Finite Group Databasebeta

← #14654184

Subgroups — #14654184

Order 2816.

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

normal subgroups only

This group has 574 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#13078560C211yesmaximal, characteristic
2#13072903C211yesmaximal, characteristic
3#13068716C211yesmaximal, characteristic
4#13067149C211yesmaximal, characteristic
5#13066946C211yesmaximal, characteristic
6#13066469C211yesmaximal, characteristic
7C11×#2583C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66979C2211yescharacteristic
11C11×#398—21no—
12C11×#395—21no—
13C11×#389—22no—
14C11×#385—21no—
15C11×#385—21no—
16C4×C11×C22⋊C4C2211yescharacteristic
17#10622838—21no—
18#10622824—21no—
19#10622824C2211yescharacteristic
20#10622823—21no—
21#10622820C2211yescharacteristic
22#10622820C2211yescharacteristic
23#10622658—22no—
24#10622657—21no—
25#10622656—21no—
26#10622599—21no—
27#10622596—21no—
28#10622591—22no—
29#10622577—21no—
30#10622176—22no—
31#10622166—22no—
32#10622161—22no—
33C22×Q8×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11D412yes—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56#66979—21no—
57#66979—21no—
58#66979—21no—
59#66979—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D411yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C2×#4318—21no—
65C2×#4318—21no—
66C11×#95—22no—
67C11×#95—22no—
68C11×#95—21no—
69#66899—22no—
70#66899—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95D412yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)D412yes—
80#66872—22no—
81#66871—22no—
82#9945—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—42no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—44no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—82no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—42no—
122C22⋊Dic11—42no—
123C22⋊Dic11—41no—
124C22⋊Dic11—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129Dic11⋊C4—44no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132#4318—42no—
133#4318—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136#3095—111no—
137#2583D1111yescharacteristic
138#2484—111no—
139#1826—111no—
140#1511—111no—
141#1463—111no—
142#1284—111no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11#12111yescharacteristic
149Q8×C11—42no—
150Q8×C11—81no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—81no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C11⋊C8—42no—
187C11⋊C8—81no—
188C2×C22⋊Q8C2×D1111yescharacteristic
189C2×#117—111no—
190C22×C4⋊C4C2×D1111yescharacteristic
191#485—222no—
192#484—221no—
193#483—221no—
194#428—221no—
195#419—221no—
196#407—111no—
197#407—111no—
198#400—221no—
199#398—21no—
200#398—221no—
201#395—21no—
202#389—22no—
203#387—222no—
204#385—21no—
205#385—21no—
206#385—221no—
207#381—111no—
208#381—221no—
209C4×C22⋊C4C2×D1111yescharacteristic
210#339—222no—
211#328—222no—
212#324—222no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11#39211yescharacteristic
222C22×C11#45612yes—
223C22×C11#45812yes—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—44no—
229C4×C11—42no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—81no—
233Dic11—82no—
234Dic11—81no—
235Dic11—81no—
236C22×Q8C22⋊D1111yescharacteristic
237C23×C4C22⋊D1111yescharacteristic
238C23×C4C22⋊D1111yescharacteristic
239C23×C4C22×D1111yescharacteristic
240C2×M16—221no—
241C2×M16—221no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246#117—221no—
247#117—221no—
248#117—221no—
249#117—221no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4C22⋊D1111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C42—221no—
268C2×C42C22⋊D1112yes—
269#107—222no—
270#106—222no—
271#103—222no—
272#103—222no—
273C22⋊C8—112no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#95—22no—
278#95—22no—
279#95—21no—
280#95—112no—
281#95—222no—
282#95—222no—
283#95—222no—
284#95—221no—
285C2×C11—22no—
286C2×C11—22no—
287C2×C11—41no—
288C2×C11#200511yescharacteristic
289C2×C11#201011yescharacteristic
290C2×C11#202211yescharacteristic
291C24C2×C22⋊D1111yescharacteristic
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—42no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—222no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4#434111yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316M16—442no—
317M16—442no—
318C2×C8—222no—
319C2×C8—441no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—44no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—82no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—444no—
335C22⋊C4—24no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—442no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C42—42no—
342C42—441no—
343C42—441no—
344C11#994511yescharacteristic, complemented, Sylow
345C23—22no—
346C23—22no—
347C23—41no—
348C23#6699011yescharacteristic
349C23#6699211yescharacteristic
350C23#6700611yescharacteristic
351Q8—42no—
352Q8—81no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4#6699011yescharacteristic
385C2×C4#6699111yescharacteristic
386C2×C4#6699211yescharacteristic
387C2×C4#6699311yescharacteristic
388C8—442no—
389C8—881no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22#1062270812yes—
399C22#1062283611yescharacteristic
400C22#1062285612yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—44no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—882no—
411C4—881no—
412C4—881no—
413C2—22no—
414C2—22no—
415C2—41no—
416C2#1306965211yescharacteristic
417C2#1306968111yescharacteristic
418C2#1306974511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2583C2
socleC22×C11#392
prime radicalC24×C11C2×D4
hypercenter#2583D11
hypocenterC11#9945
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
344. C11#9945semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130729032
#130687162
#130671492
#130669462
#130664692
C11×#25832
#994511