Finite Group Databasebeta

← #14651524

Subgroups — #14651524

Order 2816.

726 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 97 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#13072275C211yesmaximal, characteristic
2#13071201C211yesmaximal, characteristic, complemented
3#13068539C211yesmaximal, characteristic, complemented
4#13067145C211yesmaximal, characteristic
5#13066470C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1510C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C2×#66989C412yescomplemented
11C2×#66930—21no—
12C11×#407C2211yescharacteristic
13C11×#381C2211yescharacteristic
14#10622833—21no—
15#10622833—21no—
16#10622824C2211yescharacteristic
17C4×C22⋊Dic11C2211yescharacteristic
18#10622820C2211yescharacteristic
19C2×#66888—22no—
20#10622587C412yescomplemented
21#10622560—22no—
22#10622556—21no—
23#10622259—22no—
24#10622259—22no—
25C11×#327—22no—
26#10622175—22no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22—21no—
33C22×Dic22—21no—
34C22×Dic22—21no—
35C22×Dic22—21no—
36C22×Dic22—44no—
37C22×Dic22C2×C412yes—
38C22×Dic22D412yes—
39C2×C11×M16—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51#66989—44no—
52C2×Dic11⋊C4—22no—
53C2×C4×Dic11—22no—
54C2×C4×Dic11C2×C412yes—
55C2×#4318—21no—
56#66930—44no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95D412yes—
61C11⋊#95—24no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66888—44no—
70#9466—111nomaximal, Sylow
71C24×C11—21no—
72C24×C11C2×D411yescharacteristic
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—42no—
76C2×D4×C11—44no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—42no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—24no—
89C22×Dic11—22no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—42no—
96C22×Dic11C22⋊C412yes—
97C22×Dic11C22⋊C412yes—
98C2×Dic22—24no—
99C2×Dic22—24no—
100C2×Dic22—22no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22—22no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×Dic22—42no—
107C2×Dic22—42no—
108C2×Dic22—42no—
109C2×Dic22—42no—
110C2×Dic22—44no—
111C2×Dic22—44no—
112C11×M16—42no—
113C2×C8×C11—41no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C22⋊Dic11—42no—
120C22⋊Dic11—42no—
121C22⋊Dic11—44no—
122C22⋊Dic11—44no—
123Dic11⋊C4—44no—
124C4×Dic11—42no—
125C4×Dic11—44no—
126#4318—42no—
127C2×C11⋊C8—41no—
128#2436—111no—
129#2310—111no—
130#1784—111no—
131#1510—111no—
132#1510D1111yescharacteristic
133#1284—111no—
134#1284—111no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11—41no—
141C23×C11—42no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11#12011yescharacteristic
144C23×C11#12311yescharacteristic
145D4×C11—81no—
146D4×C11—81no—
147D4×C11—82no—
148D4×C11—82no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—24no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11#9914yes—
182Dic22—44no—
183Dic22—44no—
184Dic22—44no—
185Dic22—44no—
186C8×C11—81no—
187C11⋊C8—81no—
188C23×Q8—111no—
189C2×#124—112no—
190C2×#121C2×D1111yescharacteristic
191C2×#117—221no—
192C2×#101—222no—
193#407—111no—
194#407C2×D1111yescharacteristic
195#393—222no—
196#391—112no—
197#391—222no—
198#391—222no—
199#386—221no—
200#386—221no—
201#381—111no—
202#381—221no—
203#381C2×D1111yescharacteristic
204C4×C22⋊C4—111no—
205#327—22no—
206#327—222no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—44no—
215C22×C11—84no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#38611yescharacteristic
220C22×C11C2×#9912yes—
221C22×C11#45412yes—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—82no—
227C4×C11—81no—
228Dic11—24no—
229Dic11—42no—
230Dic11—82no—
231Dic11—82no—
232C22×Q8—112no—
233C22×Q8—112no—
234C22×Q8—221no—
235C22×Q8—221no—
236C22×Q8—221no—
237C22×Q8—221no—
238C22×Q8—444no—
239C22×D4—21no—
240C22×D4C4×D1111yescharacteristic
241C23×C4—111no—
242C23×C4—111no—
243C23×C4C22×D1111yescharacteristic
244C2×M16—21no—
245C2×M16—221no—
246#124—444no—
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251#117—444no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4C4×D1111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—222no—
257C2×C22⋊C4—222no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—112no—
261C2×C42—222no—
262#101—444no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—221no—
266C22⋊C8—221no—
267#95—21no—
268#95—112no—
269#95—222no—
270#95—222no—
271#95—224no—
272#95—221no—
273#95—221no—
274#95C22⋊D1112yes—
275C2×C11—22no—
276C2×C11—22no—
277C2×C11—41no—
278C2×C11—161no—
279C2×C11#188811yescharacteristic
280C2×C11#189811yescharacteristic
281C2×C11#191211yescharacteristic
282C24—21no—
283C24D4×D1111yescharacteristic
284C2×Q8—224no—
285C2×Q8—224no—
286C2×Q8—222no—
287C2×Q8—222no—
288C2×Q8—222no—
289C2×Q8—222no—
290C2×Q8—442no—
291C2×Q8—442no—
292C2×Q8—444no—
293C2×Q8—442no—
294C2×Q8—442no—
295C2×Q8—444no—
296C2×Q8—442no—
297C2×Q8—442no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—44no—
302C2×D4—41no—
303C2×D4—41no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—42no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4—224no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—442no—
317C22×C4C2×C4×D1111yescharacteristic
318C22×C4#433911yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4#434111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323M16—42no—
324M16—442no—
325C2×C8—41no—
326C2×C8—441no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—444no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—444no—
334C22⋊C4—444no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C42—442no—
338C42—444no—
339C11#946611yescharacteristic, complemented, Sylow
340C23—22no—
341C23—22no—
342C23—41no—
343C23—42no—
344C23—42no—
345C23—41no—
346C23—42no—
347C23C22⋊C4×D1111yescharacteristic
348C23#6693611yescharacteristic
349C23#6699011yescharacteristic
350Q8—444no—
351Q8—444no—
352Q8—444no—
353Q8—444no—
354D4—81no—
355D4—81no—
356D4—82no—
357D4—82no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—114no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—224no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4(C22⋊D11)⋊C411yescharacteristic
388C2×C4#6693711yescharacteristic
389C2×C4C4×C22⋊D1111yescharacteristic
390C2×C4#6699111yescharacteristic
391C8—81no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—44no—
401C22—84no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22D11×#9912yes—
406C22#1062256911yescharacteristic
407C22#1062281412yes—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—82no—
413C4—81no—
414C4—224no—
415C4—442no—
416C4—882no—
417C4—882no—
418C2—22no—
419C2—22no—
420C2—41no—
421C2—161no—
422C2#1306901611yescharacteristic
423C2#1306906611yescharacteristic
424C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1510C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1510D11
hypocenterC11#9466
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #13071201C2semidirect
3. #13068539C2semidirect
5. #13066470C2semidirect
6. #13066468C2semidirect
10. C2×#66989C4semidirect
20. #10622587C4semidirect
339. C11#9466semidirect

Maximal subgroups

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

subgroupindex
#130722752
#130712012
#130685392
#130671452
#130664702
#130664682
C11×#15102
#946611