Finite Group Databasebeta

← #14656389

Subgroups — #14656389

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622294C211yesmaximal, characteristic
2C2×#10622463C211yesmaximal, characteristic
3C2×#10622464C211yesmaximal, characteristic
4#13069552C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic
6C2×#10622124C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66882—21no—
15C2×#66881—21no—
16C2×#66880—21no—
17C2×#66880—21no—
18C2×#66880—22no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622464—22no—
21#10622464—22no—
22#10622463—22no—
23#10622463—22no—
24#10622294—22no—
25#10622294—22no—
26#10622188—22no—
27#10622124—22no—
28#10622119—22no—
29C22×Dic22—21no—
30C22×Dic22—21no—
31C22×Dic22D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922D412yes—
51#66922D412yes—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C4⋊C8D412yes—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62#66882—24no—
63#66881—24no—
64#66880—24no—
65#66880—28no—
66#66880—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#10277—111nomaximal, Sylow
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—22no—
80C2×Dic22—22no—
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—42no—
87C2×Dic22—42no—
88C2×Dic22—82no—
89C2×Dic22Q1612yes—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C4×Dic11—41no—
116C4×Dic11—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—42no—
119C2×#487—111no—
120C2×#477—111no—
121C2×#475—111no—
122#1984—111no—
123C2×#333—111no—
124C2×#332—111no—
125#1277D1111yescharacteristic
126C23×C11#12111yescharacteristic
127C2×C4×C11—22no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12711yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13512yes—
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13712yes—
138C2×C4×C11#13711yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—82no—
148C2×Dic11—82no—
149Dic22—22no—
150Dic22—22no—
151Dic22—41no—
152Dic22—41no—
153Dic22—44no—
154Dic22—82no—
155Dic22—81no—
156Dic22—81no—
157Dic22—82no—
158C8×C11—42no—
159C8×C11—42no—
160C8×C11—42no—
161C11⋊C8—81no—
162C2×C4⋊Q8—111no—
163C2×C4⋊Q8—111no—
164C2×C4×Q8—111no—
165#487—222no—
166#487—222no—
167#477—222no—
168#477—222no—
169#475—222no—
170#475—222no—
171C2×#107—221no—
172C2×#106—221no—
173C2×C4⋊C8—111no—
174C2×C4⋊C8C2×D1111yescharacteristic
175C2×C4⋊C8C2×D1111yescharacteristic
176C2×#103—221no—
177C2×#103—221no—
178C2×#103—222no—
179C2×C4×C8C2×D1111yescharacteristic
180#336—222no—
181#333—222no—
182#332—222no—
183C22×C11#39211yescharacteristic
184C22×C11#46412yes—
185C22×C11#46711yescharacteristic
186C22×C11#47011yescharacteristic
187C22×C11#47112yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11#45111yescharacteristic
191C4×C11#45111yescharacteristic
192C4×C11#45212yes—
193C4×C11#45211yescharacteristic
194C4×C11#45211yescharacteristic
195C4×C11#49511yescharacteristic
196C4×C11#49711yescharacteristic
197Dic11—42no—
198Dic11—82no—
199Dic11—82no—
200Dic11—81no—
201C22×Q8—111no—
202C22×Q8—221no—
203C22×Q8—221no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—221no—
207C22×C8D4412yes—
208C4⋊Q8—112no—
209C4⋊Q8—112no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4×Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219C4×Q8—221no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C42—221no—
227C2×C42C22×D1111yescharacteristic
228#107—224no—
229#106—224no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8D4412yes—
235C4⋊C8D4412yes—
236#103—224no—
237#103—224no—
238#103—228no—
239C4×C8—21no—
240C4×C8—21no—
241C2×C11#168412yes—
242C2×C11#170412yes—
243C2×C11#200111yescharacteristic
244C2×C11#201511yescharacteristic
245C2×C11#201911yescharacteristic
246C2×Q8—112no—
247C2×Q8—221no—
248C2×Q8—221no—
249C2×Q8—221no—
250C2×Q8—222no—
251C2×Q8—222no—
252C2×Q8—221no—
253C2×Q8—221no—
254C2×Q8—441no—
255C2×Q8—441no—
256C2×Q8—442no—
257C2×Q8—442no—
258C2×Q8—882no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4C2×D4411yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4#434311yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—441no—
276C2×C8—442no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—222no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C42—441no—
290C42—441no—
291C42C2×D4411yescharacteristic
292C42C2×D4411yescharacteristic
293C42D4×D1111yescharacteristic
294C42D4×D1111yescharacteristic
295C11#1027711yescharacteristic, complemented, Sylow
296C23#6694811yescharacteristic
297Q8—222no—
298Q8—222no—
299Q8—441no—
300Q8—441no—
301Q8—444no—
302Q8—882no—
303Q8—882no—
304Q8—881no—
305Q8—881no—
306C2×C4—22no—
307C2×C4—222no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—882no—
315C2×C4—882no—
316C2×C4#6692711yescharacteristic
317C2×C4#6693511yescharacteristic
318C2×C4#6693511yescharacteristic
319C2×C4#6693511yescharacteristic
320C2×C4#6694811yescharacteristic
321C2×C4#6694811yescharacteristic
322C2×C4#6695712yes—
323C2×C4#6696212yes—
324C2×C4#6696511yescharacteristic
325C2×C4#6696811yescharacteristic
326C2×C4#6696811yescharacteristic
327C2×C4Q16×D1111yescharacteristic
328C8—42no—
329C8—42no—
330C8—42no—
331C8—881no—
332C22#1062228411yescharacteristic
333C22#1062245812yes—
334C22#1062248111yescharacteristic
335C22#1062250011yescharacteristic
336C22#1062251112yes—
337C4—21no—
338C4—21no—
339C4—442no—
340C4—882no—
341C4—881no—
342C4—882no—
343C4#1062230911yescharacteristic
344C4#1062232811yescharacteristic
345C4#1062234612yes—
346C4#1062239611yescharacteristic
347C4#1062239611yescharacteristic
348C4#1062242111yescharacteristic
349C4#1062242111yescharacteristic
350C2#1306807512yes—
351C2#1306819912yes—
352C2#1306962711yescharacteristic
353C2#1306971311yescharacteristic
354C2#1306973311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socle, prime radicalC23×C11#121
hypercenter#1277D11
hypocenterC11#10277
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
295. C11#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106224632
C2×#106224642
#130695522
C2×#106221192
C2×#106221242
C11×#12772
#1027711