Finite Group Databasebeta

← #14782526

Subgroups — #14782526

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622846C212yesmaximal
2#13071023C211yesmaximal, characteristic, complemented
3#13070034C212yesmaximal, complemented
4#13070029C212yesmaximal, complemented
5#13070024C212yesmaximal, complemented
6#13070019C212yesmaximal, complemented
7#13068332C212yesmaximal, complemented
8C2×#10622162C211yesmaximal, characteristic, complemented
9C11×#2297C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66979C2212yes—
14C23×C11⋊C8C2212yes—
15C11×#391C2211yescharacteristic
16C11×#391C2211yescharacteristic
17C11×#390C2211yescharacteristic
18C11×#390C2211yescharacteristic
19C11×#386—22no—
20C4×C11×C22⋊C4—22no—
21#10622846—28no—
22C2×#66899C2214yes—
23C2×#66896C2214yes—
24#10622825—22no—
25#10622549C2212yes—
26#10622548C2212yes—
27C4×C4⋊Dic11—22no—
28#10622167C2214yes—
29#10622167C2214yes—
30#10622162C2212yes—
31#10622162C2212yes—
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41D414yes—
36C22×Q8×C11C2311yescharacteristic
37C22×D4×C11—21no—
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C11×#117—24no—
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C42×C11—24no—
49C2×C42×C11—21no—
50C2×C42×C11D412yes—
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54#66979—24no—
55#66979—24no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2314yes—
59C2×C4×Dic11—22no—
60C22×C11⋊C8—24no—
61C22×C11⋊C8—24no—
62C22×C11⋊C8—24no—
63C22×C11⋊C8C2314yes—
64C11×#95—22no—
65C11×#95—22no—
66#66899—28no—
67#66896—28no—
68C11⋊#95—24no—
69#23627—111nomaximal, Sylow
70C24×C11—21no—
71C24×C11C2×D411yescharacteristic
72C11×#41—216no—
73C11×#41—48no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11C2×D412yes—
78C2×D4×C11—24no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11C2×D412yes—
85C22×C4×C11—24no—
86C22×C4×C11—21no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11#4112yes—
99C22×C4×C11#4114yes—
100C22×C4×C11#4114yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—24no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C22⋊C4—44no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—44no—
108C42×C11—24no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11—42no—
112C22⋊Dic11—44no—
113C4⋊Dic11—24no—
114C4⋊Dic11—24no—
115C4⋊Dic11—44no—
116C4⋊Dic11—44no—
117C4×Dic11—44no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—48no—
122C2×#416—112no—
123#2297D1111yescharacteristic
124#2285—111no—
125#2074—112no—
126#2073—112no—
127#2072—112no—
128#2071—112no—
129#1735—112no—
130C2×#336—111no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11#12112yes—
139C23×C11#12312yes—
140C23×C11#12412yes—
141C23×C11C22×D411yescharacteristic
142Q8×C11—24no—
143Q8×C11—42no—
144D4×C11—24no—
145D4×C11—48no—
146D4×C11—42no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—48no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—48no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11#12112yes—
162C2×C4×C11#12318yes—
163C2×C4×C11#12312yes—
164C2×C4×C11#12412yes—
165C2×C4×C11#12618yes—
166C2×C4×C11#13514yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C11C2×#4112yes—
170C2×C4×C11C2×#4112yes—
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C11⋊C8—44no—
175C22×#41C2×D1111yescharacteristic
176C23×C8—112no—
177C2×#117—112no—
178C2×#117C2×D1111yescharacteristic
179C22×C42C2×D1111yescharacteristic
180#416—228no—
181C2×#103—114no—
182C2×#102—114no—
183#391C2×D1111yescharacteristic
184#391C2×D1111yescharacteristic
185#390C2×D1111yescharacteristic
186#390C2×D1111yescharacteristic
187#386—22no—
188#384—112no—
189#382—112no—
190#380—222no—
191C4×C4⋊C4—222no—
192C4×C22⋊C4—22no—
193#340—114no—
194#340—114no—
195#336—112no—
196#336—112no—
197C22×C11—24no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—24no—
201C22×C11—42no—
202C22×C11—44no—
203C22×C11—82no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#39714yes—
207C22×C11C2×#12111yescharacteristic
208C22×C11C2×#12311yescharacteristic
209C22×C11C2×#12411yescharacteristic
210C22×C11C2×#13512yes—
211C22×C11#57512yes—
212C4×C11—24no—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#39714yes—
218C4×C11C2×#12312yes—
219C4×C11C2×#12612yes—
220Dic11—84no—
221C2×#41—22no—
222C2×#41—24no—
223C2×#41—24no—
224C2×#41D4414yes—
225C22×Q8C22×D1111yescharacteristic
226C22×D4—21no—
227C22×D4C22×D1111yescharacteristic
228C23×C4—21no—
229C23×C4C22⋊D1112yes—
230C23×C4C22×D1111yescharacteristic
231C22×C8—114no—
232C22×C8—224no—
233C22×C8—224no—
234C22×C8—224no—
235#117—24no—
236#117—224no—
237#117—224no—
238C2×C4⋊C4—114no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4C22×D1111yescharacteristic
242C2×C4⋊C4C22×D1111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—222no—
247C2×C42—24no—
248C2×C42—21no—
249C2×C42—222no—
250C2×C42C22⋊D1112yes—
251C2×C42C22×D1111yescharacteristic
252C2×C42C22×D1111yescharacteristic
253#103—228no—
254#102—228no—
255#95—22no—
256#95—22no—
257#95—224no—
258C2×C11—24no—
259C2×C11—82no—
260C2×C11C2×#39711yescharacteristic
261C2×C11#303512yes—
262C2×C11#309112yes—
263C2×C11#313111yescharacteristic
264C2×C11#313511yescharacteristic
265C24—21no—
266C24C2×C22⋊D1111yescharacteristic
267#41—216no—
268#41—48no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8C2×D4412yes—
273C2×D4—24no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4C2×D4412yes—
280C22×C4—24no—
281C22×C4—21no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—224no—
290C22×C4C2×D4412yes—
291C22×C4#433912yes—
292C22×C4#434114yes—
293C22×C4#434114yes—
294C22×C4C2×C22⋊D1112yes—
295C22×C4C2×C22⋊D1112yes—
296C22×C4C2×C22⋊D1111yescharacteristic
297C22×C4C23×D1111yescharacteristic
298C2×C8—224no—
299C2×C8—224no—
300C2×C8—224no—
301C2×C8—448no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—224no—
305C4⋊C4—224no—
306C4⋊C4—444no—
307C4⋊C4—444no—
308C22⋊C4—44no—
309C22⋊C4—42no—
310C22⋊C4—44no—
311C22⋊C4—444no—
312C42—24no—
313C42—22no—
314C42—22no—
315C42—42no—
316C42—444no—
317C11#2362711yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—42no—
324C23—42no—
325C23#6698312yes—
326C23#6698812yes—
327C23#6698912yes—
328C23C22×C22⋊D1111yescharacteristic
329Q8—24no—
330Q8—42no—
331D4—24no—
332D4—48no—
333D4—42no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—48no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—48no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—444no—
349C2×C4—444no—
350C2×C4—444no—
351C2×C4#6693218yes—
352C2×C4#6693918yes—
353C2×C4#6698312yes—
354C2×C4#6698812yes—
355C2×C4#6698912yes—
356C2×C4#6700314yes—
357C2×C4C22×D4411yescharacteristic
358C2×C4C2×#433911yescharacteristic
359C2×C4C2×#434112yes—
360C2×C4C2×#434112yes—
361C8—444no—
362C22—24no—
363C22—22no—
364C22—22no—
365C22—24no—
366C22—44no—
367C22—42no—
368C22—81no—
369C22—81no—
370C22—82no—
371C22#1062256614yes—
372C22C2×#6698311yescharacteristic
373C22C2×#6698811yescharacteristic
374C22C2×#6698911yescharacteristic
375C22C2×#6700312yes—
376C22#1062335312yes—
377C4—24no—
378C4—42no—
379C4—42no—
380C4—81no—
381C4—81no—
382C4—884no—
383C4#1062256614yes—
384C4C2×#6693212yes—
385C4C2×#6693912yes—
386C2—24no—
387C2—82no—
388C2C2×#1062256611yescharacteristic
389C2#1307807112yes—
390C2#1307852512yes—
391C2#1307893811yescharacteristic
392C2#1307896111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#23627
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. #13071023C2semidirect
3. #13070034C2semidirect
4. #13070029C2semidirect
5. #13070024C2semidirect
6. #13070019C2semidirect
7. #13068332C2semidirect
8. C2×#10622162C2semidirect
317. C11#23627semidirect

Maximal subgroups

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

subgroupindex
C2×#106228462
#130710232
#130700342
#130700292
#130700242
#130700192
#130683322
C2×#106221622
C11×#22972
#2362711