Finite Group Databasebeta

← #14745300

Subgroups — #14745300

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#13080965C211yesmaximal, characteristic
2#13080926C212yesmaximal, complemented
3#13068225C211yesmaximal, characteristic, complemented
4#13068193C212yesmaximal, complemented
5#13068012C211yesmaximal, characteristic, complemented
6#13068010C211yesmaximal, characteristic, complemented
7#13067830C212yesmaximal, complemented
8#13067766C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11C11×#3380C211yesmaximal, characteristic, complemented
12C11×#554C2212yes—
13#10623082C2212yes—
14C11×#500C2211yescharacteristic
15C11×#499—21no—
16C11×#478—22no—
17C11×#476C2212yes—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8—21no—
20C4×C11×D8C2211yescharacteristic
21#10622770—21no—
22#10622706C2212yes—
23#10622697C2212yes—
24#10622694C2212yes—
25#10622665—22no—
26#10622660—22no—
27#10622644C2212yes—
28C4×#4325C2211yescharacteristic
29#10622625C2212yes—
30#10622620C2212yes—
31#10622584—22no—
32#10622579—22no—
33D11×#107—21no—
34#10622387—22no—
35C8×D44C2211yescharacteristic
36#10622295C2211yescharacteristic
37#10622184C2212yes—
38Q8⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2212yes—
40#10622124C2212yes—
41#10622121C2211yescharacteristic
42#10622118C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×#4339—22no—
46C2×C11×D8D411yescharacteristic
47C11×C4⋊Q8C2312yes—
48C11×#125—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—42no—
51C4×Q8×C11C2311yescharacteristic
52C4×D4×C11—22no—
53C4×D4×C11C2312yes—
54C2×C11×C4⋊C4—22no—
55C2×#4326—22no—
56C2×#4325D411yescharacteristic
57#66991—22no—
58#66977—22no—
59C2×#4318—22no—
60C2×C8×D11—21no—
61C4⋊C4×D11—22no—
62#66936—42no—
63C4×D44C2311yescharacteristic
64#66922C2312yes—
65C11×#107—21no—
66C11×#107—21no—
67C11×#107D411yescharacteristic
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2311yescharacteristic
71C11×#102—22no—
72C11×#102D412yes—
73C4×C8×C11—21no—
74C4×C8×C11C2311yescharacteristic
75#66899—42no—
76#66899D411yescharacteristic
77#66896—22no—
78C22⋊(C11⋊C8)—22no—
79(C2×D11)⋊C8—21no—
80#66882—21no—
81#66882—21no—
82#66874—22no—
83#66874—22no—
84#66874—22no—
85#66873—22no—
86#66873D411yescharacteristic
87#66872—22no—
88#66872D411yescharacteristic
89#66871—22no—
90C4⋊(C11⋊C8)C2311yescharacteristic
91C4⋊(C11⋊C8)C2312yes—
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#19903—111nomaximal, Sylow
95C2×Q8×C11—22no—
96C2×Q8×C11C2×D411yescharacteristic
97C2×D4×C11C2×D412yes—
98C22×C4×C11—22no—
99C22×C4×C11—42no—
100C2×C22⋊D11—42no—
101#4339—44no—
102#4339—82no—
103C2×D44C2×D411yescharacteristic
104C2×C4×D11—21no—
105C2×C4×D11—42no—
106C2×Dic22—22no—
107C11×D8—22no—
108C2×C8×C11—21no—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4C2×D411yescharacteristic
117C11×C4⋊C4C2×D412yes—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—42no—
120C42×C11—21no—
121C42×C11C2411yescharacteristic
122C22⋊Dic11—42no—
123#4326—82no—
124#4325—22no—
125(C2×D11)⋊C4—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11C2×D411yescharacteristic
129Dic11⋊C4—42no—
130#4318—82no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136C8×D11—42no—
137#3380D1111yescharacteristic, complemented
138#3334—111no—
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—22no—
149C22×D11—21no—
150Q8×C11—21no—
151Q8×C11—21no—
152Q8×C11—82no—
153D4×C11—22no—
154D4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—162no—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11H(5,𝔽2)11yescharacteristic
165C22⋊D11—84no—
166C2×Dic11—21no—
167C2×Dic11—42no—
168D44—21no—
169D44#13512yes—
170C4×D11—41no—
171C4×D11—41no—
172C4×D11—84no—
173Dic22—42no—
174Dic22—42no—
175C8×C11—21no—
176C8×C11—41no—
177C8×C11#13712yes—
178C11⋊C8—21no—
179C11⋊C8—21no—
180C11⋊C8—41no—
181C11⋊C8—41no—
182C11⋊C8—42no—
183#554C2×D1112yes—
184#547—112no—
185#500—111no—
186#500C2×D1111yescharacteristic
187#499—21no—
188#487—112no—
189#487—112no—
190#483—222no—
191#480—222no—
192#478—22no—
193#476—112no—
194#476C2×D1112yes—
195#474—112no—
196#470—222no—
197#466—221no—
198#462—112no—
199#452—222no—
200C8×Q8C2×D1111yescharacteristic
201C4×SD16—111no—
202C4×D8—21no—
203C4×D8C2×D1111yescharacteristic
204#436—112no—
205C8×D4—111no—
206C2×#107—221no—
207#417—222no—
208#335—111no—
209#334—111no—
210#333—112no—
211#332—112no—
212Q8⋊C8—111no—
213D4⋊C8—112no—
214D4⋊C8—111no—
215C82—111no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11D4211yescharacteristic
220C2×D11—22no—
221C2×D11—41no—
222C2×D11—41no—
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—82no—
228C4×C11C2×#13511yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C4×C11#57611yescharacteristic
231C4×C11#57811yescharacteristic
232Dic11—41no—
233Dic11—82no—
234C2×#41—222no—
235C2×Q16—222no—
236C2×SD16—111no—
237C2×D8C22⋊D1111yescharacteristic
238C2×M16—222no—
239C22×C8—221no—
240C4⋊Q8—112no—
241C4⋊Q8C22×D1112yes—
242#125—22no—
243#123—442no—
244C22⋊Q8—22no—
245C22⋊Q8—42no—
246C22⋊Q8—222no—
247#121—222no—
248C4×Q8C22×D1111yescharacteristic
249C4×D4—22no—
250C4×D4—111no—
251C4×D4C22×D1112yes—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—222no—
254#107—21no—
255#107—21no—
256#107—221no—
257#107—221no—
258#107—222no—
259#107C22⋊D1111yescharacteristic
260#106—22no—
261#106—111no—
262#106—222no—
263C4⋊C8—21no—
264C4⋊C8—112no—
265C4⋊C8—111no—
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—222no—
278C22⋊C8—221no—
279C4×C8—21no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8C22×D1111yescharacteristic
283C2×C11—82no—
284C2×C11#327611yescharacteristic
285C2×C11#328011yescharacteristic
286C2×C11#329011yescharacteristic
287D11—42no—
288#41—444no—
289#41—882no—
290C2×Q8—22no—
291C2×Q8—222no—
292C2×Q8D4×D1111yescharacteristic
293C2×D4—111no—
294C2×D4—442no—
295C2×D4C2×C22⋊D1112yes—
296C22×C4—22no—
297C22×C4—42no—
298C22×C4—221no—
299C22×C4—442no—
300Q16—882no—
301SD16—222no—
302D8—22no—
303M16—882no—
304C2×C8—21no—
305C2×C8—111no—
306C2×C8—111no—
307C2×C8—222no—
308C2×C8—221no—
309C2×C8—221no—
310C2×C8—442no—
311C2×C8C2×C22⋊D1111yescharacteristic
312C2×C8C2×C22⋊D1111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—111no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—442no—
322C4⋊C4D4×D1111yescharacteristic
323C4⋊C4C2×C22⋊D1112yes—
324C22⋊C4—22no—
325C22⋊C4—42no—
326C22⋊C4—221no—
327C22⋊C4—442no—
328C42—21no—
329C42C23×D1111yescharacteristic
330C11#1990311yescharacteristic, complemented, Sylow
331C23—22no—
332C23—221no—
333Q8—21no—
334Q8—21no—
335Q8—82no—
336Q8—442no—
337Q8—442no—
338D4—22no—
339D4—22no—
340D4—112no—
341D4—221no—
342D4—884no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—162no—
350C2×C4—221no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—442no—
354C2×C4—884no—
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#6699512yes—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—222no—
370C22—441no—
371C22—441no—
372C22D4×C22⋊D1111yescharacteristic
373C4—21no—
374C4—41no—
375C4—42no—
376C4—41no—
377C4—82no—
378C4—441no—
379C4—882no—
380C4D11×#13511yescharacteristic
381C4#1062330011yescharacteristic
382C4C2×#6699511yescharacteristic
383C4#1062336911yescharacteristic
384C2—82no—
385C2—442no—
386C2#1308026211yescharacteristic
387C2#1308029511yescharacteristic
388C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3380C2
socleC22×C11D42
prime radical#13080965C2
hypercenter#3380D11
hypocenterC11#19903
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3380

Complements

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

NH ≅ G/Ntype
2. #13080926C2semidirect
3. #13068225C2semidirect
4. #13068193C2semidirect
5. #13068012C2semidirect
6. #13068010C2semidirect
7. #13067830C2semidirect
8. #13067766C2semidirect
9. #13067501C2semidirect
10. C8×#4325C2semidirect
11. C11×#3380C2semidirect
137. #3380D11semidirect
330. C11#19903semidirect

Maximal subgroups

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

subgroupindex
#130809652
#130809262
#130682252
#130681932
#130680122
#130680102
#130678302
#130677662
#130675012
C8×#43252
C11×#33802
#1990311