Finite Group Databasebeta

← #14664705

Subgroups — #14664705

Order 2816.

412 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073992C211yesmaximal, characteristic
2#13068695C211yesmaximal, characteristic
3D11×#324C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066623C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622842C411yescharacteristic
12#10622739—21no—
13#10622602—21no—
14#10622596C2211yescharacteristic
15#10622586—21no—
16D11×C22⋊C8—21no—
17#10622281—21no—
18#10622279C411yescharacteristic
19#10622274C411yescharacteristic
20#10622260—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
34#66999—41no—
35#66999—41no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11—21no—
47C2×#4318—21no—
48C2×C8×D11—41no—
49C4⋊C4×D11—41no—
50C4⋊C4×D11—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—41no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11854—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C2×Q8×C11—41no—
65C2×Q8×C11—81no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—41no—
85C2×C4×D11—81no—
86C2×C4×D11—81no—
87C11×M16—41no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—81no—
93(C2×D11)⋊C4—24no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—81no—
105C4×Dic11—81no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C8×D11—82no—
111#2583—111no—
112#1821—111no—
113C2×#324—111no—
114#1354—111no—
115#1354D1111yescharacteristic, complemented
116#1346—111no—
117#1346—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—22no—
122C22×D11—41no—
123C22×D11#9911yescharacteristic
124C22×D11#9911yescharacteristic
125Q8×C11—82no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C4×D11—41no—
154C4×D11—41no—
155C4×D11—41no—
156C4×D11—41no—
157C4×D11—42no—
158C4×D11—81no—
159C4×D11—81no—
160C4×D11—81no—
161C8×C11—81no—
162C8×C11—81no—
163C11⋊C8—81no—
164C11⋊C8—81no—
165C2×C22⋊Q8—111no—
166C22×C4⋊C4—111no—
167#407—221no—
168C2×C22⋊C8—221no—
169#398—111no—
170#398—111no—
171#395—111no—
172#395C2×D1111yescharacteristic
173#389—221no—
174#389—221no—
175#385—221no—
176#385—221no—
177C4×C22⋊C4—111no—
178#343—111no—
179#343—221no—
180#343C2×D1111yescharacteristic
181#324—111no—
182#324—221no—
183#324C2×D1111yescharacteristic
184C22×C11—21no—
185C22×C11—21no—
186C22×C11C2×#9911yescharacteristic
187C22×C11#41611yescharacteristic
188C22×C11#42111yescharacteristic
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—42no—
195C2×D11—42no—
196C2×D11#35612yes—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—81no—
203Dic11—42no—
204Dic11—41no—
205Dic11—41no—
206Dic11—41no—
207Dic11—81no—
208C22×Q8C4×D1111yescharacteristic
209C23×C4—111no—
210C23×C4—111no—
211C23×C4—111no—
212C2×M16—21no—
213C2×M16—221no—
214C22×C8—441no—
215C22⋊Q8—441no—
216C22⋊Q8—441no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—441no—
227C2×C4⋊C4—441no—
228C2×C4⋊C4C22×D1111yescharacteristic
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C42—221no—
232C22⋊C8—21no—
233C22⋊C8—221no—
234C22⋊C8—441no—
235C22⋊C8—441no—
236C22⋊C8—441no—
237#95—21no—
238#95—111no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95C4×D1111yescharacteristic
243C2×C11—21no—
244C2×C11—21no—
245C2×C11#151611yescharacteristic
246C2×C11#212111yescharacteristic
247C2×C11C2×#35611yescharacteristic
248D11—22no—
249D11—41no—
250C24—111no—
251C2×Q8—41no—
252C2×Q8—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—441no—
269C22×C4—881no—
270C22×C4—881no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274M16—41no—
275M16—41no—
276M16—441no—
277M16—441no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—882no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—881no—
294C22⋊C4—224no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C42—881no—
298C11#1185411yescharacteristic, complemented, Sylow
299C23—111no—
300C23—111no—
301C23—222no—
302C23—221no—
303C23—221no—
304C23—441no—
305C23C22⋊C4×D1111yescharacteristic
306Q8—82no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—222no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4#6696911yescharacteristic
341C2×C4#6697211yescharacteristic
342C8—81no—
343C8—81no—
344C8—881no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—112no—
349C22—221no—
350C22—221no—
351C22—221no—
352C22—221no—
353C22—221no—
354C22—442no—
355C22—442no—
356C22D11×#9911yescharacteristic
357C22#1062241711yescharacteristic
358C22#1062243411yescharacteristic
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—442no—
366C4—441no—
367C4—441no—
368C4—441no—
369C4—881no—
370C2—21no—
371C2—21no—
372C2—222no—
373C2—441no—
374C2#1306717111yescharacteristic
375C2#1307025911yescharacteristic
376C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11854
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #13066646C2semidirect
5. #13066623C2semidirect
6. #13066621C2semidirect
7. C11×#1354C2semidirect
115. #1354D11semidirect
298. C11#11854semidirect

Maximal subgroups

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

subgroupindex
#130739922
#130686952
D11×#3242
#130666462
#130666232
#130666212
C11×#13542
#1185411