Finite Group Databasebeta

← #14647130

Subgroups — #14647130

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66979C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3#13066456C212yesmaximal, complemented
4#13066456C212yesmaximal, complemented
5C4×C11×C22⋊C8C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66979C411yescharacteristic
8C2×#66979C411yescharacteristic
9C2×C11×C22⋊C8—21no—
10C2×C4×C8×C11C2212yes—
11C4×C22⋊Dic11—21no—
12C4×C22⋊Dic11—21no—
13C2×C22⋊(C11⋊C8)—21no—
14C4×C4⋊Dic11C411yescharacteristic
15C4×C4⋊Dic11C411yescharacteristic
16C4×C4⋊Dic11C2211yescharacteristic
17C4×C4⋊Dic11C2211yescharacteristic
18#10622545—21no—
19C42×Dic11—21no—
20C2×C4⋊(C11⋊C8)C2212yes—
21C11×#336—21no—
22#10622162—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C8×C11—22no—
27C2×C42×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35#66979—22no—
36#66979—22no—
37#66979—22no—
38#66979C814yescomplemented
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—22no—
50C11×C22⋊C8—24no—
51C4×C8×C11—22no—
52C4×C8×C11—22no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—42no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60#8708—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C2×C812yes—
77C22×C4×C11M1612yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×C8×C11—24no—
86C2×C8×C11—42no—
87C2×C8×C11—42no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11#4112yes—
93C42×C11#4112yes—
94C22⋊Dic11—24no—
95C22⋊Dic11—24no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11C2×C812yes—
101C4⋊Dic11C2×C812yes—
102C4⋊Dic11M1612yes—
103C4⋊Dic11M1612yes—
104C4×Dic11—24no—
105C4×Dic11—24no—
106C4×Dic11—42no—
107C4×Dic11—42no—
108C4×Dic11—42no—
109C4×Dic11—41no—
110C4×Dic11—41no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C4×#117—111no—
115#1797—111no—
116C4×C22⋊C8D1111yescharacteristic
117#1279—112no—
118#1279—112no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C22⋊C812yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—44no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11C22⋊C812yes—
144C2×C4×C11#10412yes—
145C2×C4×C11#11711yescharacteristic
146C2×C4×C11#11711yescharacteristic
147C2×C4×C11#12312yes—
148C2×C4×C11#12312yes—
149C2×C4×C11C22×C811yescharacteristic
150C2×C4×C11C2×M1611yescharacteristic
151C2×C4×C11C2×M1611yescharacteristic
152C2×C4×C11C2×M1611yescharacteristic
153C2×C4×C11#13512yes—
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C8×C11—44no—
169C11⋊C8—82no—
170C2×#117—111no—
171C2×#117—111no—
172C22×C42C2×D1111yescharacteristic
173C2×C4⋊C8—112no—
174C2×C22⋊C8—21no—
175C2×C22⋊C8—221no—
176C2×C4×C8C2×D1112yes—
177C4×C4⋊C4—111no—
178C4×C4⋊C4—111no—
179C4×C4⋊C4—111no—
180C4×C4⋊C4—111no—
181C4×C22⋊C4—221no—
182C4×C22⋊C4—221no—
183#376—221no—
184C43—221no—
185#336—21no—
186#336—221no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11#38111yescharacteristic
195C22×C11C2×C22⋊C811yescharacteristic
196C22×C11#40711yescharacteristic
197C22×C11#41611yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C22×C11#42111yescharacteristic
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—41no—
205C4×C11#43111yescharacteristic
206C4×C11#43111yescharacteristic
207C4×C11#43211yescharacteristic
208C4×C11#43211yescharacteristic
209C4×C11#48212yes—
210C4×C11#48512yes—
211Dic11—42no—
212Dic11—42no—
213Dic11—42no—
214Dic11—42no—
215C23×C4C4×D1111yescharacteristic
216C23×C4D4411yescharacteristic
217C23×C4C22⋊D1111yescharacteristic
218C22×C8—22no—
219C22×C8—222no—
220#117—114no—
221#117—222no—
222#117—222no—
223#117—222no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—111no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42—221no—
233C2×C42—221no—
234C2×C42—221no—
235C2×C42—221no—
236C2×C42—221no—
237C2×C42—221no—
238C2×C42C4×D1111yescharacteristic
239C2×C42D4411yescharacteristic
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—222no—
243C4⋊C8—222no—
244C22⋊C8—24no—
245C22⋊C8—442no—
246C4×C8—22no—
247C4×C8—22no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—221no—
252C2×C11—42no—
253C2×C11#147611yescharacteristic
254C2×C11#147711yescharacteristic
255C2×C11#148811yescharacteristic
256C2×C11#148911yescharacteristic
257C2×C11#181711yescharacteristic
258C2×C11#182511yescharacteristic
259C2×C11#182611yescharacteristic
260C24(C2×D11)⋊C411yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4C8×D1112yes—
277C22×C4#431312yes—
278C22×C4(C2×D11)⋊C411yescharacteristic
279C22×C4(C2×D11)⋊C411yescharacteristic
280C22×C4(C2×D11)⋊C411yescharacteristic
281C22×C4C2×C4×D1111yescharacteristic
282C22×C4C2×D4411yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C2×C8—24no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—442no—
288C2×C8—442no—
289C2×C8—442no—
290C4⋊C4—112no—
291C4⋊C4—112no—
292C4⋊C4—112no—
293C4⋊C4—112no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C22⋊C4—224no—
299C22⋊C4—224no—
300C42—21no—
301C42—21no—
302C42—22no—
303C42—22no—
304C42—224no—
305C42—224no—
306C42—442no—
307C42—442no—
308C42—442no—
309C42—441no—
310C42—441no—
311C42#434112yes—
312C42#434112yes—
313C11#870811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23(C2×D11)⋊C812yes—
321C23C2×(C2×D11)⋊C411yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4#6686912yes—
351C2×C4(C2×D11)⋊C812yes—
352C2×C4#6693011yescharacteristic
353C2×C4#6693011yescharacteristic
354C2×C4#6693912yes—
355C2×C4C2×C8×D1111yescharacteristic
356C2×C4C2×#431311yescharacteristic
357C2×C4#6695712yes—
358C2×C4M16×D1111yescharacteristic
359C2×C4M16×D1111yescharacteristic
360C2×C4#6696111yescharacteristic
361C2×C4#6696211yescharacteristic
362C2×C4#6698812yes—
363C8—44no—
364C8—882no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22C2×#6686911yescharacteristic
373C22#1062255611yescharacteristic
374C22#1062261811yescharacteristic
375C22C2×(C2×D11)⋊C811yescharacteristic
376C22#1062272611yescharacteristic
377C22#1062273911yescharacteristic
378C22#1062274611yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—442no—
384C4—442no—
385C4—442no—
386C4—442no—
387C4#1062233111yescharacteristic
388C4#1062233111yescharacteristic
389C4#1062233211yescharacteristic
390C4#1062233211yescharacteristic
391C4#1062233612yes—
392C4#1062235012yes—
393C2—42no—
394C2#1306699911yescharacteristic
395C2#1306700411yescharacteristic
396C2#1306705111yescharacteristic
397C2#1306705611yescharacteristic
398C2#1306868211yescharacteristic
399C2#1306871211yescharacteristic
400C2#1306871611yescharacteristic
subgroupG/H
centerC22×C4C2×D44
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×C22⋊C8D11
hypocenterC11#8708
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #13066456C2semidirect
4. #13066456C2semidirect
38. #66979C8semidirect
313. C11#8708semidirect

Maximal subgroups

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

subgroupindex
C4×#669792
#130685962
#130664562
C4×C11×C22⋊C82
#870811