Finite Group Databasebeta

← #29695368

Subgroups — #29695368

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×#16840409C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3#21454551C211yesmaximal, characteristic, complemented
4C2×#16839744C211yesmaximal, characteristic, complemented
5C2×#100×D61C211yesmaximal, characteristic, complemented
6#21446665C211yesmaximal, characteristic, complemented
7#21446665C211yesmaximal, characteristic, complemented
8#21446286C211yesmaximal, characteristic, complemented
9#21446286C211yesmaximal, characteristic, complemented
10#21446283C211yesmaximal, characteristic, complemented
11#21445810C211yesmaximal, characteristic, complemented
12#21445745C211yesmaximal, characteristic, complemented
13#21445738C211yesmaximal, characteristic, complemented
14#21445610C211yesmaximal, characteristic, complemented
15C61×#1900C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21#16840409—21no—
22#16840409—21no—
23#16840409—21no—
24#16840409—21no—
25#16840409—21no—
26#16840409—21no—
27#16840409—21no—
28#16840409—21no—
29C2×#14519764C2211yescharacteristic
30C2×#14519759C412yes—
31C2×#14519757C2211yescharacteristic
32C2×#14519748C412yes—
33C2×#14519745C412yes—
34C2×#14519739C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×C22⋊C4×D61C412yes—
37#16839838—21no—
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41#16839831—21no—
42#16839830—21no—
43C8×C22⋊D61—21no—
44#16839825—21no—
45#16839785C2211yescharacteristic, complemented
46#16839785C2211yescharacteristic, complemented
47#16839744—24no—
48C2×#14519695C2211yescharacteristic, complemented
49C2×#14519695C2211yescharacteristic, complemented
50C2×#14519695C2211yescharacteristic, complemented
51C2×#14519695C2211yescharacteristic, complemented
52C2×#14519694C2211yescharacteristic
53C2×#14519694C2211yescharacteristic
54C2×#14519693C2211yescharacteristic
55C2×#14519693C2211yescharacteristic
56C2×#14519693C2211yescharacteristic
57C2×#14519693C2211yescharacteristic
58#100×D61—24no—
59#16839726C2211yescharacteristic, complemented
60#16839725C2211yescharacteristic
61#16839725C2211yescharacteristic
62M16×Dic61C2211yescharacteristic, complemented
63M16×Dic61C2211yescharacteristic, complemented
64#16839531C2211yescharacteristic, complemented
65#16839531C2211yescharacteristic, complemented
66C22×M16×C61C2211yescharacteristic, complemented
67C2×#121×C61C2211yescharacteristic
68C2×#100×C61C2211yescharacteristic
69C2×#100×C61C2211yescharacteristic
70C61×#407C2211yescharacteristic, complemented
71C61×#343C2211yescharacteristic, complemented
72C61×#343C2211yescharacteristic, complemented
73C24×D61C2×C412yes—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222—22no—
79C2×#11758222—22no—
80C2×#11758222—41no—
81C2×#11758222—41no—
82C22×Dic122C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C22⋊D61C2×C412yes—
85C22×C22⋊D61C2×C412yes—
86C22×C22⋊D61C2×C411yescharacteristic
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
98C2×#11758194—21no—
99C2×#11758194—22no—
100C2×#11758194—41no—
101C2×#11758194C2311yescharacteristic
102C2×#11758194C2311yescharacteristic
103C2×#11758194C2311yescharacteristic
104C2×#11758194C2311yescharacteristic
105C2×#11758189—21no—
106C2×#11758189—21no—
107M16×D61—22no—
108M16×D61—22no—
109M16×D61—41no—
110M16×D61—41no—
111C22×#92418—21no—
112C2×C8×D61—21no—
113C2×C8×D61—21no—
114#14519764—21no—
115#14519764—21no—
116#14519764—21no—
117#14519764—21no—
118#14519759—22no—
119#14519759—22no—
120#14519759—22no—
121#14519759—22no—
122#14519757—21no—
123#14519757—21no—
124#14519757—21no—
125#14519757—21no—
126#14519748—22no—
127#14519748—22no—
128#14519748—22no—
129#14519748—22no—
130#14519745—22no—
131#14519745—22no—
132#14519745—22no—
133#14519745—22no—
134#14519739—21no—
135#14519739—21no—
136#14519739—21no—
137#14519739—21no—
138C4×C22⋊D61D411yescharacteristic
139C4×C22⋊D61D411yescharacteristic
140C4×C22⋊D61D411yescharacteristic
141C4×C22⋊D61D411yescharacteristic
142C4×C22⋊D61D411yescharacteristic
143C4×C22⋊D61D411yescharacteristic
144C4×C22⋊D61D411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C2×C4⋊Dic61C2×C412yes—
147C2×#11758196C2×C411yescharacteristic
148C2×C22⋊Dic61C2×C412yes—
149C2×C22⋊Dic61C2×C412yes—
150C2×C22⋊Dic61C2×C411yescharacteristic
151C2×#11758198C2×C412yes—
152C2×#11758198C2×C412yes—
153C2×#11758198C2×C411yescharacteristic
154C22⋊C4×D61—22no—
155C22⋊C4×D61—22no—
156C22⋊C4×D61—22no—
157C22⋊C4×D61—22no—
158C2×C4×Dic61C2311yescharacteristic
159#14519706—21no—
160#14519706—21no—
161#14519706—21no—
162#14519706—21no—
163#14519695—22no—
164#14519695—22no—
165#14519695—41no—
166#14519695—41no—
167#14519694—22no—
168#14519694—41no—
169#14519693—22no—
170#14519693—22no—
171#14519693—22no—
172#14519693D414yescomplemented
173C22⋊#92418—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519687—21no—
180#14519687—21no—
181C8×Dic61—21no—
182C8×Dic61—21no—
183C22×D4×C61C2×C412yes—
184C22×D4×C61C2311yescharacteristic
185C23×C4×C61C2311yescharacteristic
186C2×M16×C61—21no—
187C2×M16×C61—22no—
188C2×M16×C61—41no—
189C2×M16×C61C2311yescharacteristic
190C2×M16×C61C2311yescharacteristic
191C2×M16×C61C2311yescharacteristic
192C2×M16×C61C2311yescharacteristic
193C22×C8×C61—21no—
194#121×C61—21no—
195#121×C61—21no—
196#121×C61—21no—
197#121×C61—21no—
198C2×C4⋊C4×C61C2311yescharacteristic
199C2×C22⋊C4×C61C2×C412yes—
200#100×C61—22no—
201#100×C61—41no—
202C22⋊C8×C61—21no—
203C22⋊C8×C61—21no—
204C24×C61C22×C412yes—
205C24×C61C22×C411yescharacteristic
206C23×D61—22no—
207C23×D61—22no—
208C23×D61—24no—
209C23×D61—42no—
210C23×D61—44no—
211C23×D61—82no—
212C23×D61C22×C411yescharacteristic
213C23×D61C22×C412yes—
214C2×D4×C61—22no—
215C2×D4×C61—22no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—82no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C412yes—
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C2×C22⋊D61—24no—
237C2×C22⋊D61—24no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—42no—
241C2×C22⋊D61—42no—
242C2×C22⋊D61—42no—
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C22×Dic61C22×C412yes—
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C22×C411yescharacteristic
250C22×Dic61C22×C411yescharacteristic
251D4×D61—42no—
252D4×D61—42no—
253D4×D61—42no—
254D4×D61—42no—
255D4×D61—42no—
256D4×D61—42no—
257D4×D61—42no—
258D4×D61—42no—
259#11758222—42no—
260#11758222—42no—
261#11758222—42no—
262#11758222—42no—
263#11758222—42no—
264#11758222—42no—
265#11758222—42no—
266#11758222—42no—
267C2×D244—21no—
268C2×D244—21no—
269C2×D244—21no—
270C2×D244—21no—
271C2×D244C2×D412yes—
272C2×D244#4112yes—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—24no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—22no—
282C2×C4×D61—42no—
283C2×C4×D61—82no—
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×Dic122—21no—
289C2×Dic122—21no—
290C2×Dic122—21no—
291C2×Dic122—21no—
292C2×Dic122—21no—
293C2×Dic122—21no—
294M16×C61—21no—
295M16×C61—21no—
296M16×C61—21no—
297M16×C61—21no—
298M16×C61—21no—
299M16×C61—21no—
300M16×C61—21no—
301M16×C61—42no—
302M16×C61C2×D412yes—
303C2×C8×C61—21no—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C2×C8×C61—21no—
307C2×C8×C61—42no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C22⋊C4×C61—22no—
311C22⋊C4×C61—22no—
312C22⋊Dic61—22no—
313C22⋊Dic61—22no—
314C22⋊Dic61—22no—
315C22⋊Dic61—22no—
316C22⋊Dic61C22⋊C411yescharacteristic
317C22⋊Dic61C22⋊C411yescharacteristic
318C22⋊Dic61C22⋊C411yescharacteristic
319C22⋊Dic61C22⋊C411yescharacteristic
320#11758198—22no—
321#11758198—22no—
322#11758198—22no—
323#11758198—22no—
324#11758198C22⋊C411yescharacteristic
325#11758198C22⋊C411yescharacteristic
326#11758198C22⋊C411yescharacteristic
327#11758198C22⋊C411yescharacteristic
328C4⋊Dic61—22no—
329C4⋊Dic61—22no—
330#11758196C22⋊C411yescharacteristic
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338#11758194—21no—
339#11758194—21no—
340#11758194—21no—
341#11758194—21no—
342#11758194—21no—
343#11758194—21no—
344#11758194—21no—
345#11758194—42no—
346#11758194C2×D412yes—
347C2×#92418—21no—
348C2×#92418—21no—
349C2×#92418—21no—
350C2×#92418—21no—
351C2×#92418—42no—
352#11758189—42no—
353#11758189—42no—
354C8×D61—42no—
355C8×D61—42no—
356C23×C61—21no—
357C23×C61—21no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—42no—
364C23×C61—42no—
365C23×C61C2×C22⋊C411yescharacteristic
366C23×C61C2×C22⋊C411yescharacteristic
367C23×C61C23×C411yescharacteristic
368C22×D61—22no—
369C22×D61—21no—
370C22×D61—21no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—41no—
374C22×D61—44no—
375C22×D61—44no—
376C22×D61—44no—
377C22×D61—42no—
378C22×D61—42no—
379C22×D61—44no—
380C22×D61—82no—
381C22×D61—82no—
382C22×D61—88no—
383C22×D61—88no—
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C4×D414yes—
387D4×C61—41no—
388D4×C61—41no—
389D4×C61—41no—
390D4×C61—41no—
391D4×C61—82no—
392D4×C61—82no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—22no—
404C2×C4×C61—42no—
405C2×C4×C61C2×C22⋊C411yescharacteristic
406C2×C4×C61C2×C22⋊C411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C2×#4111yescharacteristic
411C2×C4×C61H(5,𝔽2)11yescharacteristic
412C2×C4×C61H(5,𝔽2)11yescharacteristic
413C22⋊D61—22no—
414C22⋊D61—22no—
415C22⋊D61—41no—
416C22⋊D61—41no—
417C22⋊D61—44no—
418C22⋊D61—44no—
419C22⋊D61—44no—
420C22⋊D61—44no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C2×C22⋊C411yescharacteristic
433C2×Dic61C2×C22⋊C411yescharacteristic
434D244—22no—
435D244—22no—
436D244—22no—
437D244—22no—
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—44no—
447C4×D61—44no—
448C4×D61—82no—
449C4×D61—82no—
450Dic122—41no—
451Dic122—41no—
452Dic122—41no—
453Dic122—41no—
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—21no—
466C22×C61—21no—
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—42no—
472C22×C61—42no—
473C22×C61—42no—
474C22×C61—81no—
475C22×C61—81no—
476C22×C61—82no—
477C22×C61—82no—
478C22×C61C22×C22⋊C411yescharacteristic
479C22×C61C2×C4×D411yescharacteristic
480C22×C61#51811yescharacteristic
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—24no—
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—42no—
488C2×D61—42no—
489C2×D61—44no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—44no—
493C2×D61—88no—
494C2×D61—88no—
495C2×D61#41312yescomplemented
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—42no—
499C4×C61D4211yescharacteristic
500C4×C61D4211yescharacteristic
501C4×C61#54611yescharacteristic
502C4×C61#54611yescharacteristic
503Dic61—21no—
504Dic61—21no—
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#1967—611no—
517#1901—611no—
518#1901—611no—
519#1900—611no—
520#1900D6111yescharacteristic, complemented
521#1800—611no—
522#1785—611no—
523#1783—611no—
524C4×#100—611no—
525C2×C61—21no—
526C2×C61—21no—
527C2×C61—41no—
528C2×C61—41no—
529C2×C61—82no—
530C2×C61D4×C22⋊C411yescharacteristic
531C2×C61C2×#41311yescharacteristic
532C2×C61#288811yescharacteristic
533D61—22no—
534D61—41no—
535D61—44no—
536C22×#41—611no—
537C23×D4—611no—
538C22×M16—611no—
539C22×M16—611no—
540C22×M16—611no—
541C22×M16C2×D6111yescharacteristic, complemented
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×#124—611no—
551C2×#123—612no—
552C2×C22⋊Q8—611no—
553C2×#121—612no—
554C2×#121C2×D6111yescharacteristic
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#423—611no—
569#413—1224no—
570C2×#101—611no—
571C2×#101—611no—
572C2×#101—611no—
573C2×#101—611no—
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#407C2×D6111yescharacteristic, complemented
587C4×M16—611no—
588C4×M16—611no—
589#343—611no—
590#343—611no—
591#343C2×D6111yescharacteristic, complemented
592#343C2×D6111yescharacteristic, complemented
593C61#2240811yescharacteristic, complemented, Sylow
594C25—612no—
595C2×#41—1222no—
596C2×#41—1222no—
597C2×#41—1221no—
598C2×#41—1221no—
599C2×#41—1221no—
600C2×#41—1221no—
601C2×#41—2441no—
602C2×#41—2441no—
603C22×Q8—611no—
604C22×D4—611no—
605C22×D4—612no—
606C22×D4—612no—
607C22×D4—611no—
608C22×D4—1221no—
609C22×D4—1221no—
610C22×D4—1221no—
611C22×D4—1221no—
612C22×D4—1222no—
613C22×D4—1222no—
614C22×D4—2441no—
615C22×D4—2441no—
616C22×D4C4×D6112yes—
617C22×D4C22×D6111yescharacteristic
618C23×C4—611no—
619C23×C4—612no—
620C23×C4—612no—
621C23×C4C22×D6111yescharacteristic
622C2×M16—21no—
623C2×M16—22no—
624C2×M16—41no—
625C2×M16—611no—
626C2×M16—611no—
627C2×M16—611no—
628C2×M16—611no—
629C2×M16—1221no—
630C2×M16—1221no—
631C2×M16—1221no—
632C2×M16—1222no—
633C2×M16—1222no—
634C2×M16—1222no—
635C2×M16—2441no—
636C2×M16—2441no—
637C2×M16—2441no—
638C2×M16C22×D6111yescharacteristic
639C2×M16C22×D6111yescharacteristic
640C2×M16C22×D6111yescharacteristic
641C2×M16C22×D6111yescharacteristic
642C22×C8—21no—
643C22×C8—1221no—
644C22×C8—1221no—
645C22×C8—1221no—
646#124—1221no—
647#124—1221no—
648#124—1221no—
649#124—1221no—
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—21no—
659#121—21no—
660#121—21no—
661#121—21no—
662#121—1222no—
663#121—1222no—
664#121—1222no—
665#121—1222no—
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⋊C4C22×D6111yescharacteristic
685C2×C22⋊C4—611no—
686C2×C22⋊C4—611no—
687C2×C22⋊C4—612no—
688C2×C22⋊C4—612no—
689C2×C22⋊C4—612no—
690C2×C22⋊C4—612no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4C4×D6112yes—
696C2×C42—611no—
697C4⋊C8—1221no—
698C4⋊C8—1221no—
699C4⋊C8—1221no—
700C4⋊C8—1221no—
701#101—1222no—
702#101—1222no—
703#101—2441no—
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—21no—
714C22⋊C8—21no—
715C22⋊C8—1221no—
716C22⋊C8—1221no—
717C22⋊C8—1221no—
718C22⋊C8—1221no—
719C22⋊C8—1221no—
720C22⋊C8—1221no—
721#97—1221no—
722#97—1221no—
723C4×C8—1221no—
724C4×C8—1221no—
725C24—611no—
726C24—612no—
727C24—1224no—
728C24—1222no—
729C24—1222no—
730C24—4882no—
731C24—2442no—
732C24—2444no—
733C24C2×C4×D6112yes—
734C24C2×C4×D6111yescharacteristic
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—1221no—
744C2×Q8—1221no—
745C2×Q8—1221no—
746C2×Q8—1221no—
747C2×Q8—1221no—
748C2×Q8—1221no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—82no—
758C2×D4—611no—
759C2×D4—611no—
760C2×D4—611no—
761C2×D4—611no—
762C2×D4—612no—
763C2×D4—612no—
764C2×D4—1222no—
765C2×D4—1222no—
766C2×D4—1224no—
767C2×D4—1224no—
768C2×D4—1222no—
769C2×D4—1222no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
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—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—612no—
797C22×C4—1222no—
798C22×C4—1222no—
799C22×C4—1224no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1222no—
805C22×C4—1222no—
806C22×C4—4882no—
807C22×C4—2442no—
808C22×C4C2×C4×D6111yescharacteristic
809C22×C4C2×C4×D6112yes—
810C22×C4D4×D6111yescharacteristic
811C22×C4D4×D6111yescharacteristic
812C22×C4D4×D6111yescharacteristic
813C22×C4D4×D6111yescharacteristic
814C22×C4C23×D6111yescharacteristic
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—42no—
823M16—612no—
824M16—1221no—
825M16—1221no—
826M16—1221no—
827M16—1221no—
828M16—1221no—
829M16—1221no—
830M16—1221no—
831M16—2442no—
832M16—2442no—
833M16—2442no—
834M16D4×D6112yes—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—42no—
840C2×C8—1221no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—2442no—
845C2×C8—2442no—
846C2×C8—2442no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—611no—
850C4⋊C4—611no—
851C4⋊C4—611no—
852C4⋊C4—611no—
853C4⋊C4—1222no—
854C4⋊C4—1222no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—611no—
858C22⋊C4—611no—
859C22⋊C4—611no—
860C22⋊C4—611no—
861C22⋊C4—611no—
862C22⋊C4—611no—
863C22⋊C4—611no—
864C22⋊C4—611no—
865C22⋊C4—1222no—
866C22⋊C4—1222no—
867C22⋊C4—1222no—
868C22⋊C4—1222no—
869C22⋊C4—1222no—
870C22⋊C4—1222no—
871C22⋊C4—1222no—
872C22⋊C4—1222no—
873C42—611no—
874C42—611no—
875C42—611no—
876C42—611no—
877C23—21no—
878C23—21no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—41no—
883C23—41no—
884C23—42no—
885C23—42no—
886C23—611no—
887C23—611no—
888C23—614no—
889C23—1222no—
890C23—1222no—
891C23—1221no—
892C23—1221no—
893C23—1222no—
894C23—4882no—
895C23—4882no—
896C23—4888no—
897C23—4888no—
898C23—2441no—
899C23—2442no—
900C23—2442no—
901C23—2444no—
902C23—2444no—
903C23—2444no—
904C23—2444no—
905C23C22⋊C4×D6111yescharacteristic
906C23C22⋊C4×D6111yescharacteristic
907C23C22×C4×D6111yescharacteristic
908Q8—2441no—
909Q8—2441no—
910Q8—2441no—
911Q8—2441no—
912D4—41no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—82no—
917D4—82no—
918D4—1222no—
919D4—1222no—
920D4—1222no—
921D4—1222no—
922D4—1222no—
923D4—1222no—
924D4—2441no—
925D4—2441no—
926D4—2444no—
927D4—2444no—
928D4—2444no—
929D4—2444no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—42no—
942C2×C4—611no—
943C2×C4—611no—
944C2×C4—611no—
945C2×C4—611no—
946C2×C4—611no—
947C2×C4—611no—
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—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—4882no—
962C2×C4—4882no—
963C2×C4—2444no—
964C2×C4—2444no—
965C2×C4—2441no—
966C2×C4—2441no—
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—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—81no—
995C22—81no—
996C22—82no—
997C22—82no—
998C22—612no—
999C22—1221no—
1000C22—1221no—
1001C22—1221no—
1002C22—1224no—
1003C22—1221no—
1004C22—1221no—
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—42no—
1019C4—1221no—
1020C4—1221no—
1021C4—1221no—
1022C4—1221no—
1023C4—1221no—
1024C4—1221no—
1025C4—2442no—
1026C4#1684039411yescharacteristic
1027C4#1684039611yescharacteristic
1028C4#1684040111yescharacteristic
1029C4#1684040411yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—41no—
1033C2—41no—
1034C2—82no—
1035C2—1222no—
1036C2—2441no—
1037C2—2444no—
1038C2#2144863711yescharacteristic
1039C2#413×D6111yescharacteristic
1040C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1900C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840409C2
cosocleC22×C4×C61C24
hypercenter#1900D61
hypocenterC61#22408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D61C2semidirect
3. #21454551C2semidirect
4. C2×#16839744C2semidirect
5. C2×#100×D61C2semidirect
6. #21446665C2semidirect
7. #21446665C2semidirect
8. #21446286C2semidirect
9. #21446286C2semidirect
10. #21446283C2semidirect
11. #21445810C2semidirect
12. #21445745C2semidirect
13. #21445738C2semidirect
14. #21445610C2semidirect
15. C61×#1900C2semidirect
18. C22×#11758194C22semidirect
45. #16839785C22semidirect
46. #16839785C22semidirect
48. C2×#14519695C22semidirect
49. C2×#14519695C22semidirect
50. C2×#14519695C22semidirect
51. C2×#14519695C22semidirect
59. #16839726C22semidirect
62. M16×Dic61C22semidirect
63. M16×Dic61C22semidirect
64. #16839531C22semidirect
65. #16839531C22semidirect
66. C22×M16×C61C22semidirect
70. C61×#407C22semidirect
71. C61×#343C22semidirect
72. C61×#343C22semidirect
172. #14519693D4semidirect
495. C2×D61#413semidirect
520. #1900D61semidirect
541. C22×M16C2×D61semidirect
586. #407C2×D61semidirect
591. #343C2×D61semidirect
592. #343C2×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×#168404092
M16×C22⋊D612
#214545512
C2×#168397442
C2×#100×D612
#214466652
#214462862
#214462832
#214458102
#214457452
#214457382
#214456102
C61×#19002
#2240861