Finite Group Databasebeta

← #14909718

Subgroups — #14909718

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2C2×#10622309C211yesmaximal, characteristic, complemented
3#13070877C212yesmaximal, complemented
4#13070848C212yesmaximal, complemented
5#13070679C212yesmaximal, complemented
6#13070672C212yesmaximal, complemented
7#13070552C211yesmaximal, characteristic, complemented
8#13070547C211yesmaximal, characteristic, complemented
9#13070535C211yesmaximal, characteristic, complemented
10#13070530C211yesmaximal, characteristic
11C11×#2162C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C22×D88C2211yescharacteristic
14C22×#4314—21no—
15#10623010—21no—
16C2×#66928—21no—
17C2×C4×C8×C11C2211yescharacteristic
18#10622729C2211yescharacteristic
19#10622728C2211yescharacteristic
20#10622727—21no—
21C2×Dic88C2212yescomplemented
22C2×#66864C2212yes—
23C2×#66864C2212yescomplemented
24C2×D176C2212yes—
25C4×Dic44C2211yescharacteristic, complemented
26#10622310—21no—
27#10622309—21no—
28#10622309—21no—
29#10622309C2212yes—
30#10622309C2212yes—
31#10622309C2211yescharacteristic, complemented
32C4×D88C2211yescharacteristic, complemented
33C4×#4314—21no—
34#10622296C2211yescharacteristic, complemented
35C11×C4⋊C16C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37C11×C22⋊C16C2211yescharacteristic
38C4×C11×C16C2212yescomplemented
39#10622147C2212yes—
40#10622147C2212yes—
41#10622141C2212yescomplemented
42#10622141C2212yescomplemented
43C22×D44—21no—
44C22×Dic22—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C2×C42×C11D411yescharacteristic
48#66983—21no—
49#66982—41no—
50C4×C22⋊D11—41no—
51C2×(C2×D11)⋊C4—41no—
52C2×(C2×D11)⋊C4—41no—
53#66977—21no—
54C2×Dic44—21no—
55C2×Dic44—42no—
56C2×Dic44C2311yescharacteristic
57C2×Dic44C2312yes—
58C2×D88—21no—
59C2×D88—42no—
60C2×D88C2311yescharacteristic
61C2×D88C2312yes—
62C2×#4314—21no—
63C2×#4314—22no—
64C2×#4314—22no—
65C2×#4314—44no—
66#66929—41no—
67#66928—22no—
68#66928—22no—
69#66928—21no—
70#66928—41no—
71#66928—41no—
72C4×D44—21no—
73#66925—41no—
74#66923—21no—
75C4×Dic22—21no—
76C2×C11×C16C2312yes—
77C2×C11×C16C2312yes—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66885—21no—
83#66885—21no—
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66881—21no—
87#66880—21no—
88#66880—21no—
89Dic88—42no—
90#66864—42no—
91#66864—42no—
92D176—42no—
93#33777—111nomaximal, Sylow
94C23×D11—41no—
95C22×C4×C11D811yescharacteristic
96C22×C4×C11D811yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100C2×D44—21no—
101C2×D44—22no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—41no—
105C2×C4×D11—41no—
106C2×Dic22—21no—
107C2×Dic22—22no—
108C2×Dic22—42no—
109C2×Dic22—42no—
110C2×Dic22—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2411yescharacteristic
117C42×C11D811yescharacteristic
118C42×C11D811yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C22⋊Dic11—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136C4×Dic11—41no—
137Dic44—22no—
138Dic44—22no—
139Dic44—22no—
140Dic44—42no—
141D88—22no—
142D88—22no—
143D88—22no—
144D88—42no—
145#4314—44no—
146#4314—42no—
147#4314—44no—
148C11×C16—22no—
149C11×C16—22no—
150#3168—111no—
151C2×#495—111no—
152#2249—112no—
153#2242—112no—
154#2211—112no—
155#2210—112no—
156#2188—111no—
157#2187—111no—
158#2185—111no—
159#2184—111no—
160#2162D1111yescharacteristic, complemented
161C23×C11C2×D811yescharacteristic
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11—82no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—41no—
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—82no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—82no—
183D44—42no—
184D44—41no—
185D44—42no—
186D44—41no—
187D44—82no—
188C4×D11—82no—
189Dic22—42no—
190Dic22—41no—
191Dic22—42no—
192Dic22—41no—
193Dic22—82no—
194C8×C11—21no—
195C8×C11—21no—
196C8×C11AGL(1,ℤ/8)12yes—
197C8×C11H(5,𝔽2)12yes—
198C22×Q16—111no—
199C22×SD16—221no—
200C22×D8—111no—
201#529—221no—
202C2×#124—221no—
203C2×Q32—112no—
204C2×SD32—112no—
205C2×SD32—112no—
206C2×D16—112no—
207#499—111no—
208#495—112no—
209#495—112no—
210#495—111no—
211#495—221no—
212#495—221no—
213#488—221no—
214#467—111no—
215#466—111no—
216#465—221no—
217C4×Q16—111no—
218C4×SD16—221no—
219C4×D8—111no—
220C2×C4×C8C2×D1111yescharacteristic
221C4⋊C16C2×D1112yescomplemented
222#358—112no—
223#358—112no—
224#357—112no—
225#357—112no—
226C22⋊C16C2×D1111yescharacteristic
227C22⋊C16C2×D1111yescharacteristic
228C4×C16C2×D1112yescomplemented
229C22×C11—21no—
230C22×C11—21no—
231C22×C11#50812yes—
232C22×C11C22×D811yescharacteristic
233C2×D11—82no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—82no—
238C2×D11—81no—
239C2×D11—164no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11#53511yescharacteristic
246C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
247Dic11—81no—
248Dic11—81no—
249Dic11—82no—
250Dic11—81no—
251C22×Q8—221no—
252C22×D4—221no—
253C2×Q16—112no—
254C2×Q16—111no—
255C2×Q16—221no—
256C2×Q16—442no—
257C2×SD16—222no—
258C2×SD16—222no—
259C2×SD16—221no—
260C2×SD16—444no—
261C2×D8—112no—
262C2×D8—111no—
263C2×D8—221no—
264C2×D8—442no—
265C22×C8D4411yescharacteristic
266C22×C8C22×D1111yescharacteristic
267#126—441no—
268#125—221no—
269#124—222no—
270#124—222no—
271#124—221no—
272#124—441no—
273#124—441no—
274#123—441no—
275C22⋊Q8—221no—
276#121—221no—
277C4×Q8—221no—
278C4×D4—221no—
279C4×D4—441no—
280#117—441no—
281C2×C22⋊C4—441no—
282C2×C22⋊C4—441no—
283C2×C42D4411yescharacteristic
284Q32—442no—
285SD32—442no—
286SD32—442no—
287D16—442no—
288C2×C16C22×D1112yes—
289C2×C16C22×D1112yes—
290#107—111no—
291#107—111no—
292#106—221no—
293#103—221no—
294#103—221no—
295#102—221no—
296#102—221no—
297C4×C8D4411yescharacteristic
298C4×C8D4411yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C4×C8C22×D1111yescharacteristic
301C2×C11—22no—
302C2×C11#320511yescharacteristic
303C2×C11C2×#50811yescharacteristic
304C2×C11#341411yescharacteristic
305D11—161no—
306D11—162no—
307C24—441no—
308C2×Q8—221no—
309C2×Q8—222no—
310C2×Q8—442no—
311C2×Q8—442no—
312C2×Q8—441no—
313C2×D4—221no—
314C2×D4—222no—
315C2×D4—442no—
316C2×D4—442no—
317C2×D4—441no—
318C2×D4—441no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4D8811yescharacteristic
322C22×C4D8811yescharacteristic
323C22×C4C2×D4411yescharacteristic
324Q16—222no—
325Q16—222no—
326Q16—222no—
327Q16—442no—
328SD16—444no—
329SD16—444no—
330SD16—442no—
331D8—222no—
332D8—222no—
333D8—222no—
334D8—442no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8C2×D4411yescharacteristic
338C2×C8C2×D4411yescharacteristic
339C2×C8C2×D4411yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C22⋊C4—442no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C42—441no—
357C42D8811yescharacteristic
358C42D8811yescharacteristic
359C42C2×D4411yescharacteristic
360C42C2×D4411yescharacteristic
361C16—22no—
362C16—22no—
363C11#3377711yescharacteristic, complemented, Sylow
364C23—441no—
365C23—442no—
366C23—882no—
367C23—882no—
368C23—882no—
369C23C2×D8811yescharacteristic
370Q8—442no—
371Q8—441no—
372Q8—442no—
373Q8—441no—
374Q8—882no—
375D4—442no—
376D4—441no—
377D4—442no—
378D4—441no—
379D4—882no—
380D4—882no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—882no—
390C2×C4—882no—
391C2×C4C2×D8811yescharacteristic
392C2×C4C2×D8811yescharacteristic
393C2×C4C2×D8811yescharacteristic
394C2×C4C2×D8811yescharacteristic
395C2×C4C2×D8811yescharacteristic
396C2×C4C22×D4411yescharacteristic
397C8—21no—
398C8—21no—
399C8#6696112yes—
400C8#6704212yes—
401C22—21no—
402C22—21no—
403C22—881no—
404C22—882no—
405C22—881no—
406C22—882no—
407C22—882no—
408C22—881no—
409C22—1764no—
410C22#1062251712yes—
411C22C22×D8811yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—881no—
418C4—881no—
419C4—882no—
420C4—881no—
421C4#1062305611yescharacteristic
422C4C2×#6696111yescharacteristic
423C2—22no—
424C2—1762no—
425C2—1761no—
426C2#1307953611yescharacteristic
427C2C2×#1062251711yescharacteristic
428C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2162C2
socleC22×C11C22×D8
prime radical#13070530C2
hypercenter#2162D11
hypocenterC11#33777
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. C2×#10622309C2semidirect
3. #13070877C2semidirect
4. #13070848C2semidirect
5. #13070679C2semidirect
6. #13070672C2semidirect
7. #13070552C2semidirect
8. #13070547C2semidirect
9. #13070535C2semidirect
11. C11×#2162C2semidirect
21. C2×Dic88C22semidirect
23. C2×#66864C22semidirect
25. C4×Dic44C22semidirect
31. #10622309C22semidirect
32. C4×D88C22semidirect
34. #10622296C22semidirect
35. C11×C4⋊C16C22semidirect
38. C4×C11×C16C22semidirect
41. #10622141C22semidirect
42. #10622141C22semidirect
160. #2162D11semidirect
221. C4⋊C16C2×D11semidirect
228. C4×C16C2×D11semidirect
363. C11#33777semidirect

Maximal subgroups

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

subgroupindex
#130791862
C2×#106223092
#130708772
#130708482
#130706792
#130706722
#130705522
#130705472
#130705352
#130705302
C11×#21622
#3377711