Finite Group Databasebeta

← #29689471

Subgroups — #29689471

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic
3#21454450C211yesmaximal, characteristic
4#21446809C211yesmaximal, characteristic, complemented
5#21446808C211yesmaximal, characteristic, complemented
6#21446807C211yesmaximal, characteristic, complemented
7#21446806C214yesmaximal, complemented
8#21445898C214yesmaximal
9C61×#1997C211yesmaximal, characteristic, complemented
10C22×Q8×D61C412yes—
11C2×#14519777C2211yescharacteristic
12C2×#14519776C412yes—
13C2×#14519776C2212yes—
14C2×#14519775C412yes—
15C4⋊Q8×D61—21no—
16C4⋊Q8×D61—21no—
17C4⋊Q8×D61—21no—
18C4⋊Q8×D61—21no—
19C4⋊Q8×D61—21no—
20C4⋊Q8×D61—21no—
21C4⋊Q8×D61—21no—
22C4⋊Q8×D61—21no—
23C2×C4⋊C4×D61C412yes—
24C2×C4⋊C4×D61C2212yes—
25C2×C42×D61C2211yescharacteristic
26#16839818—21no—
27#16839818—21no—
28#16839817—21no—
29#16839817—21no—
30#16839814—21no—
31#16839814—21no—
32#16839813—21no—
33#16839813—21no—
34#16839786C2211yescharacteristic
35#16839785C2212yes—
36#16839725C2212yes—
37#16839725C2212yes—
38C4×#11758194C2211yescharacteristic
39M16×Dic61C2212yes—
40#16839531C2214yes—
41#16839530C2214yes—
42#16839530C2214yes—
43C2×C4⋊Q8×C61C2211yescharacteristic
44C61×#423C2211yescharacteristic
45C4×M16×C61C2211yescharacteristic
46C61×#343C2214yes—
47C22×Dic122C2×C412yes—
48C22×Dic122C2×C414yes—
49C2×Q8×D61—22no—
50C2×Q8×D61—22no—
51C2×Q8×D61—22no—
52C2×Q8×D61—22no—
53C2×Q8×D61—48no—
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C414yes—
57C22×C4×D61C2311yescharacteristic
58C2×#11758194C2312yes—
59C2×#11758194C2312yes—
60#14519777—21no—
61#14519777—21no—
62#14519777—21no—
63#14519777—21no—
64#14519776—22no—
65#14519776—22no—
66#14519776—22no—
67#14519776—22no—
68#14519776—22no—
69#14519776—22no—
70#14519776—22no—
71#14519776—22no—
72#14519775—22no—
73#14519775—22no—
74#14519775—22no—
75#14519775—22no—
76C2×C4⋊Dic61C2×C412yes—
77C2×C4⋊Dic61C2312yes—
78C2×#11758196C2×C414yes—
79C2×#11758196C2×C414yes—
80C4⋊C4×D61—22no—
81C4⋊C4×D61—22no—
82C4⋊C4×D61—22no—
83C4⋊C4×D61—22no—
84C4⋊C4×D61—22no—
85C4⋊C4×D61—22no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C42×D61D411yescharacteristic
92C42×D61D411yescharacteristic
93C42×D61D411yescharacteristic
94C42×D61D411yescharacteristic
95C42×D61D411yescharacteristic
96C42×D61D411yescharacteristic
97C42×D61D411yescharacteristic
98C42×D61D411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418—21no—
101#14519706—22no—
102#14519706—22no—
103#14519689—22no—
104#14519689—22no—
105#14519689—22no—
106#14519689—22no—
107#14519688—21no—
108#14519687—22no—
109C4×#92418—21no—
110C8×Dic61—22no—
111C22×Q8×C61C2×C412yes—
112C2×M16×C61C2312yes—
113C2×M16×C61C2312yes—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C2×C4⋊C4×C61C2×C412yes—
119C2×C4⋊C4×C61C2312yes—
120C2×C42×C61C2311yescharacteristic
121C4⋊C8×C61—21no—
122C4⋊C8×C61—21no—
123#97×C61—21no—
124C4×C8×C61—21no—
125C23×D61C22×C411yescharacteristic
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61—44no—
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C414yes—
132C22×C4×C61C2411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C414yes—
137Q8×D61—48no—
138Q8×D61—48no—
139Q8×D61—48no—
140Q8×D61—48no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—24no—
147C2×C4×D61—48no—
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×Dic122—22no—
161C2×Dic122—22no—
162C2×Dic122—24no—
163C2×Dic122—24no—
164C2×Dic122—48no—
165C2×Dic122—44no—
166M16×C61—24no—
167M16×C61—22no—
168M16×C61—22no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183#11758196—24no—
184#11758196—24no—
185#11758196—24no—
186#11758196—24no—
187C4×Dic61C22⋊C411yescharacteristic
188C4×Dic61C22⋊C411yescharacteristic
189C4×Dic61C22⋊C411yescharacteristic
190C4×Dic61C22⋊C411yescharacteristic
191C4×Dic61C22⋊C411yescharacteristic
192C4×Dic61C22⋊C411yescharacteristic
193C4×Dic61C22⋊C411yescharacteristic
194C4×Dic61C22⋊C411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61C2×D411yescharacteristic
199#11758194—22no—
200#11758194—24no—
201#11758194—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204C23×C61C23×C411yescharacteristic
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—22no—
208C22×D61C2×C22⋊C411yescharacteristic
209C22×D61C2×C22⋊C411yescharacteristic
210Q8×C61—44no—
211Q8×C61—44no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—44no—
216C2×C4×C61C2×C22⋊C411yescharacteristic
217C2×C4×C61C2×C22⋊C411yescharacteristic
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C612−1+412yes—
223C2×C4×C612−1+412yes—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—24no—
228C2×Dic61—44no—
229C2×Dic61C2×C22⋊C411yescharacteristic
230C2×Dic61C2×C22⋊C411yescharacteristic
231C2×Dic61C2×C22⋊C411yescharacteristic
232C2×Dic61C2×C22⋊C411yescharacteristic
233C2×Dic61C2×C22⋊C411yescharacteristic
234C2×Dic61C2×C22⋊C411yescharacteristic
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—22no—
240C4×D61—22no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—22no—
247C4×D61—48no—
248C4×D61—48no—
249C4×D61#10014yes—
250C4×D61#10114yes—
251Dic122—48no—
252Dic122—44no—
253Dic122—44no—
254Dic122—48no—
255C8×C61—42no—
256C8×C61—42no—
257#92418—42no—
258#92418—42no—
259#21829—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61C22×C22⋊C411yescharacteristic
263C22×C61#51912yes—
264C2×D61—28no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61C2×#10012yes—
270C2×D61C2×#10112yes—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—44no—
274C4×C61C2×#10012yes—
275C4×C61C2×#10112yes—
276C4×C61#53611yescharacteristic
277C4×C61#53612yes—
278C4×C61#53611yescharacteristic
279Dic61—21no—
280Dic61—21no—
281Dic61—21no—
282Dic61—21no—
283Dic61—44no—
284Dic61C2×#10012yes—
285Dic61C2×#10112yes—
286C22×C4⋊Q8—611no—
287#2920—611no—
288#2920—611no—
289#1997—611no—
290#1997—611no—
291#1997—614no—
292#1997—611no—
293#1997D6111yescharacteristic, complemented
294#1821—614no—
295C2×C61—22no—
296C2×C61#231011yescharacteristic
297C2×C61C22×#10011yescharacteristic
298C2×C61C22×#10111yescharacteristic
299D61—22no—
300D61—22no—
301C23×Q8—612no—
302C2×C4⋊Q8—612no—
303C2×C4⋊Q8—612no—
304C2×C4⋊Q8—612no—
305C2×C4⋊Q8—611no—
306C2×C4⋊Q8—1221no—
307C2×C4⋊Q8—1221no—
308C2×C4⋊Q8—1221no—
309C2×C4⋊Q8—1221no—
310C2×C4⋊Q8—1221no—
311C2×C4⋊Q8—1221no—
312C2×C4⋊Q8—1221no—
313C2×C4⋊Q8—1221no—
314C2×C4⋊Q8C2×D6111yescharacteristic
315C22×C4⋊C4—612no—
316C22×C4⋊C4—612no—
317C22×C42—611no—
318#432—1221no—
319#432—1221no—
320#432—1221no—
321#432—1221no—
322#431—1221no—
323#431—1221no—
324#431—1221no—
325#431—1221no—
326#423—612no—
327#423—611no—
328#423C2×D6111yescharacteristic
329#407—612no—
330#407—612no—
331C4×M16—612no—
332C4×M16—611no—
333C4×M16C2×D6111yescharacteristic
334#343—614no—
335#343—614no—
336#343—614no—
337#343C2×D6114yes—
338C61#2182911yescharacteristic, complemented, Sylow
339C22×Q8—614no—
340C22×Q8—612no—
341C22×Q8—1222no—
342C22×Q8—1222no—
343C22×Q8—1222no—
344C22×Q8—1222no—
345C22×Q8—2448no—
346C22×Q8C4×D6112yes—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—614no—
351C2×M16—612no—
352C2×M16—612no—
353C2×M16C22×D6112yes—
354C2×M16C22×D6112yes—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—1222no—
360C4⋊Q8—1222no—
361C4⋊Q8—1222no—
362C4⋊Q8—1222no—
363C4⋊Q8—1222no—
364C4⋊Q8—1222no—
365C4⋊Q8—1222no—
366C4⋊Q8—1222no—
367C4⋊Q8—1222no—
368C4⋊Q8—1222no—
369C4⋊Q8—1222no—
370C4⋊Q8—1222no—
371C4⋊Q8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C2×C4⋊C4—614no—
376C2×C4⋊C4—614no—
377C2×C4⋊C4—612no—
378C2×C4⋊C4—612no—
379C2×C4⋊C4—1222no—
380C2×C4⋊C4—1222no—
381C2×C4⋊C4—1222no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4—1222no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4C4×D6112yes—
388C2×C4⋊C4C22×D6112yes—
389C2×C42—611no—
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42C22×D6111yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—1222no—
404C4⋊C8—1222no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C22⋊C8—1222no—
408C22⋊C8—1222no—
409C22⋊C8—1222no—
410C22⋊C8—1222no—
411#97—21no—
412#97—1222no—
413#97—1221no—
414C4×C8—21no—
415C4×C8—1222no—
416C4×C8—1221no—
417C24—611no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—44no—
421C2×Q8—1224no—
422C2×Q8—1224no—
423C2×Q8—1222no—
424C2×Q8—1222no—
425C2×Q8—2444no—
426C2×Q8—2448no—
427C2×Q8—2448no—
428C2×Q8—2448no—
429C2×Q8—2448no—
430C2×Q8—2448no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—614no—
447C22×C4—1224no—
448C22×C4—1224no—
449C22×C4—1224no—
450C22×C4—1224no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—2448no—
454C22×C4C2×C4×D6111yescharacteristic
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4C2×C4×D6114yes—
457C22×C4C23×D6111yescharacteristic
458M16—24no—
459M16—22no—
460M16—22no—
461M16—1222no—
462M16—1222no—
463M16—1224no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—1222no—
467C2×C8—1222no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—1224no—
473C4⋊C4—1224no—
474C4⋊C4—1224no—
475C4⋊C4—1224no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C42—611no—
481C42—611no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42D4×D6111yescharacteristic
493C42D4×D6111yescharacteristic
494C42D4×D6111yescharacteristic
495C42D4×D6111yescharacteristic
496C23—611no—
497C23—611no—
498C23—1222no—
499C23—1222no—
500C23—1222no—
501C23C22×C4×D6111yescharacteristic
502Q8—44no—
503Q8—44no—
504Q8—2444no—
505Q8—2448no—
506Q8—2448no—
507Q8—2444no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—614no—
515C2×C4—614no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1224no—
536C2×C4—2448no—
537C2×C4—2448no—
538C2×C4—2444no—
539C2×C4C22⋊C4×D6111yescharacteristic
540C2×C4C22⋊C4×D6111yescharacteristic
541C2×C4C22⋊C4×D6111yescharacteristic
542C2×C4C22⋊C4×D6111yescharacteristic
543C2×C4C2×D4×D6111yescharacteristic
544C2×C4C2×D4×D6111yescharacteristic
545C2×C4#1451982412yes—
546C2×C4#1451982512yes—
547C8—42no—
548C8—42no—
549C8—2442no—
550C8—2442no—
551C22—21no—
552C22—21no—
553C22—612no—
554C22—612no—
555C22—1228no—
556C22—1221no—
557C22—1221no—
558C22—1221no—
559C22—1221no—
560C22C2×C22⋊C4×D6111yescharacteristic
561C22#1684023812yes—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—612no—
566C4—612no—
567C4—1221no—
568C4—1221no—
569C4—1221no—
570C4—1221no—
571C4—2444no—
572C4#100×D6112yes—
573C4#101×D6112yes—
574C4#1684033211yescharacteristic
575C4#1684033512yes—
576C4#1684033711yescharacteristic
577C2—22no—
578C2—1222no—
579C2—1222no—
580C2#2144840211yescharacteristic
581C2C2×#100×D6111yescharacteristic
582C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1997C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1997D61
hypocenterC61#21829
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #21446809C2semidirect
5. #21446808C2semidirect
6. #21446807C2semidirect
7. #21446806C2semidirect
9. C61×#1997C2semidirect
293. #1997D61semidirect
338. C61#21829semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
#214544512
#214544502
#214468092
#214468082
#214468072
#214468062
#214458982
C61×#19972
#2182961