Finite Group Databasebeta

← #14664392

Subgroups — #14664392

Order 2816.

516 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073564C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic
3#13066951C211yesmaximal, characteristic
4#13066641C211yesmaximal, characteristic, complemented
5#13066640C211yesmaximal, characteristic, complemented
6#13066639C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×#66949—21no—
9C2×#66941C411yescharacteristic, complemented
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C2×#66931—21no—
12C11×#399C2211yescharacteristic
13#10622605C411yescharacteristic, complemented
14#10622589—21no—
15#10622570—21no—
16C2×#66870—21no—
17#10622562C2211yescharacteristic
18C22⋊C4×Dic11—21no—
19#10622339—21no—
20#10622290C411yescharacteristic, complemented
21#10622262C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×C22⋊D11D411yescharacteristic
28C23×Dic11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×Dic22—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4D411yescharacteristic
48C2×C4×Dic11—21no—
49C2×C4×Dic11—41no—
50C2×C4×Dic11C2×C411yescharacteristic
51C2×#4313—41no—
52#66949—44no—
53#66941—41no—
54#66941—41no—
55(C22⋊D11)⋊C4—41no—
56(C22⋊D11)⋊C4—41no—
57#66931—44no—
58C11×C22⋊C8—21no—
59C11×#95C2×C411yescharacteristic
60C11⋊#95—41no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#66870—24no—
65#11788—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11C22⋊C411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—22no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—41no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—42no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—42no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—41no—
100C22⋊Dic11—22no—
101C22⋊Dic11—42no—
102C22⋊Dic11—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106C4⋊Dic11—41no—
107C4⋊Dic11—42no—
108Dic11⋊C4—24no—
109Dic11⋊C4—41no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—42no—
116C4×Dic11—82no—
117C2×C11⋊C8—41no—
118#4313—82no—
119#2542—111no—
120C4×#99—111no—
121#1465—111no—
122#1352—111no—
123#1352—111no—
124#1352—111no—
125#1352D1111yescharacteristic, complemented
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#13711yescharacteristic
132C23×C11#13711yescharacteristic
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—41no—
137C22×D11—41no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C22⋊D11—42no—
152C22⋊D11—42no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169C2×Dic11#9911yescharacteristic
170C2×Dic11#9911yescharacteristic
171C2×Dic11#10412yes—
172C4×D11—42no—
173C4×D11—81no—
174Dic22—82no—
175Dic22—82no—
176C8×C11—81no—
177C11⋊C8—81no—
178C2×C4⋊Q8—111no—
179C2×C22⋊Q8—221no—
180C2×C22⋊Q8—221no—
181C2×C4×D4—111no—
182C2×#99—221no—
183#407—221no—
184#399—111no—
185#399—111no—
186#399—111no—
187#399C2×D1111yescharacteristic
188#390—221no—
189#384—221no—
190C4×C4⋊C4—111no—
191C4×C22⋊C4—221no—
192#342—111no—
193#342C2×D1111yescharacteristic
194#324—221no—
195#323—111no—
196#323C2×D1111yescharacteristic
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—81no—
206C22×C11C2×#9911yescharacteristic
207C22×C11#41911yescharacteristic
208C22×C11C2×#10411yescharacteristic
209C2×D11—42no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—81no—
214C4×C11—42no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—82no—
218C4×C11—81no—
219Dic11—21no—
220Dic11—22no—
221Dic11—42no—
222Dic11—41no—
223Dic11—82no—
224Dic11—81no—
225Dic11#35312yes—
226C22×Q8—221no—
227C22×D4—111no—
228C23×C4—111no—
229C23×C4—111no—
230C2×M16—441no—
231C4⋊Q8—441no—
232C4⋊Q8—441no—
233C22⋊Q8—444no—
234C22⋊Q8—444no—
235C4×D4—441no—
236C4×D4—441no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4C4×D1111yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4C22×D1111yescharacteristic
254C2×C42—111no—
255C2×C42—221no—
256C2×C42—441no—
257#99—224no—
258C22⋊C8—21no—
259C22⋊C8—221no—
260C22⋊C8—441no—
261#95—111no—
262#95—441no—
263#95C4×D1111yescharacteristic
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—41no—
267C2×C11—41no—
268C2×C11#150811yescharacteristic
269C2×C11#212311yescharacteristic
270C2×C11C2×#35311yescharacteristic
271D11—81no—
272C24—111no—
273C24D4×D1111yescharacteristic
274C2×Q8—441no—
275C2×Q8—441no—
276C2×Q8—442no—
277C2×Q8—442no—
278C2×D4—222no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—442no—
295C22×C4—442no—
296C22×C4—441no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299M16—882no—
300C2×C8—41no—
301C2×C8—441no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—224no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C22⋊C4—22no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—222no—
316C22⋊C4—441no—
317C22⋊C4—442no—
318C22⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—441no—
321C42—221no—
322C42—221no—
323C42—442no—
324C42—882no—
325C11#1178811yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—441no—
334C23—441no—
335C23C22⋊C4×D1111yescharacteristic
336C23#6696811yescharacteristic
337C23#6697111yescharacteristic
338Q8—882no—
339Q8—882no—
340D4—442no—
341D4—442no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—111no—
356C2×C4—111no—
357C2×C4—112no—
358C2×C4—222no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—222no—
362C2×C4—221no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—442no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—881no—
376C8—81no—
377C8—881no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—81no—
387C22—442no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—881no—
392C22D11×#9911yescharacteristic
393C22#1062241511yescharacteristic
394C22D11×#10411yescharacteristic
395C4—42no—
396C4—41no—
397C4—41no—
398C4—82no—
399C4—81no—
400C4—112no—
401C4—222no—
402C4—221no—
403C4—442no—
404C4—441no—
405C4—882no—
406C4—881no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—881no—
412C2#1306713411yescharacteristic
413C2#1307026811yescharacteristic
414C2D11×#35311yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11788
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #13066641C2semidirect
5. #13066640C2semidirect
6. #13066639C2semidirect
7. C11×#1352C2semidirect
9. C2×#66941C4semidirect
13. #10622605C4semidirect
20. #10622290C4semidirect
21. #10622262C4semidirect
125. #1352D11semidirect
325. C11#11788semidirect

Maximal subgroups

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

subgroupindex
#130735642
#130684032
#130669512
#130666412
#130666402
#130666392
C11×#13522
#1178811