Finite Group Databasebeta

← #14656313

Subgroups — #14656313

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13069411C211yesmaximal, characteristic, complemented
4C2×#10622124C211yesmaximal, characteristic, complemented
5C2×#10622182C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#459C211yesmaximal, characteristic
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324—22no—
12C2×#66922C2211yescharacteristic
13C11×#459—22no—
14C11×#459—22no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102—21no—
17C2×#66896—21no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622689—22no—
20#10622689—22no—
21#10622620—22no—
22#10622620—22no—
23C2×#66871—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622182—22no—
28#10622124—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C2×C11×D8—24no—
36C2×C11×D8—42no—
37C2×C11×D8—42no—
38C22×C8×C11—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127D412yes—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4324—28no—
51C2×#4324—44no—
52C2×#4324—44no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D412yes—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#102—24no—
65#66896—24no—
66C22⋊(C11⋊C8)—44no—
67#66871—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#10266—111nomaximal, Sylow
75C24×C11—21no—
76C24×C11—41no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—82no—
95C2×D4×C11SD1612yescomplemented
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—41no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—42no—
108C2×Dic22—42no—
109C11×D8—48no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121#4324—416no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8D814yescomplemented
134C2×#492—111no—
135C2×#474—111no—
136C2×#459D1111yescharacteristic
137#1954—111no—
138C2×#332—111no—
139C2×#331—111no—
140#1277—111no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—82no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—44no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—81no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—82no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12711yescharacteristic
177C2×C4×C11C2×D812yes—
178C2×C4×C11C2×SD1611yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C2×Dic11—42no—
184C2×Dic11—82no—
185Dic22—44no—
186Dic22—81no—
187Dic22—81no—
188C8×C11—42no—
189C11⋊C8—24no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C22×SD16—222no—
193C22×D8—21no—
194C2×C4⋊Q8—111no—
195C2×#127C2×D1111yescharacteristic
196C2×C4×D4C2×D1111yescharacteristic
197#492—222no—
198#492—222no—
199#474—222no—
200#474—222no—
201#459—22no—
202#459—22no—
203C2×#107—221no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×#102—21no—
208C2×#102—221no—
209C2×C22⋊C8—222no—
210C2×C4×C8—111no—
211#332—222no—
212#331—222no—
213C22×C11—44no—
214C22×C11—42no—
215C22×C11—82no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—162no—
222C22×C11—162no—
223C22×C11#39211yescharacteristic
224C22×C11#45912yes—
225C22×C11#46511yescharacteristic
226C22×C11#46811yescharacteristic
227C22×C11#47112yes—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—81no—
231C4×C11#44712yes—
232C4×C11#44811yescharacteristic
233C4×C11#44911yescharacteristic
234C4×C11#45011yescharacteristic
235C4×C11#45211yescharacteristic
236C4×C11#49311yescharacteristic
237C4×C11#49611yescharacteristic
238Dic11—82no—
239C22×Q8—221no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—21no—
245C2×SD16—228no—
246C2×SD16—444no—
247C2×SD16—444no—
248C2×D8—24no—
249C2×D8—42no—
250C2×D8—42no—
251C22×C8—21no—
252C22×C8—112no—
253C22×C8—221no—
254C22×C8—221no—
255C4⋊Q8—112no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259#127—21no—
260#127—21no—
261#127—21no—
262#127C22⋊D1112yes—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C42C22×D1111yescharacteristic
272#107—224no—
273C4⋊C8—21no—
274C4⋊C8—112no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8—221no—
278C4⋊C8C22⋊D1112yes—
279#102—24no—
280#102—224no—
281C22⋊C8—444no—
282C4×C8—221no—
283C4×C8—221no—
284C2×C11—82no—
285C2×C11—162no—
286C2×C11#166512yes—
287C2×C11#168512yes—
288C2×C11#200011yescharacteristic
289C2×C11#201111yescharacteristic
290C2×C11#201911yescharacteristic
291C24—21no—
292C24—41no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—22no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—82no—
315C2×D4#432412yescomplemented
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—441no—
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325SD16—4416no—
326D8—48no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—114no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—442no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42D4×D1111yescharacteristic
347C42D4×D1111yescharacteristic
348C42C2×C22⋊D1111yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C11#1026611yescharacteristic, complemented, Sylow
351C23—22no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—82no—
358C23—82no—
359C23—81no—
360C23—81no—
361C23#6699211yescharacteristic
362Q8—444no—
363Q8—881no—
364Q8—881no—
365D4—22no—
366D4—22no—
367D4—44no—
368D4—42no—
369D4—41no—
370D4—42no—
371D4—41no—
372D4—82no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—82no—
384C2×C4—442no—
385C2×C4—882no—
386C2×C4D8×D1112yes—
387C2×C4#6696412yes—
388C2×C4#6698511yescharacteristic
389C2×C4C2×#432411yescharacteristic
390C2×C4#6699011yescharacteristic
391C2×C4#6699011yescharacteristic
392C2×C4#6699111yescharacteristic
393C2×C4#6699211yescharacteristic
394C2×C4#6699311yescharacteristic
395C2×C4#6700311yescharacteristic
396C2×C4#6700411yescharacteristic
397C2×C4#6700611yescharacteristic
398C8—42no—
399C8—224no—
400C8—442no—
401C8—881no—
402C22—42no—
403C22—44no—
404C22—82no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22—162no—
411C22—162no—
412C22#1062265411yescharacteristic
413C22#1062265511yescharacteristic
414C22#1062276312yes—
415C22#1062281312yes—
416C22#1062283611yescharacteristic
417C4—21no—
418C4—21no—
419C4—81no—
420C4—882no—
421C4#1062265011yescharacteristic
422C4#1062265311yescharacteristic
423C4#1062276411yescharacteristic
424C4#1062276711yescharacteristic
425C4#1062276912yes—
426C4#1062283111yescharacteristic
427C4#1062285211yescharacteristic
428C2—82no—
429C2—162no—
430C2#1306795512yes—
431C2#1306807912yes—
432C2#1306961911yescharacteristic
433C2#1306968511yescharacteristic
434C2#1306973011yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11#121
hypercenterC2×#459D11
hypocenterC11#10266
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. C2×#10622620C2semidirect
3. #13069411C2semidirect
4. C2×#10622124C2semidirect
5. C2×#10622182C2semidirect
6. #13066450C2semidirect
95. C2×D4×C11SD16semidirect
133. C2×C11⋊C8D8semidirect
315. C2×D4#4324semidirect
350. C11#10266semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106226202
#130694112
C2×#106221242
C2×#106221822
#130664502
C2×C11×#4592
#1026611