Finite Group Databasebeta

← #14664388

Subgroups — #14664388

Order 2816.

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

normal subgroups only

This group has 460 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#13073784C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic
3#13066951C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic, complemented
5#13066637C211yesmaximal, characteristic, complemented
6#13066636C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C2×#66997C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#393C2211yescharacteristic
11#10622844C411yescharacteristic, complemented
12#10622570—21no—
13C2×#66870—21no—
14#10622560C2211yescharacteristic
15#10622555—21no—
16C22⋊C4×Dic11—21no—
17#10622339—21no—
18#10622286C411yescharacteristic, complemented
19#10622280—21no—
20#10622263—21no—
21#10622262C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37#66997—41no—
38#66997—41no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11—21no—
47C2×C4×Dic11—41no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×#4313—41no—
50(C22⋊D11)⋊C4—41no—
51(C22⋊D11)⋊C4—41no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62#66870—24no—
63#11787—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11C22⋊C411yescharacteristic
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
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—41no—
90C2×Dic22—81no—
91C2×C8×C11—41no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—81no—
96C22⋊Dic11—22no—
97C22⋊Dic11—41no—
98C22⋊Dic11—81no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—81no—
101(C2×D11)⋊C4—81no—
102Dic11⋊C4—41no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—42no—
110C4×Dic11—82no—
111C2×C11⋊C8—41no—
112#4313—82no—
113#2563—111no—
114C4×#99—111no—
115#1465—111no—
116#1351—111no—
117#1351—111no—
118#1351—111no—
119#1351D1111yescharacteristic, complemented
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11C2×C22⋊C411yescharacteristic
125C23×C11#13711yescharacteristic
126C23×C11#13711yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—41no—
131C22×D11—41no—
132Q8×C11—82no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C22⋊D11—42no—
147C22⋊D11—42no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—22no—
151C2×Dic11—21no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11#9911yescharacteristic
165C2×Dic11#9911yescharacteristic
166C2×Dic11#10412yes—
167C4×D11—42no—
168C4×D11—81no—
169Dic22—82no—
170C8×C11—81no—
171C11⋊C8—81no—
172C2×C4⋊Q8—111no—
173C2×C4×D4—111no—
174C2×#99—221no—
175#407—221no—
176#393—111no—
177#393—111no—
178#393—111no—
179#393C2×D1111yescharacteristic
180#390—221no—
181#382—221no—
182#380—221no—
183#380—221no—
184C4×C4⋊C4—111no—
185C4×C22⋊C4—221no—
186#342—111no—
187#342C2×D1111yescharacteristic
188#324—221no—
189#323—111no—
190#323C2×D1111yescharacteristic
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—81no—
200C22×C11C2×#9911yescharacteristic
201C22×C11#41911yescharacteristic
202C22×C11C2×#10411yescharacteristic
203C2×D11—42no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—81no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11—81no—
213Dic11—21no—
214Dic11—22no—
215Dic11—41no—
216Dic11—81no—
217Dic11—82no—
218Dic11—81no—
219Dic11#35412yes—
220C22×Q8—111no—
221C22×Q8C4×D1111yescharacteristic
222C22×D4—111no—
223C23×C4—111no—
224C23×C4—111no—
225C2×M16—441no—
226C4⋊Q8—441no—
227C4⋊Q8—441no—
228C4×D4—441no—
229C4×D4—441no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4C22×D1111yescharacteristic
242C2×C42—111no—
243C2×C42—221no—
244C2×C42—441no—
245#99—224no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C22⋊C8—441no—
249#95—21no—
250#95—111no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—441no—
255#95C4×D1111yescharacteristic
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—41no—
259C2×C11—41no—
260C2×C11#150811yescharacteristic
261C2×C11#212211yescharacteristic
262C2×C11C2×#35411yescharacteristic
263D11—81no—
264C24—111no—
265C24D4×D1111yescharacteristic
266C2×Q8—41no—
267C2×Q8—81no—
268C2×Q8—441no—
269C2×Q8—881no—
270C2×D4—222no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—441no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—441no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291M16—882no—
292C2×C8—41no—
293C2×C8—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—442no—
298C4⋊C4—442no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—222no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—881no—
307C22⋊C4—881no—
308C22⋊C4—881no—
309C42—221no—
310C42—221no—
311C42—442no—
312C42—882no—
313C11#1178711yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—441no—
322C23—441no—
323C23C22⋊C4×D1111yescharacteristic
324C23#6696811yescharacteristic
325C23#6697111yescharacteristic
326Q8—82no—
327Q8—882no—
328D4—442no—
329D4—442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—112no—
346C2×C4—222no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—441no—
353C2×C4—442no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4—881no—
363C2×C4—881no—
364C8—81no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—442no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—881no—
380C22D11×#9911yescharacteristic
381C22#1062241511yescharacteristic
382C22D11×#10411yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—82no—
387C4—81no—
388C4—112no—
389C4—222no—
390C4—221no—
391C4—441no—
392C4—881no—
393C4—882no—
394C4—881no—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—881no—
400C2#1306713411yescharacteristic
401C2#1307026411yescharacteristic
402C2D11×#35411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11787
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #13066638C2semidirect
5. #13066637C2semidirect
6. #13066636C2semidirect
7. C11×#1351C2semidirect
8. C2×#66997C4semidirect
11. #10622844C4semidirect
18. #10622286C4semidirect
21. #10622262C4semidirect
119. #1351D11semidirect
313. C11#11787semidirect

Maximal subgroups

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

subgroupindex
#130737842
#130684032
#130669512
#130666382
#130666372
#130666362
C11×#13512
#1178711