Finite Group Databasebeta

← #14647236

Subgroups — #14647236

Order 2816.

498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071214C211yesmaximal, characteristic
2C2×#10622163C211yesmaximal, characteristic
3#13066463C212yesmaximal, complemented
4#13066462C212yesmaximal, complemented
5C2×C11×#323C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C2×C11×C22⋊C8C2212yes—
8#10622860C411yescharacteristic
9#10622860C411yescharacteristic
10#10622825C411yescharacteristic
11#10622825C411yescharacteristic
12C4×C22⋊Dic11C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622564—21no—
16#10622564—21no—
17#10622564—21no—
18#10622564—21no—
19C11×#323—21no—
20C11×#323—21no—
21#10622163—21no—
22#10622163—21no—
23C25×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C22×C8×C11—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11C2×C411yescharacteristic
38C2×C22⋊Dic11C2×C411yescharacteristic
39C2×C22⋊Dic11C2×C411yescharacteristic
40C2×C22⋊Dic11C2×C411yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C22×C11⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54#8736—111nomaximal, Sylow
55C24×C11—21no—
56C24×C11—21no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—81no—
60C24×C11—81no—
61C24×C11C22⋊C411yescharacteristic
62C24×C11C22⋊C411yescharacteristic
63C24×C11C22×C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—81no—
67C22×C4×C11—81no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4112yes—
73C22×C4×C11#4112yes—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×C8×C11—42no—
79C2×C8×C11—82no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C22⋊Dic11—22no—
85C22⋊Dic11—22no—
86C22⋊Dic11—22no—
87C22⋊Dic11—22no—
88C22⋊Dic11—81no—
89C22⋊Dic11—81no—
90C22⋊Dic11—81no—
91C22⋊Dic11—81no—
92C4⋊Dic11—81no—
93C4⋊Dic11—81no—
94C4×Dic11—81no—
95C4×Dic11—81no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—82no—
98#2312—111no—
99C2×#323—111no—
100C2×#323D1111yescharacteristic
101#1282—112no—
102#1282—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—81no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11—84no—
122C23×C11—84no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#11711yescharacteristic
125C23×C11#11711yescharacteristic
126C23×C11#13112yes—
127C23×C11#13112yes—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#12312yes—
139C2×C4×C11#12312yes—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C8×C11—82no—
153C11⋊C8—82no—
154C22×C22⋊C4C2×D1111yescharacteristic
155C2×C22⋊C8—112no—
156C2×C22⋊C8C2×D1112yes—
157#388—221no—
158#388—221no—
159#388—221no—
160#388—221no—
161#380—111no—
162#380—111no—
163#379—111no—
164#379—111no—
165C4×C22⋊C4—111no—
166C4×C22⋊C4—111no—
167#323—21no—
168#323—21no—
169#323—221no—
170#323—221no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—84no—
190C22×C11—84no—
191C22×C11#38111yescharacteristic
192C22×C11#40811yescharacteristic
193C22×C11#40811yescharacteristic
194C22×C11#43312yes—
195C22×C11#43312yes—
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—41no—
199C4×C11—41no—
200Dic11—81no—
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204C25C4×D1111yescharacteristic
205C23×C4C4×D1111yescharacteristic
206C23×C4C22×D1111yescharacteristic
207C22×C8—22no—
208C22×C8—222no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4D4411yescharacteristic
222C2×C22⋊C4D4411yescharacteristic
223C2×C22⋊C4C22⋊D1111yescharacteristic
224C2×C22⋊C4C22⋊D1111yescharacteristic
225C2×C42—221no—
226C2×C42—221no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—222no—
230C22⋊C8—222no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—22no—
238C2×C11—22no—
239C2×C11—81no—
240C2×C11—81no—
241C2×C11#181811yescharacteristic
242C2×C11#182811yescharacteristic
243C2×C11#182911yescharacteristic
244C24—21no—
245C24—21no—
246C24—22no—
247C24—22no—
248C24—81no—
249C24—81no—
250C24(C2×D11)⋊C411yescharacteristic
251C24(C2×D11)⋊C411yescharacteristic
252C24C2×C4×D1111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4C2×D4411yescharacteristic
264C22×C4#434112yes—
265C22×C4#434112yes—
266C22×C4C2×C22⋊D1111yescharacteristic
267C2×C8—42no—
268C2×C8—82no—
269C2×C8—442no—
270C2×C8—882no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—222no—
278C22⋊C4—222no—
279C22⋊C4—222no—
280C22⋊C4—222no—
281C22⋊C4—881no—
282C22⋊C4—881no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C42—881no—
286C42—881no—
287C11#873611yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—42no—
301C23—42no—
302C23—81no—
303C23—81no—
304C23—81no—
305C23—81no—
306C23—84no—
307C23—84no—
308C23#6693011yescharacteristic
309C23#6693011yescharacteristic
310C23#6695412yes—
311C23#6696012yes—
312C23C2×(C2×D11)⋊C411yescharacteristic
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4#6693912yes—
336C2×C4#6698812yes—
337C8—82no—
338C8—882no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—42no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—84no—
358C22—84no—
359C22#1062233312yes—
360C22#1062233312yes—
361C22#1062255611yescharacteristic
362C22#1062272311yescharacteristic
363C22#1062274211yescharacteristic
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—881no—
369C4—881no—
370C4—881no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2—22no—
375C2—22no—
376C2—81no—
377C2—81no—
378C2#1306868511yescharacteristic
379C2#1306872211yescharacteristic
380C2#1306872511yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#323C2
socleC22×C11#381
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#323D11
hypocenterC11#8736
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #13066463C2semidirect
4. #13066462C2semidirect
287. C11#8736semidirect

Maximal subgroups

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

subgroupindex
#130712142
C2×#106221632
#130664632
#130664622
C2×C11×#3232
#873611