Finite Group Databasebeta

← #14672082

Subgroups — #14672082

Order 2816.

724 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 107 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#13073562C211yesmaximal, characteristic
2C2×#10622112C214yesmaximal, complemented
3#13068604C211yesmaximal, characteristic, complemented
4C4×C11×#99C211yesmaximal, characteristic, complemented
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66993C2212yes—
7C2×#66983—21no—
8C2×#66983—21no—
9C2×#66927C411yescharacteristic, complemented
10C2×C11×#99C2212yes—
11C4×C11×C22⋊C4—21no—
12C2×#66898C2212yes—
13#10622825—21no—
14#10622601C412yescomplemented
15#10622573—21no—
16#10622573—21no—
17C4×C4⋊Dic11C411yescharacteristic, complemented
18C11×#342—21no—
19#10622164—21no—
20#10622112—28no—
21C22×D4×C11C2311yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—22no—
25C22×C22⋊D11—22no—
26C22×D44—21no—
27C22×D44—21no—
28C22×D44C2×C412yes—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11—41no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C22⋊Dic11—22no—
38#66993—24no—
39#66993—24no—
40#66983—44no—
41#66983—44no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—41no—
46C2×C4×Dic11C2×C412yes—
47#66927—41no—
48#66927—41no—
49C11×#99—22no—
50C11×#99D414yescomplemented
51C11×#95—41no—
52#66898—24no—
53C11⋊#95—21no—
54C11⋊#95—41no—
55#13223—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C23×D11—22no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11C2×D412yes—
62C2×D4×C11#4112yes—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C2×C22⋊D11—44no—
76C2×C22⋊D11—44no—
77C2×C22⋊D11—44no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—82no—
81C2×C22⋊D11—82no—
82C22×Dic11—22no—
83C22×Dic11—42no—
84C2×D44—24no—
85C2×D44—42no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—82no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—24no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—42no—
98C42×C11—21no—
99C42×C11—21no—
100C42×C11—82no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—44no—
105C4⋊Dic11—24no—
106C4⋊Dic11—82no—
107C4×Dic11—24no—
108#2541—111no—
109C2×#353—114no—
110#1799—111no—
111C4×#99D1111yescharacteristic, complemented
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11C2×C22⋊C411yescharacteristic
121C23×C11#12112yes—
122C23×C11#12411yescharacteristic
123C23×C11#12711yescharacteristic
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131D4×C11—42no—
132D4×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—44no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11#9911yescharacteristic
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11C4×D412yes—
152C22⋊D11—88no—
153C22⋊D11—84no—
154C22⋊D11—84no—
155C2×Dic11—24no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—82no—
159C2×Dic11—82no—
160C2×Dic11—82no—
161D44—84no—
162D44—82no—
163D44—84no—
164D44—82no—
165C2×#127—112no—
166C2×#127—111no—
167C2×#121—221no—
168C2×#121—221no—
169C2×C4×D4C2×D1111yescharacteristic
170C2×#99—112no—
171C2×#99C2×D1112yes—
172#392—221no—
173#392—221no—
174#390—112no—
175#380—221no—
176C4×C4⋊C4—111no—
177C4×C22⋊C4—21no—
178#353—228no—
179#342—21no—
180#342—221no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—22no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—42no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11#39011yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11#41011yescharacteristic
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—82no—
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—84no—
211C4×C11#35312yescomplemented
212Dic11—44no—
213Dic11—162no—
214C22×D4—112no—
215C22×D4—222no—
216C22×D4—222no—
217C22×D4—221no—
218C22×D4—221no—
219C22×D4C22×D1111yescharacteristic
220C23×C4D4411yescharacteristic
221C23×C4C22⋊D1111yescharacteristic
222#127—224no—
223#127—224no—
224#127—441no—
225#127—441no—
226#121—444no—
227#121—444no—
228C4×D4—41no—
229C4×D4—41no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—441no—
232C2×C4⋊C4C4×D1111yescharacteristic
233C2×C22⋊C4—22no—
234C2×C22⋊C4—222no—
235C2×C22⋊C4—222no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4D4411yescharacteristic
238C2×C22⋊C4C22⋊D1111yescharacteristic
239C2×C42—41no—
240C2×C42—112no—
241C2×C42C4×D1111yescharacteristic
242#99—22no—
243#99—224no—
244#99D4414yescomplemented
245#95—41no—
246#95—221no—
247#95—441no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—41no—
251C2×C11—42no—
252C2×C11—41no—
253C2×C11#196411yescharacteristic
254C2×C11C2×#35311yescharacteristic
255C2×C11#212811yescharacteristic
256D11—162no—
257C24—222no—
258C24C2×D4411yescharacteristic
259C24C2×C22⋊D1111yescharacteristic
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—224no—
263C2×D4—442no—
264C2×D4—442no—
265C2×D4—442no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—444no—
269C2×D4—444no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—444no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—882no—
276C2×D4—882no—
277C2×D4—882no—
278C2×D4C2×D4412yes—
279C2×D4#433912yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—222no—
288C22×C4—442no—
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4(C2×D11)⋊C411yescharacteristic
293C22×C4C2×C4×D1111yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—224no—
296C4⋊C4—882no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—444no—
302C22⋊C4—444no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C42—21no—
306C42—21no—
307C42—82no—
308C42—224no—
309C11#1322311yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—442no—
319C23—442no—
320C23—442no—
321C23—442no—
322C23—442no—
323C23—442no—
324C23—442no—
325C23#6692711yescharacteristic
326C23#6692811yescharacteristic
327C23C2×(C2×D11)⋊C411yescharacteristic
328C23#6698312yes—
329D4—42no—
330D4—42no—
331D4—884no—
332D4—882no—
333D4—884no—
334D4—884no—
335D4—884no—
336D4—888no—
337D4—882no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—224no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—882no—
358C2×C4—882no—
359C2×C4—882no—
360C2×C4#6687011yescharacteristic
361C2×C4#6687011yescharacteristic
362C2×C4C4×D4412yes—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—882no—
378C22—882no—
379C22—882no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22—882no—
384C22#1062255211yescharacteristic
385C22C2×#6687011yescharacteristic
386C22#1062261911yescharacteristic
387C4—22no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—84no—
393C4—444no—
394C4—1762no—
395C4#1062211212yescomplemented
396C2—21no—
397C2—21no—
398C2—42no—
399C2—41no—
400C2—41no—
401C2—1762no—
402C2#1306945211yescharacteristic
403C2C2×#1062211211yescharacteristic
404C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical#13073562C2
cosocleC22×D4×C11C23
hypercenterC4×#99D11
hypocenterC11#13223
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10622112C2semidirect
3. #13068604C2semidirect
4. C4×C11×#99C2semidirect
9. C2×#66927C4semidirect
14. #10622601C4semidirect
17. C4×C4⋊Dic11C4semidirect
50. C11×#99D4semidirect
111. C4×#99D11semidirect
211. C4×C11#353semidirect
244. #99D44semidirect
309. C11#13223semidirect
395. C4#10622112semidirect

Maximal subgroups

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

subgroupindex
#130735622
C2×#106221122
#130686042
C4×C11×#992
#1322311