Finite Group Databasebeta

← #29680985

Subgroups — #29680985

Order 15616.

1550 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2C2×#16839803C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic
4C2×#16839762C211yesmaximal, characteristic
5#389×D61C211yesmaximal, characteristic, complemented
6#21446089C211yesmaximal, characteristic, complemented
7#21446085C211yesmaximal, characteristic, complemented
8#21446083C211yesmaximal, characteristic, complemented
9#21446079C211yesmaximal, characteristic, complemented
10#21446073C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446063C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445511C211yesmaximal, characteristic, complemented
15C61×#1863C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C4×#11758226—24no—
20C4×#11758226—24no—
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×D244—21no—
23C2×C4×D244C2211yescharacteristic
24C2×#14519739—21no—
25C2×#14519739C2211yescharacteristic
26C2×#14519735—21no—
27C2×#14519735C2211yescharacteristic
28C2×C4⋊C4×D61—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C42×D61—21no—
32C2×C42×D61C2211yescharacteristic
33#16839803—24no—
34C2×#14519710C2211yescharacteristic
35C2×#14519709C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37#16839762—24no—
38#16839762C418yescomplemented
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45#16839661C2211yescharacteristic
46#16839660C2211yescharacteristic
47#16839659—21no—
48#16839658C2211yescharacteristic
49#16839657—21no—
50#95×D61—21no—
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839517C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226C2×C414yes—
68C2×#11758226D414yes—
69C2×#11758226Q814yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—22no—
84C2×#11758189—22no—
85C2×#11758189C2×C414yescomplemented
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88Q8×Dic61—22no—
89Q8×Dic61—22no—
90C4×D244—28no—
91C4×D244—22no—
92C4×D244—22no—
93#14519739—28no—
94#14519739—22no—
95#14519739—22no—
96#14519735—28no—
97#14519735—22no—
98#14519735D414yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—44no—
112C4⋊C4×D61C2×C414yescomplemented
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121C42×D61—28no—
122C42×D61—22no—
123C42×D61—22no—
124#14519710—22no—
125#14519709—22no—
126#14519708—22no—
127#14519701—22no—
128#14519701C2×C414yescomplemented
129#14519699—22no—
130#14519699C2×C414yescomplemented
131#14519697—22no—
132#14519697C2×C414yescomplemented
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C22×Q8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C4×Q8×C61—22no—
140C4×Q8×C61—22no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61C2311yescharacteristic
148#107×C61—22no—
149#103×C61—22no—
150#103×C61C2×C414yescomplemented
151#95×C61—21no—
152C23×D61—21no—
153C23×D61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61C22×C412yes—
158C2×Q8×C61C2×D412yes—
159C2×Q8×C61C2×Q812yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173#11758226—28no—
174#11758226—28no—
175#11758226—28no—
176#11758226C4⋊C4116yescomplemented
177C2×D244—24no—
178C2×D244—24no—
179C2×D244—24no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244C22×C412yes—
184C2×D244C2×D412yes—
185C2×D244C2×Q812yes—
186C2×C4×D61—24no—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—41no—
197C2×C4×D61—41no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×Q812yes—
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×C61—21no—
218C2×C8×C61C22×C412yes—
219C4⋊C4×C61—24no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61C22×C412yes—
226C4⋊C4×C61C2×D412yes—
227C42×C61—24no—
228C42×C61—21no—
229C42×C61—21no—
230#11758198—24no—
231#11758198—24no—
232#11758198—24no—
233C4⋊Dic61—24no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—42no—
239C4⋊Dic61C22×C412yes—
240C4⋊Dic61C2×D412yes—
241#11758196—24no—
242#11758196—42no—
243#11758196—42no—
244#11758196—42no—
245C4×Dic61—24no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—22no—
249C4×Dic61—24no—
250C4×Dic61—22no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257#11758189—28no—
258#11758189—44no—
259C23×C61C22×D411yescharacteristic
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61C4×D412yes—
272C22×D61#12012yes—
273C22×D61C22⋊Q812yes—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61C2×C4⋊C414yescomplemented
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61#13712yes—
296C2×C4×C61C23×C411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×Q811yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C4×D412yes—
317C2×Dic61#12012yes—
318C2×Dic61C22⋊Q812yes—
319C2×Dic61AGL(1,ℤ/8)12yes—
320D244—216no—
321D244—22no—
322D244—22no—
323D244—22no—
324D244C2×C4⋊C414yescomplemented
325C4×D61—216no—
326C4×D61—44no—
327C4×D61—48no—
328C4×D61—44no—
329C4×D61—48no—
330C4×D61—48no—
331C4×D61—84no—
332C4×D61C2×C4⋊C414yes—
333C4×D61C4×D414yes—
334C4×D61C22⋊Q814yes—
335C4×D61#12314yes—
336C8×C61—22no—
337C8×C61—41no—
338#92418—22no—
339#92418—41no—
340#20875—611nomaximal, Sylow
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C2×#12011yescharacteristic
343C22×C61C2×C22⋊Q811yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61C2×#13711yescharacteristic
346C22×C61#57511yescharacteristic
347C22×C61#57511yescharacteristic
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—24no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61#38514yes—
362C4×C61—22no—
363C4×C61—24no—
364C4×C61—42no—
365C4×C61—41no—
366C4×C61—42no—
367C4×C61—81no—
368C4×C61C22×C4⋊C411yescharacteristic
369C4×C61C2×C4×D411yescharacteristic
370C4×C61C2×C22⋊Q811yescharacteristic
371C4×C61C2×#12311yescharacteristic
372Dic61—22no—
373Dic61—42no—
374Dic61—41no—
375Dic61—42no—
376Dic61—81no—
377Dic61#38514yes—
378C2×C4×#41—611no—
379C2×#428—611no—
380C2×#417—611no—
381C2×#417—611no—
382C2×#389—611no—
383#1865—611no—
384#1865—611no—
385#1864—611no—
386#1864—611no—
387#1863—611no—
388#1863D6111yescharacteristic, complemented
389#1862—611no—
390#1862—611no—
391#1736—611no—
392#1728—611no—
393C2×C61C2×#38511yescharacteristic
394C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
395C2×C61C4×#13711yescharacteristic
396C2×C61#300611yescharacteristic
397C2×C61#300711yescharacteristic
398C2×C61#307911yescharacteristic
399C2×C61#308011yescharacteristic
400D61—24no—
401D61—44no—
402C22×#41—611no—
403C22×M16—611no—
404C22×M16—611no—
405C4×#41—1224no—
406C4×#41—1224no—
407C2×C4×Q8—611no—
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C2×C4×D4—1221no—
412C2×C4×D4—1221no—
413C2×#117—611no—
414C2×#117—1221no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—1221no—
418C22×C42—611no—
419C22×C42—1221no—
420#428—1224no—
421C2×#107—611no—
422C2×#107C2×D6111yescharacteristic
423C2×#106—611no—
424C2×#106—611no—
425#417—618no—
426#417—1224no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103C2×D6111yescharacteristic
430C2×#103C2×D6111yescharacteristic
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435#389—611no—
436#389—611no—
437#389—611no—
438#389—1221no—
439#389—1221no—
440#389C2×D6111yescharacteristic
441C2×#95—1221no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic
446#336—611no—
447#336—611no—
448#336—611no—
449#336C2×D6111yescharacteristic
450C61#2087511yescharacteristic, complemented, Sylow
451C2×#41—614no—
452C2×#41—614no—
453C2×#41—614no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C2×M16—614no—
469C2×M16—1222no—
470C2×M16—1222no—
471C2×M16—1222no—
472C2×M16—1222no—
473C2×M16—1222no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—1222no—
481C4×Q8—1222no—
482C4×D4—1222no—
483C4×D4—1222no—
484C4×D4—1228no—
485C4×D4—1222no—
486C4×D4—1228no—
487C4×D4—1222no—
488#117—614no—
489#117—1222no—
490#117—1228no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—614no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—2444no—
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C42—21no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—611no—
517C2×C42—1222no—
518C2×C42—1222no—
519C2×C42—1228no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42C22×D6111yescharacteristic
523#107—22no—
524#107—1222no—
525#106—1222no—
526#106—1222no—
527#103—22no—
528#103—614no—
529#103—1222no—
530#103C4×D6114yescomplemented
531#102—614no—
532#102—614no—
533#102—1222no—
534#102—1222no—
535#95—21no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—611no—
540C24—1221no—
541#41—6116no—
542#41—1228no—
543#41—1228no—
544#41—1228no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C4×D6112yes—
549C2×Q8D4×D6112yes—
550C2×Q8Q8×D6112yes—
551C2×D4—612no—
552C2×D4—612no—
553C2×D4—612no—
554C2×D4—1224no—
555C2×D4—1224no—
556C2×D4—1224no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—611no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1224no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1222no—
585C22×C4—1221no—
586C22×C4—2441no—
587C22×C4—2441no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600M16—1228no—
601M16—2444no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8C2×C4×D6112yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—2442no—
629C4⋊C4—2442no—
630C4⋊C4—2442no—
631C4⋊C4—2442no—
632C4⋊C4C2×C4×D6112yes—
633C4⋊C4D4×D6112yes—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C42—24no—
638C42—21no—
639C42—21no—
640C42—1222no—
641C42—1222no—
642C42—1224no—
643C42—1224no—
644C42—1221no—
645C42—1221no—
646C23—612no—
647C23—612no—
648C23—612no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23C2×D4×D6111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8C4⋊C4×D6114yescomplemented
665D4—614no—
666D4—12216no—
667D4—1222no—
668D4—1222no—
669D4—1222no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—614no—
691C2×C4—614no—
692C2×C4—614no—
693C2×C4—614no—
694C2×C4—612no—
695C2×C4—12216no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—4884no—
704C2×C4—2444no—
705C2×C4—2448no—
706C2×C4—2444no—
707C2×C4—2448no—
708C2×C4—2448no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4#1451980912yes—
717C2×C4C22×C4×D6111yescharacteristic
718C2×C4C2×D4×D6111yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4C2×Q8×D6111yescharacteristic
721C2×C4#41×D6111yescharacteristic
722C2×C4#41×D6111yescharacteristic
723C8—22no—
724C8—41no—
725C8—1222no—
726C8—2441no—
727C22—614no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1224no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22C4×D4×D6111yescharacteristic
742C22#120×D6111yescharacteristic
743C22C22⋊Q8×D6111yescharacteristic
744C22AGL(1,ℤ/8)×D6111yescharacteristic
745C22C2×#1451980911yescharacteristic
746C22#1684055911yescharacteristic
747C22#1684056111yescharacteristic
748C4—24no—
749C4—22no—
750C4—42no—
751C4—41no—
752C4—42no—
753C4—81no—
754C4—614no—
755C4—1222no—
756C4—4881no—
757C4—2442no—
758C4—2441no—
759C4—2442no—
760C4C2×C4⋊C4×D6111yescharacteristic
761C4C4×D4×D6111yescharacteristic
762C4C22⋊Q8×D6111yescharacteristic
763C4#123×D6111yescharacteristic
764C2—1224no—
765C2—2444no—
766C2#385×D6111yescharacteristic
767C2#2145462411yescharacteristic
768C2C4×#1451980911yescharacteristic
769C2#2145506811yescharacteristic
770C2#2145507811yescharacteristic
771C2#2145563311yescharacteristic
772C2#2145563811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1863C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1863D61
hypocenterC61#20875
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
2. C2×#16839803C2semidirect
5. #389×D61C2semidirect
6. #21446089C2semidirect
7. #21446085C2semidirect
8. #21446083C2semidirect
9. #21446079C2semidirect
10. #21446073C2semidirect
11. #21446067C2semidirect
12. #21446063C2semidirect
13. #21445537C2semidirect
14. #21445511C2semidirect
15. C61×#1863C2semidirect
38. #16839762C4semidirect
85. C2×#11758189C2×C4semidirect
112. C4⋊C4×D61C2×C4semidirect
128. #14519701C2×C4semidirect
130. #14519699C2×C4semidirect
132. #14519697C2×C4semidirect
150. #103×C61C2×C4semidirect
176. #11758226C4⋊C4semidirect
277. Q8×C61C2×C4⋊C4semidirect
324. D244C2×C4⋊C4semidirect
388. #1863D61semidirect
450. C61#20875semidirect
530. #103C4×D61semidirect
664. Q8C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
C2×#168398032
C2×#168397622
#389×D612
#214460892
#214460852
#214460832
#214460792
#214460732
#214460672
#214460632
#214455372
#214455112
C61×#18632
#2087561