Finite Group Databasebeta

← #14656295

Subgroups — #14656295

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622703C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic
4#13069551C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—21no—
10C22×#4314—21no—
11C2×#66927C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66899—21no—
16C2×#66885—21no—
17#10622703—22no—
18#10622703—22no—
19#10622701—22no—
20#10622701—22no—
21C2×#66873—22no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622461—22no—
25#10622461—22no—
26C11×#332—22no—
27#10622188—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4326—24no—
44C2×#4326—42no—
45C2×#4326—42no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8D412yes—
51C2×#4314—24no—
52C2×#4314—42no—
53C2×#4314—42no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927D412yes—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66#66899—24no—
67#66885—24no—
68#66873—28no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#10263—111nomaximal, Sylow
74C23×D11—41no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—42no—
99C2×D44—82no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22D812yes—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—42no—
110C2×C8×C11—41no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119#4326—48no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#4314—48no—
133C2×#486—111no—
134C2×#462—111no—
135C2×#460—111no—
136#1984—111no—
137C2×#332D1111yescharacteristic, complemented
138C2×#331—111no—
139#1277—111no—
140C23×C11#12111yescharacteristic
141C22×D11—42no—
142C22×D11—82no—
143C22×D11—81no—
144C22×D11—81no—
145C22×D11—82no—
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×C11#13511yescharacteristic
162C2×C4×C11#13512yes—
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13712yes—
166C2×Dic11—22no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171D44—42no—
172D44—42no—
173D44—44no—
174D44—82no—
175D44—82no—
176D44—81no—
177D44—81no—
178D44—81no—
179D44—81no—
180Dic22—22no—
181Dic22—22no—
182Dic22—41no—
183Dic22—41no—
184C8×C11—42no—
185C8×C11—81no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188C22×Q16—221no—
189C22×SD16—221no—
190C2×C4⋊Q8C2×D1111yescharacteristic
191C2×#127—111no—
192C2×C4×Q8—111no—
193#486—222no—
194#486—222no—
195#462—222no—
196#462—222no—
197#460—222no—
198#460—222no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×C4⋊C8C2×D1111yescharacteristic
202C2×#103—221no—
203C2×#102—222no—
204C2×#102—221no—
205C2×C4×C8—111no—
206#336—222no—
207#332—22no—
208#331—222no—
209C22×C11#39211yescharacteristic
210C22×C11#46412yes—
211C22×C11#46611yescharacteristic
212C22×C11#46911yescharacteristic
213C22×C11#47112yes—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—162no—
218C2×D11—162no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11#44711yescharacteristic
223C4×C11#44711yescharacteristic
224C4×C11#44911yescharacteristic
225C4×C11#44911yescharacteristic
226C4×C11#45212yes—
227C4×C11#49511yescharacteristic
228C4×C11#49711yescharacteristic
229Dic11—42no—
230Dic11—81no—
231C22×Q8—21no—
232C22×Q8—111no—
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×Q16—224no—
237C2×Q16—442no—
238C2×Q16—442no—
239C2×SD16—224no—
240C2×SD16—442no—
241C2×SD16—442no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—112no—
245C22×C8—221no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8D4412yes—
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×Q8—221no—
257C4×Q8—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—221no—
262C2×C42—221no—
263C2×C42C22×D1111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270#103—224no—
271#102—228no—
272#102—224no—
273C4×C8—221no—
274C4×C8—221no—
275C2×C11#168212yes—
276C2×C11#170212yes—
277C2×C11#199911yescharacteristic
278C2×C11#201511yescharacteristic
279C2×C11#201911yescharacteristic
280D11—162no—
281C24—441no—
282C2×Q8—22no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—112no—
289C2×Q8—221no—
290C2×Q8—221no—
291C2×Q8—221no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—442no—
302C2×D4—441no—
303C2×D4—442no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—882no—
307C22×C4—41no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4#433911yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313Q16—448no—
314SD16—448no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—441no—
325C2×C8—441no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C42—441no—
335C42—441no—
336C42C2×D4411yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C11#1026311yescharacteristic, complemented, Sylow
341C23—442no—
342C23—882no—
343C23—881no—
344C23—881no—
345C23—882no—
346C23#6693711yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—81no—
350Q8—81no—
351Q8—222no—
352Q8—222no—
353Q8—441no—
354Q8—441no—
355D4—442no—
356D4—442no—
357D4—444no—
358D4—882no—
359D4—882no—
360D4—881no—
361D4—881no—
362D4—881no—
363D4—881no—
364C2×C4—22no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—222no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—442no—
373C2×C4#6693511yescharacteristic
374C2×C4#6693511yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4D8×D1111yescharacteristic
377C2×C4#6696411yescharacteristic
378C2×C4#6696711yescharacteristic
379C2×C4#6696912yes—
380C2×C4#6696911yescharacteristic
381C2×C4#6697112yes—
382C2×C4#6698311yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699311yescharacteristic
385C8—42no—
386C8—81no—
387C8—442no—
388C8—442no—
389C22—882no—
390C22—882no—
391C22—882no—
392C22—1762no—
393C22—1762no—
394C22#1062236712yes—
395C22#1062238811yescharacteristic
396C22#1062239511yescharacteristic
397C22#1062241112yes—
398C22#1062257311yescharacteristic
399C4—21no—
400C4—21no—
401C4—82no—
402C4—442no—
403C4—881no—
404C4#1062238611yescharacteristic
405C4#1062239411yescharacteristic
406C4#1062242312yes—
407C4#1062276911yescharacteristic
408C4#1062278111yescharacteristic
409C4#1062278511yescharacteristic
410C4#1062280311yescharacteristic
411C2—1762no—
412C2#1306806312yes—
413C2#1306818712yes—
414C2#1306961311yescharacteristic
415C2#1306971111yescharacteristic
416C2#1306972911yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#332D11
hypocenterC11#10263
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
2. C2×#10622703C2semidirect
4. #13069551C2semidirect
6. #13066450C2semidirect
7. C2×C11×#332C2semidirect
137. C2×#332D11semidirect
340. C11#10263semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106227032
C2×#106224612
#130695512
C2×#106221232
#130664502
C2×C11×#3322
#1026311