Finite Group Databasebeta

← #14645273

Subgroups — #14645273

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622184C212yesmaximal, complemented
4C2×#10622185C212yesmaximal, complemented
5C2×C11×#533C211yesmaximal, characteristic
6C11×#533—24no—
7C11×#533—24no—
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#125—21no—
11C2×C11×C22⋊Q8—21no—
12C2×C11×C22⋊Q8C412yes—
13C2×C4×Q8×C11—21no—
14C2×C4×Q8×C11C412yes—
15C2×C11×#117—21no—
16C22×C42×C11C2211yescharacteristic
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622185—24no—
22#10622184—24no—
23#10622162—21no—
24#10622162—21no—
25C22×Q8×C11—21no—
26C22×Q8×C11C2×C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C11×C4⋊Q8—22no—
31C11×C4⋊Q8—22no—
32C11×C4⋊Q8D414yes—
33C11×C4⋊Q8D414yes—
34C11×#125—28no—
35C11×C22⋊Q8—28no—
36C11×C22⋊Q8—24no—
37C11×C22⋊Q8—24no—
38C4×Q8×C11—28no—
39C4×Q8×C11—24no—
40C4×Q8×C11—24no—
41C11×#117—28no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11D411yescharacteristic
54C2×C42×C11D411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C22×C11⋊C8—22no—
57C22×C11⋊C8—22no—
58C22⋊(C11⋊C8)—42no—
59C22⋊(C11⋊C8)—42no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—22no—
63C4⋊(C11⋊C8)—22no—
64#8343—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—24no—
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—42no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11C22⋊C414yes—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11SD1612yes—
90C22×C4×C11Q1612yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×C4⋊C4—28no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4C22⋊C414yes—
101C11×C22⋊C4—28no—
102C42×C11—28no—
103C42×C11—21no—
104C42×C11—21no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11C2×D412yes—
108C42×C11C2×D412yes—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—42no—
115C2×#533D1111yescharacteristic
116#1797—111no—
117#1797—111no—
118C2×#333—112no—
119C2×#332—112no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11#10312yes—
127C23×C11C2×C22⋊C411yescharacteristic
128Q8×C11—44no—
129Q8×C11—44no—
130Q8×C11—44no—
131Q8×C11—44no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11#10312yes—
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11#12012yes—
158C2×C4×C11#12012yes—
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11C2×Q1611yescharacteristic
161C2×C4×C11#13512yes—
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11#13712yes—
164C2×C4×C11#13711yescharacteristic
165C11⋊C8—82no—
166C11⋊C8—82no—
167#533—24no—
168#533—24no—
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×#125—21no—
172C2×C22⋊Q8—21no—
173C2×C22⋊Q8Dic1112yes—
174C2×C4×Q8—21no—
175C2×C4×Q8Dic1112yes—
176C2×#117—21no—
177C22×C42C2×D1111yescharacteristic
178C2×C4⋊C8—112no—
179C2×C4⋊C8—112no—
180C2×C22⋊C8—221no—
181C2×C22⋊C8—221no—
182#336—221no—
183#336—221no—
184#333—224no—
185#332—224no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11#37911yescharacteristic
194C22×C11#41311yescharacteristic
195C22×C11#41311yescharacteristic
196C22×C11C2×#10311yescharacteristic
197C22×C11#41611yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11#41911yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—44no—
205C4×C11—41no—
206C4×C11—44no—
207C4×C11#44812yes—
208C4×C11#44912yes—
209C4×C11#45112yes—
210C4×C11#45212yes—
211C22×Q8—21no—
212C22×Q8C2×Dic1112yes—
213C23×C4C2×Dic1111yescharacteristic
214C23×C4C22⋊D1111yescharacteristic
215C23×C4C22⋊D1111yescharacteristic
216C22×C8—222no—
217C22×C8—222no—
218C4⋊Q8—22no—
219C4⋊Q8—22no—
220C4⋊Q8C22⋊D1114yes—
221C4⋊Q8C22⋊D1114yes—
222#125—28no—
223C22⋊Q8—28no—
224C22⋊Q8—24no—
225C22⋊Q8—24no—
226C4×Q8—28no—
227C4×Q8—24no—
228C4×Q8—24no—
229#117—28no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×Dic1112yes—
236C2×C22⋊C4—22no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42C2×Dic1111yescharacteristic
241C2×C42C22⋊D1111yescharacteristic
242C2×C42C22⋊D1111yescharacteristic
243C2×C42C22×D1111yescharacteristic
244C4⋊C8—222no—
245C4⋊C8—222no—
246C4⋊C8—222no—
247C4⋊C8—222no—
248C22⋊C8—442no—
249C22⋊C8—442no—
250C2×C11—42no—
251C2×C11#154211yescharacteristic
252C2×C11#155011yescharacteristic
253C2×C11#155411yescharacteristic
254C2×C11#155911yescharacteristic
255C2×C11#178511yescharacteristic
256C2×C11#178711yescharacteristic
257C2×C11#178811yescharacteristic
258C24C22⋊Dic1111yescharacteristic
259C2×Q8—22no—
260C2×Q8—24no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—41no—
264C2×Q8—42no—
265C2×Q8—41no—
266C2×Q8C22⋊Dic1114yes—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4#432512yes—
280C22×C4#432612yes—
281C22×C4C22⋊Dic1111yescharacteristic
282C22×C4C22⋊Dic1111yescharacteristic
283C22×C4C22⋊Dic1111yescharacteristic
284C22×C4C22×Dic1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287C2×C8—442no—
288C2×C8—442no—
289C2×C8—442no—
290C2×C8—442no—
291C2×C8—442no—
292C2×C8—442no—
293C4⋊C4—28no—
294C4⋊C4—28no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4C22⋊Dic1114yes—
300C22⋊C4—28no—
301C42—28no—
302C42—21no—
303C42—21no—
304C42—22no—
305C42—22no—
306C42C2×C22⋊D1112yes—
307C42C2×C22⋊D1112yes—
308C11#834311yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23#6689912yes—
316C23C2×C22⋊Dic1111yescharacteristic
317Q8—44no—
318Q8—44no—
319Q8—44no—
320Q8—44no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4#6689912yes—
344C2×C4C2×#432511yescharacteristic
345C2×C4#6699512yes—
346C2×C4C2×#432611yescharacteristic
347C2×C4#6700211yescharacteristic
348C2×C4#6700312yes—
349C2×C4#6700411yescharacteristic
350C2×C4C2×C22⋊Dic1111yescharacteristic
351C2×C4C2×C22⋊Dic1111yescharacteristic
352C2×C4#6700612yes—
353C2×C4#6700612yes—
354C8—882no—
355C8—882no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22C2×#6689911yescharacteristic
364C22#1062283811yescharacteristic
365C22#1062284511yescharacteristic
366C22#1062284611yescharacteristic
367C22#1062285011yescharacteristic
368C22#1062285011yescharacteristic
369C22#1062286011yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—44no—
375C4—41no—
376C4—44no—
377C4#1062284012yes—
378C4#1062284112yes—
379C4#1062285112yes—
380C4#1062285212yes—
381C2—42no—
382C2#1306727311yescharacteristic
383C2#1306730611yescharacteristic
384C2#1306732611yescharacteristic
385C2#1306734611yescharacteristic
386C2#1306854411yescharacteristic
387C2#1306855111yescharacteristic
388C2#1306855611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#533C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#533D11
hypocenterC11#8343
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. C2×#10622184C2semidirect
4. C2×#10622185C2semidirect
308. C11#8343semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221842
C2×#106221852
C2×C11×#5332
#834311