Finite Group Databasebeta

← #14745322

Subgroups — #14745322

Order 2816.

604 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#13081040C211yesmaximal, characteristic
2#13080910C212yesmaximal, complemented
3#13068225C211yesmaximal, characteristic, complemented
4#13068189C212yesmaximal, complemented
5#13068020C211yesmaximal, characteristic, complemented
6#13068002C211yesmaximal, characteristic, complemented
7#13067843C212yesmaximal, complemented
8#13067781C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11Q8×C11×D8C211yesmaximal, characteristic, complemented
12D4×Q8×C11C2212yes—
13#10623094C2212yes—
14C11×#500—21no—
15C11×#500C2211yescharacteristic
16C11×#474—22no—
17C11×#474C2212yes—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8—21no—
20C4×C11×D8C2211yescharacteristic
21#10622840—22no—
22#10622838—22no—
23#10622770—21no—
24#10622706C2212yes—
25#10622696C2212yes—
26#10622694C2212yes—
27#10622662—22no—
28#10622658—22no—
29C4×#4325C2211yescharacteristic
30#10622634C2212yes—
31#10622625C2212yes—
32#10622621C2212yes—
33#10622493—21no—
34#10622397—22no—
35C8×D44C2211yescharacteristic
36#10622295C2211yescharacteristic
37#10622185C2212yes—
38Q8⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2212yes—
40#10622121C2211yescharacteristic
41#10622119C2212yes—
42#10622118C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C22×Q8×C11—22no—
46C2×C11×D8D411yescharacteristic
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2312yes—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—42no—
51C4×Q8×C11C2311yescharacteristic
52C4×D4×C11—22no—
53C4×D4×C11C2312yes—
54C2×#4325—22no—
55C2×#4325D411yescharacteristic
56#66991—22no—
57#66983—22no—
58#66979—22no—
59C2×#4318—22no—
60C2×C8×D11—21no—
61#66945—22no—
62#66938—42no—
63C4×D44C2311yescharacteristic
64#66922C2312yes—
65C11×#107—21no—
66C11×#107—21no—
67C11×#107—22no—
68C11×#107D411yescharacteristic
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2311yescharacteristic
71C11×#102—22no—
72C11×#102D412yes—
73C4×C8×C11—21no—
74C4×C8×C11C2311yescharacteristic
75#66899—22no—
76#66899—22no—
77#66899—22no—
78#66899—22no—
79#66899D411yescharacteristic
80#66896—22no—
81C22⋊(C11⋊C8)—22no—
82(C2×D11)⋊C8—21no—
83#66882—21no—
84#66882—21no—
85#66874—42no—
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#19905—111nomaximal, Sylow
95C2×Q8×C11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11—44no—
98C2×Q8×C11—82no—
99C2×Q8×C11C2×D411yescharacteristic
100C2×D4×C11C2×D412yes—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C2×C22⋊D11—42no—
104C2×D44C2×D411yescharacteristic
105C2×C4×D11—21no—
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⋊C4C2×D411yescharacteristic
116C11×C4⋊C4C2×D412yes—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—42no—
119C42×C11—21no—
120C42×C11C2411yescharacteristic
121C22⋊Dic11—42no—
122#4325—22no—
123#4325—82no—
124(C2×D11)⋊C4—21no—
125(C2×D11)⋊C4—42no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11C2×D411yescharacteristic
129C4×Dic11—42no—
130#4318—82no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136C8×D11—42no—
137Q8×D8D1111yescharacteristic, complemented
138#3341—111no—
139#3329—112no—
140#1710—111no—
141#1703—112no—
142#1676—111no—
143#1673—111no—
144#1646—112no—
145#1637—112no—
146#1589—111no—
147C8×SD16—111no—
148C23×C11—22no—
149C22×D11—21no—
150Q8×C11—21no—
151Q8×C11—42no—
152Q8×C11—42no—
153Q8×C11—84no—
154Q8×C11#13512yes—
155D4×C11—22no—
156D4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—84no—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11H(5,𝔽2)11yescharacteristic
167C22⋊D11—162no—
168C2×Dic11—21no—
169C2×Dic11—42no—
170D44—21no—
171D44—21no—
172C4×D11—41no—
173C4×D11—41no—
174Dic22—82no—
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#555—112no—
184D4×Q8C2×D1112yes—
185#500—21no—
186#500—111no—
187#500C2×D1111yescharacteristic
188#487—112no—
189#487—112no—
190#485—222no—
191#482—222no—
192#477—112no—
193#476—112no—
194#474—22no—
195#474C2×D1112yes—
196#468—222no—
197#466—221no—
198#461—112no—
199#448—222no—
200C8×Q8C2×D1111yescharacteristic
201C4×SD16—111no—
202C4×D8—21no—
203C4×D8C2×D1111yescharacteristic
204#436—112no—
205C8×D4—111no—
206#427—221no—
207#419—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—41no—
221C2×D11—41no—
222C2×D11—41no—
223C4×C11—22no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11—41no—
227C4×C11—82no—
228C4×C11C2×#13511yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C4×C11#57611yescharacteristic
231C4×C11#57811yescharacteristic
232Dic11—41no—
233Dic11—82no—
234C22×Q8—22no—
235C2×SD16—111no—
236C2×SD16—222no—
237C2×D8C22⋊D1111yescharacteristic
238C2×M16—222no—
239C22×C8—221no—
240C4⋊Q8—22no—
241C4⋊Q8—112no—
242C4⋊Q8C22×D1112yes—
243#124—442no—
244C22⋊Q8—22no—
245C22⋊Q8—42no—
246#121—222no—
247#121—222no—
248C4×Q8C22×D1111yescharacteristic
249C4×D4—22no—
250C4×D4—111no—
251C4×D4C22×D1112yes—
252#117—222no—
253#117—222no—
254#107—21no—
255#107—21no—
256#107—22no—
257#107—221no—
258#107—221no—
259#107—222no—
260#107C22⋊D1111yescharacteristic
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—222no—
272#103—442no—
273#102—22no—
274#102—111no—
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—81no—
288C2×Q8—22no—
289C2×Q8—42no—
290C2×Q8—44no—
291C2×Q8—82no—
292C2×Q8—222no—
293C2×Q8D4×D1111yescharacteristic
294C2×D4—111no—
295C2×D4—442no—
296C2×D4C2×C22⋊D1112yes—
297C22×C4—22no—
298C22×C4—42no—
299C22×C4—221no—
300SD16—222no—
301SD16—882no—
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—111no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4D4×D1111yescharacteristic
321C4⋊C4C2×C22⋊D1112yes—
322C22⋊C4—22no—
323C22⋊C4—42no—
324C22⋊C4—221no—
325C22⋊C4—442no—
326C22⋊C4—442no—
327C42—21no—
328C42—442no—
329C42C23×D1111yescharacteristic
330C11#1990511yescharacteristic, complemented, Sylow
331C23—22no—
332C23—221no—
333Q8—21no—
334Q8—42no—
335Q8—42no—
336Q8—84no—
337Q8—882no—
338Q8#6696512yes—
339D4—22no—
340D4—22no—
341D4—221no—
342D4—221no—
343D4—1762no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—84no—
351C2×C4—221no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—442no—
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—441no—
370C22—441no—
371C22—441no—
372C22D4×C22⋊D1111yescharacteristic
373C4—21no—
374C4—22no—
375C4—41no—
376C4—42no—
377C4—82no—
378C4—441no—
379C4—882no—
380C4C2×#6696511yescharacteristic
381C4#1062328811yescharacteristic
382C4C2×#6699511yescharacteristic
383C4#1062336911yescharacteristic
384C2—82no—
385C2—881no—
386C2#1308026211yescharacteristic
387C2#1308030111yescharacteristic
388C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×D8C2
socleC22×C11D42
prime radical#13081040C2
hypercenterQ8×D8D11
hypocenterC11#19905
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
2. #13080910C2semidirect
3. #13068225C2semidirect
4. #13068189C2semidirect
5. #13068020C2semidirect
6. #13068002C2semidirect
7. #13067843C2semidirect
8. #13067781C2semidirect
9. #13067501C2semidirect
10. C8×#4325C2semidirect
11. Q8×C11×D8C2semidirect
137. Q8×D8D11semidirect
330. C11#19905semidirect

Maximal subgroups

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

subgroupindex
#130810402
#130809102
#130682252
#130681892
#130680202
#130680022
#130678432
#130677812
#130675012
C8×#43252
Q8×C11×D82
#1990511