Finite Group Databasebeta

← #14664157

Subgroups — #14664157

Order 2816.

470 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#66897C211yesmaximal, characteristic, complemented
2#13066934C211yesmaximal, characteristic, complemented
3#13066643C212yesmaximal, complemented
4#13066619C212yesmaximal, complemented
5C11×#2635C211yesmaximal, characteristic
6C2×C11×#121C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#400C2211yescharacteristic
9C11×#399C411yescharacteristic
10C11×#394—21no—
11C11×#394C2211yescharacteristic
12C11×#392—21no—
13C11×#392C411yescharacteristic
14C11×#388—21no—
15C11×#386—21no—
16C11×#381C411yescharacteristic
17C2×#66897—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C4×#4318—21no—
20#10622168C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C22×D4×C11D411yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×#121—41no—
30C11×#121—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×#4318—22no—
46C22×C11⋊C8—41no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52#66897—24no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—41no—
55#66867—41no—
56C4×C11⋊C8—41no—
57#11737—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22⋊C411yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C2×D4×C11—81no—
68C2×D4×C11—81no—
69C2×D4×C11—81no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—81no—
80C22×C4×C11—81no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—81no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—81no—
95C11×C22⋊C4—81no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C42×C11—21no—
99C42×C11—21no—
100#4318—24no—
101#4318—42no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—82no—
105#2635D1111yescharacteristic
106C4×#100—111no—
107#1459—111no—
108#1353—112no—
109#1345—112no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#10412yes—
127C23×C11C2×C22⋊C411yescharacteristic
128D4×C11—44no—
129D4×C11—82no—
130D4×C11—84no—
131D4×C11—84no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#9911yescharacteristic
155C2×C4×C11#9911yescharacteristic
156C2×C4×C11#13512yes—
157C11⋊C8—44no—
158C11⋊C8—82no—
159C2×#121Dic1111yescharacteristic
160C2×C4×D4C2×D1111yescharacteristic
161C2×#100—221no—
162C2×C22⋊C8—221no—
163C4×M16—221no—
164#400C2×D1111yescharacteristic
165#399Dic1111yescharacteristic
166#394—21no—
167#394C2×D1111yescharacteristic
168#392—21no—
169#392Dic1111yescharacteristic
170#388—21no—
171#386—21no—
172#381Dic1111yescharacteristic
173#343—112no—
174#324—112no—
175#323—221no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—42no—
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—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11C2×#9911yescharacteristic
196C22×C11#41611yescharacteristic
197C22×C11C2×#10411yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—22no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C2×Dic1111yescharacteristic
210C22×D4C22⋊D1111yescharacteristic
211C23×C4C2×Dic1111yescharacteristic
212C23×C4C22⋊D1111yescharacteristic
213C2×M16—222no—
214C22×C8—441no—
215#121—41no—
216#121—41no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic1111yescharacteristic
221C2×C4⋊C4C22×D1111yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4C2×Dic1111yescharacteristic
229C2×C22⋊C4C22⋊D1111yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231#100—224no—
232C22⋊C8—222no—
233C22⋊C8—441no—
234#97—441no—
235C4×C8—441no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95C2×Dic1111yescharacteristic
240#95C2×Dic1111yescharacteristic
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—42no—
244C2×C11—81no—
245C2×C11—161no—
246C2×C11#150111yescharacteristic
247C2×C11#212111yescharacteristic
248C2×C11#213411yescharacteristic
249C24—21no—
250C24C22⋊Dic1111yescharacteristic
251C24C22⋊Dic1111yescharacteristic
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—81no—
259C2×D4—81no—
260C2×D4—81no—
261C2×D4—81no—
262C2×D4—81no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4C22⋊Dic1111yescharacteristic
273C22×C4C22⋊Dic1111yescharacteristic
274C22×C4C22×Dic1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277M16—224no—
278M16—442no—
279C2×C8—442no—
280C2×C8—442no—
281C2×C8—882no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C42—21no—
295C42—21no—
296C11#1173711yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#6690112yes—
314C23C2×C22⋊Dic1111yescharacteristic
315D4—44no—
316D4—82no—
317D4—84no—
318D4—84no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4#6689811yescharacteristic
342C2×C4#6689811yescharacteristic
343C2×C4#6700312yes—
344C8—444no—
345C8—882no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22C2×#6689811yescharacteristic
366C22#1062284611yescharacteristic
367C22C2×#6690111yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—81no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—81no—
381C2—161no—
382C2#1306710711yescharacteristic
383C2#1307026211yescharacteristic
384C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2635C2
socleC22×C11C2×#99
cosocleC2×C11×C4⋊C4C23
hypercenter#2635D11
hypocenterC11#11737
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C4×#66897C2semidirect
2. #13066934C2semidirect
3. #13066643C2semidirect
4. #13066619C2semidirect
296. C11#11737semidirect

Maximal subgroups

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

subgroupindex
C4×#668972
#130669342
#130666432
#130666192
C11×#26352
#1173711