Finite Group Databasebeta

← #14738506

Subgroups — #14738506

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic, complemented
2#13079999C211yesmaximal, characteristic
3#13079175C211yesmaximal, characteristic
4#13068122C212yesmaximal, complemented
5#13068088C212yesmaximal, complemented
6#13068074C212yesmaximal, complemented
7#13068060C212yesmaximal, complemented
8#13067375C211yesmaximal, characteristic, complemented
9#13067353C211yesmaximal, characteristic, complemented
10#13067349C211yesmaximal, characteristic
11C11×#2960C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#446—21no—
16C11×#446C2212yes—
17C8×Q8×C11—21no—
18C8×Q8×C11C2212yes—
19C11×#424—21no—
20C11×#423C2211yescharacteristic
21C11×#405—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622727—21no—
24#10622727—21no—
25#10622707—21no—
26#10622703—21no—
27#10622700—21no—
28#10622696—21no—
29#10622665—22no—
30#10622662—22no—
31#10622644C2212yes—
32#10622640C2212yes—
33#10622634C2212yes—
34#10622633C2212yes—
35#10622537C2211yescharacteristic
36#10622537C2211yescharacteristic
37#10622307C2211yescharacteristic
38#10622306C2211yescharacteristic
39C4×#4314—21no—
40C4×#4314—21no—
41#10622294C2211yescharacteristic
42#10622293C2211yescharacteristic
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C2×#4339—21no—
50C2×C11×M16—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8D412yes—
58C4×Q8×C11—21no—
59C4×Q8×C11C2312yes—
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4325—22no—
64#66983—21no—
65#66983—21no—
66#66979—21no—
67#66977—21no—
68#66977—21no—
69C2×#4318—21no—
70C2×#4318—21no—
71C2×#4314—21no—
72C2×#4314—21no—
73#66928—21no—
74#66927C2311yescharacteristic
75C4×D44—21no—
76C4×D44—21no—
77#66923—21no—
78#66922C2311yescharacteristic
79#66922C2311yescharacteristic
80#66922C2311yescharacteristic
81C4×Dic22—21no—
82C4×Dic22—21no—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2312yes—
87C11×#97—22no—
88C4×C8×C11—22no—
89C4×C8×C11D411yescharacteristic
90C4×C8×C11D411yescharacteristic
91C4×C8×C11C2311yescharacteristic
92C4×C8×C11C2311yescharacteristic
93#66899—22no—
94#66899—22no—
95#66885—21no—
96#66885—21no—
97#66881—21no—
98#66881—21no—
99#66880—21no—
100#66880—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#19351—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—41no—
116#4339—82no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C11×M16—42no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—41no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C42×C11—22no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144C22⋊Dic11—41no—
145#4326—82no—
146#4325—82no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158#4318—81no—
159#4318—81no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162#4314—42no—
163#4314—42no—
164#3255—111no—
165#3254—111no—
166#3167—111no—
167#2960D1111yescharacteristic, complemented
168#1692—112no—
169#1686—112no—
170#1684—112no—
171#1682—112no—
172#1567—111no—
173#1561—111no—
174#1560—111no—
175C23×C11#12111yescharacteristic
176C22×D11—41no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—42no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C22⋊D11—82no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197D44—41no—
198D44—41no—
199D44—41no—
200D44—41no—
201D44—81no—
202C4×D11—82no—
203Dic22—41no—
204Dic22—41no—
205Dic22—41no—
206Dic22—41no—
207Dic22—81no—
208C8×C11—21no—
209C8×C11—21no—
210C8×C11—21no—
211C8×C11—42no—
212C8×C11#13712yes—
213C11⋊C8—42no—
214C11⋊C8—42no—
215#533—111no—
216#533C2×D1111yescharacteristic
217#532—111no—
218#498—111no—
219#492—111no—
220#487—111no—
221#486—111no—
222#477—112no—
223#475—112no—
224#475—221no—
225#474—221no—
226#470—222no—
227#468—222no—
228#465—221no—
229#465—221no—
230#462—112no—
231#462—221no—
232#461—221no—
233#460—112no—
234#446—21no—
235#446C2×D1112yes—
236C8×Q8—21no—
237C8×Q8C2×D1112yes—
238C4×SD16—221no—
239C4×SD16—221no—
240#424—21no—
241#423—111no—
242#423—111no—
243#423C2×D1111yescharacteristic
244#405—21no—
245C2×C4×C8C2×D1111yescharacteristic
246#335—112no—
247#335—112no—
248#333—112no—
249#332—112no—
250#332—112no—
251#331—112no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11C2×#12111yescharacteristic
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11#47112yes—
265C4×C11C2×#13711yescharacteristic
266C4×C11#57511yescharacteristic
267C4×C11#57611yescharacteristic
268C4×C11#57811yescharacteristic
269Dic11—81no—
270Dic11—81no—
271Dic11—81no—
272C2×#41—221no—
273C2×Q16—222no—
274C2×SD16—222no—
275C2×SD16—221no—
276C2×SD16—221no—
277C2×M16—21no—
278C2×M16—221no—
279C2×M16—221no—
280C22×C8C22⋊D1111yescharacteristic
281C22×C8C22⋊D1111yescharacteristic
282C4⋊Q8—111no—
283C4⋊Q8—111no—
284C4⋊Q8—111no—
285C4⋊Q8D4411yescharacteristic
286C4⋊Q8D4411yescharacteristic
287#127—111no—
288#125—21no—
289#125—221no—
290#124—221no—
291C22⋊Q8—21no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8D4412yes—
295#121—221no—
296#121—221no—
297C4×Q8—21no—
298C4×Q8—221no—
299C4×Q8—221no—
300C4×Q8C22×D1112yes—
301C4×D4—221no—
302C4×D4—221no—
303#117—21no—
304#117—221no—
305C2×C42C22×D1111yescharacteristic
306#107—222no—
307#106—221no—
308#106—221no—
309#106—222no—
310C4⋊C8—22no—
311C4⋊C8—22no—
312C4⋊C8—21no—
313C4⋊C8—112no—
314C4⋊C8—112no—
315C4⋊C8—221no—
316C4⋊C8—221no—
317C4⋊C8C22×D1112yes—
318#103—222no—
319#103—222no—
320#103—221no—
321#103—221no—
322#103—222no—
323#102—221no—
324#102—221no—
325#102—222no—
326#97—22no—
327C4×C8—22no—
328C4×C8C22⋊D1111yescharacteristic
329C4×C8C22⋊D1111yescharacteristic
330C4×C8C22×D1111yescharacteristic
331C4×C8C22×D1111yescharacteristic
332C2×C11—41no—
333C2×C11#303711yescharacteristic
334C2×C11#306111yescharacteristic
335C2×C11C2×#47111yescharacteristic
336D11—161no—
337#41—882no—
338C2×Q8—21no—
339C2×Q8—221no—
340C2×Q8—221no—
341C2×Q8—221no—
342C2×Q8C2×D4412yes—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—441no—
347C22×C4—441no—
348C22×C4C2×D4411yescharacteristic
349C22×C4#433911yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—882no—
352SD16—442no—
353SD16—442no—
354SD16—882no—
355M16—42no—
356M16—881no—
357M16—881no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C2×C22⋊D1111yescharacteristic
366C2×C8C2×C22⋊D1111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4C2×D4412yes—
381C22⋊C4—22no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C42—22no—
386C42—441no—
387C42C2×D4411yescharacteristic
388C42#433911yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1935111yescharacteristic, complemented, Sylow
392C23—441no—
393C23#6698311yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—42no—
397Q8—441no—
398Q8—441no—
399Q8—441no—
400Q8—441no—
401Q8—881no—
402D4—441no—
403D4—441no—
404D4—441no—
405D4—441no—
406D4—881no—
407D4—882no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—882no—
419C2×C4#6698311yescharacteristic
420C2×C4#6698311yescharacteristic
421C2×C4#6698311yescharacteristic
422C2×C4C22×D4411yescharacteristic
423C2×C4C2×#433911yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—21no—
426C8—21no—
427C8—21no—
428C8—42no—
429C8—442no—
430C8—442no—
431C8#6699512yes—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—881no—
436C22—881no—
437C22—881no—
438C22C2×#6698311yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—881no—
445C4—881no—
446C4—881no—
447C4#1062275412yes—
448C4#1062328311yescharacteristic
449C4#1062328411yescharacteristic
450C4C2×#6699511yescharacteristic
451C4#1062335311yescharacteristic
452C2—41no—
453C2—1761no—
454C2#1307808811yescharacteristic
455C2#1307828611yescharacteristic
456C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2960D11
hypocenterC11#19351
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #13080007C2semidirect
4. #13068122C2semidirect
5. #13068088C2semidirect
6. #13068074C2semidirect
7. #13068060C2semidirect
8. #13067375C2semidirect
9. #13067353C2semidirect
11. C11×#2960C2semidirect
167. #2960D11semidirect
391. C11#19351semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130799992
#130791752
#130681222
#130680882
#130680742
#130680602
#130673752
#130673532
#130673492
C11×#29602
#1935111