Finite Group Databasebeta

← #14664301

Subgroups — #14664301

Order 2816.

462 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073990C211yesmaximal, characteristic
2D11×#343C211yesmaximal, characteristic
3#13066944C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic, complemented
5#13066645C211yesmaximal, characteristic, complemented
6#13066622C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66950C411yescharacteristic
10C2×C4⋊C4×D11C2211yescharacteristic
11C11×#398C2211yescharacteristic
12#10622602—21no—
13#10622598—21no—
14#10622593C411yescharacteristic
15#10622592C2211yescharacteristic
16#10622339—21no—
17#10622281—21no—
18#10622279C411yescharacteristic
19#10622269C411yescharacteristic
20#10622260—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4C2×C411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11—21no—
45C2×#4318—21no—
46M16×D11—24no—
47M16×D11—42no—
48C2×#4313—41no—
49C2×#4313—41no—
50C2×C8×D11—41no—
51#66950—41no—
52#66950—41no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11768—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
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—22no—
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—21no—
85C2×C4×D11—81no—
86C2×C4×D11—81no—
87C2×Dic22—41no—
88C2×Dic22—81no—
89C11×M16—22no—
90C11×M16—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97(C2×D11)⋊C4—24no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—42no—
102C4⋊Dic11—81no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—42no—
106Dic11⋊C4—81no—
107C4×Dic11—81no—
108#4318—22no—
109#4318—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#4313—44no—
113#4313—82no—
114C8×D11—44no—
115#2583—111no—
116C2×#343—111no—
117#1463—111no—
118#1354—111no—
119#1354—111no—
120#1346—111no—
121#1346D1111yescharacteristic, complemented
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—22no—
126C22×D11—41no—
127C22×D11#9911yescharacteristic
128C22×D11#9911yescharacteristic
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—22no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11#10412yes—
156C4×D11—22no—
157C4×D11—22no—
158C4×D11—22no—
159C4×D11—22no—
160C4×D11—42no—
161C4×D11—81no—
162C4×D11—81no—
163C4×D11—81no—
164Dic22—82no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169C22×M16—221no—
170C2×C22⋊Q8—111no—
171C22×C4⋊C4—111no—
172#407—221no—
173#398—111no—
174#398C2×D1111yescharacteristic
175#395—111no—
176#395—111no—
177#389—221no—
178#389—221no—
179#385—221no—
180#385—221no—
181C4×C22⋊C4—111no—
182#343—111no—
183#343—221no—
184#343C2×D1111yescharacteristic
185#324—111no—
186#324—221no—
187#324C2×D1111yescharacteristic
188C22×C11—21no—
189C22×C11—21no—
190C22×C11C2×#9911yescharacteristic
191C22×C11#41711yescharacteristic
192C22×C11C2×#10411yescharacteristic
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11#35612yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—81no—
207Dic11—22no—
208Dic11—42no—
209Dic11—41no—
210Dic11—41no—
211Dic11—81no—
212C22×Q8—111no—
213C23×C4—111no—
214C23×C4—111no—
215C23×C4—111no—
216C2×M16—21no—
217C2×M16—224no—
218C2×M16—221no—
219C2×M16—441no—
220C2×M16—441no—
221C2×M16—442no—
222C22×C8—441no—
223C22⋊Q8—441no—
224C22⋊Q8—441no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—441no—
234C2×C4⋊C4—441no—
235C2×C4⋊C4C4×D1111yescharacteristic
236C2×C4⋊C4C22×D1111yescharacteristic
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C42—221no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242C22⋊C8—441no—
243#95—21no—
244#95—111no—
245#95—221no—
246#95—221no—
247#95—221no—
248#95C4×D1111yescharacteristic
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#150411yescharacteristic
252C2×C11#212111yescharacteristic
253C2×C11C2×#35611yescharacteristic
254D11—22no—
255D11—41no—
256C24—111no—
257C2×Q8—441no—
258C2×Q8—881no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—222no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—881no—
276C22×C4—881no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280M16—22no—
281M16—41no—
282M16—222no—
283M16—444no—
284M16—441no—
285M16—882no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—444no—
289C2×C8—441no—
290C2×C8—441no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—442no—
299C4⋊C4—442no—
300C4⋊C4—881no—
301C4⋊C4—881no—
302C22⋊C4—224no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—881no—
306C11#1176811yescharacteristic, complemented, Sylow
307C23—111no—
308C23—111no—
309C23—222no—
310C23—221no—
311C23—221no—
312C23—441no—
313C23C22⋊C4×D1111yescharacteristic
314Q8—882no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—112no—
328C2×C4—222no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4#6696411yescharacteristic
349C2×C4#6696811yescharacteristic
350C8—42no—
351C8—81no—
352C8—442no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—112no—
357C22—221no—
358C22—221no—
359C22—221no—
360C22—221no—
361C22—221no—
362C22—442no—
363C22—442no—
364C22D11×#9911yescharacteristic
365C22#1062238411yescharacteristic
366C22D11×#10411yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—222no—
374C4—442no—
375C4—441no—
376C4—441no—
377C4—881no—
378C2—21no—
379C2—21no—
380C2—222no—
381C2—441no—
382C2#1306711711yescharacteristic
383C2#1307026111yescharacteristic
384C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11768
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #13066647C2semidirect
5. #13066645C2semidirect
6. #13066622C2semidirect
7. C11×#1346C2semidirect
121. #1346D11semidirect
306. C11#11768semidirect

Maximal subgroups

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

subgroupindex
#130739902
D11×#3432
#130669442
#130666472
#130666452
#130666222
C11×#13462
#1176811