Finite Group Databasebeta

← #14642340

Subgroups — #14642340

Order 2816.

426 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 93 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#13076980C211yesmaximal, characteristic
2#13068731C211yesmaximal, characteristic, complemented
3#13068363C211yesmaximal, characteristic, complemented
4#13066440C211yesmaximal, characteristic, complemented
5#13066438C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic
7C11×#1270C211yesmaximal, characteristic
8C2×#66932—21no—
9C11×#390C2211yescharacteristic
10#10622834C411yescharacteristic
11#10622834C411yescharacteristic
12C2×#66879—21no—
13C2×Dic11⋊C8—21no—
14#10622598C411yescharacteristic
15#10622586C411yescharacteristic
16#10622564—21no—
17#10622558—21no—
18#10622557—21no—
19C42×Dic11C2211yescharacteristic
20#10622541C2211yescharacteristic
21C11×#336C2211yescharacteristic
22C11×#336C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11C2×C411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66932—42no—
52#66932—42no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66879—24no—
57Dic11⋊C8—42no—
58#7706—111nomaximal, Sylow
59C24×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×C8×C11—22no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11—41no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—41no—
93C4⋊Dic11—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—22no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—41no—
105C4×Dic11—41no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#2860—111no—
113#1831—111no—
114#1745—111no—
115#1271—111no—
116#1271—111no—
117#1270—111no—
118#1270D1111yescharacteristic
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11C2×C22⋊C411yescharacteristic
127D4×C11—81no—
128D4×C11—81no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#13111yescharacteristic
139C2×C4×C11#13111yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11#10412yes—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C2×#126—221no—
167C2×C4⋊C8—221no—
168C2×#97—221no—
169#390—111no—
170#390—111no—
171#390C2×D1111yescharacteristic
172#389—111no—
173#389—111no—
174#389—111no—
175#388—221no—
176#388—221no—
177#388—221no—
178C43—111no—
179#336—111no—
180#336—111no—
181#336—221no—
182#336—221no—
183#336C2×D1111yescharacteristic
184#336C2×D1111yescharacteristic
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#40811yescharacteristic
193C22×C11#41011yescharacteristic
194C22×C11#41311yescharacteristic
195C22×C11#41711yescharacteristic
196C22×C11#41811yescharacteristic
197C22×C11C2×#10411yescharacteristic
198C22×C11#42111yescharacteristic
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206Dic11—22no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210Dic11—81no—
211Dic11—81no—
212C22×D4C4×D1111yescharacteristic
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—221no—
216C22×C8—221no—
217#126—442no—
218#126—442no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4C4×D1111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C42—111no—
232C2×C42—111no—
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—442no—
239#97—224no—
240#95—221no—
241#95—221no—
242#95—221no—
243C2×C11—161no—
244C2×C11#147311yescharacteristic
245C2×C11#148311yescharacteristic
246C2×C11#149611yescharacteristic
247C2×C11#150511yescharacteristic
248C2×C11#151211yescharacteristic
249C2×C11#152911yescharacteristic
250C2×C11#155711yescharacteristic
251C24—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4—41no—
256C22×C4—21no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4C2×C4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—222no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—441no—
278C4⋊C4—41no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C22⋊C4—442no—
293C22⋊C4—442no—
294C42—41no—
295C42—222no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42—221no—
300C42—221no—
301C42—221no—
302C42—441no—
303C42—441no—
304C11#770611yescharacteristic, complemented, Sylow
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23C22⋊C4×D1111yescharacteristic
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—112no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4#6695411yescharacteristic
343C2×C4#6696011yescharacteristic
344C2×C4#6696411yescharacteristic
345C2×C4#6696411yescharacteristic
346C2×C4#6696711yescharacteristic
347C2×C4#6696811yescharacteristic
348C8—42no—
349C8—81no—
350C8—442no—
351C8—881no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22#1062234011yescharacteristic
360C22#1062235311yescharacteristic
361C22#1062235811yescharacteristic
362C22#1062238311yescharacteristic
363C22#1062238411yescharacteristic
364C22D11×#10411yescharacteristic
365C22#1062243411yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—81no—
373C4—222no—
374C4—441no—
375C4—441no—
376C4—441no—
377C4—881no—
378C4—881no—
379C2—161no—
380C2#1306698211yescharacteristic
381C2#1306702611yescharacteristic
382C2#1306708311yescharacteristic
383C2#1306712211yescharacteristic
384C2#1306715111yescharacteristic
385C2#1306722011yescharacteristic
386C2#1306733511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1270D11
hypocenterC11#7706
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13068731C2semidirect
3. #13068363C2semidirect
4. #13066440C2semidirect
5. #13066438C2semidirect
304. C11#7706semidirect

Maximal subgroups

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

subgroupindex
#130769802
#130687312
#130683632
#130664402
#130664382
#130664372
C11×#12702
#770611