Finite Group Databasebeta

← #14783524

Subgroups — #14783524

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622738C211yesmaximal, characteristic, complemented
2C2×#10622737C212yesmaximal, complemented
3#13077061C212yesmaximal
4#13070132C218yesmaximal, complemented
5C2×C11⋊#338C211yesmaximal, characteristic, complemented
6C11×#2879C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C22×C11×M16C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×#4318C2212yes—
11C22×#4318C2212yes—
12C11×#408—22no—
13C11×#408—22no—
14C11×#407C2214yes—
15#10622847—24no—
16#10622847—24no—
17#10622820C2218yes—
18#10622738—22no—
19#10622738C2214yes—
20#10622737—24no—
21#10622737C2218yes—
22C2×#66886—24no—
23C2×#66883—22no—
24C11⋊#338C2214yes—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—21no—
28C2×C11×#41—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C22×Q8×C11Q811yescharacteristic
34C22×D4×C11Q812yes—
35C22×D4×C11Q811yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16—21no—
41C2×C11×M16—22no—
42C2×C11×M16—22no—
43C2×C11×M16D412yes—
44C2×C11×M16C2312yes—
45C2×C11×M16C2312yes—
46C22×C8×C11—21no—
47C22×C8×C11D412yes—
48C2×#4318—22no—
49C2×#4318—22no—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318—22no—
53C2×#4318—22no—
54C2×#4318—22no—
55C2×#4318—22no—
56C2×#4318—22no—
57C2×#4318D414yes—
58C2×#4318C2314yes—
59C2×#4318C2314yes—
60C22×C11⋊C8—22no—
61C22×C11⋊C8D414yes—
62C11×C22⋊C8—28no—
63C22⋊(C11⋊C8)—216no—
64#66886—216no—
65#66883—28no—
66#23723—111nomaximal, Sylow
67C24×C11C2×Q812yes—
68C24×C11C2×Q811yescharacteristic
69C11×#41—42no—
70C11×#41—42no—
71C11×#41—42no—
72C11×#41—42no—
73C11×#41—41no—
74C11×#41—41no—
75C11×#41—42no—
76C11×#41—41no—
77C11×#41—42no—
78C11×#41—41no—
79C2×Q8×C11—22no—
80C2×Q8×C11—22no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×D4×C11—24no—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×Q812yes—
100C22×C4×C11C2×Q811yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C11×M16—24no—
107C11×M16—24no—
108C11×M16—24no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—42no—
115C2×C8×C11C2×D414yes—
116#4318—24no—
117#4318—24no—
118#4318—24no—
119#4318—24no—
120#4318—24no—
121#4318—24no—
122#4318—42no—
123#4318—42no—
124C2×C11⋊C8—24no—
125C2×C11⋊C8—24no—
126C2×C11⋊C8—24no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8C2×D418yes—
130C2×#430—112no—
131C2×#430—111no—
132#2879—112no—
133#2879D1111yescharacteristic
134#2091—118no—
135C2×#338—111no—
136C23×C11—24no—
137C23×C11—22no—
138C23×C11—81no—
139C23×C11—82no—
140C23×C11C22⋊Q812yes—
141C23×C11C22⋊Q812yes—
142C23×C11C22⋊Q811yescharacteristic
143C23×C11C22⋊Q811yescharacteristic
144C23×C11C22×Q811yescharacteristic
145Q8×C11—41no—
146Q8×C11—42no—
147Q8×C11—41no—
148D4×C11—42no—
149D4×C11—44no—
150D4×C11—42no—
151D4×C11—41no—
152D4×C11—42no—
153D4×C11—41no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—44no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11C22⋊Q812yes—
160C2×C4×C11C22⋊Q812yes—
161C2×C4×C11C22⋊Q811yescharacteristic
162C2×C4×C11C22⋊Q811yescharacteristic
163C2×C4×C11#12312yes—
164C2×C4×C11#12312yes—
165C2×C4×C11#12312yes—
166C2×C4×C11#12312yes—
167C2×C4×C11#12311yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×C4×C11#12312yes—
170C2×C4×C11#12711yescharacteristic
171C2×C4×C11#12712yes—
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C22×D412yes—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11C2×#4112yes—
177C8×C11—24no—
178C8×C11—42no—
179C11⋊C8—28no—
180C11⋊C8—44no—
181C22×#41C2×D1111yescharacteristic
182C22×M16—112no—
183C22×M16—112no—
184C22×M16C2×D1111yescharacteristic
185C22×M16C2×D1111yescharacteristic
186#430—118no—
187#430—114no—
188#430—224no—
189#430—222no—
190C2×#108—224no—
191C2×#108—222no—
192#408—22no—
193#408—22no—
194#408—224no—
195#408—224no—
196#407—118no—
197#407C2×D1114yes—
198#338—114no—
199C22×C11—41no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—48no—
205C22×C11—44no—
206C22×C11—42no—
207C22×C11#39911yescharacteristic
208C22×C11#39912yes—
209C22×C11#39911yescharacteristic
210C22×C11C2×C22⋊Q812yes—
211C22×C11C2×C22⋊Q811yescharacteristic
212C4×C11—42no—
213C4×C11#39911yescharacteristic
214C4×C11#39912yes—
215C4×C11#39911yescharacteristic
216C4×C11C2×#12312yes—
217C4×C11C2×#12311yescharacteristic
218C4×C11C2×#12711yescharacteristic
219C2×#41—21no—
220C2×#41—21no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—22no—
224C2×#41—22no—
225C2×#41—21no—
226C2×#41—21no—
227C22×Q8Dic2211yescharacteristic
228C22×D4Dic2212yes—
229C22×D4Dic2211yescharacteristic
230C23×C4C22×D1112yes—
231C23×C4C22×D1111yescharacteristic
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—21no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—114no—
238C2×M16—114no—
239C2×M16—114no—
240C2×M16—222no—
241C2×M16—222no—
242C2×M16—222no—
243C2×M16—222no—
244C2×M16—222no—
245C2×M16—222no—
246C2×M16—222no—
247C2×M16—222no—
248C2×M16—222no—
249C2×M16C22⋊D1112yes—
250C2×M16C22×D1112yes—
251C2×M16C22×D1112yes—
252C22×C8—21no—
253C22×C8—114no—
254C22×C8—222no—
255C22×C8C22⋊D1112yes—
256#108—2216no—
257#108—228no—
258C22⋊C8—28no—
259C22⋊C8—2216no—
260C2×C11—22no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—22no—
264C2×C11—21no—
265C2×C11—82no—
266C2×C11C2×#39911yescharacteristic
267C24C2×Dic2212yes—
268C24C2×Dic2211yescharacteristic
269#41—42no—
270#41—42no—
271#41—42no—
272#41—42no—
273#41—41no—
274#41—41no—
275#41—42no—
276#41—42no—
277#41—41no—
278#41—41no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×D4—24no—
284C2×D4—24no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—21no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4C2×Dic2212yes—
296C22×C4C2×Dic2211yescharacteristic
297C22×C4#433911yescharacteristic
298C22×C4#433911yescharacteristic
299C22×C4D4×D1112yes—
300C22×C4D4×D1112yes—
301C22×C4#434112yes—
302C22×C4#434112yes—
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C23×D1111yescharacteristic
306M16—24no—
307M16—24no—
308M16—24no—
309M16—41no—
310M16—41no—
311M16—224no—
312M16—224no—
313M16—224no—
314M16—224no—
315M16—224no—
316M16—224no—
317M16—442no—
318M16—442no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—42no—
323C2×C8—118no—
324C2×C8—224no—
325C2×C8—224no—
326C2×C8—224no—
327C2×C8—442no—
328C2×C8—442no—
329C2×C8C2×C22⋊D1114yes—
330C11#2372311yescharacteristic, complemented, Sylow
331C23—24no—
332C23—22no—
333C23—81no—
334C23—82no—
335C23#6693112yes—
336C23#6693112yes—
337C23#6697711yescharacteristic
338C23#6697711yescharacteristic
339C23C22×Dic2211yescharacteristic
340Q8—41no—
341Q8—42no—
342Q8—41no—
343D4—42no—
344D4—44no—
345D4—42no—
346D4—41no—
347D4—42no—
348D4—41no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4#6693112yes—
355C2×C4#6693112yes—
356C2×C4#6693612yes—
357C2×C4#6693612yes—
358C2×C4#6693612yes—
359C2×C4#6693612yes—
360C2×C4#6697711yescharacteristic
361C2×C4#6697711yescharacteristic
362C2×C4#6698811yescharacteristic
363C2×C4#6698811yescharacteristic
364C2×C4#6698812yes—
365C2×C4#6699312yes—
366C2×C4#6699311yescharacteristic
367C2×C4#6699311yescharacteristic
368C2×C4C2×#433911yescharacteristic
369C2×C4C2×D4×D1112yes—
370C2×C4C2×#434112yes—
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—24no—
373C8—42no—
374C8—228no—
375C8—444no—
376C22—41no—
377C22—42no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—48no—
382C22—44no—
383C22—42no—
384C22#1062256211yescharacteristic
385C22#1062256212yes—
386C22#1062256211yescharacteristic
387C22C2×#6693112yes—
388C22C2×#6697711yescharacteristic
389C4—42no—
390C4#1062256211yescharacteristic
391C4#1062256212yes—
392C4#1062256211yescharacteristic
393C4C2×#6693612yes—
394C4C2×#6698811yescharacteristic
395C4C2×#6699311yescharacteristic
396C2—22no—
397C2—21no—
398C2—21no—
399C2—22no—
400C2—21no—
401C2—82no—
402C2C2×#1062256211yescharacteristic
subgroupG/H
centerC4C2×#66993
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2879C2
socleC2×C11C2×#399
prime radicalC22×C11×#41C22
hypercenter#2879D11
hypocenterC11#23723
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
1. C2×#10622738C2semidirect
2. C2×#10622737C2semidirect
4. #13070132C2semidirect
5. C2×C11⋊#338C2semidirect
330. C11#23723semidirect

Maximal subgroups

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

subgroupindex
C2×#106227382
C2×#106227372
#130770612
#130701322
C2×C11⋊#3382
C11×#28792
#2372311