Finite Group Databasebeta

← #14664834

Subgroups — #14664834

Order 2816.

510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073572C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic, complemented
3#13066621C212yesmaximal, complemented
4#13066618C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66992—21no—
8C2×#66983C411yescharacteristic
9C11×#423—21no—
10C2×C11×#100—21no—
11#10622826—21no—
12C2×C11⋊#95C411yescharacteristic
13C2×C22⋊(C11⋊C8)—21no—
14#10622604C2211yescharacteristic
15#10622596C2211yescharacteristic
16#10622573C411yescharacteristic
17#10622571—21no—
18#10622566C411yescharacteristic
19#10622553—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C23×Dic11—21no—
29C22×D44C2×C411yescharacteristic
30C2×C11×M16—22no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38#66992—42no—
39#66992—42no—
40#66983—41no—
41#66983—41no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×Dic11⋊C4—21no—
48C22×C11⋊C8—41no—
49C11×C4⋊C8—41no—
50C11×C4⋊C8—41no—
51C11×#100—42no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)—41no—
59#11884—111nomaximal, Sylow
60C24×C11C22⋊C411yescharacteristic
61C24×C11C22⋊C411yescharacteristic
62C23×D11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11D812yes—
66C2×D4×C11SD1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—81no—
72C22×C4×C11—81no—
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—81no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11—81no—
90C2×D44—41no—
91C2×D44—81no—
92C11×M16—42no—
93C11×M16—42no—
94C2×C8×C11—42no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—21no—
99C42×C11—21no—
100C22⋊Dic11—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—81no—
107C4⋊Dic11—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—82no—
112#2543—111no—
113#1800D1111yescharacteristic, complemented
114#1459—111no—
115#1346—112no—
116#1345—112no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#10212yes—
126C23×C11#10212yes—
127C23×C11C2×C22⋊C411yescharacteristic
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135D4×C11—42no—
136D4×C11—42no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11#9911yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C22⋊D11—84no—
155C22⋊D11—84no—
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—84no—
166D44—82no—
167C8×C11—82no—
168C11⋊C8—82no—
169C2×#121—111no—
170C2×#121—221no—
171C2×C4×D4C2×D1111yescharacteristic
172#423—21no—
173C2×#100—21no—
174C2×C22⋊C8—221no—
175#398—111no—
176#397—111no—
177#394—111no—
178#392—111no—
179#388—221no—
180#386—221no—
181#386—221no—
182C2×#95—111no—
183#343C2×D1112yes—
184#324—112no—
185#323—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11C2×#9911yescharacteristic
199C22×C11C2×#10211yescharacteristic
200C22×C11#42111yescharacteristic
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—41no—
215Dic11—42no—
216Dic11—81no—
217Dic11—81no—
218C22×D4—111no—
219C22×D4—221no—
220C22×D4—221no—
221C22×D4C22⋊D1111yescharacteristic
222C23×C4—221no—
223C23×C4C4×D1111yescharacteristic
224C23×C4D4411yescharacteristic
225C2×M16—22no—
226C22×C8—441no—
227#121—442no—
228#121—442no—
229#121—441no—
230#121—441no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4C22×D1111yescharacteristic
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4C4×D1111yescharacteristic
242C2×C22⋊C4D4411yescharacteristic
243C2×C42C22⋊D1111yescharacteristic
244C4⋊C8—41no—
245C4⋊C8—41no—
246#100—42no—
247C22⋊C8—222no—
248C22⋊C8—441no—
249#95—111no—
250#95—111no—
251#95—221no—
252#95—221no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—42no—
257C2×C11—42no—
258C2×C11#151911yescharacteristic
259C2×C11#212111yescharacteristic
260C2×C11#213211yescharacteristic
261D11—161no—
262C24—221no—
263C24(C2×D11)⋊C411yescharacteristic
264C24(C2×D11)⋊C411yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—441no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—442no—
273C2×D4—881no—
274C2×D4—881no—
275C2×D4#432312yes—
276C2×D4#432512yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—81no—
282C22×C4—81no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—881no—
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4C2×D4411yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294M16—42no—
295M16—42no—
296C2×C8—42no—
297C2×C8—442no—
298C2×C8—882no—
299C4⋊C4—41no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—881no—
312C42—21no—
313C42—21no—
314C11#1188411yescharacteristic, complemented, Sylow
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23—441no—
330C23#6687312yes—
331C23#6687312yes—
332C23C2×(C2×D11)⋊C411yescharacteristic
333D4—42no—
334D4—42no—
335D4—882no—
336D4—884no—
337D4—884no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—222no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—884no—
361C2×C4#6687011yescharacteristic
362C2×C4#6687011yescharacteristic
363C2×C4C2×#432311yescharacteristic
364C2×C4C2×#432511yescharacteristic
365C8—82no—
366C8—882no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22C2×#6687011yescharacteristic
387C22C2×#6687311yescharacteristic
388C22#1062261811yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—442no—
397C4—881no—
398C4—881no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—1761no—
404C2#1306718311yescharacteristic
405C2#1307026311yescharacteristic
406C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1800C2
socleC22×C11C2×#99
prime radical#13073572C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1800D11
hypocenterC11#11884
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13066934C2semidirect
3. #13066621C2semidirect
4. #13066618C2semidirect
5. C11×#1800C2semidirect
113. #1800D11semidirect
314. C11#11884semidirect

Maximal subgroups

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

subgroupindex
#130735722
#130669342
#130666212
#130666182
C11×#18002
#1188411