Finite Group Databasebeta

← #14664674

Subgroups — #14664674

Order 2816.

572 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071951C211yesmaximal, characteristic
2C2×#10622166C211yesmaximal, characteristic, complemented
3#13066645C212yesmaximal, complemented
4#13066618C212yesmaximal, complemented
5C11×#1821C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66982—21no—
9C11×#407—21no—
10#10622826—21no—
11#10622824C411yescharacteristic
12C2×C22⋊(C11⋊C8)—21no—
13#10622604C411yescharacteristic
14#10622604C2211yescharacteristic
15#10622602—21no—
16#10622602—21no—
17#10622592C411yescharacteristic
18#10622592C2211yescharacteristic
19C11×#343—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C2×#4339—41no—
28C2×#4339—41no—
29C2×#4339—44no—
30C22×D44C2×C411yescharacteristic
31C22×C4×D11—21no—
32C22×Dic22C2×C411yescharacteristic
33C2×C11×M16—22no—
34C2×C11×C4⋊C4—41no—
35C2×C11×C4⋊C4—41no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41#66982—44no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C22×C11⋊C8—41no—
49C11×C22⋊C8—41no—
50C11×C22⋊C8—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11848—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—24no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84#4339—44no—
85#4339—44no—
86#4339—44no—
87#4339—44no—
88C2×D44—41no—
89C2×D44—42no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×Dic22—41no—
94C2×Dic22—42no—
95C11×M16—42no—
96C11×M16—42no—
97C2×C8×C11—42no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C22⋊Dic11—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—82no—
111#2406—111no—
112#1821D1111yescharacteristic, complemented
113C2×#324—111no—
114#1354—112no—
115#1345—112no—
116C23×C11—22no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11#9911yescharacteristic
121C23×C11#9911yescharacteristic
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—22no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11#13512yes—
150C22⋊D11—44no—
151C22⋊D11—44no—
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161D44—42no—
162D44—42no—
163C4×D11—48no—
164Dic22—42no—
165Dic22—42no—
166C8×C11—82no—
167C11⋊C8—82no—
168C22×#41—111no—
169C2×#123—221no—
170C22×C4⋊C4C2×D1111yescharacteristic
171#407—21no—
172C2×C22⋊C8—221no—
173#395—111no—
174#395—111no—
175#394—111no—
176#394—111no—
177#386—221no—
178#385—221no—
179#385—221no—
180#381—111no—
181#343—21no—
182#343C2×D1112yes—
183#324—112no—
184#324—221no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11AΣL(1,𝔽16)12yes—
195C22×C11C2×#9911yescharacteristic
196C22×C11#41611yescharacteristic
197C22×C11#42111yescharacteristic
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—22no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211Dic11—42no—
212Dic11—81no—
213Dic11—81no—
214C2×#41—441no—
215C2×#41—441no—
216C2×#41—444no—
217C22×Q8—111no—
218C22×D4—111no—
219C22×D4—221no—
220C23×C4—221no—
221C23×C4C4×D1111yescharacteristic
222C23×C4D4411yescharacteristic
223C23×C4C22⋊D1111yescharacteristic
224C2×M16—22no—
225C22×C8—441no—
226#123—444no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4C4×D1111yescharacteristic
232C2×C4⋊C4D4411yescharacteristic
233C2×C4⋊C4C22⋊D1111yescharacteristic
234C2×C4⋊C4C22×D1111yescharacteristic
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C22⋊C8—41no—
241C22⋊C8—41no—
242C22⋊C8—222no—
243C22⋊C8—441no—
244#95—111no—
245#95—111no—
246#95—221no—
247#95—221no—
248#95—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—22no—
252C2×C11—41no—
253C2×C11#151611yescharacteristic
254C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
255C2×C11#213311yescharacteristic
256D11—82no—
257C24—221no—
258C24(C2×D11)⋊C411yescharacteristic
259#41—444no—
260#41—444no—
261#41—444no—
262#41—444no—
263C2×Q8—441no—
264C2×Q8—442no—
265C2×D4—224no—
266C2×D4—441no—
267C2×D4—442no—
268C2×D4—442no—
269C2×D4—441no—
270C2×D4—441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4(C2×D11)⋊C411yescharacteristic
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C2×D4411yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293M16—42no—
294M16—42no—
295C2×C8—42no—
296C2×C8—442no—
297C2×C8—882no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—442no—
303C4⋊C4—442no—
304C22⋊C4—442no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C11#1184811yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—22no—
313C23—41no—
314C23—222no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23#6687011yescharacteristic
322C23#6687011yescharacteristic
323C23C2×(C2×D11)⋊C411yescharacteristic
324Q8—442no—
325Q8—442no—
326D4—442no—
327D4—442no—
328D4—444no—
329D4—444no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—222no—
350C2×C4—448no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4#6700312yes—
360C8—82no—
361C8—882no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—442no—
372C22—442no—
373C22—442no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22#1062211312yes—
379C22C2×#6687011yescharacteristic
380C22#1062261511yescharacteristic
381C22#1062261811yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—442no—
389C4—881no—
390C4—881no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—882no—
396C2#1306717011yescharacteristic
397C2C2×#1062211311yescharacteristic
398C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1821C2
socleC22×C11C2×#99
prime radicalC22×#4339C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1821D11
hypocenterC11#11848
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. C2×#10622166C2semidirect
3. #13066645C2semidirect
4. #13066618C2semidirect
5. C11×#1821C2semidirect
112. #1821D11semidirect
309. C11#11848semidirect

Maximal subgroups

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

subgroupindex
#130719512
C2×#106221662
#130666452
#130666182
C11×#18212
#1184811