Finite Group Databasebeta

← #14656286

Subgroups — #14656286

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic, complemented
5C2×#10622124C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C22×#4323—21no—
10C22×#4314—21no—
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66896—21no—
16C2×#66896—22no—
17C2×(C2×D11)⋊C8—22no—
18C2×#66880—21no—
19#10622685—22no—
20#10622685—22no—
21#10622683—22no—
22#10622683—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622454—22no—
26#10622454—22no—
27C11×#331—22no—
28#10622124—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127D412yes—
41C2×C42×C11C2311yescharacteristic
42C2×#4323—24no—
43C2×#4323—42no—
44C2×#4323—42no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8D412yes—
51C2×#4314—24no—
52C2×#4314—42no—
53C2×#4314—42no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66#66896—28no—
67#66896—24no—
68(C2×D11)⋊C8—44no—
69#66880—24no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#10261—111nomaximal, Sylow
75C24×C11—41no—
76C23×D11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—82no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—41no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44D812yes—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×C8×C11—22no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—42no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4323—48no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#4314—48no—
136C2×#486—111no—
137C2×#461—111no—
138C2×#459—111no—
139#1954—111no—
140C2×#332—111no—
141C2×#331D1111yescharacteristic, complemented
142#1277—111no—
143C23×C11—42no—
144C23×C11—82no—
145C23×C11—81no—
146C23×C11—81no—
147C23×C11—82no—
148C23×C11#12111yescharacteristic
149C22×D11—22no—
150C22×D11—41no—
151C22×D11—42no—
152C22×D11—41no—
153C22×D11—42no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—44no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11#13512yes—
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181D44—22no—
182D44—22no—
183D44—41no—
184D44—41no—
185C4×D11—82no—
186C4×D11—81no—
187C4×D11—81no—
188Dic22—42no—
189Dic22—42no—
190Dic22—81no—
191Dic22—81no—
192C8×C11—42no—
193C8×C11—81no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C22×SD16—221no—
197C22×D8—221no—
198C2×C4⋊Q8—111no—
199C2×#127C2×D1111yescharacteristic
200C2×C4×D4—111no—
201#486—222no—
202#486—222no—
203#461—222no—
204#461—222no—
205#459—222no—
206#459—222no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×C4⋊C8C2×D1111yescharacteristic
210C2×#103—221no—
211C2×#102—221no—
212C2×#102—222no—
213C2×C22⋊C8—222no—
214C2×C4×C8—111no—
215#332—222no—
216#331—22no—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—162no—
221C22×C11—162no—
222C22×C11#39211yescharacteristic
223C22×C11#46312yes—
224C22×C11#46611yescharacteristic
225C22×C11#46911yescharacteristic
226C22×C11#47112yes—
227C2×D11—44no—
228C2×D11—42no—
229C2×D11—82no—
230C2×D11—81no—
231C2×D11—81no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11#44711yescharacteristic
235C4×C11#44711yescharacteristic
236C4×C11#44911yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#44912yes—
239C4×C11#49511yescharacteristic
240C4×C11#49611yescharacteristic
241Dic11—82no—
242Dic11—81no—
243C22×Q8—221no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—111no—
248C23×C4—221no—
249C2×SD16—224no—
250C2×SD16—442no—
251C2×SD16—442no—
252C2×D8—224no—
253C2×D8—442no—
254C2×D8—442no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—112no—
258C22×C8—221no—
259C4⋊Q8—112no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C4⋊Q8—221no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127D4412yes—
267C4×D4—221no—
268C4×D4—221no—
269C4×D4—221no—
270C4×D4—221no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C42C22×D1111yescharacteristic
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—112no—
280C4⋊C8—221no—
281C4⋊C8C22⋊D1112yes—
282#103—224no—
283#102—224no—
284#102—228no—
285C22⋊C8—444no—
286C4×C8—221no—
287C4×C8—221no—
288C2×C11—162no—
289C2×C11#168112yes—
290C2×C11#170112yes—
291C2×C11#199911yescharacteristic
292C2×C11#201211yescharacteristic
293C2×C11#201911yescharacteristic
294D11—82no—
295C24—41no—
296C24—221no—
297C2×Q8—222no—
298C2×Q8—441no—
299C2×Q8—441no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—82no—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—221no—
323C22×C4—441no—
324C22×C4—441no—
325C22×C4—442no—
326C22×C4—442no—
327C22×C4—441no—
328C22×C4#433911yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331SD16—448no—
332D8—448no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—221no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—221no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42C2×D4411yescharacteristic
353C42D4×D1111yescharacteristic
354C42D4×D1111yescharacteristic
355C42C2×C22⋊D1111yescharacteristic
356C11#1026111yescharacteristic, complemented, Sylow
357C23—42no—
358C23—82no—
359C23—81no—
360C23—81no—
361C23—82no—
362C23—222no—
363C23—441no—
364C23—442no—
365C23—441no—
366C23—442no—
367C23#6693711yescharacteristic
368Q8—442no—
369Q8—442no—
370Q8—881no—
371Q8—881no—
372D4—42no—
373D4—42no—
374D4—44no—
375D4—82no—
376D4—82no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—222no—
382D4—222no—
383D4—441no—
384D4—441no—
385C2×C4—22no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4—882no—
394C2×C4#6693511yescharacteristic
395C2×C4#6693511yescharacteristic
396C2×C4#6693711yescharacteristic
397C2×C4D8×D1111yescharacteristic
398C2×C4#6696412yes—
399C2×C4#6696411yescharacteristic
400C2×C4#6696711yescharacteristic
401C2×C4#6696912yes—
402C2×C4#6696911yescharacteristic
403C2×C4#6698311yescharacteristic
404C2×C4#6699011yescharacteristic
405C2×C4#6699311yescharacteristic
406C8—42no—
407C8—81no—
408C8—442no—
409C8—442no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22—444no—
416C22—442no—
417C22—881no—
418C22—882no—
419C22—881no—
420C22#1062236112yes—
421C22#1062238811yescharacteristic
422C22#1062239511yescharacteristic
423C22#1062240012yes—
424C22#1062257311yescharacteristic
425C4—21no—
426C4—21no—
427C4—882no—
428C4—881no—
429C4#1062238611yescharacteristic
430C4#1062239411yescharacteristic
431C4#1062239412yes—
432C4#1062276711yescharacteristic
433C4#1062276911yescharacteristic
434C4#1062278111yescharacteristic
435C4#1062278511yescharacteristic
436C2—162no—
437C2—882no—
438C2#1306805212yes—
439C2#1306817612yes—
440C2#1306961311yescharacteristic
441C2#1306969511yescharacteristic
442C2#1306973211yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11#121
prime radicalC2×#10622685C2
hypercenterC2×#331D11
hypocenterC11#10261
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
2. C2×#10622454C2semidirect
4. #13069409C2semidirect
5. C2×#10622124C2semidirect
6. #13066450C2semidirect
7. C2×C11×#331C2semidirect
141. C2×#331D11semidirect
356. C11#10261semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
C2×#106224542
C2×#106226852
#130694092
C2×#106221242
#130664502
C2×C11×#3312
#1026111