Finite Group Databasebeta

← #14664805

Subgroups — #14664805

Order 2816.

644 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 99 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
2#13066934C211yesmaximal, characteristic, complemented
3#13066612C214yesmaximal, complemented
4C11×#1799C211yesmaximal, characteristic, complemented
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66993—21no—
7C2×#66983—21no—
8C2×#66983—21no—
9C2×#66927C411yescharacteristic, complemented
10C2×C11×#99—21no—
11C11×#380—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622601—21no—
14#10622573C412yescomplemented
15#10622573C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17C11×#342C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×C22⋊D11—22no—
24C22×C22⋊D11—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44C2×C412yes—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36#66993—42no—
37#66993—42no—
38#66983—44no—
39#66983—44no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×C4⋊Dic11—21no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—41no—
45#66927—41no—
46#66927—41no—
47C11×#99—42no—
48C11×#95—41no—
49C11⋊#95C2×C412yes—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—41no—
52#11877—111nomaximal, Sylow
53C24×C11C22⋊C411yescharacteristic
54C24×C11C2×D411yescharacteristic
55C23×D11—22no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11D812yes—
59C2×D4×C11SD1612yes—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—44no—
73C2×C22⋊D11—44no—
74C2×C22⋊D11—44no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—82no—
78C2×C22⋊D11—82no—
79C22×Dic11—22no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—42no—
83C2×D44—42no—
84C2×D44—42no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—82no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—82no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—42no—
95C42×C11—21no—
96C42×C11—21no—
97(C2×D11)⋊C4—44no—
98(C2×D11)⋊C4—44no—
99C4⋊Dic11—24no—
100C4×Dic11—42no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—82no—
103#2541—111no—
104#1799D1111yescharacteristic, complemented
105#1459—111no—
106#1343—114no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10212yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11C2×D811yescharacteristic
118C23×C11C2×SD1611yescharacteristic
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122C22×D11—42no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—42no—
126D4×C11—42no—
127D4×C11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11—82no—
144C2×C4×C11#9911yescharacteristic
145C2×C4×C11#9911yescharacteristic
146C2×C4×C11#10212yes—
147C22⋊D11—88no—
148C22⋊D11—84no—
149C22⋊D11—84no—
150C2×Dic11—24no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153D44—82no—
154D44—84no—
155D44—84no—
156D44—82no—
157C11⋊C8—82no—
158C2×#127—111no—
159C2×#127—221no—
160C2×#121—221no—
161C2×#121—221no—
162C2×C4×D4C2×D1111yescharacteristic
163C2×#99—21no—
164C2×C22⋊C8—221no—
165#392—112no—
166#392—112no—
167#390—221no—
168#380—21no—
169C4×C4⋊C4—111no—
170#342C2×D1112yes—
171#324—221no—
172#323—112no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11C2×#9911yescharacteristic
188C22×C11C2×#10211yescharacteristic
189C22×C11#42111yescharacteristic
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C2×D11—82no—
197C4×C11—21no—
198C4×C11—22no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—162no—
203C4×C11#35312yes—
204Dic11—44no—
205C22×D4—112no—
206C22×D4—222no—
207C22×D4—222no—
208C22×D4—221no—
209C22×D4—221no—
210C22×D4C22⋊D1111yescharacteristic
211C23×C4D4411yescharacteristic
212C23×C4C22⋊D1111yescharacteristic
213C22×C8—441no—
214#127—441no—
215#127—441no—
216#127—442no—
217#127—442no—
218#121—444no—
219#121—444no—
220C4×D4—41no—
221C4×D4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4D4411yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—222no—
227C2×C22⋊C4—222no—
228C2×C22⋊C4C4×D1111yescharacteristic
229C2×C22⋊C4C22×D1111yescharacteristic
230C2×C42—221no—
231C2×C42C4×D1111yescharacteristic
232#99—42no—
233C22⋊C8—222no—
234C22⋊C8—441no—
235#95—41no—
236#95—112no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—41no—
240C2×C11—42no—
241C2×C11—41no—
242C2×C11#151911yescharacteristic
243C2×C11#212211yescharacteristic
244C2×C11C2×#35311yescharacteristic
245D11—162no—
246C24—222no—
247C24(C2×D11)⋊C411yescharacteristic
248C24C2×C22⋊D1111yescharacteristic
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—442no—
252C2×D4—442no—
253C2×D4—442no—
254C2×D4—442no—
255C2×D4—442no—
256C2×D4—444no—
257C2×D4—444no—
258C2×D4—444no—
259C2×D4—442no—
260C2×D4—442no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—442no—
264C2×D4—882no—
265C2×D4—882no—
266C2×D4—882no—
267C2×D4#432312yes—
268C2×D4#432512yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—222no—
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4(C2×D11)⋊C411yescharacteristic
279C22×C4(C2×D11)⋊C411yescharacteristic
280C22×C4C2×C4×D1111yescharacteristic
281C22×C4C2×D4411yescharacteristic
282C2×C8—442no—
283C2×C8—882no—
284C4⋊C4—41no—
285C4⋊C4—82no—
286C4⋊C4—224no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—444no—
292C22⋊C4—444no—
293C42—21no—
294C42—21no—
295C42—442no—
296C11#1187711yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—442no—
306C23—442no—
307C23—442no—
308C23—442no—
309C23—442no—
310C23—442no—
311C23—442no—
312C23#6687312yes—
313C23C2×(C2×D11)⋊C411yescharacteristic
314C23C2×#432311yescharacteristic
315C23C2×#432511yescharacteristic
316D4—42no—
317D4—42no—
318D4—884no—
319D4—882no—
320D4—884no—
321D4—888no—
322D4—884no—
323D4—884no—
324D4—882no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—224no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4#6687011yescharacteristic
345C2×C4#6687011yescharacteristic
346C2×C4#6687312yes—
347C8—882no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—882no—
363C22—882no—
364C22—882no—
365C22—882no—
366C22—882no—
367C22—882no—
368C22—882no—
369C22C2×#6687011yescharacteristic
370C22C2×#6687311yescharacteristic
371C22#1062261811yescharacteristic
372C4—22no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—162no—
378C4—444no—
379C4#1062211212yes—
380C2—21no—
381C2—21no—
382C2—41no—
383C2—42no—
384C2—41no—
385C2—1762no—
386C2#1306718311yescharacteristic
387C2#1307026511yescharacteristic
388C2C2×#1062211211yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radical#13073562C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1799D11
hypocenterC11#11877
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13066934C2semidirect
3. #13066612C2semidirect
4. C11×#1799C2semidirect
9. C2×#66927C4semidirect
14. #10622573C4semidirect
16. C4×C4⋊Dic11C4semidirect
104. #1799D11semidirect
296. C11#11877semidirect

Maximal subgroups

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

subgroupindex
#130735622
#130669342
#130666122
C11×#17992
#1187711