Finite Group Databasebeta

← #14656368

Subgroups — #14656368

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622705C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic
3C2×#10622700C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—22no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66885—21no—
15C2×(C2×D11)⋊C8—22no—
16C2×#66882—21no—
17#10622705—22no—
18#10622705—22no—
19#10622700—22no—
20#10622700—22no—
21C2×#66873—21no—
22C2×#66871—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622459—22no—
26#10622459—22no—
27C11×#332—22no—
28#10622120—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×#4326—28no—
43C2×#4326—44no—
44C2×#4326—44no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8D412yes—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63#66885—24no—
64(C2×D11)⋊C8—44no—
65#66882—24no—
66#66873—24no—
67#66871—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10274—111nomaximal, Sylow
73C23×D11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—41no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44Q1612yescomplemented
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C4×D11—42no—
93C2×C4×D11—42no—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C2×Dic22—42no—
97C2×Dic22—42no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—42no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111#4326—416no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8D814yes—
126C2×#494—111no—
127C2×#474—111no—
128C2×#474—111no—
129#1954—111no—
130C2×#332—111no—
131C2×#332D1111yescharacteristic, complemented
132#1277—111no—
133C23×C11#12111yescharacteristic
134C22×D11—22no—
135C22×D11—41no—
136C22×D11—42no—
137C22×D11—41no—
138C22×D11—42no—
139Q8×C11—44no—
140Q8×C11—81no—
141Q8×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×C4×C11C2×D812yes—
152C2×C4×C11C2×Q1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)12yes—
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161D44—22no—
162D44—22no—
163D44—41no—
164D44—41no—
165C4×D11—82no—
166C4×D11—81no—
167C4×D11—81no—
168Dic22—44no—
169Dic22—81no—
170Dic22—81no—
171C8×C11—42no—
172C8×C11—81no—
173C11⋊C8—24no—
174C11⋊C8—42no—
175C22×Q16—222no—
176C2×C4⋊Q8—111no—
177C2×C4⋊Q8C2×D1111yescharacteristic
178C2×C4×D4—111no—
179#494—222no—
180#494—222no—
181#474—222no—
182#474—222no—
183#474—222no—
184#474—222no—
185C2×#107—221no—
186C2×#107—221no—
187C2×C4⋊C8—111no—
188C2×C4⋊C8C2×D1111yescharacteristic
189C2×C4⋊C8C2×D1111yescharacteristic
190C2×#102—221no—
191C2×#102—221no—
192C2×C22⋊C8—222no—
193C2×C4×C8—111no—
194#332—22no—
195#332—222no—
196C22×C11#39211yescharacteristic
197C22×C11#45912yes—
198C22×C11#46711yescharacteristic
199C22×C11#47011yescharacteristic
200C22×C11#47312yes—
201C2×D11—44no—
202C2×D11—42no—
203C2×D11—82no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—82no—
209C4×C11#44712yes—
210C4×C11#45111yescharacteristic
211C4×C11#45111yescharacteristic
212C4×C11#45211yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#49311yescharacteristic
215C4×C11#49611yescharacteristic
216Dic11—82no—
217Dic11—81no—
218C22×Q8—21no—
219C22×Q8—221no—
220C22×D4—111no—
221C23×C4—221no—
222C2×Q16—228no—
223C2×Q16—444no—
224C2×Q16—444no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—112no—
228C22×C8—221no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—112no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8D4412yes—
237C4×D4—221no—
238C4×D4—221no—
239C4×D4—221no—
240C4×D4—221no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C42C22×D1111yescharacteristic
248#107—224no—
249#107—224no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—112no—
254C4⋊C8—221no—
255C4⋊C8C22⋊D1112yes—
256#102—224no—
257#102—224no—
258C22⋊C8—444no—
259C4×C8—221no—
260C4×C8—221no—
261C2×C11#166912yes—
262C2×C11#168912yes—
263C2×C11#200111yescharacteristic
264C2×C11#201111yescharacteristic
265C2×C11#202011yescharacteristic
266D11—82no—
267C24—221no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—222no—
273C2×Q8—441no—
274C2×Q8—442no—
275C2×Q8—442no—
276C2×D4—112no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C22×C4—41no—
283C22×C4—221no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—441no—
289C22×C4#433911yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292Q16—4416no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—42no—
297C2×C8—41no—
298C2×C8—114no—
299C2×C8—222no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8—441no—
303C2×C8—441no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—221no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—221no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C42C2×D4411yescharacteristic
317C42D4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C11#1027411yescharacteristic, complemented, Sylow
321C23—222no—
322C23—441no—
323C23—442no—
324C23—442no—
325C23—441no—
326C23#6693711yescharacteristic
327Q8—44no—
328Q8—81no—
329Q8—81no—
330Q8—444no—
331Q8—881no—
332Q8—881no—
333D4—222no—
334D4—222no—
335D4—441no—
336D4—441no—
337C2×C4—22no—
338C2×C4—42no—
339C2×C4—82no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—882no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4—882no—
347C2×C4#6693511yescharacteristic
348C2×C4#6693511yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4D8×D1112yes—
351C2×C4#6696712yes—
352C2×C4#6696811yescharacteristic
353C2×C4#6696911yescharacteristic
354C2×C4Q16×D1111yescharacteristic
355C2×C4#6697111yescharacteristic
356C2×C4#6698311yescharacteristic
357C2×C4#6699011yescharacteristic
358C2×C4#6699311yescharacteristic
359C8—42no—
360C8—81no—
361C8—224no—
362C8—442no—
363C22—442no—
364C22—444no—
365C22—882no—
366C22—881no—
367C22—881no—
368C22#1062236812yes—
369C22#1062239912yes—
370C22#1062242611yescharacteristic
371C22#1062242911yescharacteristic
372C22#1062257311yescharacteristic
373C4—21no—
374C4—21no—
375C4—82no—
376C4—881no—
377C4—882no—
378C4#1062238612yes—
379C4#1062242111yescharacteristic
380C4#1062242311yescharacteristic
381C4#1062276411yescharacteristic
382C4#1062278611yescharacteristic
383C4#1062278911yescharacteristic
384C4#1062279911yescharacteristic
385C2—882no—
386C2#1306798012yes—
387C2#1306810412yes—
388C2#1306962511yescharacteristic
389C2#1306968811yescharacteristic
390C2#1306973611yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11#10274
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×#10622705C2semidirect
5. C2×#10622120C2semidirect
6. #13066450C2semidirect
7. C2×C11×#332C2semidirect
89. C2×D44Q16semidirect
131. C2×#332D11semidirect
320. C11#10274semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
C2×#106224592
C2×#106227002
#130694092
C2×#106221202
#130664502
C2×C11×#3322
#1027411