Finite Group Databasebeta

← #13080204

Subgroups — #13080204

Order 1408.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623348C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic, complemented
3C2×#66969C211yesmaximal, characteristic, complemented
4#10623130C211yesmaximal, characteristic, complemented
5C11×#448C211yesmaximal, characteristic, complemented
6#10622789C211yesmaximal, characteristic, complemented
7#10622786C211yesmaximal, characteristic, complemented
8#10622776C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622424C211yesmaximal, characteristic, complemented
11#10622420C211yesmaximal, characteristic, complemented
12#10622411C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622341C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×#4339C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C11×#121C2211yescharacteristic
23#67000—21no—
24#67000C2211yescharacteristic
25#66999—21no—
26#66999C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30#66995—24no—
31C2×#4325C2211yescharacteristic
32C2×#4325C2211yescharacteristic
33#66993—21no—
34#66993C2211yescharacteristic
35#66992—21no—
36C2×#4323C2211yescharacteristic
37#66983—21no—
38#66983C2211yescharacteristic
39C4×C22⋊D11—21no—
40C4×C22⋊D11C2211yescharacteristic
41C2×#4318C2211yescharacteristic
42#66969—24no—
43C2×D88C2211yescharacteristic
44C2×#4314C2211yescharacteristic
45C2×C8×D11C2211yescharacteristic
46#66948C2211yescharacteristic
47#66940C2211yescharacteristic
48#66937—21no—
49(C22⋊D11)⋊C4—21no—
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×C22⋊C8C2211yescharacteristic
53#66896C2211yescharacteristic
54#66885C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic
56#66880C2211yescharacteristic
57#66879C2211yescharacteristic
58Dic11⋊C8C2211yescharacteristic
59#66873C2211yescharacteristic
60#66872C2211yescharacteristic
61C2×Q8×C11—21no—
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11C2311yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11D411yescharacteristic
76C22×Dic11—21no—
77#4343—22no—
78#4343—41no—
79#4341—22no—
80#4341—41no—
81#4339—22no—
82#4339—41no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44C2311yescharacteristic
86C2×D44C2311yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11C2311yescharacteristic
90C2×Dic22C2311yescharacteristic
91C11×SD16—22no—
92C11×SD16—41no—
93C2×C8×C11C2311yescharacteristic
94C2×C8×C11C2311yescharacteristic
95C11×C4⋊C4C2311yescharacteristic
96C11×C22⋊C4—21no—
97C22⋊Dic11D411yescharacteristic
98#4326—22no—
99#4326D414yescomplemented
100#4325—22no—
101#4325—22no—
102#4323—22no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4D411yescharacteristic
109C4⋊Dic11—21no—
110C4⋊Dic11C2311yescharacteristic
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4D411yescharacteristic
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11C2311yescharacteristic
117#4318—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120D88—41no—
121#4314—22no—
122C8×D11—22no—
123#3271—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11C2×D411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11C2×D411yescharacteristic
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11—21no—
132Q8×C11—42no—
133Q8×C11C2×D412yes—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—42no—
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2411yescharacteristic
145C22⋊D11—41no—
146C22⋊D11—42no—
147C22⋊D11—42no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C22⋊D11—81no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—42no—
154C2×Dic11C2×D411yescharacteristic
155C2×Dic11C2×D411yescharacteristic
156C2×Dic11C2×D411yescharacteristic
157D44—21no—
158D44—21no—
159D44—21no—
160D44—21no—
161D44—42no—
162D44—81no—
163C4×D11—21no—
164C4×D11—21no—
165C4×D11—42no—
166C4×D11—42no—
167Dic22—21no—
168Dic22C2×D412yes—
169C8×C11—21no—
170C8×C11—21no—
171C11⋊C8—21no—
172C11⋊C8C2×D412yes—
173C2×#137—111no—
174C2×#135—111no—
175#550—111no—
176#548—111no—
177#496—111no—
178#469—111no—
179#465—111no—
180#464—111no—
181#460—111no—
182#452—111no—
183#449—111no—
184#449—111no—
185#448D1111yescharacteristic, complemented
186#441—111no—
187#435—111no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C22×D411yescharacteristic
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C4×C11—21no—
205C4×C11—22no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11C22×D411yescharacteristic
209C4×C11H(5,𝔽2)11yescharacteristic
210Dic11—22no—
211Dic11—21no—
212Dic11—21no—
213Dic11—21no—
214Dic11—41no—
215C2×#41—111no—
216C2×#41—111no—
217C2×#41—111no—
218C22×Q8C2×D1111yescharacteristic
219#137—224no—
220#135—224no—
221C2×Q16—111no—
222C2×Q16—111no—
223C2×SD16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16C2×D1111yescharacteristic
227C2×SD16C2×D1111yescharacteristic
228C2×D8—111no—
229C2×D8—111no—
230C2×M16—111no—
231C22×C8—111no—
232#127—111no—
233#127—221no—
234#124—111no—
235#124—221no—
236C22⋊Q8—111no—
237C22⋊Q8—221no—
238#121—111no—
239#121—111no—
240#121—221no—
241#121—221no—
242#121—221no—
243#121C2×D1111yescharacteristic
244C4×Q8—111no—
245C4×Q8—111no—
246C4×D4—111no—
247C4×D4—221no—
248C4×D4—221no—
249#106—111no—
250C4⋊C8—111no—
251#103—111no—
252#103C2×D1111yescharacteristic
253#103C2×D1111yescharacteristic
254#102—111no—
255#102—111no—
256#102—111no—
257C22⋊C8—111no—
258C22⋊C8C2×D1111yescharacteristic
259#97—111no—
260C2×C11—41no—
261C2×C11—81no—
262C2×C11D4211yescharacteristic
263C2×C11#57511yescharacteristic
264C2×C11#57711yescharacteristic
265D11—41no—
266D11—81no—
267D11—81no—
268#41—222no—
269#41—222no—
270#41—222no—
271#41—441no—
272#41—441no—
273#41—441no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—111no—
278C2×Q8C22×D1111yescharacteristic
279C2×Q8C22×D1111yescharacteristic
280C2×D4—21no—
281C2×D4—111no—
282C2×D4—111no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4C22×D1111yescharacteristic
292C22×C4—21no—
293C22×C4—111no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4C22×D1111yescharacteristic
298Q16—114no—
299Q16—222no—
300SD16—22no—
301SD16—41no—
302SD16—222no—
303SD16—222no—
304SD16—222no—
305D8—222no—
306D8—441no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8—222no—
311C2×C8C22×D1111yescharacteristic
312C2×C8C22×D1111yescharacteristic
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4C22×D1111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—111no—
321C22⋊C4—111no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C42—111no—
328C42—221no—
329C42—221no—
330C11#327111yescharacteristic, complemented, Sylow
331C23—21no—
332C23—111no—
333C23—221no—
334C23—221no—
335C23D4×D1111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—42no—
340Q8—112no—
341Q8—221no—
342Q8D4×D1112yes—
343D4—21no—
344D4—21no—
345D4—81no—
346D4—221no—
347D4—221no—
348D4—221no—
349D4—221no—
350D4—442no—
351D4—441no—
352D4—442no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—881no—
357D4—881no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4D4×D1111yescharacteristic
375C2×C4C23×D1111yescharacteristic
376C8—21no—
377C8—21no—
378C8—112no—
379C8—221no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—221no—
387C22—221no—
388C22—221no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22C2×D4×D1111yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—41no—
400C4—221no—
401C4—221no—
402C4—221no—
403C4—222no—
404C4—441no—
405C4C2×D4×D1111yescharacteristic
406C4#6703711yescharacteristic
407C2—41no—
408C2—81no—
409C2—441no—
410C2—881no—
411C2—881no—
412C2#1062312111yescharacteristic
413C2#1062329311yescharacteristic
414C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#448C2
socleC22×C11C22×D4
hypercenter#448D11
hypocenterC11#3271
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #10623348C2semidirect
2. C2×#66995C2semidirect
3. C2×#66969C2semidirect
4. #10623130C2semidirect
5. C11×#448C2semidirect
6. #10622789C2semidirect
7. #10622786C2semidirect
8. #10622776C2semidirect
9. #10622652C2semidirect
10. #10622424C2semidirect
11. #10622420C2semidirect
12. #10622411C2semidirect
13. #10622402C2semidirect
14. #10622347C2semidirect
15. #10622341C2semidirect
99. #4326D4semidirect
185. #448D11semidirect
330. C11#3271semidirect

Maximal subgroups

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

subgroupindex
#106233482
C2×#669952
C2×#669692
#106231302
C11×#4482
#106227892
#106227862
#106227762
#106226522
#106224242
#106224202
#106224112
#106224022
#106223472
#106223412
#327111