4×#14519698C211yesmaximal, characteristic, complemented
12#21445633C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840234—24no—
20#16840234C418yescomplemented
21C2×C4×D244C2211yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C22×#11758198—21no—
31C2×C22⋊C4×D61—21no—
32#16839765C418yescomplemented
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39#102×D61C418yescomplemented
40#16839719—24no—
41C2×#14519687C2211yescharacteristic, complemented
42C2×C4×#92418C2211yescharacteristic, complemented
43C2×C8×Dic61C2211yescharacteristic, complemented
44C4⋊C4×Dic61C2211yescharacteristic, complemented
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758196—21no—
47C4×C4⋊Dic61C2211yescharacteristic, complemented
48#16839613—21no—
49C4×#11758198—21no—
50#16839609—21no—
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic, complemented
61C4×C4⋊C4×C61C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C2×D4×D61C2×C414yes—
72C2×D4×D61C2×C414yes—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61C2×C414yescomplemented
86C4×D244—22no—
87C4×D244C2×C414yescomplemented
88D4×Dic61—22no—
89D4×Dic61C2×C414yescomplemented
90#14519739—22no—
91#14519739C2×C414yescomplemented
92C4×C22⋊D61—28no—
93#14519737—28no—
94#14519735—22no—
95#14519735—22no—
96#14519735C2×C414yes—
97#14519735C2×C414yescomplemented
98#14519734C2×C414yes—
99#14519734D414yes—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196D411yescharacteristic
105C2×#11758196D411yescharacteristic
106C4⋊C4×D61—22no—
107C4⋊C4×D61C2×C414yescomplemented
108C2×C22⋊Dic61—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—28no—
114C2×#11758198D411yescharacteristic
115C2×#11758198D411yescharacteristic
116C22⋊C4×D61—28no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519699C2×C414yescomplemented
124#14519699C2×C414yescomplemented
125#14519698C2×C414yescomplemented
126#14519698C2×C414yescomplemented
127#14519697C2×C414yescomplemented
128#14519697C2×C414yescomplemented
129#14519687—22no—
130C4×#92418—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C4×D4×C61—22no—
140C4×D4×C61C2×C414yescomplemented
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147#102×C61C2×C414yescomplemented
148#102×C61C2×C414yescomplemented
149#97×C61—22no—
150#95×C61—21no—
151C24×C61—21no—
152C23×D61—21no—
153C23×D61—24no—
154C23×D61—24no—
155C23×D61—24no—
156C23×D61—81no—
157C23×D61—81no—
158C23×D61—81no—
159C23×D61—81no—
160C23×D61C2×D411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C22×C412yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—81no—
172C22×C4×C61—81no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—24no—
183C22×Dic61—81no—
184C22×Dic61—81no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188D4×D61—28no—
189D4×D61—28no—
190D4×D61—28no—
191D4×D61C42116yescomplemented
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C412yes—
196C2×D244C22×C412yes—
197C2×D244C22×C412yes—
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—81no—
202C2×C4×D61—81no—
203C2×C4×D61—81no—
204C2×C4×D61—81no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C22×C412yes—
210C2×C4×D61C2×D412yes—
211C2×C4×D61#4112yes—
212C2×C4×D61#4112yes—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61C22×C412yes—
218C2×C8×C61C22×C412yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61C22×C412yes—
223C4⋊C4×C61C22×C412yes—
224C4⋊C4×C61C22×C412yes—
225C22⋊C4×C61—24no—
226C42×C61—81no—
227C42×C61C22×C412yes—
228C42×C61C2×D412yes—
229C22⋊Dic61—24no—
230#11758198—24no—
231#11758198—24no—
232#11758198—24no—
233#11758198—24no—
234#11758198C22⋊C414yes—
235#11758198C22⋊C414yes—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61C22×C412yes—
240C4⋊Dic61C22×C412yes—
241C4⋊Dic61C22×C412yes—
242#11758196—24no—
243#11758196C22⋊C414yes—
244#11758196C22⋊C414yes—
245C4×Dic61—24no—
246C4×Dic61—24no—
247C4×Dic61—81no—
248C4×Dic61—81no—
249C4×Dic61—81no—
250C4×Dic61C22×C412yes—
251C4×Dic61C2×D412yes—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257C2×#92418C22×C412yes—
258#11758189—28no—
259C8×D61—28no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61C22×D411yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—216no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61C2×C22⋊C412yes—
287C22×D61C4×D412yes—
288C22×D61C4×D412yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61C2×C4214yes—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—84no—
307C2×C4×C61C2×C22⋊C412yes—
308C2×C4×C61C2×C22⋊C412yes—
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C22⋊D61—216no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—84no—
330C2×Dic61C2×C22⋊C412yes—
331C2×Dic61C2×C22⋊C412yes—
332C2×Dic61C2×C22⋊C412yes—
333C2×Dic61C4×D412yes—
334C2×Dic61C4×D412yes—
335D244—22no—
336D244—22no—
337D244—22no—
338D244C2×C4214yes—
339C4×D61—84no—
340C4×D61—84no—
341C4×D61—84no—
342C4×D61C2×C4214yes—
343C4×D61#11714yes—
344C4×D61C4×D414yes—
345C4×D61C4×D414yes—
346C8×C61—22no—
347C8×C61—22no—
348#92418—22no—
349#92418—22no—
350#20416—611nomaximal, Sylow
351C22×C61—24no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61C22×C22⋊C411yescharacteristic
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C2×C4×D411yescharacteristic
361C22×C61#57611yescharacteristic
362C22×C61#57611yescharacteristic
363C22×C61#57711yescharacteristic
364C22×C61#57711yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—24no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—816no—
379C2×D61C4×C22⋊C414yes—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61C22×C4211yescharacteristic
386C4×C61C2×#11711yescharacteristic
387C4×C61C2×C4×D411yescharacteristic
388C4×C61C2×C4×D411yescharacteristic
389Dic61—22no—
390Dic61—22no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394Dic61C4×C22⋊C414yes—
395C2×#518—611no—
396C2×#418—611no—
397C22×#102—611no—
398C2×#405—611no—
399#2274—611no—
400#1762—611no—
401#1762—611no—
402#1762—611no—
403#1762D6111yescharacteristic, complemented
404C4×#102—611no—
405C4×#102—611no—
406C4×#102—611no—
407C4×#102—611no—
408#1736—611no—
409#1735—611no—
410C2×C61—44no—
411C2×C61C2×C4×C22⋊C411yescharacteristic
412C2×C61#289711yescharacteristic
413C2×C61#289711yescharacteristic
414C2×C61#294611yescharacteristic
415C2×C61#294611yescharacteristic
416C2×C61#294811yescharacteristic
417C2×C61#294911yescharacteristic
418D61—24no—
419D61—44no—
420C23×D4—611no—
421C22×M16—611no—
422C23×C8—611no—
423#518—618no—
424#518—1224no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4—611no—
428C2×C4×D4—1221no—
429C2×C4×D4—1221no—
430C2×C4×D4C2×D6111yescharacteristic
431C2×#117—611no—
432C2×#117—611no—
433C2×#117—611no—
434C22×C4⋊C4—611no—
435C22×C22⋊C4—1221no—
436C22×C22⋊C4—1221no—
437#418—618no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—618no—
445C2×#102C2×D6111yescharacteristic
446C2×#102C2×D6111yescharacteristic
447#405—1224no—
448C2×#97—611no—
449C2×#97C2×D6111yescharacteristic, complemented
450C2×C4×C8—611no—
451C2×C4×C8—611no—
452C4×C4⋊C4—611no—
453C4×C4⋊C4—611no—
454C4×C4⋊C4—611no—
455C4×C4⋊C4—1221no—
456C4×C4⋊C4—1221no—
457C4×C4⋊C4C2×D6111yescharacteristic, complemented
458C4×C22⋊C4—1221no—
459C4×C22⋊C4—1221no—
460#340—611no—
461#340—611no—
462#340—611no—
463#340—611no—
464#340—611no—
465#340—611no—
466#340C2×D6111yescharacteristic, complemented
467#340C2×D6111yescharacteristic, complemented
468C61#2041611yescharacteristic, complemented, Sylow
469C25—1221no—
470C22×D4—614no—
471C22×D4—614no—
472C22×D4—614no—
473C22×D4—611no—
474C22×D4—1222no—
475C22×D4—1222no—
476C22×D4—1222no—
477C22×D4—1221no—
478C22×D4C22×D6111yescharacteristic
479C23×C4—21no—
480C23×C4—611no—
481C23×C4—1221no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C2×M16—614no—
486C2×M16—1222no—
487C2×M16—1222no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—614no—
491C22×C8—1222no—
492C22×C8—1222no—
493C22×C8C22×D6111yescharacteristic
494C22×C8C22×D6111yescharacteristic
495C4×D4—22no—
496C4×D4—614no—
497C4×D4—614no—
498C4×D4—614no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1228no—
502C4×D4—1228no—
503C4×D4—1222no—
504C4×D4C4×D6114yescomplemented
505#117—614no—
506#117—614no—
507#117—614no—
508#117—614no—
509#117—1222no—
510#117—1222no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1228no—
526C2×C22⋊C4—1228no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C42—21no—
533C2×C42—611no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#102—614no—
541#102—614no—
542#102—614no—
543#102—614no—
544#102—614no—
545#102—614no—
546#102C4×D6114yescomplemented
547#102C4×D6114yescomplemented
548#97—22no—
549#97—1222no—
550C4×C8—1222no—
551C4×C8—1222no—
552#95—21no—
553#95—1221no—
554#95—1221no—
555#95—1221no—
556C24—21no—
557C24—611no—
558C24—1224no—
559C24—1224no—
560C24—1224no—
561C24—1221no—
562C24—4881no—
563C24—4881no—
564C24—4881no—
565C24—4881no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—6116no—
570C2×D4—612no—
571C2×D4—612no—
572C2×D4—612no—
573C2×D4—1228no—
574C2×D4—1228no—
575C2×D4—1228no—
576C2×D4—1224no—
577C2×D4—1224no—
578C2×D4—1224no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4C2×C4×D6112yes—
583C2×D4C2×C4×D6112yes—
584C2×D4C2×C4×D6112yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—611no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1224no—
607C22×C4—4881no—
608C22×C4—4881no—
609C22×C4—4881no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4D4×D6111yescharacteristic
616C22×C4D4×D6111yescharacteristic
617C22×C4C23×D6111yescharacteristic
618M16—1228no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—612no—
624C2×C8—612no—
625C2×C8—1228no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8C2×C4×D6112yes—
631C2×C8C2×C4×D6112yes—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—612no—
640C4⋊C4—1224no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4C2×C4×D6112yes—
645C4⋊C4C2×C4×D6112yes—
646C4⋊C4C2×C4×D6112yes—
647C22⋊C4—24no—
648C22⋊C4—614no—
649C22⋊C4—614no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C42—81no—
656C42—612no—
657C42—612no—
658C42—1224no—
659C42—1224no—
660C42—4881no—
661C42—4881no—
662C42—4881no—
663C42C2×C4×D6112yes—
664C42D4×D6112yes—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—612no—
673C23—612no—
674C23—612no—
675C23—12216no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—4884no—
684C23—4884no—
685C23—4884no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23C2×D4×D6111yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—614no—
698D4—12216no—
699D4—1222no—
700D4—1222no—
701D4—1222no—
702D4C42×D6114yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—614no—
721C2×C4—614no—
722C2×C4—614no—
723C2×C4—614no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—4884no—
734C2×C4—4884no—
735C2×C4—4884no—
736C2×C4—4884no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4C22⋊C4×D6112yes—
744C2×C4C22⋊C4×D6112yes—
745C2×C4C22×C4×D6111yescharacteristic
746C2×C4C22×C4×D6111yescharacteristic
747C2×C4C22×C4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4#41×D6111yescharacteristic
750C2×C4#41×D6111yescharacteristic
751C8—22no—
752C8—22no—
753C8—1222no—
754C8—1222no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—614no—
763C22—1222no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1224no—
770C22—48816no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22C2×C22⋊C4×D6111yescharacteristic
778C22C4×D4×D6111yescharacteristic
779C22C4×D4×D6111yescharacteristic
780C22#1684056611yescharacteristic
781C22#1684056611yescharacteristic
782C22#1684057111yescharacteristic
783C22#1684057211yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—614no—
790C4—1222no—
791C4—1222no—
792C4—2442no—
793C4—2442no—
794C4—2442no—
795C4C2×C42×D6111yescharacteristic
796C4#117×D6111yescharacteristic
797C4C4×D4×D6111yescharacteristic
798C4C4×D4×D6111yescharacteristic
799C2—44no—
800C2—1224no—
801C2—2444no—
802C2C4×C22⋊C4×D6111yescharacteristic
803C2#2145434311yescharacteristic
804C2#2145434411yescharacteristic
805C2#2145464811yescharacteristic
806C2#2145465011yescharacteristic
807C2#2145466811yescharacteristic
808C2#2145467511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#20416
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
4. C2×#16839719C2semidirect
5. #21448173C2semidirect
6. #21445646C2semidirect
7. #21445645C2semidirect
8. #21445643C2semidirect
9. C4×#14519697C2semidirect
10. #102×Dic61C2semidirect
11. C4×#14519698C2semidirect
12. #21445633C2semidirect
13. #21445537C2semidirect
14. #21445534C2semidirect
15. C61×#1762C2semidirect
20. #16840234C4semidirect
32. #16839765C4semidirect
39. #102×D61C4semidirect
41. C2×#14519687C22semidirect
42. C2×C4×#92418C22semidirect
43. C2×C8×Dic61C22semidirect
44. C4⋊C4×Dic61C22semidirect
45. C4⋊C4×Dic61C22semidirect
47. C4×C4⋊Dic61C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
60. C2×#97×C61C22semidirect
61. C4×C4⋊C4×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
80. C2×#11758189C2×C4semidirect
85. C2×C8×D61C2×C4semidirect
87. C4×D244C2×C4semidirect
89. D4×Dic61C2×C4semidirect
91. #14519739C2×C4semidirect
97. #14519735C2×C4semidirect
107. C4⋊C4×D61C2×C4semidirect
123. #14519699C2×C4semidirect
124. #14519699C2×C4semidirect
125. #14519698C2×C4semidirect
126. #14519698C2×C4semidirect
127. #14519697C2×C4semidirect
128. #14519697C2×C4semidirect
140. C4×D4×C61C2×C4semidirect
147. #102×C61C2×C4semidirect
148. #102×C61C2×C4semidirect
191. D4×D61C42semidirect
403. #1762D61semidirect
449. C2×#97C2×D61semidirect
457. C4×C4⋊C4C2×D61semidirect
466. #340C2×D61semidirect
467. #340C2×D61semidirect
468. C61#20416semidirect
504. C4×D4C4×D61semidirect
546. #102C4×D61semidirect
547. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
C2×#168397652
C2×#102×D612
C2×#168397192
#214481732
#214456462
#214456452
#214456432
C4×#145196972
#102×Dic612
C4×#145196982
#214456332
#214455372
#214455342
C61×#17622
#2041661