Finite Group Databasebeta

← #14745296

Subgroups — #14745296

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081481C211yesmaximal, characteristic, complemented
2#13080932C212yesmaximal, complemented
3#13068225C211yesmaximal, characteristic, complemented
4#13068189C212yesmaximal, complemented
5#13068015C211yesmaximal, characteristic, complemented
6#13068007C211yesmaximal, characteristic, complemented
7#13067829C212yesmaximal, complemented
8#13067767C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11C11×#3334C211yesmaximal, characteristic
12C11×#547C2212yes—
13#10623074C2212yes—
14C11×#500C2211yescharacteristic
15C11×#480—22no—
16C11×#474C2212yes—
17C11×#466—21no—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C2×C11×#107—21no—
21#10622852—22no—
22#10622845—22no—
23D8×Dic11—21no—
24#10622706C2212yes—
25#10622703C2212yes—
26#10622694C2212yes—
27#10622665—22no—
28#10622656—22no—
29C4×#4324C2211yescharacteristic
30#10622625C2212yes—
31#10622621C2212yes—
32#10622621C2212yes—
33#10622491—21no—
34#10622379—22no—
35#10622295C2211yescharacteristic
36C8×Dic22C2211yescharacteristic
37#10622185C2212yes—
38D4⋊(C11⋊C8)C2212yes—
39D4⋊(C11⋊C8)C2211yescharacteristic
40#10622122C2211yescharacteristic
41#10622119C2212yes—
42#10622118C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×C11×#41—22no—
46C2×C11×D8D411yescharacteristic
47C22×C8×C11—21no—
48C11×C4⋊Q8C2312yes—
49C11×#123—42no—
50C11×C22⋊Q8—22no—
51C11×#121—22no—
52C4×D4×C11C2312yes—
53C4×D4×C11C2311yescharacteristic
54C2×C11×C4⋊C4—22no—
55C2×#4326—22no—
56D4×Dic11—22no—
57C2×#4324D411yescharacteristic
58C2×C4⋊Dic11—22no—
59#66977—22no—
60C2×#4318—22no—
61#66943—22no—
62#66931—42no—
63#66922C2312yes—
64C4×Dic22C2311yescharacteristic
65C11×#107—21no—
66C11×#107—21no—
67C11×#107—22no—
68C11×#107D411yescharacteristic
69C11×C4⋊C8C2311yescharacteristic
70C11×#102—22no—
71C11×#102D412yes—
72C11×C22⋊C8—21no—
73C4×C8×C11C2311yescharacteristic
74#66899—22no—
75#66899—22no—
76#66899—22no—
77#66896—22no—
78#66896—22no—
79#66896D411yescharacteristic
80C22⋊(C11⋊C8)—22no—
81#66882—21no—
82#66882—21no—
83Dic11⋊C8—21no—
84C8×Dic11—21no—
85#66874—42no—
86#66874D411yescharacteristic
87#66872—22no—
88#66872—22no—
89#66872D411yescharacteristic
90C4⋊(C11⋊C8)C2311yescharacteristic
91C4⋊(C11⋊C8)C2312yes—
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#19903—111nomaximal, Sylow
95C11×#41—44no—
96C11×#41—82no—
97C2×Q8×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11C2×D412yes—
100C2×D4×C11C2×D411yescharacteristic
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×Dic11—42no—
105C2×Dic22—22no—
106C2×Dic22C2×D411yescharacteristic
107C11×D8—22no—
108C2×C8×C11—21no—
109C2×C8×C11—42no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4C2×D411yescharacteristic
116C11×C4⋊C4C2×D412yes—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—21no—
119C11×C22⋊C4—42no—
120C42×C11C2411yescharacteristic
121C22⋊Dic11—42no—
122#4326—82no—
123#4324—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—42no—
127C4⋊Dic11C2×D411yescharacteristic
128Dic11⋊C4—21no—
129Dic11⋊C4—42no—
130C4×Dic11—21no—
131#4318—82no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137#3380—111no—
138#3334D1111yescharacteristic
139#3331—112no—
140#1710—111no—
141#1703—112no—
142#1675—111no—
143#1674—111no—
144#1644—112no—
145#1635—112no—
146#1589—111no—
147C8×SD16—111no—
148C23×C11—21no—
149C23×C11—22no—
150Q8×C11—42no—
151Q8×C11—42no—
152D4×C11—22no—
153D4×C11—21no—
154D4×C11—22no—
155D4×C11—84no—
156D4×C11#13512yes—
157C2×C4×C11—22no—
158C2×C4×C11—21no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—84no—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11H(5,𝔽2)11yescharacteristic
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—42no—
171C2×Dic11—162no—
172Dic22—21no—
173Dic22—21no—
174Dic22—82no—
175C8×C11—21no—
176C8×C11—41no—
177C8×C11#13712yes—
178C11⋊C8—21no—
179C11⋊C8—21no—
180C11⋊C8—41no—
181C11⋊C8—42no—
182C11⋊C8—41no—
183#554—112no—
184#547C2×D1112yes—
185#500—111no—
186#500C2×D1111yescharacteristic
187#499—221no—
188#487—112no—
189#487—112no—
190#483—222no—
191#480—22no—
192#478—222no—
193#476—112no—
194#476—112no—
195#474C2×D1112yes—
196#470—222no—
197#466—21no—
198#462—112no—
199#452—222no—
200C8×Q8—111no—
201C4×SD16—111no—
202C4×D8—221no—
203C4×D8C2×D1111yescharacteristic
204#436—112no—
205C8×D4C2×D1111yescharacteristic
206C2×#107—21no—
207#417—222no—
208#335—111no—
209#334—111no—
210#333—112no—
211#332—112no—
212Q8⋊C8—111no—
213D4⋊C8—111no—
214D4⋊C8—112no—
215C82—111no—
216C22×C11—22no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11D4211yescharacteristic
223C4×C11—21no—
224C4×C11—41no—
225C4×C11—42no—
226C4×C11—82no—
227C4×C11C2×#13511yescharacteristic
228C4×C11C2×#13711yescharacteristic
229C4×C11#57611yescharacteristic
230C4×C11#57811yescharacteristic
231Dic11—41no—
232Dic11—41no—
233Dic11—82no—
234C2×#41—22no—
235C2×Q16—222no—
236C2×SD16—111no—
237C2×D8C22⋊D1111yescharacteristic
238C2×M16—222no—
239C22×C8—21no—
240C4⋊Q8—112no—
241C4⋊Q8C22×D1112yes—
242#125—222no—
243#123—42no—
244C22⋊Q8—22no—
245C22⋊Q8—222no—
246C22⋊Q8—442no—
247#121—22no—
248C4×Q8—111no—
249C4×D4—222no—
250C4×D4C22×D1111yescharacteristic
251C4×D4C22×D1112yes—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—222no—
254#107—21no—
255#107—21no—
256#107—22no—
257#107—221no—
258#107—221no—
259#107C22⋊D1111yescharacteristic
260#106—111no—
261#106—222no—
262#106—222no—
263C4⋊C8—111no—
264C4⋊C8—112no—
265C4⋊C8—221no—
266C4⋊C8C22×D1111yescharacteristic
267#103—111no—
268#103—222no—
269#103—222no—
270#103—222no—
271#103—442no—
272#102—22no—
273#102—111no—
274#102—222no—
275#102—222no—
276#102C22⋊D1112yes—
277C22⋊C8—21no—
278C22⋊C8—222no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—221no—
282C4×C8C22×D1111yescharacteristic
283C2×C11—42no—
284C2×C11—82no—
285C2×C11#327611yescharacteristic
286C2×C11#328011yescharacteristic
287C2×C11#329011yescharacteristic
288#41—44no—
289#41—82no—
290C2×Q8—22no—
291C2×Q8—111no—
292C2×Q8—222no—
293C2×D4—42no—
294C2×D4D4×D1111yescharacteristic
295C2×D4C2×C22⋊D1112yes—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—442no—
300Q16—882no—
301SD16—222no—
302D8—22no—
303M16—882no—
304C2×C8—21no—
305C2×C8—42no—
306C2×C8—111no—
307C2×C8—111no—
308C2×C8—222no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8C2×C22⋊D1111yescharacteristic
312C2×C8C2×C22⋊D1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—42no—
316C4⋊C4—111no—
317C4⋊C4—221no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—442no—
321C4⋊C4—442no—
322C4⋊C4D4×D1111yescharacteristic
323C4⋊C4C2×C22⋊D1112yes—
324C22⋊C4—22no—
325C22⋊C4—21no—
326C22⋊C4—42no—
327C22⋊C4—442no—
328C42—221no—
329C42C23×D1111yescharacteristic
330C11#1990311yescharacteristic, complemented, Sylow
331C23—21no—
332C23—22no—
333Q8—42no—
334Q8—42no—
335Q8—221no—
336Q8—221no—
337Q8—882no—
338D4—21no—
339D4—22no—
340D4—22no—
341D4—84no—
342D4#6696512yes—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—84no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—442no—
354C2×C4—1762no—
355C2×C4C2×D4×D1111yescharacteristic
356C2×C4#6703711yescharacteristic
357C2×C4C22×C22⋊D1111yescharacteristic
358C8—21no—
359C8—41no—
360C8—221no—
361C8—221no—
362C8—441no—
363C8—442no—
364C8—441no—
365C8#6700412yes—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22D4×C22⋊D1111yescharacteristic
373C4—21no—
374C4—41no—
375C4—42no—
376C4—82no—
377C4—441no—
378C4—441no—
379C4—882no—
380C4C2×#6696511yescharacteristic
381C4#1062328811yescharacteristic
382C4C2×#6700411yescharacteristic
383C4#1062336911yescharacteristic
384C2—42no—
385C2—82no—
386C2#1308025811yescharacteristic
387C2#1308030111yescharacteristic
388C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3334C2
socleC22×C11D42
hypercenter#3334D11
hypocenterC11#19903
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13081481C2semidirect
2. #13080932C2semidirect
3. #13068225C2semidirect
4. #13068189C2semidirect
5. #13068015C2semidirect
6. #13068007C2semidirect
7. #13067829C2semidirect
8. #13067767C2semidirect
9. #13067501C2semidirect
10. C8×#4324C2semidirect
330. C11#19903semidirect

Maximal subgroups

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

subgroupindex
#130814812
#130809322
#130682252
#130681892
#130680152
#130680072
#130678292
#130677672
#130675012
C8×#43242
C11×#33342
#1990311