Finite Group Databasebeta

← #14656372

Subgroups — #14656372

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×#10622697C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic
3#13069410C211yesmaximal, characteristic
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622185C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C2×C11×#487C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#487—22no—
12C11×#487—22no—
13C2×C11×#103—22no—
14C2×C4×C8×C11C2211yescharacteristic
15C2×(C2×D11)⋊C8—22no—
16#10622700—22no—
17#10622700—22no—
18#10622697—22no—
19#10622697—22no—
20C2×#66873—21no—
21C2×#66873—21no—
22C2×#66872—21no—
23C2×#66871—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622185—22no—
28#10622184—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×C8×C11D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C11×C4⋊Q8D412yes—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44—21no—
56C11×#103—28no—
57C4×C8×C11—21no—
58C4×C8×C11—21no—
59(C2×D11)⋊C8—44no—
60#66873—24no—
61#66873—24no—
62#66872—24no—
63#66871—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69C4⋊(C11⋊C8)D412yes—
70#10275—111nomaximal, Sylow
71C23×D11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×Q8×C11—82no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44Q1612yes—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×#487D1111yescharacteristic, complemented
123C2×#476—111no—
124C2×#474—111no—
125#1954—111no—
126C2×#333—111no—
127C2×#332—111no—
128#1277—111no—
129C23×C11#12111yescharacteristic
130C22×D11—22no—
131C22×D11—41no—
132C22×D11—42no—
133C22×D11—41no—
134C22×D11—42no—
135Q8×C11—44no—
136Q8×C11—82no—
137Q8×C11—82no—
138Q8×C11—81no—
139Q8×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—82no—
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×Q1611yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11#13512yes—
154C2×C4×C11AGL(1,ℤ/8)12yes—
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—42no—
159D44—22no—
160D44—22no—
161D44—41no—
162D44—41no—
163C4×D11—82no—
164C4×D11—81no—
165C4×D11—81no—
166C8×C11—42no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×C4⋊Q8C2×D1111yescharacteristic
172C2×C4×D4—111no—
173#487—22no—
174#487—22no—
175#476—222no—
176#476—222no—
177#474—222no—
178#474—222no—
179C2×#107—221no—
180C2×#106—221no—
181C2×C4⋊C8—111no—
182C2×C4⋊C8—111no—
183C2×C4⋊C8—111no—
184C2×#103—22no—
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—82no—
204C4×C11—82no—
205C4×C11#44912yes—
206C4×C11#45111yescharacteristic
207C4×C11#45111yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#49511yescharacteristic
211C4×C11#49611yescharacteristic
212Dic11—81no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×D4—111no—
216C23×C4—221no—
217C22×C8—221no—
218C22×C8—221no—
219C22×C8—221no—
220C22×C8C22⋊D1112yes—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22⋊D1112yes—
228C4⋊Q8C22⋊D1112yes—
229C4×D4—221no—
230C4×D4—221no—
231C4×D4—221no—
232C4×D4—221no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C22⋊C4—221no—
239C2×C42C22×D1111yescharacteristic
240#107—224no—
241#106—224no—
242C4⋊C8—112no—
243C4⋊C8—112no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248#103—28no—
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—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—82no—
268C2×D4—112no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—221no—
277C22×C4—441no—
278C22×C4—442no—
279C22×C4—442no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282C22×C4#434111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8—441no—
294C2×C8—442no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42D4×D1111yescharacteristic
308C42D4×D1111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C11#1027511yescharacteristic, complemented, Sylow
312C23—222no—
313C23—442no—
314C23—441no—
315C23—441no—
316C23—442no—
317C23#6699111yescharacteristic
318Q8—44no—
319Q8—82no—
320Q8—82no—
321Q8—81no—
322Q8—81no—
323D4—222no—
324D4—222no—
325D4—441no—
326D4—441no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—441no—
333C2×C4—442no—
334C2×C4—882no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4Q16×D1111yescharacteristic
338C2×C4#6697111yescharacteristic
339C2×C4#6697111yescharacteristic
340C2×C4#6697211yescharacteristic
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700212yes—
347C2×C4#6700312yes—
348C2×C4#6700611yescharacteristic
349C8—42no—
350C8—442no—
351C8—442no—
352C8—881no—
353C22—444no—
354C22—442no—
355C22—881no—
356C22—882no—
357C22—881no—
358C22#1062267012yes—
359C22#1062279012yes—
360C22#1062280111yescharacteristic
361C22#1062280211yescharacteristic
362C22#1062283611yescharacteristic
363C4—21no—
364C4—21no—
365C4—82no—
366C4—82no—
367C4—881no—
368C4#1062267111yescharacteristic
369C4#1062267211yescharacteristic
370C4#1062279911yescharacteristic
371C4#1062279911yescharacteristic
372C4#1062280011yescharacteristic
373C4#1062280011yescharacteristic
374C4#1062285112yes—
375C2—882no—
376C2#1306806412yes—
377C2#1306818812yes—
378C2#1306962311yescharacteristic
379C2#1306969311yescharacteristic
380C2#1306972811yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#487C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#487D11
hypocenterC11#10275
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. C2×#10622184C2semidirect
5. C2×#10622185C2semidirect
6. #13066451C2semidirect
7. C2×C11×#487C2semidirect
122. C2×#487D11semidirect
311. C11#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106227002
#130694102
C2×#106221842
C2×#106221852
#130664512
C2×C11×#4872
#1027511