Finite Group Databasebeta

← #13080173

Subgroups — #13080173

Order 1408.

478 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×#66969C211yesmaximal, characteristic, complemented
2C2×#66968C211yesmaximal, characteristic, complemented
3#10623107C211yesmaximal, characteristic, complemented
4#10623086C211yesmaximal, characteristic, complemented
5C11×#440C211yesmaximal, characteristic, complemented
6#10622644C211yesmaximal, characteristic, complemented
7#10622629C211yesmaximal, characteristic, complemented
8#10622500C211yesmaximal, characteristic, complemented
9#10622499C211yesmaximal, characteristic, complemented
10#10622423C211yesmaximal, characteristic, complemented
11#10622421C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic, complemented
13#10622394C211yesmaximal, characteristic, complemented
14#10622328C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×#4341C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22C4×D4×C11C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27#66983—21no—
28C2×C4⋊Dic11—21no—
29#66969—24no—
30#66968—24no—
31C2×Dic44C2211yescharacteristic
32C2×Dic44C2211yescharacteristic
33C2×#4314C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36C2×C8×D11C2211yescharacteristic
37#66950—21no—
38#66950C2211yescharacteristic
39#66950C2211yescharacteristic
40#66950C2211yescharacteristic
41#66948—21no—
42#66948C2211yescharacteristic
43#66939—21no—
44#66939—21no—
45#66928—21no—
46#66928C2211yescharacteristic
47C4×D44—21no—
48C4×D44C2211yescharacteristic
49#66922C2211yescharacteristic
50C11×#107C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C11×#97C2211yescharacteristic
54(C2×D11)⋊C8C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic
56#66874C2211yescharacteristic
57#66874C2211yescharacteristic
58#66874C2211yescharacteristic
59#66873C2211yescharacteristic
60C4⋊(C11⋊C8)C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68#4343—22no—
69#4343—41no—
70Q8×D11—22no—
71Q8×D11—41no—
72#4341—22no—
73#4341—22no—
74#4341—41no—
75#4341—41no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44D411yescharacteristic
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11C2311yescharacteristic
83C2×C4×D11C2311yescharacteristic
84C2×Dic22—21no—
85C2×Dic22C2311yescharacteristic
86C2×Dic22C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C11×SD16D414yescomplemented
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C11×C4⋊C4—21no—
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C42×C11—21no—
96C42×C11C2311yescharacteristic
97#4326—22no—
98#4326—22no—
99#4324—22no—
100#4323—22no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4D411yescharacteristic
108(C2×D11)⋊C4D411yescharacteristic
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11D411yescharacteristic
115C2×C11⋊C8C2311yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117Dic44—22no—
118Dic44—41no—
119#4314—22no—
120#4314—41no—
121#4313—22no—
122C8×D11—22no—
123#3269—111nomaximal, Sylow
124C23×C11—21no—
125C22×D11—21no—
126C22×D11C2×D411yescharacteristic
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11C2×D412yes—
130D4×C11—21no—
131D4×C11C2×D412yes—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2411yescharacteristic
139C22⋊D11—42no—
140C22⋊D11—42no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148D44—21no—
149D44—21no—
150D44—41no—
151D44—42no—
152D44—42no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—42no—
158C4×D11—42no—
159Dic22—21no—
160Dic22—21no—
161Dic22—21no—
162Dic22—21no—
163Dic22—21no—
164Dic22—21no—
165Dic22—42no—
166C8×C11—21no—
167C8×C11C2×D412yes—
168C11⋊C8—21no—
169C11⋊C8—21no—
170C2×#137—111no—
171C2×#135—111no—
172#548—111no—
173#547—111no—
174#497—111no—
175#468—111no—
176#467—111no—
177#463—111no—
178#462—111no—
179#452—111no—
180#452—111no—
181#451—111no—
182#449—111no—
183#440D1111yescharacteristic, complemented
184#435—111no—
185C22×C11—22no—
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—21no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C4×C11—22no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11C22×D411yescharacteristic
204C4×C11H(5,𝔽2)11yescharacteristic
205Dic11—21no—
206Dic11—21no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41—111no—
212C2×#41—111no—
213C22×Q8—111no—
214#137—224no—
215#135—224no—
216C2×Q16—111no—
217C2×Q16—111no—
218C2×Q16—111no—
219C2×Q16—111no—
220C2×SD16—111no—
221C2×SD16—111no—
222C2×SD16—111no—
223C2×SD16C2×D1111yescharacteristic
224C2×D8—111no—
225C2×M16—111no—
226C22×C8—111no—
227C4⋊Q8—111no—
228#124—111no—
229#124—221no—
230#123—221no—
231#123—221no—
232C22⋊Q8—111no—
233C22⋊Q8—111no—
234C22⋊Q8—111no—
235C22⋊Q8—221no—
236#121—111no—
237#121—221no—
238#121—221no—
239C4×Q8C2×D1111yescharacteristic
240C4×D4—111no—
241C4×D4—221no—
242C4×D4C2×D1111yescharacteristic
243C2×C4⋊C4—221no—
244#107C2×D1111yescharacteristic
245C4⋊C8—111no—
246#103—111no—
247#103—111no—
248#103—111no—
249#103C2×D1111yescharacteristic
250#102—111no—
251#102C2×D1111yescharacteristic
252C22⋊C8—111no—
253C22⋊C8—111no—
254#97C2×D1111yescharacteristic
255C2×C11—42no—
256C2×C11D4211yescharacteristic
257C2×C11#57511yescharacteristic
258C2×C11#57811yescharacteristic
259D11—41no—
260D11—41no—
261D11—81no—
262#41—222no—
263#41—222no—
264#41—222no—
265#41—441no—
266#41—441no—
267#41—441no—
268C2×Q8—111no—
269C2×Q8—111no—
270C2×Q8—111no—
271C2×Q8—221no—
272C2×Q8—222no—
273C2×Q8—441no—
274C2×Q8C22×D1111yescharacteristic
275C2×D4—111no—
276C2×D4—111no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4C22×D1111yescharacteristic
282C22×C4—21no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289Q16—222no—
290Q16—222no—
291Q16—222no—
292Q16—441no—
293SD16—222no—
294SD16—222no—
295SD16—441no—
296SD16D4414yescomplemented
297D8—222no—
298M16—222no—
299C2×C8—111no—
300C2×C8—111no—
301C2×C8—222no—
302C2×C8C22×D1111yescharacteristic
303C2×C8C22×D1111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—111no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4C22×D1111yescharacteristic
312C4⋊C4C22×D1111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—111no—
315C22⋊C4—111no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C22⋊C4—221no—
322C42—21no—
323C42C22×D1111yescharacteristic
324C11#326911yescharacteristic, complemented, Sylow
325C23—21no—
326C23—111no—
327C23—111no—
328C23—221no—
329Q8—21no—
330Q8—221no—
331Q8—221no—
332Q8—221no—
333Q8—221no—
334Q8—221no—
335Q8—221no—
336Q8—442no—
337Q8C2×D4412yes—
338D4—21no—
339D4—221no—
340D4—221no—
341D4—441no—
342D4—442no—
343D4—442no—
344D4—442no—
345D4—442no—
346D4C2×D4412yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
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—221no—
369C8—221no—
370C8C2×D4412yes—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—221no—
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—441no—
392C4—441no—
393C4—441no—
394C4C22×D4411yescharacteristic
395C4#6704211yescharacteristic
396C2—42no—
397C2—441no—
398C2—441no—
399C2—881no—
400C2D4×D4411yescharacteristic
401C2#1062330411yescharacteristic
402C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3269
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#66969C2semidirect
2. C2×#66968C2semidirect
3. #10623107C2semidirect
4. #10623086C2semidirect
5. C11×#440C2semidirect
6. #10622644C2semidirect
7. #10622629C2semidirect
8. #10622500C2semidirect
9. #10622499C2semidirect
10. #10622423C2semidirect
11. #10622421C2semidirect
12. #10622396C2semidirect
13. #10622394C2semidirect
14. #10622328C2semidirect
15. #10622319C2semidirect
88. C11×SD16D4semidirect
183. #440D11semidirect
296. SD16D44semidirect
324. C11#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#669692
C2×#669682
#106231072
#106230862
C11×#4402
#106226442
#106226292
#106225002
#106224992
#106224232
#106224212
#106223962
#106223942
#106223282
#106223192
#326911