Finite Group Databasebeta

← #14658151

Subgroups — #14658151

Order 2816.

438 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079437C211yesmaximal, characteristic
2#13069082C211yesmaximal, characteristic
3#13069050C211yesmaximal, characteristic
4#13068823C211yesmaximal, characteristic
5#13067189C211yesmaximal, characteristic
6#13066523C211yesmaximal, characteristic
7C11×#1472C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13#10622841—21no—
14C2×#66899—21no—
15#10622825C2211yescharacteristic
16#10622820C2211yescharacteristic
17C2×#66888—21no—
18C2×#66883—21no—
19#10622665—21no—
20#10622665—21no—
21#10622663—21no—
22#10622656—21no—
23#10622584—21no—
24C11×#324—22no—
25#10622192—21no—
26#10622190—21no—
27#10622167—21no—
28#10622105—22no—
29C22×Q8×C11D411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C22×Dic22D411yescharacteristic
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×#4326—21no—
44C2×#4326—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47#66977—21no—
48#66977—21no—
49#66977—21no—
50#66977—21no—
51C2×Dic11⋊C4—21no—
52C2×#4318—21no—
53C2×#4318—21no—
54C2×#4318—42no—
55C2×#4318D411yescharacteristic
56C2×#4318D411yescharacteristic
57C22×C11⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8D412yes—
62#66899—21no—
63#66899—21no—
64#66899—42no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#66888—42no—
69#66883—42no—
70#66874—21no—
71#66874—21no—
72#66872—21no—
73#66872—21no—
74#10563—111nomaximal, Sylow
75C24×C11#4111yescharacteristic
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—41no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—81no—
112#4326—81no—
113#4326—81no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120#4318—22no—
121#4318—22no—
122#4318—41no—
123#4318—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#3195—111no—
132#1901—111no—
133#1894—111no—
134#1855—111no—
135#1520—111no—
136#1472D1111yescharacteristic
137#1305—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11#12111yescharacteristic
143C23×C11#12311yescharacteristic
144C23×C11#12411yescharacteristic
145Q8×C11—42no—
146Q8×C11—41no—
147Q8×C11—41no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173Dic22—41no—
174Dic22—41no—
175Dic22—81no—
176C8×C11—42no—
177C8×C11—81no—
178C11⋊C8—42no—
179C11⋊C8—41no—
180C11⋊C8—41no—
181C22×M16—111no—
182C2×C22⋊Q8—111no—
183C2×C22⋊Q8C2×D1111yescharacteristic
184#483—221no—
185#483—221no—
186#470—221no—
187#470—221no—
188#451—221no—
189#451—221no—
190C2×#108—221no—
191C2×#103—221no—
192C2×#101—221no—
193#407—111no—
194#407C2×D1111yescharacteristic
195C2×C22⋊C8C2×D1111yescharacteristic
196#380—111no—
197#343—221no—
198#341—221no—
199#340—221no—
200#328—222no—
201#324—22no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#39411yescharacteristic
213C22×C11#47111yescharacteristic
214C22×C11#47311yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11B(4,𝔽2)11yescharacteristic
221C4×C11#45811yescharacteristic
222Dic11—81no—
223Dic11—81no—
224Dic11—161no—
225C22×Q8—111no—
226C22×Q8D4411yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C2×Q16—221no—
229C2×Q16—221no—
230C2×M16—21no—
231C2×M16—111no—
232C2×M16—111no—
233C2×M16—221no—
234C2×M16—221no—
235C2×M16—442no—
236C22×C8—21no—
237C22×C8—221no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—221no—
243C22⋊Q8—221no—
244C22⋊Q8—221no—
245C22⋊Q8—221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4D4411yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254#108—442no—
255#106—221no—
256#106—221no—
257#103—221no—
258#103—221no—
259#103—221no—
260#103—221no—
261#103—442no—
262#101—442no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268C22⋊C8C22⋊D1112yes—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—41no—
273C2×C11—41no—
274C2×C11#204411yescharacteristic
275C2×C11#204911yescharacteristic
276C2×C11#205211yescharacteristic
277C24#433911yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—221no—
283C2×Q8—221no—
284C2×Q8—441no—
285C2×Q8—441no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4C2×D4411yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C22×C4#434111yescharacteristic
297C22×C4#434111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299Q16—881no—
300Q16—881no—
301M16—41no—
302M16—41no—
303M16—222no—
304M16—222no—
305M16—441no—
306M16—441no—
307M16—441no—
308M16—441no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—222no—
314C2×C8—221no—
315C2×C8—221no—
316C2×C8—441no—
317C2×C8—441no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—881no—
333C11#1056311yescharacteristic, complemented, Sylow
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#6693611yescharacteristic
339C23#6693811yescharacteristic
340C23#6698311yescharacteristic
341Q8—42no—
342Q8—41no—
343Q8—41no—
344Q8—441no—
345Q8—441no—
346Q8—881no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4—881no—
368C2×C4#6693511yescharacteristic
369C2×C4#6693911yescharacteristic
370C2×C4#6699111yescharacteristic
371C2×C4#6699211yescharacteristic
372C8—42no—
373C8—81no—
374C8—442no—
375C8—441no—
376C8—441no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1062257411yescharacteristic
388C22#1062275411yescharacteristic
389C22#1062275611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—881no—
396C4—881no—
397C4—1761no—
398C4#1062235411yescharacteristic
399C4#1062235511yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1306986611yescharacteristic
405C2#1306989511yescharacteristic
406C2#1306991411yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1472C2
socleC22×C11#394
prime radicalC24×C11#41
hypercenter#1472D11
hypocenterC11#10563
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
333. C11#10563semidirect

Maximal subgroups

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

subgroupindex
#130794372
#130690822
#130690502
#130688232
#130671892
#130665232
C11×#14722
#1056311