Finite Group Databasebeta

← #14655428

Subgroups — #14655428

Order 2816.

536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079615C211yesmaximal, characteristic
2C2×#10622699C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic, complemented
4#13067231C211yesmaximal, characteristic, complemented
5#13066967C211yesmaximal, characteristic
6#13066516C211yesmaximal, characteristic, complemented
7C11×#3230C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4326—21no—
11C22×#4325—21no—
12C2×#66928C2211yescharacteristic
13C11×#500—21no—
14C11×#487—21no—
15C11×#484—22no—
16C11×#477—22no—
17C11×#431C2211yescharacteristic
18#10622702—21no—
19#10622699—22no—
20#10622699—21no—
21#10622699—22no—
22#10622663—21no—
23#10622659—21no—
24#10622641—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622185—22no—
29#10622181—22no—
30#10622106—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×Dic22D411yescharacteristic
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—24no—
50C2×#4326—22no—
51C2×#4326—44no—
52C2×#4325—24no—
53C2×#4325—22no—
54C2×#4325—44no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C22×C11⋊C8—21no—
58#66928—21no—
59#66928—21no—
60#66928—21no—
61#66928—21no—
62C11×#107—24no—
63C11×C4⋊C8—21no—
64C11×#103—24no—
65C11×C22⋊C8D412yes—
66C4×C8×C11—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66874—22no—
70#66873—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74#66867—21no—
75#66867—21no—
76#66867D412yes—
77#10133—111nomaximal, Sylow
78C23×D11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—42no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—42no—
96C2×C8×C11—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113#4326—48no—
114#4326—82no—
115#4325—48no—
116#4325—82no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#3230D1111yescharacteristic, complemented
126#3215—111no—
127C2×#497—111no—
128#1556—111no—
129#1531—111no—
130#1469—111no—
131#1302—111no—
132C23×C11#12111yescharacteristic
133C22×D11—41no—
134C22×D11—42no—
135C22×D11—81no—
136C22×D11—81no—
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—82no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×Dic11—41no—
156C2×Dic11—81no—
157D44—42no—
158D44—42no—
159Dic22—42no—
160Dic22—42no—
161C8×C11—42no—
162C11⋊C8—24no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C22×Q16—221no—
166C22×SD16—221no—
167#533C2×D1111yescharacteristic
168C2×C4⋊Q8C2×D1111yescharacteristic
169C2×#124—111no—
170#500—21no—
171#497—222no—
172#497—222no—
173#497—221no—
174#489—221no—
175#487—21no—
176#484—22no—
177#477—22no—
178#464—222no—
179#451—221no—
180#450—221no—
181#432—111no—
182#432—111no—
183#431C2×D1111yescharacteristic
184C2×#97—111no—
185#332—222no—
186#330—222no—
187#323—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#39211yescharacteristic
191C22×C11#47312yes—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—162no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11#45312yes—
205Dic11—81no—
206C22×Q8—21no—
207C22×Q8—111no—
208C22×D4—111no—
209C2×Q16—224no—
210C2×Q16—222no—
211C2×Q16—444no—
212C2×SD16—224no—
213C2×SD16—222no—
214C2×SD16—444no—
215C22×C8—221no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8C22⋊D1112yes—
220C4⋊Q8C22⋊D1111yescharacteristic
221C4⋊Q8C22⋊D1111yescharacteristic
222#125—21no—
223#124—221no—
224#124—221no—
225#124—221no—
226#124—221no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#107—24no—
238C4⋊C8—21no—
239C4⋊C8—112no—
240C4⋊C8—221no—
241#103—24no—
242#103—222no—
243#102—222no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246C22⋊C8C22⋊D1112yes—
247#97—112no—
248#97—221no—
249#97—221no—
250#97—221no—
251C4×C8—21no—
252C2×C11—22no—
253C2×C11#200211yescharacteristic
254C2×C11#200911yescharacteristic
255C2×C11#202011yescharacteristic
256D11—161no—
257C24—221no—
258C2×Q8—21no—
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—41no—
264C2×Q8—221no—
265C2×Q8—221no—
266C2×Q8—442no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—442no—
270C22×C4—41no—
271C22×C4—221no—
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275Q16—448no—
276Q16—882no—
277SD16—448no—
278SD16—882no—
279C2×C8—22no—
280C2×C8—224no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C42—41no—
300C42D4×D1111yescharacteristic
301C42D4×D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C42C2×C22⋊D1111yescharacteristic
304C11#1013311yescharacteristic, complemented, Sylow
305C23—441no—
306C23—442no—
307C23—881no—
308C23—881no—
309C23#6699111yescharacteristic
310Q8—42no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314Q8—82no—
315Q8—442no—
316Q8—442no—
317D4—442no—
318D4—442no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—441no—
327C2×C4—881no—
328C2×C4#6699011yescharacteristic
329C2×C4#6699011yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4#6699211yescharacteristic
332C2×C4#6699311yescharacteristic
333C2×C4#6700611yescharacteristic
334C8—42no—
335C8—224no—
336C8—442no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22—881no—
341C22—881no—
342C22—881no—
343C22—1762no—
344C22#1062280512yes—
345C22#1062283611yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—81no—
353C4—81no—
354C4—881no—
355C4#1062281112yes—
356C2—22no—
357C2—1761no—
358C2#1306962811yescharacteristic
359C2#1306967611yescharacteristic
360C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3230D11
hypocenterC11#10133
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #13067333C2semidirect
4. #13067231C2semidirect
6. #13066516C2semidirect
7. C11×#3230C2semidirect
125. #3230D11semidirect
304. C11#10133semidirect

Maximal subgroups

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

subgroupindex
#130796152
C2×#106226992
#130673332
#130672312
#130669672
#130665162
C11×#32302
#1013311