Finite Group Databasebeta

← #14647383

Subgroups — #14647383

Order 2816.

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

normal subgroups only

This group has 446 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#13071557C211yesmaximal, characteristic
2C4×#66887C211yesmaximal, characteristic
3#13066956C211yesmaximal, characteristic
4#13066509C211yesmaximal, characteristic, complemented
5#13066482C211yesmaximal, characteristic, complemented
6#13066481C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C11×#376C2211yescharacteristic
12C2×#66887—21no—
13#10622553—21no—
14C4×(C2×D11)⋊C4—21no—
15#10622550C2211yescharacteristic
16#10622539C2211yescharacteristic
17C4×#4318C2211yescharacteristic
18#10622280C411yescharacteristic
19#10622279C411yescharacteristic
20#10622278—21no—
21#10622277C411yescharacteristic
22D11×#95C411yescharacteristic
23#10622267—21no—
24#10622192—21no—
25#10622106—21no—
26#10622106—21no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11C2×C411yescharacteristic
31C2×C11×M16—21no—
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4D411yescharacteristic
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×#4318—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#97—21no—
51C4×C8×C11—21no—
52C11×#95—21no—
53C11×#95C2×C411yescharacteristic
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66887—24no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67#8773—111nomaximal, Sylow
68C23×D11C22⋊C411yescharacteristic
69C23×D11C22⋊C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C2×D44—22no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—41no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—42no—
88C2×C4×D11—42no—
89C2×C4×D11—81no—
90C2×C4×D11—81no—
91C2×C4×D11—81no—
92C11×M16—22no—
93C11×M16—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C42×C11—42no—
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—81no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110Dic11⋊C4—81no—
111C4×Dic11—81no—
112#4318—22no—
113#4318—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2353—111no—
117C4×#100—111no—
118#1466—111no—
119#1300—111no—
120#1300D1111yescharacteristic, complemented
121#1288—111no—
122#1288—111no—
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11#10412yes—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11#11711yescharacteristic
145C2×C4×C11#11711yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—42no—
161D44—42no—
162C4×D11—81no—
163C4×D11—81no—
164C4×D11—81no—
165C4×D11—81no—
166C4×D11—84no—
167C8×C11—42no—
168C8×C11—81no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×C4×D4—111no—
172#432—111no—
173#432C2×D1111yescharacteristic
174C2×#100—221no—
175C4×M16—111no—
176C4×M16C2×D1111yescharacteristic
177#388—221no—
178#387—221no—
179#386—221no—
180#383—111no—
181#381—111no—
182#380—111no—
183C4×C22⋊C4—111no—
184C4×C22⋊C4—221no—
185#376C2×D1111yescharacteristic
186C2×#95—111no—
187#343—221no—
188#323—221no—
189#323—221no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38111yescharacteristic
193C22×C11C2×#10411yescharacteristic
194C22×C11#42111yescharacteristic
195C2×D11—22no—
196C2×D11—42no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—42no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—81no—
213Dic11—41no—
214Dic11—41no—
215Dic11—81no—
216Dic11—81no—
217C22×D4—111no—
218C23×C4—111no—
219C23×C4—111no—
220C23×C4—221no—
221C2×M16—21no—
222C2×M16—221no—
223C4×D4—221no—
224C4×D4—221no—
225C4×D4—221no—
226C4×D4—221no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C42—21no—
235C2×C42—221no—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—221no—
239#100—224no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242#97—21no—
243#97—21no—
244#97—221no—
245#97—221no—
246C4×C8—21no—
247C4×C8—221no—
248#95—21no—
249#95—111no—
250#95—111no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95C4×D1111yescharacteristic
256#95C4×D1111yescharacteristic
257C2×C11—21no—
258C2×C11—21no—
259C2×C11#182611yescharacteristic
260C2×C11#182711yescharacteristic
261C2×C11#182911yescharacteristic
262D11—42no—
263D11—81no—
264C24—111no—
265C24—111no—
266C2×D4—222no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—442no—
281C22×C4—442no—
282C22×C4—881no—
283C22×C4—881no—
284C22×C4—881no—
285C22×C4C2×C4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288M16—22no—
289M16—41no—
290M16—222no—
291M16—441no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—441no—
295C2×C8—441no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—881no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C22⋊C4—881no—
306C42—42no—
307C42—881no—
308C42#433911yescharacteristic
309C42#433911yescharacteristic
310C42#434111yescharacteristic
311C42#434311yescharacteristic
312C11#877311yescharacteristic, complemented, Sylow
313C23—112no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—221no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23C22⋊C4×D1111yescharacteristic
324D4—442no—
325D4—442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4—884no—
351C2×C4#6692511yescharacteristic
352C2×C4#6693611yescharacteristic
353C2×C4#6693611yescharacteristic
354C2×C4#6694511yescharacteristic
355C2×C4#6694711yescharacteristic
356C2×C4#6694711yescharacteristic
357C8—42no—
358C8—81no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—222no—
364C22—442no—
365C22—442no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—881no—
372C22—881no—
373C22#1062227711yescharacteristic
374C22D11×#10411yescharacteristic
375C22#1062243411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—81no—
384C4—441no—
385C4—441no—
386C4—881no—
387C4—881no—
388C2—21no—
389C2—21no—
390C2—442no—
391C2—881no—
392C2#1306871411yescharacteristic
393C2#1306871911yescharacteristic
394C2#1306872611yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1300C2
socleC22×C11#381
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1300D11
hypocenterC11#8773
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
4. #13066509C2semidirect
5. #13066482C2semidirect
6. #13066481C2semidirect
7. C11×#1300C2semidirect
120. #1300D11semidirect
312. C11#8773semidirect

Maximal subgroups

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

subgroupindex
#130715572
C4×#668872
#130669562
#130665092
#130664822
#130664812
C11×#13002
#877311