Finite Group Databasebeta

← #29695372

Subgroups — #29695372

Order 15616.

1544 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840405C211yesmaximal, characteristic
2M16×D244C211yesmaximal, characteristic, complemented
3#21454554C211yesmaximal, characteristic, complemented
4C2×#16839745C211yesmaximal, characteristic, complemented
5C2×#100×D61C211yesmaximal, characteristic, complemented
6#21446669C211yesmaximal, characteristic, complemented
7#21446284C211yesmaximal, characteristic, complemented
8#21446284C211yesmaximal, characteristic, complemented
9#21446279C211yesmaximal, characteristic, complemented
10#21446279C211yesmaximal, characteristic, complemented
11#21445808C211yesmaximal, characteristic, complemented
12#21445746C211yesmaximal, characteristic, complemented
13#21445738C211yesmaximal, characteristic, complemented
14C4×#14519693C211yesmaximal, characteristic, complemented
15C61×#1967C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic, complemented
21C2×M16×D61C2211yescharacteristic, complemented
22#16840405—21no—
23#16840405—21no—
24#16840405—21no—
25#16840405—21no—
26#16840405—21no—
27#16840405—21no—
28#16840405—21no—
29#16840405—21no—
30C2×#14519759C412yes—
31C2×#14519753C2211yescharacteristic
32C2×#14519750C412yes—
33C2×#14519748C2211yescharacteristic
34C2×#14519747C412yes—
35C2×C4×D244C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×C22⋊C4×D61C412yes—
38#16839841—21no—
39#16839839—21no—
40#16839835—21no—
41#16839835—21no—
42#16839832—21no—
43#16839832—21no—
44C8×D244—21no—
45#16839827—21no—
46#16839786C2211yescharacteristic, complemented
47#16839745—24no—
48C2×#14519696C2211yescharacteristic, complemented
49C2×#14519696C2211yescharacteristic, complemented
50C2×#14519694C2211yescharacteristic
51C2×#14519694C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic
55C2×#14519693C2211yescharacteristic
56#100×D61—24no—
57#16839725C2211yescharacteristic
58#16839725C2211yescharacteristic
59#16839725C2211yescharacteristic, complemented
60#16839725C2211yescharacteristic, complemented
61C4×#11758194C2211yescharacteristic, complemented
62#16839530C2211yescharacteristic, complemented
63#16839530C2211yescharacteristic, complemented
64#16839530C2211yescharacteristic, complemented
65#16839530C2211yescharacteristic, complemented
66C2×#124×C61C2211yescharacteristic
67C61×#423C2211yescharacteristic, complemented
68C2×#101×C61C2211yescharacteristic, complemented
69C2×#101×C61C2211yescharacteristic, complemented
70C2×#100×C61C2211yescharacteristic
71C2×#100×C61C2211yescharacteristic
72C4×M16×C61C2211yescharacteristic, complemented
73C24×D61C2×C412yes—
74C2×#11758226—22no—
75C2×#11758226—22no—
76C2×#11758226—21no—
77C2×#11758226—21no—
78C2×#11758226—21no—
79C2×#11758226—21no—
80C2×#11758226—41no—
81C2×#11758226—41no—
82C22×D244C2×C412yes—
83C22×D244C2×C411yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61C2×C412yes—
86C22×C22⋊D61C2×C412yes—
87C2×D4×D61—22no—
88C2×D4×D61—22no—
89C2×D4×D61—21no—
90C2×D4×D61—21no—
91C2×D4×D61—21no—
92C2×D4×D61—21no—
93C2×D4×D61—41no—
94C2×D4×D61—41no—
95C22×C4×D61C2×C412yes—
96C22×C4×D61C2×C412yes—
97C22×C4×D61C2311yescharacteristic
98C22×C4×D61C2311yescharacteristic
99C2×#11758194C2311yescharacteristic
100C2×#11758194C2311yescharacteristic
101C2×#11758194C2311yescharacteristic
102C2×#11758194C2311yescharacteristic
103C2×#11758189—21no—
104C2×#11758189—21no—
105C2×#11758189—21no—
106C2×#11758189—21no—
107M16×D61—22no—
108M16×D61—22no—
109M16×D61—22no—
110M16×D61—22no—
111M16×D61—41no—
112M16×D61—41no—
113M16×D61—41no—
114M16×D61—41no—
115C2×C8×D61—21no—
116C2×C8×D61—21no—
117C2×C8×D61—21no—
118C2×C8×D61—21no—
119#14519759—22no—
120#14519759—22no—
121#14519759—22no—
122#14519759—22no—
123#14519753—21no—
124#14519753—21no—
125#14519753—21no—
126#14519753—21no—
127#14519750—22no—
128#14519750—22no—
129#14519750—22no—
130#14519750—22no—
131#14519748—21no—
132#14519748—21no—
133#14519748—21no—
134#14519748—21no—
135#14519747—22no—
136#14519747—22no—
137#14519747—22no—
138#14519747—22no—
139C4×D244—21no—
140C4×D244—21no—
141C4×D244—21no—
142C4×D244—21no—
143C4×D244D411yescharacteristic
144C4×D244D411yescharacteristic
145C4×D244D411yescharacteristic
146C4×D244D411yescharacteristic
147C4×D244D411yescharacteristic
148C4×D244D411yescharacteristic
149C4×D244D411yescharacteristic
150C4×D244D411yescharacteristic
151C2×C4⋊Dic61C2×C411yescharacteristic
152C2×C4⋊Dic61C2311yescharacteristic
153C2×#11758196C2×C412yes—
154C2×C22⋊Dic61C2×C412yes—
155C2×#11758198C2×C412yes—
156C2×#11758198C2×C412yes—
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C22⋊C4×D61—22no—
160C22⋊C4×D61—22no—
161C22⋊C4×D61—22no—
162C22⋊C4×D61—22no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165#14519696—22no—
166#14519696—41no—
167#14519694—22no—
168#14519694—41no—
169#14519693—22no—
170#14519693—22no—
171#14519693—22no—
172#14519693D414yescomplemented
173#14519689—21no—
174#14519689—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182C4×#92418—21no—
183C22×Q8×C61C2311yescharacteristic
184C22×D4×C61C2311yescharacteristic
185C2×M16×C61C2311yescharacteristic
186C2×M16×C61C2311yescharacteristic
187C2×M16×C61C2311yescharacteristic
188C2×M16×C61C2311yescharacteristic
189#124×C61—21no—
190#124×C61—21no—
191#124×C61—21no—
192#124×C61—21no—
193C2×C22⋊C4×C61C2×C412yes—
194C2×C22⋊C4×C61C2×C412yes—
195C2×C42×C61C2311yescharacteristic
196C4⋊C8×C61—21no—
197C4⋊C8×C61—21no—
198#101×C61—22no—
199#101×C61—41no—
200#100×C61—22no—
201#100×C61—41no—
202#97×C61—21no—
203C4×C8×C61—21no—
204C24×C61C22×C412yes—
205C23×D61—22no—
206C23×D61—22no—
207C23×D61—24no—
208C23×D61—42no—
209C23×D61—44no—
210C23×D61—82no—
211C23×D61C22×C411yescharacteristic
212C23×D61C22×C411yescharacteristic
213C23×D61C22×C412yes—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—24no—
231C2×C22⋊D61—22no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61—82no—
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C412yes—
240#11758226—42no—
241#11758226—42no—
242#11758226—42no—
243#11758226—42no—
244#11758226—42no—
245#11758226—42no—
246#11758226—42no—
247#11758226—42no—
248D4×D61—42no—
249D4×D61—42no—
250D4×D61—42no—
251D4×D61—42no—
252D4×D61—42no—
253D4×D61—42no—
254D4×D61—42no—
255D4×D61—42no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—22no—
261C2×D244—22no—
262C2×D244—24no—
263C2×D244—42no—
264C2×D244—42no—
265C2×D244C22⋊C411yescharacteristic
266C2×D244C22⋊C411yescharacteristic
267C2×D244C22⋊C411yescharacteristic
268C2×D244C22⋊C411yescharacteristic
269C2×D244C2×D412yes—
270C2×D244#4112yes—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—24no—
280C2×C4×D61—22no—
281C2×C4×D61—22no—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×C4×D61—42no—
285C2×C4×D61—82no—
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294M16×C61—21no—
295M16×C61—21no—
296M16×C61—21no—
297M16×C61—21no—
298M16×C61—21no—
299M16×C61—21no—
300M16×C61—21no—
301M16×C61C2×D412yes—
302C2×C8×C61—21no—
303C2×C8×C61—21no—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C22⋊C4×C61—22no—
307C22⋊C4×C61—22no—
308C22⋊C4×C61—22no—
309C22⋊C4×C61—22no—
310C42×C61C2×D411yescharacteristic
311C42×C61C2×D411yescharacteristic
312C42×C61C2×D411yescharacteristic
313C42×C61C2×D411yescharacteristic
314C22⋊Dic61—22no—
315C22⋊Dic61—22no—
316#11758198—22no—
317#11758198—22no—
318#11758198—22no—
319#11758198—22no—
320#11758198C22⋊C411yescharacteristic
321#11758198C22⋊C411yescharacteristic
322#11758198C22⋊C411yescharacteristic
323#11758198C22⋊C411yescharacteristic
324#11758198C22⋊C411yescharacteristic
325#11758198C22⋊C411yescharacteristic
326#11758198C22⋊C411yescharacteristic
327#11758198C22⋊C411yescharacteristic
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61C22⋊C411yescharacteristic
331C4⋊Dic61C22⋊C411yescharacteristic
332C4⋊Dic61C22⋊C411yescharacteristic
333C4⋊Dic61C22⋊C411yescharacteristic
334#11758196—22no—
335#11758196—22no—
336#11758194—21no—
337#11758194—21no—
338#11758194—21no—
339#11758194—21no—
340#11758194—21no—
341#11758194—21no—
342#11758194—21no—
343#11758194C2×D412yes—
344C2×#92418—21no—
345C2×#92418—21no—
346C2×#92418—21no—
347C2×#92418—21no—
348#11758189—42no—
349#11758189—42no—
350#11758189—42no—
351#11758189—42no—
352C8×D61—42no—
353C8×D61—42no—
354C8×D61—42no—
355C8×D61—42no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—42no—
360C23×C61—42no—
361C23×C61C23×C411yescharacteristic
362C22×D61—22no—
363C22×D61—21no—
364C22×D61—21no—
365C22×D61—22no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—22no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—44no—
373C22×D61—44no—
374C22×D61—44no—
375C22×D61—42no—
376C22×D61—42no—
377C22×D61—44no—
378C22×D61—82no—
379C22×D61—82no—
380C22×D61—88no—
381C22×D61—88no—
382C22×D61C2×C22⋊C411yescharacteristic
383C22×D61C2×C22⋊C411yescharacteristic
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C4×D414yes—
387Q8×C61—41no—
388Q8×C61—41no—
389Q8×C61—41no—
390Q8×C61—41no—
391D4×C61—41no—
392D4×C61—41no—
393D4×C61—41no—
394D4×C61—41no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C2×C22⋊C411yescharacteristic
402C2×C4×C61C2×C22⋊C411yescharacteristic
403C2×C4×C61C2×C22⋊C411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C2×#4111yescharacteristic
408C2×C4×C61H(5,𝔽2)11yescharacteristic
409C2×C4×C61H(5,𝔽2)11yescharacteristic
410C22⋊D61—44no—
411C22⋊D61—44no—
412C22⋊D61—82no—
413C22⋊D61—82no—
414C2×Dic61—21no—
415C2×Dic61—21no—
416C2×Dic61—21no—
417C2×Dic61—21no—
418C2×Dic61—22no—
419C2×Dic61—42no—
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424D244—22no—
425D244—22no—
426D244—22no—
427D244—22no—
428D244—22no—
429D244—22no—
430D244—41no—
431D244—41no—
432D244—44no—
433D244—44no—
434C4×D61—21no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—21no—
440C4×D61—21no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—44no—
451C4×D61—44no—
452C4×D61—82no—
453C4×D61—82no—
454C8×C61—22no—
455C8×C61—41no—
456C8×C61—41no—
457C8×C61—41no—
458#92418—22no—
459#92418—41no—
460#92418—41no—
461#92418—41no—
462#22408—611nomaximal, Sylow
463C22×C61—21no—
464C22×C61—21no—
465C22×C61—42no—
466C22×C61—42no—
467C22×C61—42no—
468C22×C61—82no—
469C22×C61—82no—
470C22×C61C22×C22⋊C411yescharacteristic
471C22×C61C2×C4×D411yescharacteristic
472C22×C61#51811yescharacteristic
473C2×D61—21no—
474C2×D61—21no—
475C2×D61—21no—
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—24no—
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—42no—
486C2×D61—42no—
487C2×D61—44no—
488C2×D61—42no—
489C2×D61—42no—
490C2×D61—44no—
491C2×D61—88no—
492C2×D61—81no—
493C2×D61—81no—
494C2×D61—88no—
495C2×D61#41312yescomplemented
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—21no—
500C4×C61—42no—
501C4×C61D4211yescharacteristic
502C4×C61D4211yescharacteristic
503C4×C61#54611yescharacteristic
504C4×C61#54611yescharacteristic
505Dic61—21no—
506Dic61—21no—
507Dic61—21no—
508Dic61—21no—
509Dic61—42no—
510C2×#546—611no—
511D4×M16—611no—
512D4×M16—611no—
513C2×#413—611no—
514C22×#100—611no—
515#1967—611no—
516#1967D6111yescharacteristic, complemented
517#1901—611no—
518#1901—611no—
519#1900—611no—
520#1900—611no—
521#1800—611no—
522#1785—611no—
523#1783—611no—
524C4×#100—611no—
525C2×C61—21no—
526C2×C61—21no—
527C2×C61—82no—
528C2×C61D4×C22⋊C411yescharacteristic
529C2×C61C2×#41311yescharacteristic
530C2×C61#288811yescharacteristic
531D61—22no—
532D61—41no—
533D61—41no—
534D61—41no—
535D61—44no—
536C22×#41—611no—
537C23×D4—611no—
538C22×M16—611no—
539C22×M16—611no—
540C22×M16—611no—
541C22×M16—611no—
542#546—1221no—
543#546—1221no—
544#546—1221no—
545#546—1221no—
546#546—1221no—
547#546—1221no—
548#546—1221no—
549#546—1221no—
550C2×#124C2×D6111yescharacteristic
551C2×#123—612no—
552C2×C22⋊Q8—611no—
553C2×#121—611no—
554C2×#121—612no—
555C2×#120—612no—
556C2×C4×D4—611no—
557C2×C4×D4—611no—
558C22×C22⋊C4—612no—
559#436—1221no—
560#436—1221no—
561#435—1221no—
562#435—1221no—
563#435—1221no—
564#435—1221no—
565C8×D4—1221no—
566C8×D4—1221no—
567#423—611no—
568#423C2×D6111yescharacteristic, complemented
569#413—1224no—
570C2×#101—611no—
571C2×#101—611no—
572C2×#101C2×D6111yescharacteristic, complemented
573C2×#101C2×D6111yescharacteristic, complemented
574C2×#100—611no—
575C2×#100—611no—
576C2×#100—611no—
577C2×#100—611no—
578C2×#100—611no—
579C2×#100—611no—
580C2×#100—1224no—
581C2×#100C2×D6111yescharacteristic
582C2×#100C2×D6111yescharacteristic
583#407—611no—
584#407—611no—
585#407—611no—
586#407—611no—
587C4×M16—611no—
588C4×M16C2×D6111yescharacteristic, complemented
589#343—611no—
590#343—611no—
591#343—611no—
592#343—611no—
593C61#2240811yescharacteristic, complemented, Sylow
594C25—612no—
595C2×#41—1221no—
596C2×#41—1221no—
597C2×#41—1221no—
598C2×#41—1221no—
599C2×#41—1222no—
600C2×#41—1222no—
601C2×#41—2441no—
602C2×#41—2441no—
603C22×Q8C22×D6111yescharacteristic
604C22×D4—612no—
605C22×D4—612no—
606C22×D4—611no—
607C22×D4—612no—
608C22×D4—611no—
609C22×D4—1221no—
610C22×D4—1221no—
611C22×D4—1221no—
612C22×D4—1221no—
613C22×D4—1222no—
614C22×D4—1222no—
615C22×D4—2441no—
616C22×D4—2441no—
617C22×D4C22×D6111yescharacteristic
618C23×C4—611no—
619C23×C4—611no—
620C23×C4—612no—
621C23×C4—612no—
622C2×M16—611no—
623C2×M16—611no—
624C2×M16—611no—
625C2×M16—611no—
626C2×M16—1221no—
627C2×M16—1221no—
628C2×M16—1221no—
629C2×M16—1221no—
630C2×M16—1222no—
631C2×M16—1222no—
632C2×M16—1222no—
633C2×M16—1222no—
634C2×M16—2441no—
635C2×M16—2441no—
636C2×M16—2441no—
637C2×M16—2441no—
638C2×M16C22×D6111yescharacteristic
639C2×M16C22×D6111yescharacteristic
640C2×M16C22×D6111yescharacteristic
641C2×M16C22×D6111yescharacteristic
642C22×C8—1221no—
643C22×C8—1221no—
644C22×C8—1221no—
645C22×C8—1221no—
646#124—21no—
647#124—21no—
648#124—21no—
649#124—21no—
650#123—1222no—
651#123—1222no—
652#123—1222no—
653#123—1222no—
654C22⋊Q8—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658#121—1222no—
659#121—1222no—
660#121—1222no—
661#121—1222no—
662#121—1221no—
663#121—1221no—
664#121—1221no—
665#121—1221no—
666#120—1222no—
667#120—1222no—
668#120—1222no—
669#120—1222no—
670C4×D4—611no—
671C4×D4—611no—
672C4×D4—611no—
673C4×D4—611no—
674C4×D4—611no—
675C4×D4—611no—
676C4×D4—611no—
677C4×D4—611no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C2×C4⋊C4—611no—
683C2×C4⋊C4—612no—
684C2×C4⋊C4—611no—
685C2×C22⋊C4—611no—
686C2×C22⋊C4—611no—
687C2×C22⋊C4—612no—
688C2×C22⋊C4—612no—
689C2×C22⋊C4—612no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4C4×D6112yes—
695C2×C22⋊C4C4×D6112yes—
696C2×C42C22×D6111yescharacteristic
697C4⋊C8—21no—
698C4⋊C8—21no—
699C4⋊C8—1221no—
700C4⋊C8—1221no—
701#101—22no—
702#101—41no—
703#101—1222no—
704#101—2441no—
705#100—22no—
706#100—41no—
707#100—614no—
708#100—1222no—
709#100—1222no—
710#100—1222no—
711#100—1222no—
712#100—2441no—
713C22⋊C8—1221no—
714C22⋊C8—1221no—
715C22⋊C8—1221no—
716C22⋊C8—1221no—
717C22⋊C8—1221no—
718C22⋊C8—1221no—
719C22⋊C8—1221no—
720C22⋊C8—1221no—
721#97—21no—
722#97—1221no—
723C4×C8—21no—
724C4×C8—1221no—
725C24—611no—
726C24—612no—
727C24—611no—
728C24—1224no—
729C24—1222no—
730C24—1222no—
731C24—4882no—
732C24—2442no—
733C24—2444no—
734C24C2×C4×D6112yes—
735#41—2442no—
736#41—2442no—
737#41—2442no—
738#41—2442no—
739#41—2442no—
740#41—2442no—
741#41—2442no—
742#41—2442no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—612no—
756C2×D4—612no—
757C2×D4—611no—
758C2×D4—611no—
759C2×D4—611no—
760C2×D4—611no—
761C2×D4—1222no—
762C2×D4—1222no—
763C2×D4—1224no—
764C2×D4—1222no—
765C2×D4—1222no—
766C2×D4—1222no—
767C2×D4—1222no—
768C2×D4—1224no—
769C2×D4—1221no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—4882no—
774C2×D4—2442no—
775C2×D4—2442no—
776C2×D4—2442no—
777C2×D4—2442no—
778C2×D4—2442no—
779C2×D4—2442no—
780C2×D4—2442no—
781C2×D4—2442no—
782C2×D4—2442no—
783C2×D4—2442no—
784C2×D4—2442no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—612no—
796C22×C4—1222no—
797C22×C4—1222no—
798C22×C4—1224no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1222no—
808C22×C4—1222no—
809C22×C4—4882no—
810C22×C4—2442no—
811C22×C4C2×C4×D6112yes—
812C22×C4C2×C4×D6111yescharacteristic
813C22×C4C2×C4×D6111yescharacteristic
814C22×C4C23×D6111yescharacteristic
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—612no—
823M16—1221no—
824M16—1221no—
825M16—1221no—
826M16—1221no—
827M16—1221no—
828M16—1221no—
829M16—1221no—
830M16—2442no—
831M16—2442no—
832M16—2442no—
833M16—2442no—
834M16D4×D6112yes—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—1221no—
840C2×C8—1221no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—2442no—
844C2×C8—2442no—
845C2×C8—2442no—
846C2×C8—2442no—
847C4⋊C4—611no—
848C4⋊C4—611no—
849C4⋊C4—611no—
850C4⋊C4—611no—
851C4⋊C4—1222no—
852C4⋊C4—1222no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—611no—
860C22⋊C4—611no—
861C22⋊C4—611no—
862C22⋊C4—611no—
863C22⋊C4—611no—
864C22⋊C4—611no—
865C22⋊C4—611no—
866C22⋊C4—611no—
867C22⋊C4—1222no—
868C22⋊C4—1222no—
869C22⋊C4—1222no—
870C22⋊C4—1222no—
871C22⋊C4—1222no—
872C22⋊C4—1222no—
873C42D4×D6111yescharacteristic
874C42D4×D6111yescharacteristic
875C42D4×D6111yescharacteristic
876C42D4×D6111yescharacteristic
877C23—22no—
878C23—22no—
879C23—22no—
880C23—42no—
881C23—42no—
882C23—611no—
883C23—611no—
884C23—611no—
885C23—611no—
886C23—614no—
887C23—1222no—
888C23—1221no—
889C23—1221no—
890C23—1222no—
891C23—1221no—
892C23—1221no—
893C23—1222no—
894C23—4882no—
895C23—4882no—
896C23—4888no—
897C23—4888no—
898C23—2441no—
899C23—2441no—
900C23—2441no—
901C23—2442no—
902C23—2442no—
903C23—2444no—
904C23—2444no—
905C23—2444no—
906C23—2444no—
907C23C22×C4×D6111yescharacteristic
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912D4—41no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—1222no—
917D4—1222no—
918D4—1222no—
919D4—1222no—
920D4—1222no—
921D4—1222no—
922D4—4882no—
923D4—4882no—
924D4—2441no—
925D4—2441no—
926D4—2444no—
927D4—2444no—
928D4—2444no—
929D4—2444no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—611no—
936C2×C4—611no—
937C2×C4—611no—
938C2×C4—611no—
939C2×C4—1221no—
940C2×C4—1221no—
941C2×C4—1221no—
942C2×C4—1221no—
943C2×C4—1221no—
944C2×C4—1221no—
945C2×C4—1221no—
946C2×C4—1221no—
947C2×C4—1221no—
948C2×C4—1221no—
949C2×C4—1221no—
950C2×C4—1221no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1221no—
954C2×C4—1221no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1222no—
960C2×C4—4882no—
961C2×C4—4882no—
962C2×C4—2444no—
963C2×C4—2444no—
964C2×C4—2442no—
965C2×C4C22⋊C4×D6111yescharacteristic
966C2×C4C22⋊C4×D6111yescharacteristic
967C2×C4C22⋊C4×D6111yescharacteristic
968C2×C4C22⋊C4×D6111yescharacteristic
969C2×C4C2×D4×D6111yescharacteristic
970C2×C4C2×D4×D6111yescharacteristic
971C2×C4C2×D4×D6111yescharacteristic
972C2×C4#41×D6111yescharacteristic
973C2×C4#1451982211yescharacteristic
974C2×C4#1451982311yescharacteristic
975C8—22no—
976C8—41no—
977C8—41no—
978C8—41no—
979C8—1222no—
980C8—2441no—
981C8—2441no—
982C8—2441no—
983C22—21no—
984C22—21no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—82no—
989C22—82no—
990C22—612no—
991C22—1221no—
992C22—1221no—
993C22—1221no—
994C22—1221no—
995C22—1221no—
996C22—1224no—
997C22—1221no—
998C22—1221no—
999C22—1221no—
1000C22—1221no—
1001C22—1221no—
1002C22—1221no—
1003C22—4881no—
1004C22—4881no—
1005C22—4888no—
1006C22—4888no—
1007C22—2442no—
1008C22—2442no—
1009C22—2444no—
1010C22—2444no—
1011C22—2442no—
1012C22—2442no—
1013C22C2×C22⋊C4×D6111yescharacteristic
1014C22C4×D4×D6111yescharacteristic
1015C22#1684023411yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—42no—
1021C4—1221no—
1022C4—1221no—
1023C4—1221no—
1024C4—1221no—
1025C4—2442no—
1026C4#1684039611yescharacteristic
1027C4#1684039711yescharacteristic
1028C4#1684040511yescharacteristic
1029C4#1684040911yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—82no—
1033C2—1222no—
1034C2—2441no—
1035C2—2441no—
1036C2—2441no—
1037C2—2444no—
1038C2#2144864011yescharacteristic
1039C2#413×D6111yescharacteristic
1040C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1967C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840405C2
cosocleC22×C4×C61C24
hypercenter#1967D61
hypocenterC61#22408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1967

Complements

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

NH ≅ G/Ntype
2. M16×D244C2semidirect
3. #21454554C2semidirect
4. C2×#16839745C2semidirect
5. C2×#100×D61C2semidirect
6. #21446669C2semidirect
7. #21446284C2semidirect
8. #21446284C2semidirect
9. #21446279C2semidirect
10. #21446279C2semidirect
11. #21445808C2semidirect
12. #21445746C2semidirect
13. #21445738C2semidirect
14. C4×#14519693C2semidirect
15. C61×#1967C2semidirect
20. C2×M16×D61C22semidirect
21. C2×M16×D61C22semidirect
46. #16839786C22semidirect
48. C2×#14519696C22semidirect
49. C2×#14519696C22semidirect
59. #16839725C22semidirect
60. #16839725C22semidirect
61. C4×#11758194C22semidirect
62. #16839530C22semidirect
63. #16839530C22semidirect
64. #16839530C22semidirect
65. #16839530C22semidirect
67. C61×#423C22semidirect
68. C2×#101×C61C22semidirect
69. C2×#101×C61C22semidirect
72. C4×M16×C61C22semidirect
172. #14519693D4semidirect
495. C2×D61#413semidirect
516. #1967D61semidirect
568. #423C2×D61semidirect
572. C2×#101C2×D61semidirect
573. C2×#101C2×D61semidirect
588. C4×M16C2×D61semidirect
593. C61#22408semidirect

Maximal subgroups

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

subgroupindex
C2×#168404052
M16×D2442
#214545542
C2×#168397452
C2×#100×D612
#214466692
#214462842
#214462792
#214458082
#214457462
#214457382
C4×#145196932
C61×#19672
#2240861