Finite Group Databasebeta

← #14654499

Subgroups — #14654499

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
1#13079440C211yesmaximal, characteristic
2C2×#10622335C211yesmaximal, characteristic
3C2×#10622334C211yesmaximal, characteristic
4#13068694C211yesmaximal, characteristic
5#13066979C211yesmaximal, characteristic
6#13066979C211yesmaximal, characteristic
7C11×#1298C211yesmaximal, characteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622750—22no—
16C2×#66882—21no—
17C2×#66881—21no—
18C2×#66880—21no—
19C2×#66880—21no—
20#10622352—21no—
21#10622352—21no—
22#10622335—22no—
23#10622335—22no—
24#10622334—21no—
25#10622334—21no—
26#10622334—22no—
27#10622334—22no—
28#10622192—22no—
29#10622107—22no—
30#10622107—22no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C22×Dic22D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C2×C11×M16D412yes—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D412yes—
48#66977—21no—
49#66977—21no—
50#66977—21no—
51#66977—21no—
52#66977—21no—
53#66977—21no—
54#66977—21no—
55#66977—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×#4318—21no—
59C2×Dic44—22no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C11×C22⋊C8D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#66882—24no—
69#66881—22no—
70#66881—24no—
71#66880—22no—
72#66880—22no—
73#66880—24no—
74#66880—24no—
75#9995—111nomaximal, Sylow
76C24×C11#4111yescharacteristic
77C22×C4×C11—42no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11—82no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—42no—
97C2×Dic22—42no—
98C11×M16—42no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120#4318—42no—
121C2×C11⋊C8—41no—
122Dic44—82no—
123#3195—111no—
124C2×#484—111no—
125C2×#483—111no—
126#1821—111no—
127#1472—111no—
128#1472—111no—
129#1298D1111yescharacteristic
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11#12111yescharacteristic
134C23×C11#12111yescharacteristic
135C23×C11#12111yescharacteristic
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—82no—
154C2×Dic11—82no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—82no—
158Dic22—42no—
159Dic22—42no—
160Dic22—42no—
161Dic22—42no—
162C8×C11—42no—
163C8×C11—42no—
164C8×C11—42no—
165C11⋊C8—81no—
166C2×C22⋊Q8—111no—
167C2×C22⋊Q8—111no—
168C22×C4⋊C4—111no—
169#484—222no—
170#484—222no—
171#483—222no—
172#483—221no—
173#483—221no—
174#483—222no—
175#470—222no—
176#451—221no—
177#451—221no—
178C2×#107—221no—
179C2×#106—221no—
180C2×#103—221no—
181C2×#103—221no—
182#407—111no—
183#407C2×D1111yescharacteristic
184C2×C22⋊C8C2×D1111yescharacteristic
185C2×C22⋊C8C2×D1111yescharacteristic
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#45812yes—
204Dic11—81no—
205Dic11—82no—
206Dic11—81no—
207Dic11—81no—
208Dic11—81no—
209C22×Q8—111no—
210C22×Q8—111no—
211C23×C4—221no—
212C23×C4C22×D1111yescharacteristic
213C2×Q16—222no—
214C2×M16—221no—
215C2×M16D4412yes—
216C22×C8—21no—
217C22×C8—21no—
218C22⋊Q8—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C22⋊Q8—221no—
223C22⋊Q8—221no—
224C22⋊Q8—221no—
225C22⋊Q8—221no—
226C2×C4⋊C4—112no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238#107—224no—
239#106—224no—
240#106—222no—
241#103—224no—
242#103—224no—
243#103—222no—
244#103—222no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251C22⋊C8D4412yes—
252C22⋊C8D4412yes—
253C2×C11—22no—
254C2×C11—22no—
255C2×C11—41no—
256C2×C11#201911yescharacteristic
257C2×C11#202011yescharacteristic
258C2×C11#202211yescharacteristic
259C24#434311yescharacteristic
260C2×Q8—221no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—442no—
265C2×Q8—442no—
266C22×C4—42no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—222no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4—882no—
275C22×C4C2×D4411yescharacteristic
276C22×C4C2×D4411yescharacteristic
277C22×C4C2×D4411yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281Q16—882no—
282M16—42no—
283M16—442no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—441no—
290C4⋊C4—222no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—222no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C11#999511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23#6694811yescharacteristic
311C23#6694811yescharacteristic
312C23#6694811yescharacteristic
313Q8—442no—
314Q8—442no—
315Q8—442no—
316Q8—442no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—882no—
331C2×C4—882no—
332C2×C4—882no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4#6692711yescharacteristic
336C2×C4#6693511yescharacteristic
337C2×C4#6693511yescharacteristic
338C2×C4#6693511yescharacteristic
339C8—42no—
340C8—42no—
341C8—42no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1062228411yescharacteristic
352C22#1062250912yes—
353C22#1062251112yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—881no—
358C4—882no—
359C4—881no—
360C4—881no—
361C4—881no—
362C4#1062235512yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1306973311yescharacteristic
367C2#1306973811yescharacteristic
368C2#1306974811yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1298C2
socleC22×C11#392
prime radicalC24×C11#41
hypercenter#1298D11
hypocenterC11#9995
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1298

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
#130794402
C2×#106223352
C2×#106223342
#130686942
#130669792
C11×#12982
#999511