Finite Group Databasebeta

← #14656302

Subgroups — #14656302

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic
3C2×#10622696C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—21no—
10C22×#4314—21no—
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66899—21no—
16C2×(C2×D11)⋊C8—22no—
17C2×#66880—21no—
18#10622696—22no—
19#10622696—22no—
20#10622691—22no—
21#10622691—22no—
22C2×#66871—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622454—22no—
26#10622454—22no—
27C11×#332—22no—
28#10622124—22no—
29C22×Q8×C11—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—24no—
43C2×#4325—42no—
44C2×#4325—42no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8D412yes—
51C2×#4314—24no—
52C2×#4314—42no—
53C2×#4314—42no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66#66899—24no—
67(C2×D11)⋊C8—44no—
68#66880—24no—
69#66871—28no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#10264—111nomaximal, Sylow
75C23×D11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—41no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44D812yes—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—42no—
97C2×C4×D11—42no—
98C2×Dic22—22no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—42no—
108C2×C8×C11—41no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#4325—48no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8SD1614yescomplemented
132#4314—48no—
133C2×#500—111no—
134C2×#461—111no—
135C2×#461—111no—
136#1954—111no—
137C2×#332—111no—
138C2×#332D1111yescharacteristic, complemented
139#1277—111no—
140C23×C11#12111yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—42no—
144C22×D11—41no—
145C22×D11—42no—
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—81no—
149Q8×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—42no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×SD1612yes—
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13712yes—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171D44—22no—
172D44—22no—
173D44—41no—
174D44—41no—
175C4×D11—82no—
176C4×D11—81no—
177C4×D11—81no—
178Dic22—42no—
179Dic22—42no—
180Dic22—81no—
181Dic22—81no—
182C8×C11—42no—
183C8×C11—81no—
184C11⋊C8—24no—
185C11⋊C8—42no—
186C22×SD16—221no—
187C22×SD16—221no—
188C2×C4⋊Q8—111no—
189C2×C4⋊Q8C2×D1111yescharacteristic
190C2×C4×D4—111no—
191#500—222no—
192#500—222no—
193#461—222no—
194#461—222no—
195#461—222no—
196#461—222no—
197C2×#107—222no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#103—221no—
202C2×#103—221no—
203C2×C22⋊C8—222no—
204C2×C4×C8—111no—
205#332—22no—
206#332—222no—
207C22×C11#39211yescharacteristic
208C22×C11#46112yes—
209C22×C11#46611yescharacteristic
210C22×C11#46911yescharacteristic
211C22×C11#47312yes—
212C2×D11—44no—
213C2×D11—42no—
214C2×D11—82no—
215C2×D11—81no—
216C2×D11—81no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—82no—
220C4×C11#44711yescharacteristic
221C4×C11#44711yescharacteristic
222C4×C11#44812yes—
223C4×C11#44911yescharacteristic
224C4×C11#44911yescharacteristic
225C4×C11#49211yescharacteristic
226C4×C11#49711yescharacteristic
227Dic11—82no—
228Dic11—81no—
229C22×Q8—21no—
230C22×Q8—221no—
231C22×D4—111no—
232C23×C4—221no—
233C2×SD16—224no—
234C2×SD16—224no—
235C2×SD16—442no—
236C2×SD16—442no—
237C2×SD16—442no—
238C2×SD16—442no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—112no—
242C22×C8—221no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—112no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8D4412yes—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—221no—
254C4×D4—221no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C42C22×D1111yescharacteristic
262#107—228no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8C22⋊D1112yes—
269#103—224no—
270#103—224no—
271C22⋊C8—444no—
272C4×C8—221no—
273C4×C8—221no—
274C2×C11#167312yes—
275C2×C11#169312yes—
276C2×C11#199911yescharacteristic
277C2×C11#201311yescharacteristic
278C2×C11#202011yescharacteristic
279D11—82no—
280C24—221no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—222no—
288C2×Q8—441no—
289C2×Q8—441no—
290C2×Q8—441no—
291C2×Q8—441no—
292C2×Q8—441no—
293C2×D4—112no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C22×C4—41no—
300C22×C4—221no—
301C22×C4—441no—
302C22×C4—441no—
303C22×C4—442no—
304C22×C4—442no—
305C22×C4—441no—
306C22×C4#433911yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309SD16—448no—
310SD16—448no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—42no—
315C2×C8—41no—
316C2×C8—114no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—441no—
321C2×C8—441no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—221no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C42C2×D4411yescharacteristic
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C11#1026411yescharacteristic, complemented, Sylow
339C23—222no—
340C23—441no—
341C23—442no—
342C23—441no—
343C23—442no—
344C23#6693711yescharacteristic
345Q8—42no—
346Q8—42no—
347Q8—81no—
348Q8—81no—
349Q8—442no—
350Q8—442no—
351Q8—881no—
352Q8—881no—
353D4—222no—
354D4—222no—
355D4—441no—
356D4—441no—
357C2×C4—22no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4—881no—
368C2×C4—882no—
369C2×C4#6693511yescharacteristic
370C2×C4#6693511yescharacteristic
371C2×C4#6693711yescharacteristic
372C2×C4D8×D1111yescharacteristic
373C2×C4#6696411yescharacteristic
374C2×C4SD16×D1112yes—
375C2×C4#6696711yescharacteristic
376C2×C4#6696911yescharacteristic
377C2×C4#6697112yes—
378C2×C4#6698311yescharacteristic
379C2×C4#6699011yescharacteristic
380C2×C4#6699311yescharacteristic
381C8—42no—
382C8—81no—
383C8—224no—
384C8—442no—
385C22—442no—
386C22—444no—
387C22—882no—
388C22—881no—
389C22—881no—
390C22#1062236812yes—
391C22#1062238811yescharacteristic
392C22#1062239511yescharacteristic
393C22#1062243112yes—
394C22#1062257311yescharacteristic
395C4—21no—
396C4—21no—
397C4—82no—
398C4—882no—
399C4—881no—
400C4#1062238611yescharacteristic
401C4#1062239411yescharacteristic
402C4#1062241912yes—
403C4#1062276911yescharacteristic
404C4#1062278511yescharacteristic
405C4#1062278811yescharacteristic
406C4#1062280311yescharacteristic
407C2—882no—
408C2#1306800412yes—
409C2#1306812812yes—
410C2#1306961311yescharacteristic
411C2#1306970011yescharacteristic
412C2#1306973611yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11#10264
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
5. C2×#10622124C2semidirect
6. #13066450C2semidirect
7. C2×C11×#332C2semidirect
131. C2×C11⋊C8SD16semidirect
138. C2×#332D11semidirect
338. C11#10264semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106224542
C2×#106226962
#130694092
C2×#106221242
#130664502
C2×C11×#3322
#1026411