Finite Group Databasebeta

← #29695706

Subgroups — #29695706

Order 15616.

1472 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊D61C211yesmaximal, characteristic
2#21454551C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic, complemented
5#21448282C211yesmaximal, characteristic, complemented
6#21446736C211yesmaximal, characteristic, complemented
7#21446645C211yesmaximal, characteristic, complemented
8#21446265C211yesmaximal, characteristic, complemented
9#21446264C211yesmaximal, characteristic, complemented
10#21446119C211yesmaximal, characteristic, complemented
11#21446118C211yesmaximal, characteristic, complemented
12#21445837C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#104×Dic61C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic, complemented
18C2×M16×D61C2211yescharacteristic, complemented
19#16840431C411yescharacteristic, complemented
20Q8×C22⋊D61C411yescharacteristic, complemented
21#16840423C411yescharacteristic, complemented
22#16840419C411yescharacteristic, complemented
23#16840411—21no—
24#16840411C411yescharacteristic, complemented
25#16840406—21no—
26#16840406C411yescharacteristic, complemented
27#16840400—21no—
28#16840400C411yescharacteristic, complemented
29D4×C22⋊D61—21no—
30D4×C22⋊D61C411yescharacteristic, complemented
31#16840308—21no—
32#16840308C2211yescharacteristic
33#16840273—21no—
34#16840273C2211yescharacteristic
35#16840269—21no—
36#16840269C2211yescharacteristic
37#41×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519736C2211yescharacteristic, complemented
41C2×#14519734C2211yescharacteristic, complemented
42#16839837—21no—
43#16839836—21no—
44#16839830—21no—
45#16839825—21no—
46#16839785C2211yescharacteristic, complemented
47#16839779—24no—
48#16839777—24no—
49C2×#14519705C2211yescharacteristic, complemented
50C2×#14519705C2211yescharacteristic, complemented
51C2×#14519704C2211yescharacteristic
52C2×#14519704C2211yescharacteristic
53C2×#14519704C2211yescharacteristic, complemented
54C2×#14519704C2211yescharacteristic, complemented
55C2×#14519703C2211yescharacteristic, complemented
56C2×#14519703C2211yescharacteristic, complemented
57#16839725C2211yescharacteristic, complemented
58M16×Dic61C2211yescharacteristic, complemented
59#16839662—21no—
60#16839659—21no—
61#16839654—21no—
62#16839650—21no—
63C4×#11758196C2211yescharacteristic, complemented
64C4×#11758198C2211yescharacteristic, complemented
65C42×Dic61C2211yescharacteristic, complemented
66#16839523C2211yescharacteristic, complemented
67#16839523C2211yescharacteristic, complemented
68#16839522C2211yescharacteristic, complemented
69#16839522C2211yescharacteristic, complemented
70C22×#41×C61C2211yescharacteristic
71C2×#104×C61C2211yescharacteristic
72C2×#104×C61C2211yescharacteristic
73C2×#104×C61C2211yescharacteristic, complemented
74C2×#104×C61C2211yescharacteristic, complemented
75C61×#407C2211yescharacteristic, complemented
76C4×C22⋊C4×C61C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic
78C2×#11758222—21no—
79C2×#11758222C2311yescharacteristic
80C2×#11758224—21no—
81C2×#11758224C2×C411yescharacteristic
82#41×D61—22no—
83#41×D61—22no—
84#41×D61—41no—
85#41×D61—41no—
86C2×Q8×D61C2×C411yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61D411yescharacteristic
89C2×D4×D61—21no—
90C2×D4×D61C2×C411yescharacteristic
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93C2×#11758194—21no—
94C2×#11758194—22no—
95C2×#11758194—41no—
96C2×#11758194C2311yescharacteristic
97C2×#11758194C2311yescharacteristic
98C2×#11758189—21no—
99M16×D61—22no—
100M16×D61—41no—
101C22×#92418—21no—
102C2×C8×D61—21no—
103#14519775—21no—
104#14519775C2×C411yescharacteristic
105#14519773—21no—
106#14519773C2×C411yescharacteristic
107#14519766—21no—
108#14519766C2×C411yescharacteristic
109#14519764—21no—
110#14519764C2×C411yescharacteristic
111#14519760—21no—
112#14519760—21no—
113#14519760—21no—
114#14519758—21no—
115#14519758—21no—
116#14519758—21no—
117#14519756—21no—
118#14519756—21no—
119#14519756C2×C411yescharacteristic
120#14519756C2×C411yescharacteristic
121#14519753—21no—
122#14519753—21no—
123#14519753C2×C411yescharacteristic
124#14519753C2×C411yescharacteristic
125#14519751—21no—
126#14519751—21no—
127#14519751C2×C411yescharacteristic
128#14519751C2×C411yescharacteristic
129#14519749—21no—
130#14519749—21no—
131#14519749—21no—
132#14519749—21no—
133#14519749—21no—
134#14519749—21no—
135#14519748—21no—
136#14519748—21no—
137#14519748C2×C411yescharacteristic
138#14519748C2×C411yescharacteristic
139#14519746—21no—
140#14519746—21no—
141#14519746—21no—
142#14519745—21no—
143#14519745—21no—
144#14519745—21no—
145Q8×Dic61C2×C411yescharacteristic
146Q8×Dic61C2×C411yescharacteristic
147D4×Dic61—21no—
148D4×Dic61—21no—
149D4×Dic61C2×C411yescharacteristic
150D4×Dic61C2×C411yescharacteristic
151C4×C22⋊D61—21no—
152C4×C22⋊D61—21no—
153C4×C22⋊D61—21no—
154C4×C22⋊D61—21no—
155C4×C22⋊D61—21no—
156C4×C22⋊D61—21no—
157C4×C22⋊D61—21no—
158C4×C22⋊D61—21no—
159C4×C22⋊D61—21no—
160C4×C22⋊D61—21no—
161C4×C22⋊D61C2×C411yescharacteristic
162C4×C22⋊D61C2×C411yescharacteristic
163C4×C22⋊D61C2×C411yescharacteristic
164C4×C22⋊D61C2×C411yescharacteristic
165C4×C22⋊D61D411yescharacteristic
166C4×C22⋊D61D411yescharacteristic
167C4×C22⋊D61D411yescharacteristic
168C4×C22⋊D61D411yescharacteristic
169#14519736—21no—
170#14519736—22no—
171#14519736—41no—
172#14519736C2311yescharacteristic
173#14519734—22no—
174#14519734—41no—
175C2×C4⋊Dic61—21no—
176C2×#11758196—21no—
177C2×#11758196—21no—
178C2×#11758196—21no—
179C2×#11758196D411yescharacteristic
180C2×C22⋊Dic61—21no—
181C2×C22⋊Dic61—21no—
182C2×C22⋊Dic61D411yescharacteristic
183C2×#11758198—21no—
184C2×#11758198—21no—
185C2×#11758198—21no—
186C2×#11758198D411yescharacteristic
187C2×C4×Dic61—21no—
188C2×C4×Dic61—21no—
189C2×C4×Dic61—21no—
190C2×C4×Dic61C2311yescharacteristic
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193#14519706—21no—
194#14519706—21no—
195#14519705—22no—
196#14519705—41no—
197#14519704—22no—
198#14519704—22no—
199#14519704—22no—
200#14519704D414yescomplemented
201#14519703—22no—
202#14519703—41no—
203#14519689—21no—
204#14519689—21no—
205#14519687—21no—
206C8×Dic61—21no—
207#14519684—21no—
208#14519684—21no—
209C2×#41×C61—21no—
210C2×#41×C61—21no—
211C2×#41×C61—22no—
212C2×#41×C61—22no—
213C2×#41×C61—41no—
214C2×#41×C61—41no—
215C2×#41×C61C2×C411yescharacteristic
216C2×#41×C61C2×C411yescharacteristic
217C2×#41×C61C2311yescharacteristic
218C2×#41×C61C2311yescharacteristic
219C22×Q8×C61C2×C411yescharacteristic
220C22×D4×C61—21no—
221C22×D4×C61C2×C411yescharacteristic
222C23×C4×C61—21no—
223C23×C4×C61C2311yescharacteristic
224C2×M16×C61C2311yescharacteristic
225C2×M16×C61C2311yescharacteristic
226C2×C22⋊C4×C61—21no—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2311yescharacteristic
229#104×C61—22no—
230#104×C61—22no—
231#104×C61—41no—
232#104×C61—41no—
233C22⋊C8×C61—21no—
234C22⋊C8×C61—21no—
235#95×C61—21no—
236C24×C61—21no—
237C24×C61C2×D411yescharacteristic
238C23×D61—21no—
239C23×D61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61—22no—
243#41×C61—22no—
244#41×C61—21no—
245#41×C61—21no—
246#41×C61—21no—
247#41×C61—21no—
248#41×C61—42no—
249#41×C61—42no—
250#41×C61—41no—
251#41×C61—41no—
252#41×C61—42no—
253#41×C61—42no—
254#41×C61C2×D412yes—
255#41×C61#4112yes—
256C2×Q8×C61—21no—
257C2×Q8×C61—22no—
258C2×Q8×C61—41no—
259C2×Q8×C61C22×C411yescharacteristic
260C2×Q8×C61C22×C411yescharacteristic
261C2×D4×C61—21no—
262C2×D4×C61—22no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—41no—
268C2×D4×C61—42no—
269C2×D4×C61—42no—
270C2×D4×C61C22×C411yescharacteristic
271C2×D4×C61C22×C411yescharacteristic
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—21no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—42no—
284C22×C4×C61—42no—
285C22×C4×C61C22×C411yescharacteristic
286C22×C4×C61C22×C411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2411yescharacteristic
291C2×C22⋊D61—21no—
292C2×C22⋊D61—21no—
293C2×C22⋊D61—21no—
294C2×C22⋊D61—21no—
295C2×C22⋊D61—21no—
296C2×C22⋊D61—21no—
297C2×C22⋊D61—21no—
298C2×C22⋊D61—21no—
299C2×C22⋊D61—21no—
300C2×C22⋊D61—42no—
301C2×C22⋊D61—44no—
302C2×C22⋊D61C22⋊C411yescharacteristic
303C2×C22⋊D61C22⋊C411yescharacteristic
304C2×C22⋊D61C22⋊C411yescharacteristic
305C2×C22⋊D61C22⋊C411yescharacteristic
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61C2×D411yescharacteristic
312C22×Dic61C2×D411yescharacteristic
313C22×Dic61C2×D411yescharacteristic
314#11758226—22no—
315#11758226—41no—
316Q8×D61—22no—
317Q8×D61—41no—
318#11758224—22no—
319#11758224—41no—
320#11758224—42no—
321#11758224—42no—
322D4×D61—22no—
323D4×D61—41no—
324D4×D61—42no—
325D4×D61—42no—
326#11758222—21no—
327#11758222—21no—
328#11758222—21no—
329#11758222—21no—
330#11758222—42no—
331#11758222—42no—
332C2×D244—21no—
333C2×D244C22×C411yescharacteristic
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×C4×D61—21no—
340C2×C4×D61—21no—
341C2×C4×D61—42no—
342C2×C4×D61—42no—
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C22×C411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×Dic122—21no—
348C2×Dic122C22×C411yescharacteristic
349M16×C61—21no—
350M16×C61—21no—
351M16×C61—21no—
352M16×C61—21no—
353C2×C8×C61—21no—
354C2×C8×C61—21no—
355C22⋊C4×C61—42no—
356C42×C61—21no—
357C42×C61—21no—
358C42×C61—21no—
359C42×C61—21no—
360C22⋊Dic61—21no—
361C22⋊Dic61—21no—
362C22⋊Dic61—21no—
363C22⋊Dic61—21no—
364C22⋊Dic61—21no—
365C22⋊Dic61—21no—
366C22⋊Dic61—21no—
367C22⋊Dic61—21no—
368C22⋊Dic61—21no—
369C22⋊Dic61—42no—
370C22⋊Dic61C22⋊C411yescharacteristic
371C22⋊Dic61C22⋊C411yescharacteristic
372C22⋊Dic61C22⋊C411yescharacteristic
373C22⋊Dic61C22⋊C411yescharacteristic
374#11758198—21no—
375#11758198—21no—
376#11758198—21no—
377#11758198—21no—
378#11758198—21no—
379#11758198—21no—
380#11758198—42no—
381#11758198—42no—
382#11758198C22⋊C411yescharacteristic
383#11758198C22⋊C411yescharacteristic
384#11758198C22⋊C411yescharacteristic
385#11758198C22⋊C411yescharacteristic
386C4⋊Dic61—21no—
387C4⋊Dic61—21no—
388C4⋊Dic61—42no—
389C4⋊Dic61C22×C411yescharacteristic
390C4⋊Dic61C22×C411yescharacteristic
391#11758196—21no—
392#11758196—21no—
393#11758196—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397#11758196—42no—
398#11758196—42no—
399#11758196C22⋊C411yescharacteristic
400#11758196C22⋊C411yescharacteristic
401#11758196C22⋊C411yescharacteristic
402#11758196C22⋊C411yescharacteristic
403C4×Dic61—21no—
404C4×Dic61—21no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—42no—
410C4×Dic61—42no—
411C4×Dic61C22×C411yescharacteristic
412C4×Dic61C22×C411yescharacteristic
413C4×Dic61C2×D411yescharacteristic
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D412yescomplemented
416#11758194—21no—
417#11758194—21no—
418#11758194—21no—
419#11758194—42no—
420#11758194C2×D412yescomplemented
421C2×#92418—21no—
422C2×#92418—21no—
423C2×#92418—42no—
424#11758189—42no—
425C8×D61—42no—
426C23×C61—21no—
427C23×C61—21no—
428C23×C61—21no—
429C23×C61—21no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—42no—
433C23×C61—42no—
434C23×C61—81no—
435C23×C61C2×C22⋊C411yescharacteristic
436C23×C61C2×C22⋊C411yescharacteristic
437C23×C61C22×D411yescharacteristic
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—21no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—42no—
444C22×D61—42no—
445C22×D61—81no—
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C2×C22⋊C411yescharacteristic
448Q8×C61—21no—
449Q8×C61—21no—
450Q8×C61—21no—
451Q8×C61—42no—
452Q8×C61C4×D412yes—
453D4×C61—22no—
454D4×C61—22no—
455D4×C61—21no—
456D4×C61—21no—
457D4×C61—21no—
458D4×C61—42no—
459D4×C61—42no—
460D4×C61—42no—
461D4×C61—41no—
462D4×C61—41no—
463D4×C61C4×D412yes—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—21no—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—22no—
478C2×C4×C61—21no—
479C2×C4×C61—42no—
480C2×C4×C61—42no—
481C2×C4×C61—42no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61C2×C22⋊C411yescharacteristic
490C2×C4×C61C2×C22⋊C411yescharacteristic
491C2×C4×C61C23×C411yescharacteristic
492C2×C4×C61C22×D411yescharacteristic
493C2×C4×C61C22×D411yescharacteristic
494C2×C4×C61C2×#4111yescharacteristic
495C2×C4×C61H(5,𝔽2)11yescharacteristic
496C2×C4×C61H(5,𝔽2)11yescharacteristic
497C22⋊D61—22no—
498C22⋊D61—22no—
499C22⋊D61—41no—
500C22⋊D61—41no—
501C22⋊D61—42no—
502C22⋊D61—42no—
503C22⋊D61—42no—
504C22⋊D61—42no—
505C22⋊D61—41no—
506C22⋊D61—41no—
507C22⋊D61—42no—
508C22⋊D61—81no—
509C22⋊D61—81no—
510C22⋊D61—81no—
511C2×Dic61—21no—
512C2×Dic61—21no—
513C2×Dic61—22no—
514C2×Dic61—21no—
515C2×Dic61—21no—
516C2×Dic61—21no—
517C2×Dic61—22no—
518C2×Dic61—41no—
519C2×Dic61—42no—
520C2×Dic61—41no—
521C2×Dic61—41no—
522C2×Dic61—42no—
523C2×Dic61—41no—
524C2×Dic61—41no—
525C2×Dic61—41no—
526C2×Dic61—81no—
527C2×Dic61C2×C22⋊C411yescharacteristic
528C2×Dic61C2×C22⋊C411yescharacteristic
529C2×Dic61C2×C22⋊C411yescharacteristic
530C2×Dic61C2×C22⋊C411yescharacteristic
531C2×Dic61C2×C22⋊C411yescharacteristic
532C2×Dic61C2×C22⋊C411yescharacteristic
533D244—21no—
534D244—21no—
535D244—42no—
536C4×D61—21no—
537C4×D61—21no—
538C4×D61—21no—
539C4×D61—21no—
540C4×D61—21no—
541C4×D61—21no—
542C4×D61—21no—
543C4×D61—21no—
544C4×D61—42no—
545C4×D61—42no—
546C4×D61—41no—
547C4×D61—41no—
548Dic122—21no—
549Dic122—21no—
550Dic122—42no—
551C8×C61—41no—
552C8×C61—41no—
553#92418—22no—
554#92418—41no—
555#22435—611nomaximal, Sylow
556C22×C61—21no—
557C22×C61—21no—
558C22×C61—22no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—21no—
565C22×C61—41no—
566C22×C61—41no—
567C22×C61—41no—
568C22×C61—41no—
569C22×C61—41no—
570C22×C61—81no—
571C22×C61—81no—
572C22×C61—84no—
573C22×C61C22×C22⋊C411yescharacteristic
574C22×C61D4211yescharacteristic
575C22×C61#54611yescharacteristic
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—21no—
580C2×D61—21no—
581C2×D61—21no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—41no—
585C2×D61—81no—
586C2×D61—81no—
587C2×D61—84no—
588C4×C61—22no—
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—42no—
592C4×C61—41no—
593C4×C61—81no—
594C4×C61C2×C4×D411yescharacteristic
595C4×C61#51811yescharacteristic
596C4×C61D4211yescharacteristic
597C4×C61#54611yescharacteristic
598Dic61—21no—
599Dic61—21no—
600Dic61—21no—
601Dic61—21no—
602Dic61—21no—
603Dic61—42no—
604Dic61—41no—
605Dic61—41no—
606Dic61—41no—
607Dic61—81no—
608Dic61#42112yescomplemented
609D4×#41—611no—
610D4×M16—611no—
611C2×#421—611no—
612C2×#421—611no—
613#2293—611no—
614#1980—611no—
615#1962—611no—
616#1897—611no—
617#1897—611no—
618#1871—611no—
619#1871—611no—
620#1806—611no—
621#1789—611no—
622#1789D6111yescharacteristic, complemented
623C4×#104—611no—
624C2×C61—21no—
625C2×C61—21no—
626C2×C61—42no—
627C2×C61—41no—
628C2×C61—41no—
629C2×C61—81no—
630C2×C61D4×C22⋊C411yescharacteristic
631C2×C61C2×#42111yescharacteristic
632C2×C61#290111yescharacteristic
633D61—41no—
634D61—41no—
635D61—81no—
636C22×#41—611no—
637C22×#41C2×D6111yescharacteristic
638C22×M16—611no—
639C22×M16—611no—
640#550—611no—
641D4×Q8—611no—
642#548—611no—
643#548—611no—
644#547—611no—
645#547—1221no—
646#546—611no—
647#546—611no—
648#546—1221no—
649#546—1221no—
650D42—611no—
651D42—1221no—
652#532—611no—
653#532—1221no—
654#525—611no—
655#525—611no—
656#525—1221no—
657#525—1221no—
658C4×#41—611no—
659C2×C4×D4—611no—
660C2×C4×D4—1221no—
661C2×#117—611no—
662C2×#117—611no—
663#436—1221no—
664#435—1221no—
665#435—1221no—
666C8×D4—1221no—
667#423—611no—
668#421—1224no—
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104C2×D6111yescharacteristic
679C2×#104C2×D6111yescharacteristic
680C2×#104C2×D6111yescharacteristic, complemented
681C2×#104C2×D6111yescharacteristic, complemented
682#407—611no—
683#407C2×D6111yescharacteristic, complemented
684C4×M16—611no—
685#390—1221no—
686#389—1221no—
687#388—1221no—
688#388—1221no—
689C4×C4⋊C4—611no—
690C4×C22⋊C4—611no—
691C4×C22⋊C4C2×D6111yescharacteristic, complemented
692C43—611no—
693#339—611no—
694#339—611no—
695#339—611no—
696#339—611no—
697C61#2243511yescharacteristic, complemented, Sylow
698C2×#41—21no—
699C2×#41—21no—
700C2×#41—22no—
701C2×#41—22no—
702C2×#41—41no—
703C2×#41—41no—
704C2×#41—611no—
705C2×#41—611no—
706C2×#41—611no—
707C2×#41—1221no—
708C2×#41—1221no—
709C2×#41—1222no—
710C2×#41—1222no—
711C2×#41—2441no—
712C2×#41—2441no—
713C2×#41C4×D6111yescharacteristic
714C2×#41C4×D6111yescharacteristic
715C2×#41C22×D6111yescharacteristic
716C2×#41C22×D6111yescharacteristic
717C22×Q8—611no—
718C22×Q8C4×D6111yescharacteristic
719C22×D4—21no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—1221no—
723C22×D4—1221no—
724C22×D4C4×D6111yescharacteristic
725C23×C4—21no—
726C23×C4—611no—
727C23×C4—1221no—
728C23×C4C22×D6111yescharacteristic
729C2×M16—611no—
730C2×M16—611no—
731C2×M16—1221no—
732C2×M16—1221no—
733C2×M16—1222no—
734C2×M16—1222no—
735C2×M16—2441no—
736C2×M16—2441no—
737C2×M16C22×D6111yescharacteristic
738C2×M16C22×D6111yescharacteristic
739C22×C8—1221no—
740C22×C8—1221no—
741C4⋊Q8—611no—
742C4⋊Q8—1221no—
743#127—611no—
744#127—1221no—
745#124—611no—
746#124—611no—
747#124—1221no—
748#124—1221no—
749#123—1221no—
750#123—1221no—
751#123—1221no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755C22⋊Q8—611no—
756C22⋊Q8—611no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763#121—611no—
764#121—611no—
765#121—611no—
766#121—611no—
767#121—1221no—
768#121—1221no—
769#121—1221no—
770#121—1221no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#120—1221no—
778#120—1221no—
779#120—1221no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783C4×Q8—611no—
784C4×Q8—611no—
785C4×D4—611no—
786C4×D4—611no—
787C4×D4—611no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—1221no—
796C4×D4—1221no—
797C4×D4—1221no—
798C4×D4—1221no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807#117—611no—
808#117—1222no—
809#117—1221no—
810#117—1222no—
811#117—2441no—
812#117—2441no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C4⋊C4—1221no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—611no—
820C2×C22⋊C4—611no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C22⋊C4—1221no—
825C2×C22⋊C4—1221no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—1221no—
830C2×C42—1221no—
831C2×C42—1221no—
832C2×C42C22×D6111yescharacteristic
833C2×C42C22×D6111yescharacteristic
834C4⋊C8—1221no—
835C4⋊C8—1221no—
836#104—22no—
837#104—22no—
838#104—41no—
839#104—41no—
840#104—614no—
841#104—1222no—
842#104—1222no—
843#104—1222no—
844#104—1222no—
845#104—1222no—
846#104—2441no—
847#104—2441no—
848C22⋊C8—21no—
849C22⋊C8—21no—
850C22⋊C8—1221no—
851C22⋊C8—1221no—
852#97—1221no—
853C4×C8—1221no—
854#95—21no—
855#95—1221no—
856#95—1221no—
857C24—21no—
858C24—611no—
859C24—1221no—
860C24D4×D6111yescharacteristic
861#41—21no—
862#41—21no—
863#41—22no—
864#41—22no—
865#41—21no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—42no—
870#41—42no—
871#41—41no—
872#41—41no—
873#41—42no—
874#41—42no—
875#41—1222no—
876#41—1222no—
877#41—1221no—
878#41—1221no—
879#41—1221no—
880#41—1221no—
881#41—2442no—
882#41—2442no—
883#41—2441no—
884#41—2442no—
885#41—2442no—
886#41—2441no—
887#41D4×D6112yes—
888#41#1175822412yes—
889C2×Q8—21no—
890C2×Q8—22no—
891C2×Q8—41no—
892C2×Q8—611no—
893C2×Q8—1221no—
894C2×Q8—1222no—
895C2×Q8—2441no—
896C2×Q8C2×C4×D6111yescharacteristic
897C2×Q8C2×C4×D6111yescharacteristic
898C2×D4—21no—
899C2×D4—22no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—611no—
908C2×D4—611no—
909C2×D4—611no—
910C2×D4—611no—
911C2×D4—611no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1222no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—1221no—
923C2×D4—2441no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4—2444no—
928C2×D4C2×C4×D6111yescharacteristic
929C2×D4C2×C4×D6111yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—611no—
947C22×C4—611no—
948C22×C4—611no—
949C22×C4—611no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—2442no—
963C22×C4—2442no—
964C22×C4C2×C4×D6111yescharacteristic
965C22×C4C2×C4×D6111yescharacteristic
966C22×C4D4×D6111yescharacteristic
967C22×C4D4×D6111yescharacteristic
968C22×C4D4×D6111yescharacteristic
969C22×C4C23×D6111yescharacteristic
970M16—21no—
971M16—21no—
972M16—21no—
973M16—21no—
974M16—612no—
975M16—1221no—
976M16—1221no—
977M16—1221no—
978M16—2442no—
979M16—2442no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—1221no—
983C2×C8—1221no—
984C2×C8—2442no—
985C2×C8—2442no—
986C4⋊C4—611no—
987C4⋊C4—611no—
988C4⋊C4—611no—
989C4⋊C4—611no—
990C4⋊C4—611no—
991C4⋊C4—611no—
992C4⋊C4—1221no—
993C4⋊C4—1221no—
994C4⋊C4—1221no—
995C4⋊C4—1221no—
996C4⋊C4—1221no—
997C4⋊C4—1221no—
998C4⋊C4—1221no—
999C4⋊C4—1221no—
1000C4⋊C4—2442no—
1001C4⋊C4—2442no—
1002C4⋊C4—2442no—
1003C22⋊C4—42no—
1004C22⋊C4—611no—
1005C22⋊C4—611no—
1006C22⋊C4—611no—
1007C22⋊C4—611no—
1008C22⋊C4—611no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—1221no—
1013C22⋊C4—1221no—
1014C22⋊C4—1221no—
1015C22⋊C4—1221no—
1016C22⋊C4—1221no—
1017C22⋊C4—1221no—
1018C22⋊C4—1221no—
1019C22⋊C4—1221no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—1221no—
1027C22⋊C4—2442no—
1028C22⋊C4—2442no—
1029C22⋊C4—2442no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—611no—
1035C42—611no—
1036C42—611no—
1037C42—611no—
1038C42—612no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—2442no—
1046C42—2442no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—41no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—81no—
1056C23—611no—
1057C23—611no—
1058C23—1221no—
1059C23—1221no—
1060C23—1221no—
1061C23—4881no—
1062C23—2441no—
1063C23—2441no—
1064C23—2442no—
1065C23—2442no—
1066C23C22⋊C4×D6111yescharacteristic
1067C23C22⋊C4×D6111yescharacteristic
1068C23C2×D4×D6111yescharacteristic
1069Q8—21no—
1070Q8—21no—
1071Q8—21no—
1072Q8—42no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—2442no—
1076Q8#1451973712yes—
1077D4—22no—
1078D4—22no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—42no—
1083D4—42no—
1084D4—42no—
1085D4—41no—
1086D4—41no—
1087D4—1222no—
1088D4—1222no—
1089D4—1221no—
1090D4—1221no—
1091D4—4881no—
1092D4—4881no—
1093D4—4881no—
1094D4—2442no—
1095D4—2442no—
1096D4—2441no—
1097D4—2441no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2442no—
1102D4—2441no—
1103D4—2441no—
1104D4#1451973712yes—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—611no—
1131C2×C4—611no—
1132C2×C4—611no—
1133C2×C4—611no—
1134C2×C4—611no—
1135C2×C4—611no—
1136C2×C4—1222no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—1221no—
1147C2×C4—1221no—
1148C2×C4—1221no—
1149C2×C4—1221no—
1150C2×C4—1222no—
1151C2×C4—4881no—
1152C2×C4—2442no—
1153C2×C4—2442no—
1154C2×C4—2442no—
1155C2×C4—2441no—
1156C2×C4—2442no—
1157C2×C4—2441no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4C22⋊C4×D6111yescharacteristic
1165C2×C4C22⋊C4×D6111yescharacteristic
1166C2×C4C22×C4×D6111yescharacteristic
1167C2×C4C2×D4×D6111yescharacteristic
1168C2×C4C2×D4×D6111yescharacteristic
1169C2×C4C2×#1175822411yescharacteristic
1170C2×C4#1451982211yescharacteristic
1171C2×C4#1451982211yescharacteristic
1172C8—41no—
1173C8—41no—
1174C8—1222no—
1175C8—2441no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—22no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—81no—
1191C22—81no—
1192C22—84no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—1221no—
1198C22—1221no—
1199C22—4881no—
1200C22—4881no—
1201C22—4884no—
1202C22—2441no—
1203C22—2441no—
1204C22—2441no—
1205C22C2×C22⋊C4×D6111yescharacteristic
1206C22#1684039411yescharacteristic
1207C22#1684039911yescharacteristic
1208C4—21no—
1209C4—21no—
1210C4—22no—
1211C4—42no—
1212C4—41no—
1213C4—81no—
1214C4—612no—
1215C4—1221no—
1216C4—1221no—
1217C4—1221no—
1218C4—1221no—
1219C4—1221no—
1220C4—4881no—
1221C4—2442no—
1222C4—2441no—
1223C4—2441no—
1224C4—2441no—
1225C4C2×#1451973711yescharacteristic
1226C4#1684023511yescharacteristic
1227C4#1684039411yescharacteristic
1228C4#1684039911yescharacteristic
1229C2—21no—
1230C2—21no—
1231C2—41no—
1232C2—41no—
1233C2—42no—
1234C2—81no—
1235C2—4881no—
1236C2—2441no—
1237C2—2441no—
1238C2#2144863511yescharacteristic
1239C2#421×D6111yescharacteristic
1240C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C22×C22⋊C4
prime radical#41×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#22435
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21454551C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839777C2semidirect
5. #21448282C2semidirect
6. #21446736C2semidirect
7. #21446645C2semidirect
8. #21446265C2semidirect
9. #21446264C2semidirect
10. #21446119C2semidirect
11. #21446118C2semidirect
12. #21445837C2semidirect
13. #21445761C2semidirect
14. #104×Dic61C2semidirect
15. C61×#1789C2semidirect
17. C22×#11758194C22semidirect
18. C2×M16×D61C22semidirect
19. #16840431C4semidirect
20. Q8×C22⋊D61C4semidirect
21. #16840423C4semidirect
22. #16840419C4semidirect
24. #16840411C4semidirect
26. #16840406C4semidirect
28. #16840400C4semidirect
30. D4×C22⋊D61C4semidirect
40. C2×#14519736C22semidirect
41. C2×#14519734C22semidirect
46. #16839785C22semidirect
49. C2×#14519705C22semidirect
50. C2×#14519705C22semidirect
53. C2×#14519704C22semidirect
54. C2×#14519704C22semidirect
55. C2×#14519703C22semidirect
56. C2×#14519703C22semidirect
57. #16839725C22semidirect
58. M16×Dic61C22semidirect
63. C4×#11758196C22semidirect
64. C4×#11758198C22semidirect
65. C42×Dic61C22semidirect
66. #16839523C22semidirect
67. #16839523C22semidirect
68. #16839522C22semidirect
69. #16839522C22semidirect
73. C2×#104×C61C22semidirect
74. C2×#104×C61C22semidirect
75. C61×#407C22semidirect
76. C4×C22⋊C4×C61C22semidirect
200. #14519704D4semidirect
415. C4×Dic61C2×D4semidirect
420. #11758194C2×D4semidirect
608. Dic61#421semidirect
622. #1789D61semidirect
680. C2×#104C2×D61semidirect
681. C2×#104C2×D61semidirect
683. #407C2×D61semidirect
691. C4×C22⋊C4C2×D61semidirect
697. C61#22435semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D612
#214545512
C2×#168397792
C2×#168397772
#214482822
#214467362
#214466452
#214462652
#214462642
#214461192
#214461182
#214458372
#214457612
#104×Dic612
C61×#17892
#2243561