Finite Group Databasebeta

← #14790019

Subgroups — #14790019

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078417C212yesmaximal
2C4×#66997C211yesmaximal, characteristic
3#13069958C212yesmaximal
4#13069774C212yesmaximal
5#13069594C212yesmaximal
6#13069009C212yesmaximal
7#13068831C212yesmaximal
8#13068612C211yesmaximal, characteristic
9C11×#3502C211yesmaximal, characteristic
10Q82×C11—22no—
11C11×#557—22no—
12C11×#557—24no—
13C11×#544—22no—
14C11×#544C2212yes—
15C11×#533—22no—
16C11×#533C2212yes—
17C11×#519C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21#10622843C2211yescharacteristic
22C2×#66900C2212yes—
23#10622707—22no—
24#10622704—22no—
25#10622676—24no—
26#10622617C2214yes—
27#10622608C2214yes—
28#10622589C2211yescharacteristic
29#10622587C2211yescharacteristic
30#10622585—22no—
31C4×Dic11⋊C4—22no—
32C42×Dic11C2211yescharacteristic
33#10622537C2212yes—
34#10622170C2214yes—
35#10622170C2214yes—
36#10622168C2212yes—
37C22×Q8×C11C2311yescharacteristic
38C22×Dic22C2311yescharacteristic
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—28no—
42C11×C4⋊Q8—24no—
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D412yes—
45C11×#125—24no—
46C11×#125—28no—
47C11×#125—24no—
48C11×#125D414yes—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—22no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C11×#117—24no—
61C11×#117C2314yes—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11D412yes—
65C2×C42×C11C2311yescharacteristic
66#66997—22no—
67#66997Q814yescomplemented
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×#4318C2314yes—
78C4×Dic22—22no—
79C4×Dic22—22no—
80#66900—24no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66874—24no—
84#66874—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24315—111nomaximal, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×Q812yes—
96C2×Q8×C11#4112yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C2×Dic22—22no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×Dic22C2×Q812yes—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4C2×D414yes—
121C11×C4⋊C4C2×D414yes—
122C11×C22⋊C4—24no—
123C42×C11—28no—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—24no—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129C4⋊Dic11—22no—
130Dic11⋊C4—28no—
131Dic11⋊C4—44no—
132Dic11⋊C4—42no—
133C4×Dic11—24no—
134C4×Dic11—21no—
135C4×Dic11—22no—
136C4×Dic11—42no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139C4×Dic11C2×Q812yes—
140#4318—24no—
141#4318—24no—
142C2×C11⋊C8—24no—
143#3502D1111yescharacteristic
144#3078—112no—
145C4×C4⋊Q8—111no—
146#2060—112no—
147#2028—112no—
148#1994—112no—
149#1886—112no—
150#1857—112no—
151#1801—111no—
152C23×C11C22×D411yescharacteristic
153Q8×C11—24no—
154Q8×C11—24no—
155Q8×C11—44no—
156Q8×C11—82no—
157Q8×C11—84no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12012yes—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11C22⋊Q814yes—
170C2×C4×C11C22×D412yes—
171C2×C4×C11C22×Q811yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C112−1+412yes—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185Dic22—24no—
186Dic22—42no—
187C11⋊C8—44no—
188Q82—22no—
189#557—22no—
190#557—24no—
191#544—22no—
192#544C2×D1112yes—
193#533—22no—
194#533C2×D1112yes—
195C2×C4⋊Q8—111no—
196#519C2×D1112yes—
197C2×C4×Q8—111no—
198C2×C4×Q8C2×D1111yescharacteristic
199#479—224no—
200#477—222no—
201#475—222no—
202#428—114no—
203#423—112no—
204#419—114no—
205C2×#101—112no—
206#391—111no—
207#391—111no—
208#389—222no—
209#384—111no—
210C4×C4⋊C4—222no—
211C43—111no—
212#343—112no—
213#339—114no—
214#339—114no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11C2×#12011yescharacteristic
218C22×C11C2×C22⋊Q811yescharacteristic
219C22×C11#53611yescharacteristic
220C4×C11—24no—
221C4×C11—21no—
222C4×C11—22no—
223C4×C11—44no—
224C4×C11—42no—
225C4×C11—44no—
226C4×C11#45612yes—
227C4×C11#54812yes—
228C4×C11D4×Q812yes—
229Dic11—24no—
230Dic11—42no—
231Dic11—42no—
232Dic11—81no—
233C22×Q8—111no—
234C22×Q8C22×D1111yescharacteristic
235C2×M16—114no—
236C4⋊Q8—22no—
237C4⋊Q8—22no—
238C4⋊Q8—28no—
239C4⋊Q8—24no—
240C4⋊Q8—114no—
241C4⋊Q8—222no—
242C4⋊Q8C22⋊D1112yes—
243C4⋊Q8C22⋊D1112yes—
244#125—24no—
245#125—28no—
246#125—24no—
247#125C22⋊D1114yes—
248C22⋊Q8—22no—
249C22⋊Q8—24no—
250C22⋊Q8—22no—
251C4×Q8—24no—
252C4×Q8—24no—
253C4×Q8—24no—
254C4×Q8—24no—
255C4×Q8—22no—
256C4×Q8—22no—
257C4×Q8—22no—
258C4×Q8—22no—
259C4×Q8—222no—
260C4×Q8—222no—
261#117—24no—
262#117C22×D1114yes—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C22⋊D1112yes—
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—221no—
272C2×C42—221no—
273C2×C42—221no—
274C2×C42C22⋊D1112yes—
275C2×C42C22×D1111yescharacteristic
276#107—224no—
277#106—224no—
278C4⋊C8—222no—
279C4⋊C8—222no—
280#103—224no—
281#103—224no—
282#101—224no—
283#95—222no—
284#95—222no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#240911yescharacteristic
288C2×C11C2×#45611yescharacteristic
289C2×C11#301811yescharacteristic
290C2×Q8—24no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—112no—
296C2×Q8—221no—
297C2×Q8—222no—
298C2×Q8—222no—
299C2×Q8Q8×D1112yes—
300C2×Q8#434312yes—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4C2×C22⋊D1112yes—
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1112yes—
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C23×D1111yescharacteristic
310M16—224no—
311M16—224no—
312C2×C8—224no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—28no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—228no—
324C4⋊C4—222no—
325C4⋊C4—444no—
326C4⋊C4—442no—
327C4⋊C4C2×C22⋊D1114yes—
328C4⋊C4C2×C22⋊D1114yes—
329C22⋊C4—24no—
330C42—28no—
331C42—22no—
332C42—22no—
333C42—24no—
334C42—112no—
335C42—224no—
336C42—221no—
337C42—222no—
338C42—442no—
339C42—441no—
340C42—441no—
341C42C2×C22⋊D1112yes—
342C42C2×C22⋊D1112yes—
343C11#2431511yescharacteristic, complemented, Sylow
344C23C22×C22⋊D1111yescharacteristic
345Q8—24no—
346Q8—24no—
347Q8—44no—
348Q8—82no—
349Q8—84no—
350Q8—224no—
351Q8—442no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4#6699914yes—
372C2×C4#6700611yescharacteristic
373C2×C4#6700612yes—
374C2×C4#6700611yescharacteristic
375C2×C4C2×Q8×D1111yescharacteristic
376C2×C4C2×#434311yescharacteristic
377C2×C4#6704012yes—
378C2×C4C22×C22⋊D1112yes—
379C8—444no—
380C22—21no—
381C22—21no—
382C22C2×#6699911yescharacteristic
383C22#1062334711yescharacteristic
384C22C2×#6700611yescharacteristic
385C4—24no—
386C4—21no—
387C4—22no—
388C4—44no—
389C4—42no—
390C4—44no—
391C4—224no—
392C4—442no—
393C4—442no—
394C4—881no—
395C4#1062285912yes—
396C4Q8×C22⋊D1112yes—
397C4#1062334812yes—
398C2—21no—
399C2—21no—
400C2#1307197511yescharacteristic
401C2C2×#1062285911yescharacteristic
402C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenter#3502D11
hypocenterC11#24315
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
67. #66997Q8semidirect
343. C11#24315semidirect

Maximal subgroups

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

subgroupindex
#130784172
C4×#669972
#130699582
#130697742
#130695942
#130690092
#130688312
#130686122
C11×#35022
#2431511