Finite Group Databasebeta

← #14656993

Subgroups — #14656993

Order 2816.

438 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 75 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#13074810C211yesmaximal, characteristic, complemented
2#13069453C211yesmaximal, characteristic
3#13067145C211yesmaximal, characteristic
4#13066521C211yesmaximal, characteristic, complemented
5#13066502C211yesmaximal, characteristic, complemented
6#13066470C211yesmaximal, characteristic, complemented
7C11×#1507C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C11×#407C2211yescharacteristic
10C4×C11×C22⋊C4C2211yescharacteristic
11C2×#66898—21no—
12C2×#66898—21no—
13#10622825C2211yescharacteristic
14#10622824C2211yescharacteristic
15C4×C22⋊Dic11C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622562—21no—
18#10622561—21no—
19#10622546—21no—
20#10622541—21no—
21#10622274—21no—
22#10622270—21no—
23C11×#327—21no—
24C11×#327—21no—
25#10622175—21no—
26#10622175—21no—
27C22×D4×C11—21no—
28C22×D4×C11Q811yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C2×C11×M16—21no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—21no—
35C2×C11×C4⋊C4Q811yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×C22⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×#4318—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66898—42no—
57#66898—42no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#10384—111nomaximal, Sylow
68C24×C11—21no—
69C24×C11C2×D411yescharacteristic
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—81no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—81no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—41no—
94C11×M16—81no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—81no—
102C22⋊Dic11—22no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—81no—
107C4⋊Dic11—42no—
108C4⋊Dic11—81no—
109C4⋊Dic11—81no—
110Dic11⋊C4—42no—
111Dic11⋊C4—81no—
112Dic11⋊C4—81no—
113Dic11⋊C4—81no—
114C4×Dic11—81no—
115#4318—81no—
116C2×C11⋊C8—41no—
117#2667—111no—
118#1964—111no—
119#1510—111no—
120#1507D1111yescharacteristic
121#1305—111no—
122#1297—111no—
123#1284—111no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11#12011yescharacteristic
134C23×C11C22⋊Q811yescharacteristic
135C23×C11#12411yescharacteristic
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11C22⋊Q811yescharacteristic
158C2×C4×C11C22⋊Q811yescharacteristic
159C2×C4×C11#12411yescharacteristic
160C2×C4×C11#12411yescharacteristic
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C8×C11—81no—
177C11⋊C8—81no—
178C2×#121C2×D1111yescharacteristic
179C2×#99—221no—
180C2×#99—221no—
181#407—111no—
182#407C2×D1111yescharacteristic
183#399—221no—
184#398—221no—
185#398—221no—
186#396—221no—
187#389—221no—
188#387—221no—
189#381—111no—
190#380—111no—
191C4×C22⋊C4—111no—
192C4×C22⋊C4C2×D1111yescharacteristic
193#327—21no—
194#327—21no—
195#327—221no—
196#327—221no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—161no—
211C22×C11—161no—
212C22×C11#39311yescharacteristic
213C22×C11#45311yescharacteristic
214C22×C11#45411yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—81no—
221C4×C11—81no—
222Dic11—81no—
223Dic11—81no—
224Dic11—81no—
225Dic11—81no—
226Dic11—82no—
227C22×D4—21no—
228C22×D4Dic2211yescharacteristic
229C23×C4C22×D1111yescharacteristic
230C2×M16—21no—
231C2×M16—221no—
232#121—21no—
233#121—21no—
234#121—21no—
235#121—21no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4Dic2211yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C42—21no—
251C2×C42—221no—
252#99—442no—
253#99—442no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—221no—
257C22⋊C8—221no—
258#95—111no—
259#95—111no—
260#95—221no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95—221no—
265#95C22⋊D1111yescharacteristic
266#95C22⋊D1111yescharacteristic
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—41no—
270C2×C11—41no—
271C2×C11—161no—
272C2×C11#202711yescharacteristic
273C2×C11#203111yescharacteristic
274C2×C11#203211yescharacteristic
275C24—21no—
276C24D4×D1111yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—81no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—81no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—441no—
295C22×C4C2×Dic2211yescharacteristic
296C22×C4#433911yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4#434111yescharacteristic
299C22×C4#434111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301M16—81no—
302M16—881no—
303C2×C8—41no—
304C2×C8—441no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—881no—
310C4⋊C4—881no—
311C4⋊C4—881no—
312C4⋊C4—881no—
313C4⋊C4—881no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—222no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—881no—
322C42—81no—
323C42—881no—
324C11#1038411yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—81no—
333C23—81no—
334C23#6693111yescharacteristic
335C23#6693811yescharacteristic
336C23#6699011yescharacteristic
337D4—81no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—442no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4#6693111yescharacteristic
374C2×C4#6693811yescharacteristic
375C2×C4#6697711yescharacteristic
376C2×C4#6698911yescharacteristic
377C8—81no—
378C8—881no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—161no—
393C22—161no—
394C22#1062256011yescharacteristic
395C22#1062281111yescharacteristic
396C22#1062281411yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—81no—
404C4—881no—
405C4—881no—
406C4—881no—
407C4—881no—
408C4—882no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—161no—
414C2#1306977011yescharacteristic
415C2#1306978811yescharacteristic
416C2#1306979311yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1507C2
socleC22×C11#393
prime radicalC2×C11×#121C22
hypercenter#1507D11
hypocenterC11#10384
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
1. #13074810C2semidirect
4. #13066521C2semidirect
5. #13066502C2semidirect
6. #13066470C2semidirect
324. C11#10384semidirect

Maximal subgroups

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

subgroupindex
#130748102
#130694532
#130671452
#130665212
#130665022
#130664702
C11×#15072
#1038411