Finite Group Databasebeta

← #14745621

Subgroups — #14745621

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081511C212yesmaximal
2#13081010C211yesmaximal, characteristic, complemented
3#13068210C211yesmaximal, characteristic, complemented
4#13068120C212yesmaximal, complemented
5#13068015C211yesmaximal, characteristic, complemented
6#13067978C211yesmaximal, characteristic, complemented
7#13067828C212yesmaximal, complemented
8#13067781C212yesmaximal, complemented
9#13067513C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic
11D4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16—21no—
13D4×Q8×C11C2212yes—
14#10623110C2212yes—
15C11×#494C2211yescharacteristic
16C11×#467—21no—
17C11×#462C2212yes—
18C11×#451—22no—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622801—21no—
22#10622706C2212yes—
23#10622700C2212yes—
24#10622697—22no—
25#10622693—22no—
26#10622692C2212yes—
27#10622637C2212yes—
28#10622634C2212yes—
29#10622627—22no—
30C4×#4323C2211yescharacteristic
31#10622622—22no—
32#10622621C2212yes—
33D11×#107—21no—
34#10622422—22no—
35C8×D44C2211yescharacteristic
36#10622295C2211yescharacteristic
37#10622185C2212yes—
38Q8⋊(C11⋊C8)C2212yes—
39D4⋊(C11⋊C8)C2211yescharacteristic
40#10622121C2211yescharacteristic
41#10622119C2212yes—
42#10622117C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C22×Q8×C11—22no—
46C2×C11×Q16—22no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—44no—
50C2×C11×Q16D411yescharacteristic
51C22×C8×C11—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2312yes—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—42no—
56C4×Q8×C11C2312yes—
57C4×D4×C11—22no—
58C4×D4×C11C2311yescharacteristic
59#66999—22no—
60C2×#4323D411yescharacteristic
61C2×C8×D11—21no—
62#66949—42no—
63C4⋊C4×D11—22no—
64C4×D44—22no—
65C4×D44C2311yescharacteristic
66#66923—22no—
67#66922C2312yes—
68C11×#107D411yescharacteristic
69C11×C4⋊C8C2311yescharacteristic
70C11×#103—22no—
71C11×#103D412yes—
72C11×C22⋊C8—21no—
73C4×C8×C11C2311yescharacteristic
74#66899—22no—
75#66896—22no—
76#66896D411yescharacteristic
77(C2×D11)⋊C8—21no—
78#66882—21no—
79#66882—21no—
80#66874—42no—
81#66873—22no—
82#66873D411yescharacteristic
83#66872—22no—
84#66872—22no—
85#66872—22no—
86#66871—22no—
87#66871—22no—
88#66871D411yescharacteristic
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)C2311yescharacteristic
91C4⋊(C11⋊C8)C2312yes—
92#66867—22no—
93C4×C11⋊C8C2311yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95#19926—111nomaximal, Sylow
96C2×Q8×C11—22no—
97C2×Q8×C11—42no—
98C2×Q8×C11—44no—
99C2×Q8×C11—82no—
100C2×Q8×C11C2×D412yes—
101C2×D4×C11C2×D411yescharacteristic
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C2×D44C2×D411yescharacteristic
105C2×C4×D11—21no—
106C2×C4×D11—42no—
107C2×Dic22—22no—
108C11×Q16—22no—
109C11×Q16—44no—
110C11×Q16—42no—
111C11×Q16—81no—
112C2×C8×C11—21no—
113C2×C8×C11—42no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4C2×D411yescharacteristic
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—42no—
124C42×C11—22no—
125C42×C11C2411yescharacteristic
126#4323Q1614yescomplemented
127(C2×D11)⋊C4—21no—
128(C2×D11)⋊C4—42no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11C2×D411yescharacteristic
132Dic11⋊C4—42no—
133Dic11⋊C4—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139C8×D11—42no—
140#3384—112no—
141#3338—111no—
142D4×Q16D1111yescharacteristic, complemented
143#1707—111no—
144#1692—112no—
145#1675—111no—
146#1669—111no—
147#1644—112no—
148#1637—112no—
149#1591—111no—
150C8×D8—111no—
151C23×C11—21no—
152C22×D11—21no—
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—84no—
158D4×C11—21no—
159D4×C11C2×Q1612yes—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—84no—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11H(5,𝔽2)11yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—42no—
172D44—21no—
173D44C2×Q1612yescomplemented
174C4×D11—41no—
175C4×D11—41no—
176C4×D11—162no—
177Dic22—82no—
178C8×C11—21no—
179C8×C11—41no—
180C8×C11AGL(1,ℤ/8)12yes—
181C11⋊C8—21no—
182C11⋊C8—41no—
183C11⋊C8—41no—
184C11⋊C8—42no—
185C11⋊C8C2×Q1612yescomplemented
186C22×Q16—21no—
187#554—112no—
188D4×Q8C2×D1112yes—
189#501—222no—
190#500—111no—
191#498—112no—
192#494C2×D1111yescharacteristic
193#487—112no—
194#484—222no—
195#478—222no—
196#477—112no—
197#476—112no—
198#476—222no—
199#474—112no—
200#467—21no—
201#467—221no—
202#462C2×D1112yes—
203#451—22no—
204#446—112no—
205#442—222no—
206C4×Q16C2×D1111yescharacteristic
207C4×D8—111no—
208C8×D4—111no—
209C8×D4C2×D1111yescharacteristic
210C2×#107—221no—
211#335—111no—
212#335—111no—
213#333—112no—
214#332—112no—
215Q8⋊C8—112no—
216D4⋊C8—111no—
217D4⋊C8—111no—
218C82—111no—
219C22×C11—22no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11D4211yescharacteristic
223C2×D11—22no—
224C2×D11—41no—
225C2×D11—41no—
226C4×C11—21no—
227C4×C11—41no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11—82no—
231C4×C11C22×Q1611yescharacteristic
232C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C11#57711yescharacteristic
234C4×C11#57811yescharacteristic
235Dic11—41no—
236Dic11—82no—
237C22×Q8—22no—
238C2×Q16—22no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—44no—
242C2×Q16C22⋊D1111yescharacteristic
243C2×D8—111no—
244C22×C8—21no—
245C22×C8—221no—
246C4⋊Q8—22no—
247C4⋊Q8—112no—
248C4⋊Q8C22×D1112yes—
249#125—222no—
250C22⋊Q8—22no—
251C22⋊Q8—42no—
252C22⋊Q8—222no—
253C22⋊Q8—442no—
254C4×Q8C22×D1112yes—
255C4×D4—22no—
256C4×D4—111no—
257C4×D4—222no—
258C4×D4C22×D1111yescharacteristic
259C2×C4⋊C4—222no—
260#107—111no—
261#107—222no—
262#107—221no—
263#107—221no—
264#107—222no—
265#107C22⋊D1111yescharacteristic
266#106—222no—
267#106—222no—
268#106—222no—
269C4⋊C8—111no—
270C4⋊C8—112no—
271C4⋊C8—222no—
272C4⋊C8C22×D1111yescharacteristic
273#103—22no—
274#103—222no—
275#103—442no—
276#103C22⋊D1112yes—
277#102—111no—
278#102—111no—
279#102—222no—
280#102—222no—
281C22⋊C8—21no—
282C22⋊C8—221no—
283#97—222no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8C22×D1111yescharacteristic
287C2×C11—42no—
288C2×C11#327211yescharacteristic
289C2×C11D4×Q1611yescharacteristic
290C2×C11#329011yescharacteristic
291D11—42no—
292C2×Q8—22no—
293C2×Q8—42no—
294C2×Q8—44no—
295C2×Q8—82no—
296C2×Q8—222no—
297C2×Q8C2×C22⋊D1112yes—
298C2×D4—111no—
299C2×D4D4×D1111yescharacteristic
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—221no—
303C22×C4—442no—
304Q16—22no—
305Q16—44no—
306Q16—42no—
307Q16—81no—
308D8—114no—
309C2×C8—21no—
310C2×C8—42no—
311C2×C8—111no—
312C2×C8—111no—
313C2×C8—222no—
314C2×C8—221no—
315C2×C8—221no—
316C2×C8—442no—
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—42no—
323C4⋊C4—111no—
324C4⋊C4—222no—
325C4⋊C4—222no—
326C4⋊C4—442no—
327C4⋊C4—442no—
328C4⋊C4D4×D1111yescharacteristic
329C4⋊C4C2×C22⋊D1112yes—
330C22⋊C4—21no—
331C22⋊C4—42no—
332C22⋊C4—221no—
333C22⋊C4—442no—
334C42—22no—
335C42C23×D1111yescharacteristic
336C11#1992611yescharacteristic, complemented, Sylow
337C23—21no—
338C23—221no—
339Q8—22no—
340Q8—22no—
341Q8—42no—
342Q8—42no—
343Q8—84no—
344Q8—882no—
345D4—21no—
346D4—112no—
347D4—221no—
348D4Q16×D1112yes—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—221no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—1762no—
361C2×C4C2×D4×D1111yescharacteristic
362C2×C4#6703711yescharacteristic
363C2×C4C22×C22⋊D1111yescharacteristic
364C8—21no—
365C8—41no—
366C8—112no—
367C8—221no—
368C8—441no—
369C8—442no—
370C8—441no—
371C8#6698512yes—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—222no—
376C22—441no—
377C22—441no—
378C22D4×C22⋊D1111yescharacteristic
379C4—21no—
380C4—42no—
381C4—41no—
382C4—42no—
383C4—82no—
384C4—441no—
385C4—882no—
386C4C2×Q16×D1111yescharacteristic
387C4#1062329711yescharacteristic
388C4C2×#6698511yescharacteristic
389C4#1062336711yescharacteristic
390C2—42no—
391C2—442no—
392C2#1308021211yescharacteristic
393C2Q16×C22⋊D1111yescharacteristic
394C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×Q16C2
socleC22×C11D42
prime radicalC2×#4323D4
hypercenterD4×Q16D11
hypocenterC11#19926
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
2. #13081010C2semidirect
3. #13068210C2semidirect
4. #13068120C2semidirect
5. #13068015C2semidirect
6. #13067978C2semidirect
7. #13067828C2semidirect
8. #13067781C2semidirect
9. #13067513C2semidirect
11. D4×C11×Q16C2semidirect
126. #4323Q16semidirect
142. D4×Q16D11semidirect
173. D44C2×Q16semidirect
185. C11⋊C8C2×Q16semidirect
336. C11#19926semidirect

Maximal subgroups

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

subgroupindex
#130815112
#130810102
#130682102
#130681202
#130680152
#130679782
#130678282
#130677812
#130675132
C8×#43232
D4×C11×Q162
#1992611