Finite Group Databasebeta

← #14910136

Subgroups — #14910136

Order 2816.

528 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic, complemented
2#13079193C211yesmaximal, characteristic
3#13070769C211yesmaximal, characteristic, complemented
4#13070768C211yesmaximal, characteristic, complemented
5#13070751C212yesmaximal, complemented
6#13070728C212yesmaximal, complemented
7#13070726C212yesmaximal, complemented
8#13070659C212yesmaximal, complemented
9#13070653C211yesmaximal, characteristic, complemented
10#13070370C211yesmaximal, characteristic, complemented
11C11×#2207C211yesmaximal, characteristic, complemented
12#10623247—21no—
13#10623109—21no—
14C2×C11×SD32C2212yes—
15C11×#493C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17#10622801C2211yescharacteristic
18#10622794C2211yescharacteristic
19#10622770—21no—
20#10622770C2212yes—
21D8×Dic11—21no—
22D8×Dic11C2212yes—
23C2×#66891C2212yes—
24#10622683—21no—
25C4×#4326—21no—
26C2×#66862C2212yes—
27#10622500C2211yescharacteristic
28#10622487C2211yescharacteristic
29#10622426—21no—
30#10622405—21no—
31C4×Dic44C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33#10622295C2211yescharacteristic
34C11×C4⋊C16C2211yescharacteristic
35C11×#357C2212yes—
36#10622202C2212yes—
37#10622200C2212yes—
38#10622142C2212yes—
39#10622141C2212yes—
40Dic11⋊C16C2212yes—
41#10622127C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×#4341—41no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×D8—21no—
46C2×C11×D8C2312yes—
47C11×#127—21no—
48C4×Q8×C11—21no—
49#66999—21no—
50#66997—21no—
51C2×#4326—21no—
52#66991—22no—
53#66991—41no—
54#66989—41no—
55D4×Dic11—22no—
56D4×Dic11—41no—
57C2×Dic44C2311yescharacteristic
58C2×C8×D11D411yescharacteristic
59C2×C8×D11C2311yescharacteristic
60#66950—21no—
61#66949—41no—
62#66942—41no—
63#66941—21no—
64#66925—41no—
65C42×D11D411yescharacteristic
66#66922—21no—
67C4×Dic22—21no—
68C4×Dic22—41no—
69C11×SD32—42no—
70C2×C11×C16C2312yes—
71C11×#107C2311yescharacteristic
72C11×#103—21no—
73C4×C8×C11C2311yescharacteristic
74#66899—21no—
75#66896—22no—
76#66896—22no—
77#66891—42no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2312yes—
81#66880—21no—
82C8×Dic11D411yescharacteristic
83C8×Dic11C2311yescharacteristic
84C2×C11⋊C16C2312yes—
85#66874—21no—
86#66871—21no—
87C4×C11⋊C8D411yescharacteristic
88#66862—42no—
89#33820—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×C22⋊D11—42no—
95C22×Dic11—42no—
96#4341—84no—
97C2×C4×D11D811yescharacteristic
98C2×C4×D11D811yescharacteristic
99C2×C4×D11C2×D411yescharacteristic
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C11×Q16—21no—
104C11×Q16—21no—
105C11×D8—22no—
106C11×D8—22no—
107C11×D8—42no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116#4326—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134Dic44—21no—
135Dic44—21no—
136C8×D11—21no—
137C8×D11—21no—
138C8×D11—41no—
139C11×C16—22no—
140C11⋊C16—22no—
141#3170—111no—
142#3169—111no—
143#2227—111no—
144#2227—111no—
145#2224—112no—
146#2220—112no—
147#2220—112no—
148#2208—112no—
149#2207—111no—
150#2207D1111yescharacteristic, complemented
151#2150—111no—
152C23×C11—42no—
153C22×D11C2×D811yescharacteristic
154Q8×C11—41no—
155Q8×C11—41no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—82no—
159D4×C11—82no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—84no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—84no—
170C2×Dic11C2×D811yescharacteristic
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173C4×D11—21no—
174C4×D11—21no—
175C4×D11—22no—
176C4×D11—22no—
177Dic22—41no—
178Dic22—41no—
179Dic22—82no—
180Dic22—82no—
181C8×C11—21no—
182C8×C11H(5,𝔽2)11yescharacteristic
183C8×C112−1+411yescharacteristic
184C11⋊C8—21no—
185C11⋊C8—21no—
186#533—221no—
187#532—221no—
188C2×SD32—112no—
189C2×SD32C2×D1112yes—
190C2×M32—112no—
191#500—111no—
192#500—111no—
193#494—111no—
194#493C2×D1111yescharacteristic
195#487—221no—
196#486—221no—
197#467—111no—
198#467—111no—
199#467—221no—
200#466—112no—
201#466—221no—
202C4×Q16—111no—
203C4×Q16—221no—
204C4×Q16C2×D1111yescharacteristic
205C4×D8—112no—
206C4×D8—221no—
207C2×C4×C8—111no—
208#366—112no—
209#366—112no—
210C4⋊C16—112no—
211C4⋊C16—111no—
212C4⋊C16C2×D1111yescharacteristic
213#358—112no—
214#358—112no—
215#357—112no—
216#357C2×D1112yes—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11C22×D811yescharacteristic
221C2×D11—21no—
222C2×D11—21no—
223C2×D11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#51012yes—
228C4×C11#53711yescharacteristic
229C4×C11#57511yescharacteristic
230Dic11—21no—
231Dic11—21no—
232Dic11—81no—
233Dic11—82no—
234Dic11—81no—
235Dic11#50912yes—
236C2×#41—441no—
237C2×Q16—111no—
238C2×Q16—221no—
239C2×Q16C22×D1111yescharacteristic
240C2×D8—21no—
241C2×D8C22×D1112yes—
242C22×C8—111no—
243C22×C8—111no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247#127—21no—
248#125—441no—
249#124—441no—
250C22⋊Q8—221no—
251C22⋊Q8—221no—
252C22⋊Q8—441no—
253#121—222no—
254#121—441no—
255C4×Q8—21no—
256C4×Q8—221no—
257C4×Q8—441no—
258C4×D4—222no—
259C4×D4—441no—
260#117—441no—
261C2×C42—111no—
262SD32—42no—
263SD32—442no—
264M32—442no—
265C2×C16—112no—
266C2×C16C22×D1112yes—
267#107—111no—
268#107—112no—
269#107—221no—
270#107—221no—
271#107C22×D1111yescharacteristic
272#103—21no—
273#103—221no—
274#103—221no—
275#103—221no—
276#102—222no—
277#102—222no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8C22×D1111yescharacteristic
282C2×C11—162no—
283C2×C11#324511yescharacteristic
284C2×C11C2×#50911yescharacteristic
285C2×C11C2×#51011yescharacteristic
286D11—41no—
287#41—884no—
288C2×Q8—21no—
289C2×Q8—221no—
290C2×Q8—441no—
291C2×Q8—441no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—442no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—442no—
300Q16—21no—
301Q16—21no—
302Q16—221no—
303Q16—221no—
304Q16—442no—
305D8—22no—
306D8—22no—
307D8—42no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8—221no—
311C2×C8—221no—
312C2×C8—441no—
313C2×C8D4×D1111yescharacteristic
314C2×C8C23×D1111yescharacteristic
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—222no—
318C4⋊C4—221no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C42—41no—
331C42—111no—
332C42—111no—
333C42—111no—
334C42—441no—
335C42D4×D1111yescharacteristic
336C16—22no—
337C16—222no—
338C11#3382011yescharacteristic, complemented, Sylow
339C23—42no—
340C23—111no—
341Q8—41no—
342Q8—41no—
343Q8—441no—
344Q8—441no—
345Q8—882no—
346Q8—882no—
347D4—42no—
348D4—42no—
349D4—82no—
350D4—82no—
351D4—884no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—111no—
355C2×C4—111no—
356C2×C4—111no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—442no—
364C2×C4—884no—
365C2×C4D8×D1111yescharacteristic
366C2×C4D8×D1111yescharacteristic
367C2×C4C2×D4×D1111yescharacteristic
368C8—21no—
369C8—221no—
370C8—221no—
371C8#6703711yescharacteristic
372C8#6704311yescharacteristic
373C22—82no—
374C22—82no—
375C22—82no—
376C22—221no—
377C22—221no—
378C22—221no—
379C22C2×D8×D1111yescharacteristic
380C4—21no—
381C4—81no—
382C4—81no—
383C4—112no—
384C4—221no—
385C4—221no—
386C4—881no—
387C4—882no—
388C4—881no—
389C4#1062252812yes—
390C4#1062313911yescharacteristic
391C4#1062330411yescharacteristic
392C2—162no—
393C2—441no—
394C2#1307992411yescharacteristic
395C2D11×#50911yescharacteristic
396C2C2×#1062252811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radical#13079193C2
hypercenter#2207D11
hypocenterC11#33820
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13079199C2semidirect
3. #13070769C2semidirect
4. #13070768C2semidirect
5. #13070751C2semidirect
6. #13070728C2semidirect
7. #13070726C2semidirect
8. #13070659C2semidirect
9. #13070653C2semidirect
10. #13070370C2semidirect
11. C11×#2207C2semidirect
150. #2207D11semidirect
338. C11#33820semidirect

Maximal subgroups

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

subgroupindex
#130791992
#130791932
#130707692
#130707682
#130707512
#130707282
#130707262
#130706592
#130706532
#130703702
C11×#22072
#3382011