Finite Group Databasebeta

← #13080171

Subgroups — #13080171

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×C11×#135C211yesmaximal, characteristic, complemented
2#10623362C211yesmaximal, characteristic, complemented
3#10623355C211yesmaximal, characteristic, complemented
4C2×#66968C211yesmaximal, characteristic, complemented
5#10622852C211yesmaximal, characteristic, complemented
6#10622852C211yesmaximal, characteristic, complemented
7#10622799C211yesmaximal, characteristic, complemented
8#10622795C211yesmaximal, characteristic, complemented
9#10622787C211yesmaximal, characteristic, complemented
10#10622780C211yesmaximal, characteristic, complemented
11#10622777C211yesmaximal, characteristic, complemented
12#10622771C211yesmaximal, characteristic, complemented
13#10622766C211yesmaximal, characteristic, complemented
14#10622729C211yesmaximal, characteristic, complemented
15#10622724C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C2×#4341C2211yescharacteristic
20C11×#135—24no—
21C2×C11×Q16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic
23C2×C11×SD16C2211yescharacteristic
24C2×C11×D8C2211yescharacteristic
25C22×C8×C11C2211yescharacteristic
26#66999C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28#66997C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30C2×#4326C2211yescharacteristic
31#66992—21no—
32#66991—21no—
33#66991C2211yescharacteristic
34#66989—21no—
35#66989C2211yescharacteristic
36#66988—21no—
37D4×Dic11C2211yescharacteristic
38C2×#4324C2211yescharacteristic
39C2×#4324C2211yescharacteristic
40#66982—21no—
41C4×C22⋊D11—21no—
42C4×C22⋊D11C2211yescharacteristic
43#66977—21no—
44#66977C2211yescharacteristic
45#66977C2211yescharacteristic
46C2×Dic11⋊C4—21no—
47#66968—24no—
48C2×Dic44C2211yescharacteristic
49C2×#4313C2211yescharacteristic
50#66899C2211yescharacteristic
51#66899C2211yescharacteristic
52#66896C2211yescharacteristic
53#66896C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic
56#66882C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59#66879C2211yescharacteristic
60Dic11⋊C8C2211yescharacteristic
61C11×#41—22no—
62C11×#41—22no—
63C11×#41—41no—
64C11×#41—41no—
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11C2311yescharacteristic
70C2×D4×C11C2311yescharacteristic
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79Q8×D11—22no—
80Q8×D11—41no—
81#4341—22no—
82#4341—41no—
83C2×C4×D11—21no—
84C2×C4×D11C2311yescharacteristic
85C2×Dic22—21no—
86C2×Dic22C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C11×Q16—22no—
89C11×SD16—22no—
90C11×SD16D414yescomplemented
91C11×D8—22no—
92C2×C8×C11—22no—
93C2×C8×C11C2311yescharacteristic
94C2×C8×C11C2311yescharacteristic
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11D411yescharacteristic
102#4326—22no—
103#4326—41no—
104#4324—22no—
105#4324—41no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4D411yescharacteristic
108C4⋊Dic11—21no—
109C4⋊Dic11C2311yescharacteristic
110C4⋊Dic11C2311yescharacteristic
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4D411yescharacteristic
117C4×Dic11—21no—
118C4×Dic11C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121Dic44—22no—
122#4313—22no—
123#3269—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×D411yescharacteristic
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11C2×D412yes—
132D4×C11—21no—
133D4×C11—21no—
134D4×C11—21no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11C2×D412yes—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C2×D411yescharacteristic
145C2×C4×C11C2411yescharacteristic
146C22⋊D11—41no—
147C22⋊D11—42no—
148C22⋊D11—42no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11C2×D411yescharacteristic
156C2×Dic11C2×D411yescharacteristic
157C2×Dic11C2×D411yescharacteristic
158C4×D11—21no—
159C4×D11—21no—
160C4×D11—42no—
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×#135D1111yescharacteristic, complemented
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#440—111no—
184#435—111no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C22×D411yescharacteristic
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C4×C11—21no—
199C4×C11—22no—
200C4×C11—41no—
201C4×C11C22×D411yescharacteristic
202C4×C11H(5,𝔽2)11yescharacteristic
203Dic11—21no—
204Dic11—21no—
205Dic11—21no—
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41C2×D1111yescharacteristic
212C2×#41C2×D1111yescharacteristic
213C22×Q8—111no—
214#137—224no—
215#135—24no—
216C2×Q16—111no—
217C2×Q16—111no—
218C2×Q16—111no—
219C2×Q16C2×D1111yescharacteristic
220C2×SD16—111no—
221C2×SD16—111no—
222C2×SD16C2×D1111yescharacteristic
223C2×SD16C2×D1111yescharacteristic
224C2×D8C2×D1111yescharacteristic
225C2×M16—111no—
226C22×C8C2×D1111yescharacteristic
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×Q8—111no—
240C4×D4—111no—
241C4×D4—111no—
242C4×D4—221no—
243C2×C4⋊C4—221no—
244#107—111no—
245C4⋊C8—111no—
246#103—111no—
247#103—111no—
248#103—111no—
249#103—111no—
250#102—111no—
251#102—111no—
252C22⋊C8—111no—
253C22⋊C8—111no—
254#97—111no—
255C2×C11—41no—
256C2×C11—42no—
257C2×C11—81no—
258C2×C11D4211yescharacteristic
259C2×C11#57511yescharacteristic
260C2×C11#57811yescharacteristic
261D11—41no—
262#41—22no—
263#41—22no—
264#41—41no—
265#41—41no—
266#41—222no—
267#41—441no—
268C2×Q8—111no—
269C2×Q8—111no—
270C2×Q8—221no—
271C2×Q8—222no—
272C2×Q8—441no—
273C2×Q8C22×D1111yescharacteristic
274C2×Q8C22×D1111yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—111no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4C22×D1111yescharacteristic
281C2×D4C22×D1111yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—111no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4C22×D1111yescharacteristic
289Q16—22no—
290Q16—222no—
291Q16—222no—
292Q16—441no—
293SD16—22no—
294SD16—222no—
295SD16—441no—
296SD16C22⋊D1114yescomplemented
297D8—22no—
298M16—222no—
299C2×C8—22no—
300C2×C8—111no—
301C2×C8—111no—
302C2×C8C22×D1111yescharacteristic
303C2×C8C22×D1111yescharacteristic
304C4⋊C4—111no—
305C4⋊C4—111no—
306C4⋊C4—111no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C22⋊C4—111no—
314C22⋊C4—111no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C22⋊C4—221no—
322C42—111no—
323C42—221no—
324C11#326911yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—111no—
328C23D4×D1111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—221no—
333Q8—221no—
334Q8—221no—
335Q8—221no—
336Q8—442no—
337Q8C2×C22⋊D1112yes—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—441no—
344D4—442no—
345D4—442no—
346D4C2×C22⋊D1112yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—111no—
354C2×C4—111no—
355C2×C4—111no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4D4×D1111yescharacteristic
366C2×C4C23×D1111yescharacteristic
367C8—21no—
368C8—221no—
369C8—221no—
370C8C2×C22⋊D1112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—221no—
381C22—221no—
382C22—221no—
383C22C2×D4×D1111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—221no—
388C4—221no—
389C4—221no—
390C4—441no—
391C4—441no—
392C4—441no—
393C4—441no—
394C4#6703711yescharacteristic
395C4C22×C22⋊D1111yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—441no—
400C2#1062329911yescharacteristic
401C2#1062330211yescharacteristic
402C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#135C2
socleC22×C11C22×D4
hypercenterC2×#135D11
hypocenterC11#3269
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C11×#135C2semidirect
2. #10623362C2semidirect
3. #10623355C2semidirect
4. C2×#66968C2semidirect
5. #10622852C2semidirect
6. #10622852C2semidirect
7. #10622799C2semidirect
8. #10622795C2semidirect
9. #10622787C2semidirect
10. #10622780C2semidirect
11. #10622777C2semidirect
12. #10622771C2semidirect
13. #10622766C2semidirect
14. #10622729C2semidirect
15. #10622724C2semidirect
90. C11×SD16D4semidirect
171. C2×#135D11semidirect
296. SD16C22⋊D11semidirect
324. C11#3269semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1352
#106233622
#106233552
C2×#669682
#106228522
#106227992
#106227952
#106227872
#106227802
#106227772
#106227712
#106227662
#106227292
#106227242
#326911