Finite Group Databasebeta

← #14656377

Subgroups — #14656377

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622294C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic
3C2×#10622459C211yesmaximal, characteristic
4#13069410C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×#10622124C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66885—21no—
15C2×#66885—21no—
16C2×(C2×D11)⋊C8—22no—
17C2×#66882—21no—
18C2×#66881—21no—
19C2×#66880—22no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622459—22no—
22#10622459—22no—
23#10622455—22no—
24#10622455—22no—
25#10622294—22no—
26#10622294—22no—
27#10622124—22no—
28#10622119—22no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C22×Dic22—21no—
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C22×C11⋊C8—21no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55#66922D412yes—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C4⋊C8D412yes—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62#66885—24no—
63#66885—24no—
64(C2×D11)⋊C8—44no—
65#66882—24no—
66#66881—24no—
67#66880—28no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#10275—111nomaximal, Sylow
71C23×D11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44Q1612yes—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—42no—
87C2×C4×D11—42no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22—42no—
93C2×Dic22—42no—
94C2×Dic22—82no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—42no—
122C2×#487—111no—
123C2×#476—111no—
124C2×#474—111no—
125#1954—111no—
126C2×#333—111no—
127C2×#332—111no—
128#1277D1111yescharacteristic, complemented
129C23×C11#12111yescharacteristic
130C22×D11—22no—
131C22×D11—41no—
132C22×D11—42no—
133C22×D11—41no—
134C22×D11—42no—
135C2×C4×C11—22no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×C4×C11C2×Q1611yescharacteristic
143C2×C4×C11#13512yes—
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C2×C4×C11#13711yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—82no—
153C2×Dic11—82no—
154D44—22no—
155D44—22no—
156D44—41no—
157D44—41no—
158C4×D11—82no—
159C4×D11—81no—
160C4×D11—81no—
161Dic22—44no—
162Dic22—82no—
163Dic22—81no—
164Dic22—81no—
165Dic22—82no—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—42no—
169C11⋊C8—81no—
170C2×C4⋊Q8—111no—
171C2×C4⋊Q8—111no—
172C2×C4×D4—111no—
173#487—222no—
174#487—222no—
175#476—222no—
176#476—222no—
177#474—222no—
178#474—222no—
179C2×#107—221no—
180C2×#106—221no—
181C2×C4⋊C8—111no—
182C2×C4⋊C8C2×D1111yescharacteristic
183C2×C4⋊C8C2×D1111yescharacteristic
184C2×#103—222no—
185C2×#102—221no—
186C2×#102—221no—
187C2×C22⋊C8—222no—
188C2×C4×C8C2×D1111yescharacteristic
189#333—222no—
190#332—222no—
191C22×C11#39211yescharacteristic
192C22×C11#46312yes—
193C22×C11#46711yescharacteristic
194C22×C11#47011yescharacteristic
195C22×C11#47112yes—
196C2×D11—44no—
197C2×D11—42no—
198C2×D11—82no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11#44912yes—
204C4×C11#45111yescharacteristic
205C4×C11#45111yescharacteristic
206C4×C11#45211yescharacteristic
207C4×C11#45211yescharacteristic
208C4×C11#49511yescharacteristic
209C4×C11#49611yescharacteristic
210Dic11—82no—
211Dic11—81no—
212Dic11—82no—
213C22×Q8—221no—
214C22×Q8—221no—
215C22×D4—111no—
216C23×C4—221no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—221no—
220C22×C8D4412yes—
221C4⋊Q8—112no—
222C4⋊Q8—112no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
229C4×D4—221no—
230C4×D4—221no—
231C4×D4—221no—
232C4×D4—221no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C42C22×D1111yescharacteristic
240#107—224no—
241#106—224no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8D4412yes—
247C4⋊C8D4412yes—
248#103—228no—
249#102—224no—
250#102—224no—
251C22⋊C8—444no—
252C4×C8—21no—
253C4×C8—21no—
254C2×C11#168312yes—
255C2×C11#170312yes—
256C2×C11#200111yescharacteristic
257C2×C11#201211yescharacteristic
258C2×C11#201911yescharacteristic
259D11—82no—
260C24—221no—
261C2×Q8—222no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×Q8—441no—
265C2×Q8—442no—
266C2×Q8—442no—
267C2×Q8—882no—
268C2×D4—112no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C22×C4—221no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—442no—
280C22×C4—442no—
281C22×C4C2×D4411yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4#434311yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—441no—
294C2×C8—442no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42C2×D4411yescharacteristic
308C42C2×D4411yescharacteristic
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C11#1027511yescharacteristic, complemented, Sylow
312C23—222no—
313C23—441no—
314C23—442no—
315C23—441no—
316C23—442no—
317C23#6694811yescharacteristic
318Q8—444no—
319Q8—882no—
320Q8—882no—
321Q8—881no—
322Q8—881no—
323D4—222no—
324D4—222no—
325D4—441no—
326D4—441no—
327C2×C4—22no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—882no—
333C2×C4—882no—
334C2×C4—881no—
335C2×C4—881no—
336C2×C4—882no—
337C2×C4#6692711yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693511yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6694811yescharacteristic
342C2×C4#6694811yescharacteristic
343C2×C4#6695712yes—
344C2×C4#6696112yes—
345C2×C4#6696511yescharacteristic
346C2×C4#6696811yescharacteristic
347C2×C4#6696811yescharacteristic
348C2×C4Q16×D1111yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—881no—
353C22—444no—
354C22—442no—
355C22—881no—
356C22—882no—
357C22—881no—
358C22#1062228411yescharacteristic
359C22#1062245712yes—
360C22#1062248111yescharacteristic
361C22#1062250011yescharacteristic
362C22#1062251112yes—
363C4—21no—
364C4—21no—
365C4—881no—
366C4—882no—
367C4—882no—
368C4#1062230911yescharacteristic
369C4#1062232511yescharacteristic
370C4#1062234712yes—
371C4#1062239611yescharacteristic
372C4#1062239611yescharacteristic
373C4#1062242111yescharacteristic
374C4#1062242111yescharacteristic
375C2—882no—
376C2#1306806812yes—
377C2#1306819212yes—
378C2#1306962711yescharacteristic
379C2#1306969611yescharacteristic
380C2#1306973311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1277D11
hypocenterC11#10275
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
1. C2×#10622294C2semidirect
5. C2×#10622119C2semidirect
6. C2×#10622124C2semidirect
7. C11×#1277C2semidirect
128. #1277D11semidirect
311. C11#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106224552
C2×#106224592
#130694102
C2×#106221192
C2×#106221242
C11×#12772
#1027511