Finite Group Databasebeta

← #14908070

Subgroups — #14908070

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic
2C2×#10622794C211yesmaximal, characteristic, complemented
3#135×Dic11C211yesmaximal, characteristic
4#13070664C214yesmaximal, complemented
5#13070659C214yesmaximal, complemented
6#13070371C211yesmaximal, characteristic, complemented
7#13070337C211yesmaximal, characteristic, complemented
8#13070336C211yesmaximal, characteristic, complemented
9C2×C11×#510C211yesmaximal, characteristic
10C2×C11×#135C2211yescharacteristic
11C22×C11×Q16C2211yescharacteristic
12#41×Dic11—21no—
13C2×#66997—21no—
14C22×#4326—21no—
15C22×Dic44C2211yescharacteristic
16C11×#510—24no—
17C2×C11×Q32C2212yes—
18C2×C11×SD32C2212yes—
19C2×C11×M32C2211yescharacteristic
20#10622846—21no—
21#10622808—24no—
22Q16×Dic11C2212yes—
23#10622794—22no—
24#10622794C2214yes—
25C2×#66893C2212yes—
26SD16×Dic11—22no—
27D8×Dic11C2212yes—
28C2×#66891C2212yes—
29#10622719C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622202C2214yes—
33#10622141C2214yes—
34Dic11⋊C16C2214yes—
35C2×C11×#41—21no—
36C22×Q8×C11—21no—
37C22×Dic22—21no—
38C11×#135—22no—
39C11×#135D414yes—
40C2×C11×Q16—22no—
41C2×C11×Q16—21no—
42C2×C11×Q16—22no—
43C2×C11×Q16C2312yes—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48Q8×Dic11—22no—
49#66997—24no—
50#66997—41no—
51#66997—41no—
52C2×#4326—24no—
53C2×#4326—44no—
54D4×Dic11—22no—
55D4×Dic11—42no—
56#66979—21no—
57#66979—41no—
58C2×Dic11⋊C4—42no—
59C2×C4×Dic11—41no—
60C2×C4×Dic11D411yescharacteristic
61C22×C11⋊C8D411yescharacteristic
62C2×Dic44—22no—
63C2×Dic44—22no—
64C2×Dic44—21no—
65C2×Dic44C2312yes—
66C11×Q32—24no—
67C11×SD32—24no—
68C11×M32—22no—
69C2×C11×C16C2312yes—
70#66899—22no—
71#66896—22no—
72#66893—24no—
73#66891—24no—
74#66882C2312yes—
75#66881—21no—
76C8×Dic11D412yes—
77C8×Dic11C2312yes—
78#66876—22no—
79C2×C11⋊C16C2312yes—
80#33583—111nomaximal, Sylow
81C11×#41—24no—
82C11×#41—42no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×D4×C11—21no—
89C2×D4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—42no—
94C22×Dic11—41no—
95C22×Dic11D812yes—
96C2×Dic22—22no—
97C2×Dic22—42no—
98C2×Dic22—41no—
99C2×Dic22—42no—
100C11×Q16—21no—
101C11×Q16—22no—
102C11×Q16—22no—
103C11×Q16—42no—
104C11×Q16C2×D412yes—
105C11×SD16—24no—
106C11×D8—21no—
107C11×D8C2×D412yes—
108C2×C8×C11C2×D412yes—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11#4112yes—
111C2×C8×C11C2411yescharacteristic
112C22⋊Dic11—42no—
113C22⋊Dic11—41no—
114#4326—48no—
115C4⋊Dic11—22no—
116C4⋊Dic11—42no—
117Dic11⋊C4—44no—
118Dic11⋊C4—44no—
119C4×Dic11—42no—
120C4×Dic11—41no—
121C4×Dic11D811yescharacteristic
122C4×Dic11D811yescharacteristic
123C4×Dic11C2×D412yes—
124C2×C11⋊C8—22no—
125C2×C11⋊C8C2×D412yes—
126Dic44—22no—
127Dic44—22no—
128Dic44—42no—
129C11×C16—22no—
130C11⋊C16—22no—
131C2×#510—111no—
132C2×#510D1111yescharacteristic
133C2×#494—111no—
134C4×#135—111no—
135#2209—114no—
136#2208—114no—
137#2150—111no—
138#2141—111no—
139#2141—111no—
140C23×C11—41no—
141C23×C11C2×D811yescharacteristic
142Q8×C11—22no—
143Q8×C11—41no—
144Q8×C11—42no—
145Q8×C11—42no—
146Q8×C11—82no—
147D4×C11—22no—
148D4×C11—44no—
149D4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11#12112yes—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C2×C4×C11C22×D411yescharacteristic
158C2×Dic11—24no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—82no—
162C2×Dic11—84no—
163C2×Dic11C2×D812yes—
164C2×Dic11C2×D812yes—
165Dic22—42no—
166Dic22—42no—
167Dic22—82no—
168C8×C11#12112yes—
169C8×C11C22×D411yescharacteristic
170C8×C11C2×#4111yescharacteristic
171C11⋊C8—22no—
172C2×#135C2×D1111yescharacteristic
173C22×Q16—111no—
174C22×Q16—221no—
175C22×Q16C2×D1111yescharacteristic
176C2×C4⋊Q8—221no—
177C4×#41—221no—
178#510—24no—
179#510—224no—
180C2×Q32—112no—
181C2×Q32C2×D1112yes—
182C2×SD32—112no—
183C2×SD32C2×D1112yes—
184C2×M32—111no—
185C2×M32C2×D1111yescharacteristic
186#494—114no—
187#494—222no—
188C4×Q16—112no—
189C4×SD16—222no—
190C4×D8—112no—
191#427—111no—
192#416—221no—
193C2×C4×C8—111no—
194C4⋊C16—114no—
195#358—114no—
196#358—114no—
197C22×C11—22no—
198C22×C11—42no—
199C22×C11—82no—
200C22×C11#45912yes—
201C22×C11C22×D811yescharacteristic
202C4×C11—42no—
203C4×C11—82no—
204C4×C11#45912yes—
205C4×C11C2×#12111yescharacteristic
206C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
207Dic11—22no—
208Dic11—82no—
209Dic11—82no—
210Dic11#51014yescomplemented
211C2×#41—21no—
212C22×Q8—21no—
213C22×Q8—221no—
214#135—22no—
215#135C22⋊D1114yes—
216C2×Q16—21no—
217C2×Q16—22no—
218C2×Q16—22no—
219C2×Q16—112no—
220C2×Q16—224no—
221C2×Q16—221no—
222C2×Q16—222no—
223C2×Q16—222no—
224C2×Q16—444no—
225C2×Q16C22×D1112yes—
226C2×Q16C22×D1111yescharacteristic
227C2×SD16—21no—
228C2×D8C22×D1111yescharacteristic
229C22×C8—111no—
230C22×C8C22×D1111yescharacteristic
231C4⋊Q8—224no—
232C4⋊Q8—441no—
233C4⋊Q8—441no—
234C4×Q8—222no—
235C4×D4—222no—
236C4×D4—442no—
237#117—221no—
238#117—441no—
239C2×C4⋊C4—442no—
240C2×C42—111no—
241C2×C42—441no—
242Q32—24no—
243Q32—224no—
244SD32—24no—
245SD32—224no—
246M32—22no—
247M32—222no—
248C2×C16—112no—
249C2×C16C22×D1112yes—
250#107—112no—
251#106—221no—
252#103—222no—
253#102—222no—
254C4×C8—112no—
255C4×C8—112no—
256C2×C11—22no—
257C2×C11—82no—
258C2×C11C2×#45911yescharacteristic
259C2×C11C2×#51012yes—
260#41—24no—
261#41—42no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—222no—
268C2×Q8—441no—
269C2×Q8—442no—
270C2×Q8—442no—
271C2×D4—21no—
272C2×D4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—112no—
276C22×C4—442no—
277C22×C4—441no—
278C22×C4D4×D1111yescharacteristic
279Q16—21no—
280Q16—22no—
281Q16—22no—
282Q16—42no—
283Q16—222no—
284Q16—222no—
285Q16—448no—
286Q16—442no—
287Q16C2×C22⋊D1112yes—
288SD16—24no—
289D8—21no—
290D8C2×C22⋊D1112yes—
291C2×C8—112no—
292C2×C8—222no—
293C2×C8D4×D1111yescharacteristic
294C2×C8#434112yes—
295C2×C8C2×C22⋊D1112yes—
296C2×C8C23×D1111yescharacteristic
297C4⋊C4—222no—
298C4⋊C4—444no—
299C4⋊C4—444no—
300C4⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C42—111no—
304C42—111no—
305C42—112no—
306C42—442no—
307C42—441no—
308C16—22no—
309C16—222no—
310C11#3358311yescharacteristic, complemented, Sylow
311C23—41no—
312C23D8×D1111yescharacteristic
313Q8—22no—
314Q8—41no—
315Q8—42no—
316Q8—42no—
317Q8—82no—
318Q8—442no—
319Q8—442no—
320Q8—882no—
321D4—22no—
322D4—44no—
323D4—41no—
324C2×C4—41no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—112no—
329C2×C4—112no—
330C2×C4—224no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—884no—
334C2×C4—882no—
335C2×C4D8×D1111yescharacteristic
336C2×C4#6696412yes—
337C2×C4#6699212yes—
338C2×C4C2×D4×D1111yescharacteristic
339C8—222no—
340C8#6699212yes—
341C8C2×#434111yescharacteristic
342C8C22×C22⋊D1111yescharacteristic
343C22—22no—
344C22—42no—
345C22—82no—
346C22#1062276312yes—
347C22C2×D8×D1111yescharacteristic
348C4—42no—
349C4—82no—
350C4—114no—
351C4—222no—
352C4—882no—
353C4—882no—
354C4#1062276312yes—
355C4C2×#6696411yescharacteristic
356C4C2×#6699211yescharacteristic
357C2—22no—
358C2—82no—
359C2C2×#1062276311yescharacteristic
360C2D11×#51012yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenterC2×#510D11
hypocenterC11#33583
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#10622794C2semidirect
4. #13070664C2semidirect
5. #13070659C2semidirect
6. #13070371C2semidirect
7. #13070337C2semidirect
8. #13070336C2semidirect
210. Dic11#510semidirect
310. C11#33583semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106227942
#135×Dic112
#130706642
#130706592
#130703712
#130703372
#130703362
C2×C11×#5102
#3358311