Finite Group Databasebeta

← #14673446

Subgroups — #14673446

Order 2816.

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

normal subgroups only

This group has 476 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#13075827C211yesmaximal, characteristic
2#13068897C211yesmaximal, characteristic
3#13068826C211yesmaximal, characteristic
4#13066740C211yesmaximal, characteristic
5#13066734C211yesmaximal, characteristic
6#13066733C211yesmaximal, characteristic
7C11×#1867C211yesmaximal, characteristic
8C11×#518C2211yescharacteristic
9C2×C11×#99C2211yescharacteristic
10C11×#386C2211yescharacteristic
11C11×#385—21no—
12#10622834C2211yescharacteristic
13#10622833C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15C2×#66897C2211yescharacteristic
16#10622823—21no—
17#10622608—21no—
18#10622562—21no—
19#10622561—21no—
20#10622559—21no—
21#10622555—21no—
22#10622270—21no—
23#10622268—21no—
24C11×#342—21no—
25#10622170—21no—
26#10622164—21no—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C11×#117—21no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—41no—
51C2×C4×Dic11D411yescharacteristic
52C2×#4318—21no—
53C11×#99—21no—
54C11×#99Q812yes—
55C11×#95—21no—
56C11×#95—41no—
57#66898—21no—
58#66898Q812yes—
59#66897—21no—
60#66897Q812yes—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—41no—
66#66872—41no—
67#66871—41no—
68#13462—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11C2×Q811yescharacteristic
74C2×D4×C11C2×Q811yescharacteristic
75C2×D4×C11C2×Q811yescharacteristic
76C2×D4×C11#4111yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—81no—
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—42no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—82no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C42×C11—41no—
105C22⋊Dic11—22no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—42no—
109C22⋊Dic11—81no—
110C22⋊Dic11—81no—
111C4⋊Dic11—41no—
112C4⋊Dic11—81no—
113Dic11⋊C4—42no—
114Dic11⋊C4—81no—
115Dic11⋊C4—81no—
116Dic11⋊C4—81no—
117Dic11⋊C4—82no—
118C4×Dic11—41no—
119#4318—22no—
120#4318—41no—
121C2×C11⋊C8—41no—
122#2748—111no—
123#1867—111no—
124#1867D1111yescharacteristic
125#1856—111no—
126#1393—111no—
127#1390—111no—
128#1390—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11#12011yescharacteristic
138C23×C11C22⋊Q811yescharacteristic
139C23×C11C22⋊Q811yescharacteristic
140C23×C11C4⋊Q811yescharacteristic
141C23×C11C4⋊Q811yescharacteristic
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C22⋊Q811yescharacteristic
166C2×C4×C11C4⋊Q811yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184C11⋊C8—42no—
185#518C2×D1111yescharacteristic
186#428—221no—
187C2×#100—111no—
188C2×#99—111no—
189C2×#99C2×D1111yescharacteristic
190#399—221no—
191#398—221no—
192#396—221no—
193#390—111no—
194#387—221no—
195#386—111no—
196#386C2×D1111yescharacteristic
197#385—21no—
198#385—221no—
199#385—221no—
200#380—221no—
201#342—21no—
202#342—221no—
203#339—221no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39511yescharacteristic
221C22×C11B(4,𝔽2)11yescharacteristic
222C22×C11#45811yescharacteristic
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—81no—
230Dic11—42no—
231Dic11—81no—
232Dic11—81no—
233Dic11—82no—
234Dic11—81no—
235C22×D4C22×D1111yescharacteristic
236C23×C4—111no—
237C23×C4C22⋊D1111yescharacteristic
238C2×M16—221no—
239C4×D4—41no—
240C4×D4—41no—
241#117—21no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—441no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4C22⋊D1111yescharacteristic
260C2×C42—111no—
261#107—441no—
262#106—441no—
263#100—112no—
264#100—221no—
265#99—21no—
266#99—112no—
267#99—221no—
268#99Dic2212yes—
269#95—21no—
270#95—41no—
271#95—221no—
272#95—221no—
273#95—221no—
274#95—221no—
275#95—441no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11—41no—
281C2×C11—41no—
282C2×C11#206211yescharacteristic
283C2×C11#219711yescharacteristic
284C2×C11#220011yescharacteristic
285C24D4×D1111yescharacteristic
286C24C2×C22⋊D1111yescharacteristic
287C2×D4—41no—
288C2×D4—41no—
289C2×D4C2×Dic2211yescharacteristic
290C2×D4#433911yescharacteristic
291C2×D4Q8×D1111yescharacteristic
292C2×D4Q8×D1111yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—81no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—442no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4D4×D1111yescharacteristic
310M16—222no—
311M16—441no—
312C2×C8—441no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—82no—
316C4⋊C4—441no—
317C4⋊C4—442no—
318C4⋊C4—881no—
319C4⋊C4—881no—
320C4⋊C4—881no—
321C4⋊C4—881no—
322C4⋊C4—882no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—81no—
330C22⋊C4—222no—
331C22⋊C4—442no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—881no—
335C22⋊C4—881no—
336C42—41no—
337C42—441no—
338C11#1346211yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#6694111yescharacteristic
348C23#6694911yescharacteristic
349C23#6697711yescharacteristic
350C23#6699011yescharacteristic
351C23#6699711yescharacteristic
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
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—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—222no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4#6694111yescharacteristic
393C2×C4#6694911yescharacteristic
394C8—442no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22#1062259211yescharacteristic
412C22#1062264511yescharacteristic
413C22#1062266611yescharacteristic
414C4—21no—
415C4—21no—
416C4—81no—
417C4—82no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4—442no—
422C4—881no—
423C4—881no—
424C4—882no—
425C4—881no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—41no—
431C2—41no—
432C2#1306996911yescharacteristic
433C2#1307060311yescharacteristic
434C2#1307062111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1867C2
socleC22×C11B(4,𝔽2)
hypercenter#1867D11
hypocenterC11#13462
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1867

Complements

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

NH ≅ G/Ntype
338. C11#13462semidirect

Maximal subgroups

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

subgroupindex
#130758272
#130688972
#130688262
#130667402
#130667342
#130667332
C11×#18672
#1346211