Finite Group Databasebeta

← #14664806

Subgroups — #14664806

Order 2816.

644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068604C211yesmaximal, characteristic, complemented
2#13066934C211yesmaximal, characteristic, complemented
3#13066613C214yesmaximal, complemented
4C11×#2541C211yesmaximal, characteristic
5C2×C11×#127—21no—
6C2×C11×#127C411yescharacteristic, complemented
7C2×C11×#121—21no—
8C2×C11×#121—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C11×#392C412yescomplemented
11C11×#392C2212yes—
12C11×#390—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898—21no—
15#10622825—21no—
16C2×C22⋊(C11⋊C8)—21no—
17#10622166—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×D4×C11—22no—
21C22×D4×C11—22no—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C412yes—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#127—41no—
29C11×#127—41no—
30C11×#127—42no—
31C11×#127—42no—
32C11×#121—44no—
33C11×#121—44no—
34C4×D4×C11—41no—
35C4×D4×C11—41no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C42×C11—21no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C22⋊Dic11—22no—
45C2×C4⋊Dic11—41no—
46C22×C11⋊C8—41no—
47C11×#95C2×C412yes—
48#66898—42no—
49C11⋊#95—41no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—41no—
52#11877—111nomaximal, Sylow
53C24×C11—22no—
54C24×C11C22⋊C411yescharacteristic
55C24×C11C2×D411yescharacteristic
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—44no—
61C2×D4×C11—44no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—44no—
66C2×D4×C11—42no—
67C2×D4×C11—42no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—82no—
72C2×D4×C11—82no—
73C2×D4×C11—82no—
74C2×D4×C11D812yes—
75C2×D4×C11SD1612yes—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—42no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—44no—
94C11×C22⋊C4—44no—
95C42×C11—21no—
96C42×C11—21no—
97C42×C11—42no—
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100C4⋊Dic11—82no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—82no—
103#2541D1111yescharacteristic
104#1799—111no—
105#1459—111no—
106#1343—114no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11#10212yes—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11C2×D811yescharacteristic
125C23×C11C2×SD1611yescharacteristic
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—82no—
129D4×C11—84no—
130D4×C11—88no—
131D4×C11—84no—
132D4×C11—84no—
133D4×C11—84no—
134D4×C11—82no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11#9911yescharacteristic
152C2×C4×C11#9911yescharacteristic
153C2×C4×C11#10212yes—
154C2×Dic11—82no—
155C2×Dic11—82no—
156C2×Dic11—82no—
157C11⋊C8—82no—
158C2×#127—21no—
159C2×#127Dic1111yescharacteristic, complemented
160C2×#121—21no—
161C2×#121—21no—
162C2×C4×D4C2×D1111yescharacteristic
163C2×#99—221no—
164C2×C22⋊C8—221no—
165#392Dic1112yescomplemented
166#392C2×D1112yes—
167#390—21no—
168#380—221no—
169C4×C4⋊C4Dic1111yescharacteristic, complemented
170#342—112no—
171#324—221no—
172#323—112no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11C2×#9911yescharacteristic
195C22×C11C2×#10211yescharacteristic
196C22×C11#42111yescharacteristic
197C4×C11—21no—
198C4×C11—22no—
199C4×C11—44no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11#35312yes—
204Dic11—162no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C2×Dic1112yes—
210C22×D4C22⋊D1111yescharacteristic
211C23×C4C22⋊D1111yescharacteristic
212C23×C4C22⋊D1111yescharacteristic
213C22×C8—441no—
214#127—41no—
215#127—41no—
216#127—42no—
217#127—42no—
218#121—44no—
219#121—44no—
220C4×D4—41no—
221C4×D4—41no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—441no—
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—222no—
228C2×C22⋊C4C2×Dic1111yescharacteristic
229C2×C22⋊C4C22×D1111yescharacteristic
230C2×C42—21no—
231C2×C42C2×Dic1111yescharacteristic
232#99—442no—
233C22⋊C8—222no—
234C22⋊C8—441no—
235#95—441no—
236#95C2×Dic1112yes—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—41no—
240C2×C11—42no—
241C2×C11—41no—
242C2×C11—162no—
243C2×C11#151911yescharacteristic
244C2×C11#212211yescharacteristic
245C2×C11C2×#35311yescharacteristic
246C24—22no—
247C24C22⋊Dic1111yescharacteristic
248C24C2×C22⋊D1111yescharacteristic
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—44no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—82no—
265C2×D4—82no—
266C2×D4—82no—
267C2×D4#432312yes—
268C2×D4#432412yes—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—442no—
277C22×C4C22⋊Dic1111yescharacteristic
278C22×C4C22⋊Dic1111yescharacteristic
279C22×C4C22⋊Dic1111yescharacteristic
280C22×C4C22×Dic1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282C2×C8—442no—
283C2×C8—882no—
284C4⋊C4—24no—
285C4⋊C4—41no—
286C4⋊C4—882no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—44no—
290C22⋊C4—44no—
291C22⋊C4—442no—
292C22⋊C4—442no—
293C42—21no—
294C42—21no—
295C42—42no—
296C11#1187711yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23#6689612yes—
313C23C2×#432311yescharacteristic
314C23C2×#432411yescharacteristic
315C23C2×C22⋊Dic1111yescharacteristic
316D4—42no—
317D4—42no—
318D4—84no—
319D4—82no—
320D4—88no—
321D4—84no—
322D4—84no—
323D4—84no—
324D4—82no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—882no—
342C2×C4—882no—
343C2×C4—882no—
344C2×C4#6689612yes—
345C2×C4#6689811yescharacteristic
346C2×C4#6689811yescharacteristic
347C8—882no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—82no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22C2×#6689611yescharacteristic
370C22C2×#6689811yescharacteristic
371C22#1062284911yescharacteristic
372C4—22no—
373C4—21no—
374C4—44no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—1762no—
379C4#1062218312yes—
380C2—21no—
381C2—21no—
382C2—41no—
383C2—42no—
384C2—41no—
385C2—162no—
386C2#1306718411yescharacteristic
387C2#1307026611yescharacteristic
388C2C2×#1062218311yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2541C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2541D11
hypocenterC11#11877
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13068604C2semidirect
2. #13066934C2semidirect
3. #13066613C2semidirect
6. C2×C11×#127C4semidirect
10. C11×#392C4semidirect
13. C4×C11×C4⋊C4C4semidirect
159. C2×#127Dic11semidirect
165. #392Dic11semidirect
169. C4×C4⋊C4Dic11semidirect
296. C11#11877semidirect

Maximal subgroups

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

subgroupindex
#130686042
#130669342
#130666132
C11×#25412
#1187711