Finite Group Databasebeta

← #14654494

Subgroups — #14654494

Order 2816.

510 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#10622657C211yesmaximal, characteristic
2C2×#10622656C211yesmaximal, characteristic
3#13068694C211yesmaximal, characteristic
4#13066980C211yesmaximal, characteristic
5#13066980C211yesmaximal, characteristic
6#13066503C211yesmaximal, characteristic
7C11×#3195C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C11×#483—21no—
12C11×#483—21no—
13C11×#470—22no—
14C11×#451—21no—
15C11×#451—21no—
16C11×#407C2211yescharacteristic
17C2×#66899—21no—
18C2×#66899—21no—
19#10622820C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622657—22no—
23#10622657—22no—
24#10622656—22no—
25#10622656—22no—
26C2×#66872—21no—
27C2×#66871—21no—
28#10622192—22no—
29#10622166—22no—
30#10622166—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C2×C11×Q16—22no—
36C2×C11×M16D412yes—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11D412yes—
57C2×#4318—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C11×#106—22no—
61C11×#103—22no—
62C11×#103—22no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65#66899—24no—
66#66899—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)D412yes—
72C22⋊(C11⋊C8)D412yes—
73#66872—24no—
74#66871—24no—
75#9995—111nomaximal, Sylow
76C24×C11#4111yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C22×Dic11—82no—
98C11×Q16—82no—
99C11×M16—42no—
100C2×C8×C11—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117#4318—42no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—41no—
123#3195D1111yescharacteristic
124C2×#484—111no—
125C2×#483—111no—
126#1821—111no—
127#1472—111no—
128#1472—111no—
129#1298—111no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11#12111yescharacteristic
134C23×C11#12111yescharacteristic
135C23×C11#12111yescharacteristic
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×Dic11—42no—
159C2×Dic11—82no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C8×C11—42no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C2×C22⋊Q8C2×D1111yescharacteristic
167C2×C22⋊Q8C2×D1111yescharacteristic
168C22×C4⋊C4—111no—
169#484—222no—
170#484—222no—
171#483—21no—
172#483—21no—
173#483—222no—
174#483—222no—
175#470—22no—
176#451—21no—
177#451—21no—
178C2×#107—221no—
179C2×#106—221no—
180C2×#103—221no—
181C2×#103—221no—
182#407—111no—
183#407C2×D1111yescharacteristic
184C2×C22⋊C8—111no—
185C2×C22⋊C8—111no—
186#343—222no—
187#324—222no—
188#324—222no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—44no—
197C22×C11#39211yescharacteristic
198C22×C11#47112yes—
199C22×C11#47312yes—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11#45812yes—
208Dic11—82no—
209C22×Q8C22⋊D1111yescharacteristic
210C22×Q8C22⋊D1111yescharacteristic
211C23×C4—221no—
212C23×C4C22×D1111yescharacteristic
213C2×Q16—22no—
214C2×M16—221no—
215C2×M16C22⋊D1112yes—
216C22×C8—221no—
217C22×C8—221no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—112no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4C22⋊D1111yescharacteristic
235C2×C4⋊C4C22⋊D1111yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238#107—224no—
239#106—22no—
240#106—224no—
241#103—22no—
242#103—22no—
243#103—224no—
244#103—224no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—112no—
248C22⋊C8—112no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253C2×C11—22no—
254C2×C11—22no—
255C2×C11—41no—
256C2×C11#201911yescharacteristic
257C2×C11#202011yescharacteristic
258C2×C11#202211yescharacteristic
259C24#434111yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—42no—
265C2×Q8—42no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—222no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4—882no—
275C22×C4D4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281Q16—82no—
282M16—42no—
283M16—442no—
284C2×C8—22no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—442no—
288C2×C8—442no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C11#999511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23#6699111yescharacteristic
311C23#6699211yescharacteristic
312C23#6699211yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—42no—
316Q8—42no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—442no—
332C2×C4—882no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4#6699011yescharacteristic
336C2×C4#6699011yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—42no—
340C8—442no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1062281612yes—
352C22#1062281712yes—
353C22#1062283611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—882no—
362C4#1062285612yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1306972711yescharacteristic
367C2#1306973411yescharacteristic
368C2#1306974511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3195C2
socleC22×C11#392
prime radicalC24×C11#41
hypercenter#3195D11
hypocenterC11#9995
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
306. C11#9995semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
C2×#106226562
#130686942
#130669802
#130665032
C11×#31952
#999511