Finite Group Databasebeta

← #13080352

Subgroups — #13080352

Order 1408.

482 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×Q16×D11C211yesmaximal, characteristic, complemented
2C2×#66969C211yesmaximal, characteristic, complemented
3#10623208C211yesmaximal, characteristic, complemented
4#10623107C211yesmaximal, characteristic, complemented
5C11×#464C211yesmaximal, characteristic, complemented
6#10622800C211yesmaximal, characteristic, complemented
7#10622783C211yesmaximal, characteristic, complemented
8#10622672C211yesmaximal, characteristic, complemented
9C4×#4326C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622447C211yesmaximal, characteristic, complemented
12#10622426C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic, complemented
14#10622396C211yesmaximal, characteristic, complemented
15#10622388C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C2×#4341C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C11×#124C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66991C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31Q16×D11—24no—
32#66969—24no—
33C2×Dic44C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35C2×C8×D11C2211yescharacteristic
36C2×C8×D11C2211yescharacteristic
37#66950—21no—
38#66950C2211yescharacteristic
39#66948—21no—
40#66948C2211yescharacteristic
41#66938—21no—
42#66937—21no—
43(C22⋊D11)⋊C4—21no—
44#66931—21no—
45#66928—21no—
46#66928C2211yescharacteristic
47C4×D44—21no—
48C4×D44C2211yescharacteristic
49C4×Dic22C2211yescharacteristic
50C11×C4⋊C8C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53#66899C2211yescharacteristic
54#66885C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic
56(C2×D11)⋊C8C2211yescharacteristic
57#66880C2211yescharacteristic
58#66874C2211yescharacteristic
59#66871C2211yescharacteristic
60C4×C11⋊C8C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67#4343—22no—
68#4343—41no—
69Q8×D11—22no—
70Q8×D11—22no—
71Q8×D11—41no—
72Q8×D11—41no—
73#4341—22no—
74#4341—41no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44D411yescharacteristic
78C2×D44C2311yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11C2311yescharacteristic
83C2×C4×D11C2311yescharacteristic
84C2×Dic22—21no—
85C2×Dic22—21no—
86C2×Dic22C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C11×Q16—22no—
89C11×SD16—22no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C42×C11—21no—
97C42×C11C2311yescharacteristic
98C22⋊Dic11—21no—
99#4326—22no—
100#4326D414yescomplemented
101#4325—41no—
102#4324—41no—
103#4323—22no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110(C2×D11)⋊C4D411yescharacteristic
111C4⋊Dic11—21no—
112C4⋊Dic11D411yescharacteristic
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116C4×Dic11—21no—
117C2×C11⋊C8C2311yescharacteristic
118C2×C11⋊C8C2311yescharacteristic
119Dic44—22no—
120#4314—22no—
121C8×D11—22no—
122C8×D11—22no—
123#3285—111nomaximal, Sylow
124C23×C11—21no—
125C22×D11—21no—
126C22×D11C2×D411yescharacteristic
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11C2×D412yes—
132D4×C11—21no—
133D4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C22⋊D11—42no—
141C22⋊D11—42no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148D44—22no—
149D44—21no—
150D44—21no—
151D44—42no—
152D44—42no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—42no—
158C4×D11—42no—
159C4×D11—42no—
160Dic22—21no—
161Dic22—21no—
162Dic22—21no—
163Dic22—42no—
164Dic22—42no—
165Dic22C2×D412yes—
166C8×C11—21no—
167C8×C11—21no—
168C11⋊C8—21no—
169C11⋊C8C2×D412yes—
170C2×#135—111no—
171C22×Q16—111no—
172#548—111no—
173#548—111no—
174#495—111no—
175#467—111no—
176#466—111no—
177#464—111no—
178#464D1111yescharacteristic, complemented
179#452—111no—
180#452—111no—
181#448—111no—
182#448—111no—
183C4×Q16—111no—
184C8×D4—111no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11C22×D411yescharacteristic
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11#13512yescomplemented
198C4×C11—22no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11C22×D411yescharacteristic
204C4×C11H(5,𝔽2)11yescharacteristic
205Dic11—22no—
206Dic11—21no—
207Dic11—21no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41—111no—
212C22×Q8—111no—
213C22×Q8—111no—
214#135—224no—
215C2×Q16—111no—
216C2×Q16—111no—
217C2×Q16—111no—
218C2×Q16—224no—
219C2×Q16C2×D1111yescharacteristic
220C2×SD16—111no—
221C2×SD16—111no—
222C2×SD16—111no—
223C2×SD16C2×D1111yescharacteristic
224C2×D8—111no—
225C22×C8—111no—
226C22×C8—111no—
227#124—111no—
228#124—221no—
229#124—221no—
230#124C2×D1111yescharacteristic
231C22⋊Q8—111no—
232C22⋊Q8—111no—
233C22⋊Q8—221no—
234C22⋊Q8—221no—
235#121—111no—
236#121—111no—
237#121—221no—
238#121—221no—
239C4×Q8—111no—
240C4×Q8C2×D1111yescharacteristic
241C4×D4—111no—
242C4×D4—221no—
243C4×D4—221no—
244#107—111no—
245C4⋊C8C2×D1111yescharacteristic
246#103—111no—
247#103—111no—
248#103—111no—
249#103C2×D1111yescharacteristic
250#102—111no—
251#102C2×D1111yescharacteristic
252C22⋊C8—111no—
253C22⋊C8—111no—
254C4×C8—111no—
255C2×C11—81no—
256C2×C11D4211yescharacteristic
257C2×C11C2×#13511yescharacteristic
258C2×C11#57811yescharacteristic
259D11—22no—
260D11—41no—
261D11—81no—
262#41—222no—
263#41—222no—
264#41—441no—
265#41—441no—
266C2×Q8—111no—
267C2×Q8—111no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×Q8—222no—
271C2×Q8—222no—
272C2×Q8—441no—
273C2×Q8—441no—
274C2×Q8C22×D1111yescharacteristic
275C2×Q8C22×D1111yescharacteristic
276C2×D4—111no—
277C2×D4—111no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4C22×D1111yescharacteristic
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289Q16—22no—
290Q16—114no—
291Q16—222no—
292Q16—222no—
293SD16—22no—
294SD16—222no—
295SD16—441no—
296SD16—441no—
297D8—222no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8C22×D1111yescharacteristic
303C2×C8C22×D1111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—111no—
306C4⋊C4—111no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4C22×D1111yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—111no—
314C22⋊C4—111no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C42—21no—
322C42—221no—
323C42C22×D1111yescharacteristic
324C11#328511yescharacteristic, complemented, Sylow
325C23—21no—
326C23—111no—
327C23—111no—
328C23—221no—
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—112no—
333Q8—221no—
334Q8—221no—
335Q8—221no—
336Q8—442no—
337Q8—442no—
338Q8D4×D1112yes—
339D4—21no—
340D4—21no—
341D4—222no—
342D4—221no—
343D4—221no—
344D4—442no—
345D4—442no—
346D4—442no—
347D4—442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4D4×D1111yescharacteristic
365C2×C4D4×D1111yescharacteristic
366C2×C4C23×D1111yescharacteristic
367C8—21no—
368C8—21no—
369C8—112no—
370C8—221no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—112no—
375C22—221no—
376C22—221no—
377C22—221no—
378C22—221no—
379C22—221no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22C2×D4×D1111yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—221no—
390C4—221no—
391C4—222no—
392C4—441no—
393C4—441no—
394C4C2×D4×D1111yescharacteristic
395C4#6704211yescharacteristic
396C2—81no—
397C2—222no—
398C2—441no—
399C2—881no—
400C2#1062314011yescharacteristic
401C2D11×#13511yescharacteristic
402C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
hypercenter#464D11
hypocenterC11#3285
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D11C2semidirect
2. C2×#66969C2semidirect
3. #10623208C2semidirect
4. #10623107C2semidirect
5. C11×#464C2semidirect
6. #10622800C2semidirect
7. #10622783C2semidirect
8. #10622672C2semidirect
9. C4×#4326C2semidirect
10. #10622458C2semidirect
11. #10622447C2semidirect
12. #10622426C2semidirect
13. #10622419C2semidirect
14. #10622396C2semidirect
15. #10622388C2semidirect
100. #4326D4semidirect
178. #464D11semidirect
197. C2×D11#135semidirect
324. C11#3285semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D112
C2×#669692
#106232082
#106231072
C11×#4642
#106228002
#106227832
#106226722
C4×#43262
#106224582
#106224472
#106224262
#106224192
#106223962
#106223882
#328511