Finite Group Databasebeta

← #29689479

Subgroups — #29689479

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic
3#21454450C211yesmaximal, characteristic
4#21446810C214yesmaximal, complemented
5#21446809C211yesmaximal, characteristic, complemented
6#21446808C211yesmaximal, characteristic, complemented
7#21446807C211yesmaximal, characteristic, complemented
8#21445901C214yesmaximal
9C61×#1997C211yesmaximal, characteristic, complemented
10#16840317—21no—
11#16840317—21no—
12#16840317—21no—
13#16840317—21no—
14#16840317—21no—
15#16840317—21no—
16#16840317—21no—
17#16840317—21no—
18C2×#14519777C2211yescharacteristic
19C2×#14519768C2212yes—
20C2×#14519757C412yes—
21C2×#14519753C412yes—
22C2×Q8×Dic61C412yes—
23C2×#14519742C412yes—
24C2×#14519735C2212yes—
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×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2311yescharacteristic
51C2×#11758194C2312yes—
52C2×#11758194C2312yes—
53#14519777—21no—
54#14519777—21no—
55#14519777—21no—
56#14519777—21no—
57#14519768—22no—
58#14519768—22no—
59#14519768—22no—
60#14519768—22no—
61#14519757—22no—
62#14519757—22no—
63#14519757—22no—
64#14519757—22no—
65#14519753—22no—
66#14519753—22no—
67#14519753—22no—
68#14519753—22no—
69Q8×Dic61—22no—
70Q8×Dic61—22no—
71Q8×Dic61—22no—
72Q8×Dic61—22no—
73#14519742—22no—
74#14519742—22no—
75#14519742—22no—
76#14519742—22no—
77#14519735—22no—
78#14519735—22no—
79#14519735—22no—
80#14519735—22no—
81C2×C4⋊Dic61C2×C412yes—
82C2×C4⋊Dic61C2×C414yes—
83C2×C4⋊Dic61C2312yes—
84C2×#11758196C2×C414yes—
85C2×#11758198C2×C414yes—
86C2×C4×Dic61C2×C414yes—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90C42×D61D411yescharacteristic
91C42×D61D411yescharacteristic
92C42×D61D411yescharacteristic
93C42×D61D411yescharacteristic
94C42×D61D411yescharacteristic
95C42×D61D411yescharacteristic
96C42×D61D411yescharacteristic
97C42×D61D411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418—21no—
100#14519706—22no—
101#14519706—22no—
102#14519689—22no—
103#14519689—22no—
104#14519689—22no—
105#14519689—22no—
106#14519688—21no—
107#14519687—22no—
108C4×#92418—21no—
109C8×Dic61—22no—
110C22×Q8×C61C2×C412yes—
111C2×M16×C61C2312yes—
112C2×M16×C61C2312yes—
113C4⋊Q8×C61—21no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C2×C4⋊C4×C61C2×C412yes—
118C2×C4⋊C4×C61C2312yes—
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—21no—
121C4⋊C8×C61—21no—
122#97×C61—21no—
123C4×C8×C61—21no—
124C23×D61C22×C411yescharacteristic
125C2×Q8×C61—22no—
126C2×Q8×C61—22no—
127C2×Q8×C61—44no—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C414yes—
131C22×C4×C61C2411yescharacteristic
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C414yes—
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—42no—
139C2×C4×D61—42no—
140C2×C4×D61C22⋊C411yescharacteristic
141C2×C4×D61C22⋊C411yescharacteristic
142C2×C4×D61C22⋊C411yescharacteristic
143C2×C4×D61C22⋊C411yescharacteristic
144C2×C4×D61C22⋊C411yescharacteristic
145C2×C4×D61C22⋊C411yescharacteristic
146C2×C4×D61C22⋊C411yescharacteristic
147C2×C4×D61C22⋊C411yescharacteristic
148C2×C4×D61C2×D411yescharacteristic
149C2×C4×D61C2×D411yescharacteristic
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×Dic122—22no—
153C2×Dic122—22no—
154C2×Dic122—44no—
155M16×C61—24no—
156M16×C61—22no—
157M16×C61—22no—
158C2×C8×C61—22no—
159C2×C8×C61—22no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168#11758198—24no—
169#11758198—24no—
170C4⋊Dic61—22no—
171C4⋊Dic61—22no—
172C4⋊Dic61—22no—
173C4⋊Dic61—22no—
174C4⋊Dic61—24no—
175C4⋊Dic61—24no—
176#11758196—24no—
177#11758196—24no—
178C4×Dic61—24no—
179C4×Dic61—24no—
180C4×Dic61C22⋊C411yescharacteristic
181C4×Dic61C22⋊C411yescharacteristic
182C4×Dic61C22⋊C411yescharacteristic
183C4×Dic61C22⋊C411yescharacteristic
184C4×Dic61C22⋊C411yescharacteristic
185C4×Dic61C22⋊C411yescharacteristic
186C4×Dic61C22⋊C411yescharacteristic
187C4×Dic61C22⋊C411yescharacteristic
188C4×Dic61C2×D411yescharacteristic
189C4×Dic61C2×D411yescharacteristic
190C4×Dic61C2×D411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192#11758194—22no—
193#11758194—24no—
194#11758194—22no—
195C2×#92418—22no—
196C2×#92418—22no—
197C23×C61C23×C411yescharacteristic
198C22×D61—22no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61C2×C22⋊C411yescharacteristic
202C22×D61C2×C22⋊C411yescharacteristic
203Q8×C61—44no—
204Q8×C61—44no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—24no—
208C2×C4×C61—44no—
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61C2×C22⋊C411yescharacteristic
212C2×C4×C61C2×C22⋊C411yescharacteristic
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C612−1+412yes—
216C2×C4×C612−1+412yes—
217C2×Dic61—22no—
218C2×Dic61—24no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—44no—
222C2×Dic61C2×C22⋊C411yescharacteristic
223C2×Dic61C2×C22⋊C411yescharacteristic
224C2×Dic61C2×C22⋊C411yescharacteristic
225C2×Dic61C2×C22⋊C411yescharacteristic
226C2×Dic61C2×C22⋊C411yescharacteristic
227C2×Dic61C2×C22⋊C411yescharacteristic
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—22no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242Dic122—44no—
243Dic122—44no—
244C8×C61—42no—
245C8×C61—42no—
246#92418—42no—
247#92418—42no—
248#21831—611nomaximal, Sylow
249C22×C61—21no—
250C22×C61—21no—
251C22×C61C22×C22⋊C411yescharacteristic
252C22×C61#51912yes—
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—44no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—44no—
263C4×C61#41312yes—
264C4×C61#41312yes—
265C4×C61#53611yescharacteristic
266C4×C61#53612yes—
267C4×C61#53611yescharacteristic
268Dic61—21no—
269Dic61—21no—
270Dic61—21no—
271Dic61—21no—
272Dic61—21no—
273Dic61—21no—
274Dic61—44no—
275C2×#533—611no—
276#2920—611no—
277#2920—611no—
278#1998—614no—
279#1997—611no—
280#1997—611no—
281#1997—611no—
282#1997D6111yescharacteristic, complemented
283#1822—614no—
284C2×C61—22no—
285C2×C61#231011yescharacteristic
286C2×C61C2×#41311yescharacteristic
287C2×C61C2×#41311yescharacteristic
288D61—41no—
289D61—41no—
290#533—1221no—
291#533—1221no—
292#533—1221no—
293#533—1221no—
294#533—1221no—
295#533—1221no—
296#533—1221no—
297#533—1221no—
298C2×C4⋊Q8—611no—
299C2×C4⋊Q8C2×D6111yescharacteristic
300C2×#125—612no—
301C2×C22⋊Q8—612no—
302C2×C22⋊Q8—612no—
303C2×C4×Q8—612no—
304C2×C4×Q8—612no—
305C2×#117—612no—
306C22×C42—611no—
307#432—1221no—
308#432—1221no—
309#432—1221no—
310#432—1221no—
311#431—1221no—
312#431—1221no—
313#431—1221no—
314#431—1221no—
315#423—612no—
316#423—611no—
317#423C2×D6111yescharacteristic
318#407—612no—
319#407—612no—
320C4×M16—612no—
321C4×M16—611no—
322C4×M16C2×D6111yescharacteristic
323#343—614no—
324#343—614no—
325#343—614no—
326#343C2×D6114yes—
327C61#2183111yescharacteristic, complemented, Sylow
328C22×Q8—612no—
329C22×Q8C4×D6112yes—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C2×M16—612no—
334C2×M16—612no—
335C2×M16C22×D6112yes—
336C2×M16C22×D6112yes—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—1221no—
342C4⋊Q8—1221no—
343C4⋊Q8—1221no—
344C4⋊Q8—1221no—
345#125—1222no—
346#125—1222no—
347#125—1222no—
348#125—1222no—
349C22⋊Q8—1222no—
350C22⋊Q8—1222no—
351C22⋊Q8—1222no—
352C22⋊Q8—1222no—
353C22⋊Q8—1222no—
354C22⋊Q8—1222no—
355C22⋊Q8—1222no—
356C22⋊Q8—1222no—
357C4×Q8—1222no—
358C4×Q8—1222no—
359C4×Q8—1222no—
360C4×Q8—1222no—
361C4×Q8—1222no—
362C4×Q8—1222no—
363C4×Q8—1222no—
364C4×Q8—1222no—
365#117—1222no—
366#117—1222no—
367#117—1222no—
368#117—1222no—
369C2×C4⋊C4—614no—
370C2×C4⋊C4—614no—
371C2×C4⋊C4—612no—
372C2×C4⋊C4—612no—
373C2×C4⋊C4C4×D6112yes—
374C2×C4⋊C4C22×D6112yes—
375C2×C22⋊C4—614no—
376C2×C42—611no—
377C2×C42—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—614no—
388C2×C42C22×D6111yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—1222no—
392C4⋊C8—1222no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C22⋊C8—1222no—
396C22⋊C8—1222no—
397C22⋊C8—1222no—
398C22⋊C8—1222no—
399#97—21no—
400#97—1222no—
401#97—1221no—
402C4×C8—21no—
403C4×C8—1222no—
404C4×C8—1221no—
405C24—611no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—44no—
409C2×Q8—1222no—
410C2×Q8—1222no—
411C2×Q8—2444no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—614no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4C2×C4×D6111yescharacteristic
433C22×C4C2×C4×D6111yescharacteristic
434C22×C4C2×C4×D6114yes—
435C22×C4C23×D6111yescharacteristic
436M16—24no—
437M16—22no—
438M16—22no—
439M16—1222no—
440M16—1222no—
441M16—1224no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—1222no—
445C2×C8—1222no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—1224no—
451C4⋊C4—1224no—
452C4⋊C4—1224no—
453C4⋊C4—1224no—
454C4⋊C4—1222no—
455C4⋊C4—1222no—
456C4⋊C4—1222no—
457C4⋊C4—1222no—
458C22⋊C4—1224no—
459C22⋊C4—1224no—
460C42—611no—
461C42—611no—
462C42—611no—
463C42—611no—
464C42—611no—
465C42—611no—
466C42—611no—
467C42—611no—
468C42—611no—
469C42—611no—
470C42—611no—
471C42—611no—
472C42—1224no—
473C42—1224no—
474C42D4×D6111yescharacteristic
475C42D4×D6111yescharacteristic
476C42D4×D6111yescharacteristic
477C42D4×D6111yescharacteristic
478C23—611no—
479C23—611no—
480C23—1222no—
481C23—2441no—
482C23—2441no—
483C23C22×C4×D6111yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—2444no—
487Q8—2444no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—611no—
493C2×C4—611no—
494C2×C4—611no—
495C2×C4—611no—
496C2×C4—611no—
497C2×C4—611no—
498C2×C4—1222no—
499C2×C4—1222no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—1222no—
506C2×C4—1222no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1224no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2444no—
517C2×C4C22⋊C4×D6111yescharacteristic
518C2×C4C22⋊C4×D6111yescharacteristic
519C2×C4C22⋊C4×D6111yescharacteristic
520C2×C4C22⋊C4×D6111yescharacteristic
521C2×C4C2×D4×D6111yescharacteristic
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4#1451982412yes—
524C2×C4#1451982512yes—
525C8—42no—
526C8—42no—
527C8—2442no—
528C8—2442no—
529C22—21no—
530C22—21no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22—2444no—
538C22C2×C22⋊C4×D6111yescharacteristic
539C22#1684023812yes—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—1221no—
544C4—1221no—
545C4—1221no—
546C4—1221no—
547C4—1221no—
548C4—1221no—
549C4—2444no—
550C4#1683974312yes—
551C4#1683974512yes—
552C4#1684033211yescharacteristic
553C4#1684033512yes—
554C4#1684033711yescharacteristic
555C2—22no—
556C2—2441no—
557C2—2441no—
558C2#2144840211yescharacteristic
559C2C2×#1683974311yescharacteristic
560C2C2×#1683974511yescharacteristic
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#21831
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. #21446810C2semidirect
5. #21446809C2semidirect
6. #21446808C2semidirect
7. #21446807C2semidirect
9. C61×#1997C2semidirect
282. #1997D61semidirect
327. C61#21831semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
#214544512
#214544502
#214468102
#214468092
#214468082
#214468072
#214459012
C61×#19972
#2183161