Finite Group Databasebeta

← #14656324

Subgroups — #14656324

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4C2×#10622185C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#475C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C22×#4325—21no—
11C22×#4325—22no—
12C2×#66927C2211yescharacteristic
13C11×#475—22no—
14C11×#475—22no—
15C2×C11×#106—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—21no—
18#10622698—22no—
19#10622698—22no—
20#10622640—22no—
21#10622640—22no—
22C2×#66873—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622185—22no—
27#10622162—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4325—28no—
51C2×#4325—44no—
52C2×#4325—42no—
53C2×#4325—42no—
54C2×#4325—44no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D412yes—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927D412yes—
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66#66873—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#10268—111nomaximal, Sylow
74C23×D11—41no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11SD1612yescomplemented
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—42no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—82no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121#4325—48no—
122#4325—416no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—42no—
130C2×C11⋊C8SD1614yescomplemented
131C2×#492—111no—
132C2×#475D1111yescharacteristic, complemented
133C2×#460—111no—
134#1984—111no—
135C2×#332—111no—
136C2×#331—111no—
137#1277—111no—
138C23×C11#12111yescharacteristic
139C22×D11—42no—
140C22×D11—82no—
141C22×D11—81no—
142C22×D11—81no—
143C22×D11—82no—
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—44no—
149Q8×C11—81no—
150Q8×C11—81no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C2×C4×C11C2×SD1612yes—
166C2×C4×C11C2×SD1611yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)12yes—
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C11#13711yescharacteristic
171D44—44no—
172D44—42no—
173D44—42no—
174D44—82no—
175D44—82no—
176D44—81no—
177D44—81no—
178D44—81no—
179D44—81no—
180C8×C11—42no—
181C11⋊C8—24no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C22×SD16—222no—
185C22×SD16—221no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×#127—111no—
188C2×C4×Q8C2×D1111yescharacteristic
189#492—222no—
190#492—222no—
191#475—22no—
192#475—22no—
193#460—222no—
194#460—222no—
195C2×#106—21no—
196C2×C4⋊C8—111no—
197C2×C4⋊C8—111no—
198C2×C4⋊C8C2×D1111yescharacteristic
199C2×#103—21no—
200C2×#102—221no—
201C2×C4×C8—111no—
202#336—222no—
203#332—222no—
204#331—222no—
205C22×C11#39211yescharacteristic
206C22×C11#46012yes—
207C22×C11#46511yescharacteristic
208C22×C11#46811yescharacteristic
209C22×C11#47112yes—
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—82no—
213C2×D11—162no—
214C2×D11—162no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11#44811yescharacteristic
221C4×C11#44911yescharacteristic
222C4×C11#45012yes—
223C4×C11#45011yescharacteristic
224C4×C11#45211yescharacteristic
225C4×C11#49211yescharacteristic
226C4×C11#49611yescharacteristic
227C22×Q8—21no—
228C22×Q8C22⋊D1111yescharacteristic
229C22×D4—221no—
230C22×D4—221no—
231C22×D4—221no—
232C2×SD16—224no—
233C2×SD16—228no—
234C2×SD16—444no—
235C2×SD16—444no—
236C2×SD16—442no—
237C2×SD16—442no—
238C22×C8—21no—
239C22×C8—112no—
240C22×C8—221no—
241C22×C8—221no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C22⋊D1112yes—
246#127—112no—
247#127—221no—
248#127—221no—
249#127—221no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C22⋊D1111yescharacteristic
258C2×C42—21no—
259C2×C42C22×D1111yescharacteristic
260#106—24no—
261C4⋊C8—21no—
262C4⋊C8—112no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265C4⋊C8—221no—
266C4⋊C8C22⋊D1112yes—
267#103—24no—
268#102—224no—
269C4×C8—221no—
270C4×C8—221no—
271C2×C11#166612yes—
272C2×C11#168612yes—
273C2×C11#200011yescharacteristic
274C2×C11#201411yescharacteristic
275C2×C11#201911yescharacteristic
276D11—162no—
277C24—441no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8#432512yescomplemented
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—882no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4D4×D1111yescharacteristic
305C22×C4#434111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307SD16—4416no—
308SD16—448no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—114no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—441no—
317C2×C8—441no—
318C2×C8—442no—
319C2×C8—441no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C42—41no—
329C42—41no—
330C42D4×D1111yescharacteristic
331C42D4×D1111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C11#1026811yescharacteristic, complemented, Sylow
335C23—442no—
336C23—882no—
337C23—882no—
338C23—881no—
339C23—881no—
340C23#6699211yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—44no—
346Q8—81no—
347Q8—81no—
348D4—444no—
349D4—442no—
350D4—442no—
351D4—882no—
352D4—882no—
353D4—881no—
354D4—881no—
355D4—881no—
356D4—881no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4SD16×D1112yes—
366C2×C4#6696712yes—
367C2×C4#6699011yescharacteristic
368C2×C4#6699011yescharacteristic
369C2×C4#6699111yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6699311yescharacteristic
372C2×C4C2×#432511yescharacteristic
373C2×C4#6699511yescharacteristic
374C2×C4#6700211yescharacteristic
375C2×C4#6700311yescharacteristic
376C2×C4#6700611yescharacteristic
377C8—42no—
378C8—224no—
379C8—442no—
380C8—881no—
381C22—882no—
382C22—882no—
383C22—882no—
384C22—1762no—
385C22—1762no—
386C22#1062266111yescharacteristic
387C22#1062266211yescharacteristic
388C22#1062277612yes—
389C22#1062281612yes—
390C22#1062283611yescharacteristic
391C4—21no—
392C4—21no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4#1062265911yescharacteristic
397C4#1062266011yescharacteristic
398C4#1062278212yes—
399C4#1062278811yescharacteristic
400C4#1062278911yescharacteristic
401C4#1062284011yescharacteristic
402C4#1062285111yescharacteristic
403C2—1762no—
404C2#1306796612yes—
405C2#1306809012yes—
406C2#1306961711yescharacteristic
407C2#1306970211yescharacteristic
408C2#1306972711yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#475C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#475D11
hypocenterC11#10268
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13069553C2semidirect
4. C2×#10622185C2semidirect
6. #13066450C2semidirect
7. C2×C11×#475C2semidirect
84. C2×Q8×C11SD16semidirect
130. C2×C11⋊C8SD16semidirect
132. C2×#475D11semidirect
287. C2×Q8#4325semidirect
334. C11#10268semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226402
#130695532
C2×#106221852
C2×#106221232
#130664502
C2×C11×#4752
#1026811