Finite Group Databasebeta

← #14656392

Subgroups — #14656392

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic
3C2×#10622697C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66885—21no—
14C2×(C2×D11)⋊C8—22no—
15C2×#66881—21no—
16#10622697—22no—
17#10622697—22no—
18#10622691—22no—
19#10622691—22no—
20C2×#66873—21no—
21C2×#66872—21no—
22C2×#66871—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622455—22no—
26#10622455—22no—
27C11×#333—22no—
28#10622119—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×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8D412yes—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60#66885—24no—
61(C2×D11)⋊C8—44no—
62#66881—24no—
63#66873—24no—
64#66872—24no—
65#66871—28no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10278—111nomaximal, Sylow
71C23×D11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—41no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44Q1612yes—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×Dic22—22no—
92C2×Dic22—41no—
93C2×Dic22—82no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—42no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8SD1614yes—
121C2×#500—111no—
122C2×#476—111no—
123C2×#476—111no—
124#1954—111no—
125C2×#333—111no—
126C2×#333D1111yescharacteristic, complemented
127#1277—111no—
128C23×C11#12111yescharacteristic
129C22×D11—22no—
130C22×D11—41no—
131C22×D11—42no—
132C22×D11—41no—
133C22×D11—42no—
134Q8×C11—82no—
135Q8×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11C2×SD1612yes—
146C2×C4×C11C2×Q1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×C4×C11#13712yes—
150C2×C4×C11#13711yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—82no—
155D44—22no—
156D44—22no—
157D44—41no—
158D44—41no—
159C4×D11—82no—
160C4×D11—81no—
161C4×D11—81no—
162Dic22—82no—
163Dic22—82no—
164C8×C11—42no—
165C8×C11—81no—
166C11⋊C8—24no—
167C11⋊C8—42no—
168C2×C4⋊Q8—111no—
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×C4×D4—111no—
171#500—222no—
172#500—222no—
173#476—222no—
174#476—222no—
175#476—222no—
176#476—222no—
177C2×#107—222no—
178C2×#106—221no—
179C2×#106—221no—
180C2×C4⋊C8—111no—
181C2×C4⋊C8C2×D1111yescharacteristic
182C2×C4⋊C8C2×D1111yescharacteristic
183C2×#102—221no—
184C2×#102—221no—
185C2×C22⋊C8—222no—
186C2×C4×C8—111no—
187#333—22no—
188#333—222no—
189C22×C11#39211yescharacteristic
190C22×C11#46112yes—
191C22×C11#46711yescharacteristic
192C22×C11#47011yescharacteristic
193C22×C11#47212yes—
194C2×D11—44no—
195C2×D11—42no—
196C2×D11—82no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11#44812yes—
203C4×C11#45111yescharacteristic
204C4×C11#45111yescharacteristic
205C4×C11#45211yescharacteristic
206C4×C11#45211yescharacteristic
207C4×C11#49211yescharacteristic
208C4×C11#49711yescharacteristic
209Dic11—81no—
210Dic11—82no—
211C22×Q8—21no—
212C22×Q8—221no—
213C22×D4—111no—
214C23×C4—221no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—112no—
218C22×C8—221no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—112no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8D4412yes—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C42C22×D1111yescharacteristic
238#107—228no—
239#106—224no—
240#106—224no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—112no—
245C4⋊C8—221no—
246C4⋊C8C22⋊D1112yes—
247#102—224no—
248#102—224no—
249C22⋊C8—444no—
250C4×C8—221no—
251C4×C8—221no—
252C2×C11#167512yes—
253C2×C11#169512yes—
254C2×C11#200111yescharacteristic
255C2×C11#201311yescharacteristic
256C2×C11#201811yescharacteristic
257D11—82no—
258C24—221no—
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—82no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×Q8—882no—
265C2×D4—112no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C22×C4—41no—
272C22×C4—221no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4—442no—
276C22×C4—442no—
277C22×C4—441no—
278C22×C4#433911yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—114no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4—221no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C42C2×D4411yescharacteristic
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1027811yescharacteristic, complemented, Sylow
309C23—222no—
310C23—441no—
311C23—442no—
312C23—441no—
313C23—442no—
314C23#6693711yescharacteristic
315Q8—82no—
316Q8—82no—
317Q8—882no—
318Q8—882no—
319D4—222no—
320D4—222no—
321D4—441no—
322D4—441no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—441no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—882no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4—882no—
333C2×C4#6693511yescharacteristic
334C2×C4#6693511yescharacteristic
335C2×C4#6693711yescharacteristic
336C2×C4SD16×D1112yes—
337C2×C4#6696811yescharacteristic
338C2×C4#6696911yescharacteristic
339C2×C4Q16×D1111yescharacteristic
340C2×C4#6697111yescharacteristic
341C2×C4#6697112yes—
342C2×C4#6698311yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699311yescharacteristic
345C8—42no—
346C8—81no—
347C8—224no—
348C8—442no—
349C22—442no—
350C22—444no—
351C22—882no—
352C22—881no—
353C22—881no—
354C22#1062236212yes—
355C22#1062242611yescharacteristic
356C22#1062242911yescharacteristic
357C22#1062243112yes—
358C22#1062257311yescharacteristic
359C4—21no—
360C4—21no—
361C4—82no—
362C4—881no—
363C4—882no—
364C4#1062241912yes—
365C4#1062242111yescharacteristic
366C4#1062242311yescharacteristic
367C4#1062278611yescharacteristic
368C4#1062278811yescharacteristic
369C4#1062279911yescharacteristic
370C4#1062280311yescharacteristic
371C2—882no—
372C2#1306801412yes—
373C2#1306813812yes—
374C2#1306962511yescharacteristic
375C2#1306970011yescharacteristic
376C2#1306972411yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#333D11
hypocenterC11#10278
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
5. C2×#10622119C2semidirect
6. #13066450C2semidirect
7. C2×C11×#333C2semidirect
126. C2×#333D11semidirect
308. C11#10278semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106224552
C2×#106226972
#130694092
C2×#106221192
#130664502
C2×C11×#3332
#1027811