Finite Group Databasebeta

← #14649554

Subgroups — #14649554

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622549C211yesmaximal, characteristic, complemented
2#13068684C211yesmaximal, characteristic, complemented
3C2×#10622175C212yesmaximal
4#13066494C212yesmaximal, complemented
5C11×#2854C211yesmaximal, characteristic
6C2×C11×#123—21no—
7C2×C11×#121C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C22×C4⋊Dic11—21no—
10C11×#390C412yescomplemented
11C11×#389C412yescomplemented
12C11×#388—22no—
13C11×#386—21no—
14C11×#380C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622549—24no—
19#10622175—24no—
20#10622162—22no—
21C22×D4×C11—21no—
22C22×D4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—22no—
27C11×#123—42no—
28C11×#123—42no—
29C11×#121—22no—
30C11×#121—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11—22no—
39C2×C42×C11—22no—
40C2×C42×C11C2×C412yes—
41C2×C42×C11D412yes—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11—42no—
44C2×C4⋊Dic11—42no—
45C22×C11⋊C8—22no—
46C11×#95—22no—
47C11×#95—21no—
48C11⋊#95—24no—
49C11⋊#95—22no—
50C11⋊#95D414yes—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53#9156—111nomaximal, Sylow
54C24×C11—21no—
55C24×C11C2×D411yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—42no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11C22⋊C412yes—
75C22×C4×C11C22⋊C412yes—
76C22×C4×C11D812yes—
77C22×C4×C11SD1612yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D412yes—
81C22×C4×C11#4112yes—
82C22×Dic11—24no—
83C22×Dic11—44no—
84C22×Dic11—44no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—44no—
90C11×C22⋊C4—44no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—44no—
94C11×C22⋊C4—42no—
95C42×C11—24no—
96C42×C11—24no—
97C4⋊Dic11—48no—
98C2×C11⋊C8—44no—
99C2×C11⋊C8—42no—
100#2854D1111yescharacteristic
101C2×#382—111no—
102#1817—111no—
103C2×#327—112no—
104#1294—112no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—41no—
108C23×C11—42no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—42no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#12011yescharacteristic
114C23×C11#12311yescharacteristic
115C23×C11C2×D811yescharacteristic
116C23×C11C2×SD1611yescharacteristic
117C23×C11AGL(1,ℤ/8)11yescharacteristic
118C23×C11#13711yescharacteristic
119D4×C11—82no—
120D4×C11—81no—
121D4×C11—81no—
122D4×C11—81no—
123D4×C11—81no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11#10214yes—
146C2×C4×C11C4×D412yes—
147C2×C4×C11#12112yes—
148C2×Dic11—44no—
149C2×Dic11—44no—
150C2×Dic11—44no—
151C2×Dic11—84no—
152C2×Dic11—84no—
153C11⋊C8—82no—
154C2×#123—21no—
155C2×#121C2×D1111yescharacteristic
156C22×C4⋊C4—221no—
157C22×C42C2×D1111yescharacteristic
158C2×C22⋊C8—112no—
159#390Dic1112yescomplemented
160#389Dic1112yescomplemented
161#388—22no—
162#386—21no—
163#382—224no—
164#380C2×D1111yescharacteristic
165C2×#95—112no—
166C2×#95—221no—
167#336—222no—
168#327—224no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11#38611yescharacteristic
183C22×C11#41012yes—
184C22×C11C2×#10211yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11#42112yes—
187C22×C11#44711yescharacteristic
188C22×C11#44811yescharacteristic
189C22×C11#48011yescharacteristic
190C22×C11#48111yescharacteristic
191C4×C11—24no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11—82no—
197Dic11—84no—
198C22×D4—21no—
199C22×D4C2×Dic1111yescharacteristic
200C23×C4—222no—
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C22×C8—222no—
205#123—42no—
206#123—42no—
207#121—22no—
208#121—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—224no—
211C2×C4⋊C4—442no—
212C2×C4⋊C4—442no—
213C2×C4⋊C4C2×Dic1111yescharacteristic
214C2×C4⋊C4C2×Dic1112yes—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C2×Dic1112yes—
222C2×C42C22⋊D1112yes—
223C22⋊C8—222no—
224C22⋊C8—222no—
225#95—22no—
226#95—21no—
227#95—114no—
228#95—224no—
229#95—222no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—161no—
235C2×C11#151212yes—
236C2×C11#151712yes—
237C2×C11#187411yescharacteristic
238C2×C11#189711yescharacteristic
239C2×C11#189911yescharacteristic
240C24—21no—
241C24C2×C22⋊D1111yescharacteristic
242C2×D4—22no—
243C2×D4—42no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—224no—
261C22×C4—444no—
262C22×C4—444no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4#432312yes—
266C22×C4#432412yes—
267C22×C4C22⋊Dic1112yes—
268C22×C4C22⋊Dic1112yes—
269C22×C4D4×D1112yes—
270C22×C4#434112yes—
271C22×C4C22×Dic1111yescharacteristic
272C22×C4C2×C22⋊D1111yescharacteristic
273C2×C8—444no—
274C2×C8—442no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—44no—
278C4⋊C4—448no—
279C22⋊C4—44no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—44no—
283C22⋊C4—42no—
284C42—24no—
285C42—24no—
286C11#915611yescharacteristic, complemented, Sylow
287C23—22no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—42no—
293C23—42no—
294C23C2×#432311yescharacteristic
295C23C2×#432411yescharacteristic
296C23#6698811yescharacteristic
297C23#6699011yescharacteristic
298C23#6700211yescharacteristic
299C23#6700411yescharacteristic
300C23C2×C22⋊Dic1111yescharacteristic
301D4—82no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—444no—
328C2×C4—444no—
329C2×C4—444no—
330C2×C4—884no—
331C2×C4—884no—
332C2×C4#6689614yes—
333C2×C4D4×Dic1112yes—
334C2×C4#6699212yes—
335C8—882no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—82no—
348C22—82no—
349C22#1062264611yescharacteristic
350C22#1062264711yescharacteristic
351C22#1062264911yescharacteristic
352C22#1062265311yescharacteristic
353C22C2×#6689611yescharacteristic
354C22#1062283311yescharacteristic
355C22#1062284511yescharacteristic
356C22#1062284912yes—
357C22#1062285312yes—
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—81no—
363C4—82no—
364C4—884no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—161no—
370C2#1306715412yes—
371C2#1306717612yes—
372C2#1306893411yescharacteristic
373C2#1306906511yescharacteristic
374C2#1306907511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2854C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2854D11
hypocenterC11#9156
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#10622549C2semidirect
2. #13068684C2semidirect
4. #13066494C2semidirect
10. C11×#390C4semidirect
11. C11×#389C4semidirect
159. #390Dic11semidirect
160. #389Dic11semidirect
286. C11#9156semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
#130686842
C2×#106221752
#130664942
C11×#28542
#915611