Finite Group Databasebeta

← #14908870

Subgroups — #14908870

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic
2C2×C4×Dic44C211yesmaximal, characteristic, complemented
3#13070819C211yesmaximal, characteristic, complemented
4#13070802C211yesmaximal, characteristic
5#13070781C212yesmaximal, complemented
6#13070679C212yesmaximal, complemented
7#13070552C211yesmaximal, characteristic, complemented
8#13070535C211yesmaximal, characteristic
9#13070488C212yesmaximal, complemented
10#13070482C212yesmaximal, complemented
11C11×#2163C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13#10623010—21no—
14C2×C4×Dic22—21no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622729C2211yescharacteristic
17#10622728C2211yescharacteristic
18#10622727—21no—
19C2×#66882C2211yescharacteristic
20C2×#66880—21no—
21C2×Dic88C2212yes—
22C2×#66864C2212yes—
23C4×Dic44—21no—
24C4×Dic44—21no—
25C4×Dic44C2212yes—
26C4×Dic44C2212yes—
27C4×Dic44C2211yescharacteristic
28#10622310—21no—
29#10622309C2211yescharacteristic
30C4×D88C2211yescharacteristic
31C4×#4314—21no—
32#10622296C2211yescharacteristic
33C11×C4⋊C16C2212yes—
34C11×C22⋊C16C2211yescharacteristic
35C11×C22⋊C16C2211yescharacteristic
36C11×#346C2212yes—
37#10622147C2212yes—
38#10622143C2212yes—
39#10622142C2212yes—
40#10622141C2212yes—
41#10622141C2212yes—
42#10622141C2212yes—
43C22×Dic22—21no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C42×C11D411yescharacteristic
47#66983—21no—
48#66982—41no—
49C4×C22⋊D11—41no—
50C2×C4⋊Dic11—21no—
51#66977—21no—
52C2×Dic11⋊C4—41no—
53C2×C4×Dic11—41no—
54C2×Dic44—21no—
55C2×Dic44—24no—
56C2×Dic44C2311yescharacteristic
57C2×Dic44C2312yes—
58C2×D88C2311yescharacteristic
59C2×#4314—21no—
60#66929—41no—
61#66928—21no—
62C4×D44—21no—
63#66925—41no—
64#66923—21no—
65C4×Dic22—22no—
66C4×Dic22—22no—
67C4×Dic22—21no—
68C4×Dic22—41no—
69C4×Dic22—41no—
70C2×C11×C16C2312yes—
71C2×C11×C16C2312yes—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66885—21no—
77#66885—21no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2311yescharacteristic
81#66882C2312yes—
82#66881—21no—
83#66880—21no—
84#66880—21no—
85#66880—22no—
86#66880—22no—
87Dic88—24no—
88#66864—24no—
89#33677—111nomaximal, Sylow
90C22×C4×C11D811yescharacteristic
91C22×C4×C11D811yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—24no—
99C2×Dic22—22no—
100C2×Dic22—21no—
101C2×Dic22—42no—
102C2×Dic22—41no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C42×C11D811yescharacteristic
110C42×C11D811yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C22⋊Dic11—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—42no—
129C4×Dic11—42no—
130C4×Dic11—41no—
131Dic44—24no—
132Dic44—22no—
133Dic44—22no—
134Dic44#4114yes—
135D88—22no—
136#4314—42no—
137C11×C16—22no—
138C11×C16—22no—
139#3168—111no—
140C2×C4×Q16—111no—
141#2236—111no—
142#2233—111no—
143#2229—112no—
144#2211—112no—
145#2188—111no—
146#2185—111no—
147#2176—112no—
148#2175—112no—
149#2163D1111yescharacteristic, complemented
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152C2×C4×C11—22no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C22⋊D11—82no—
163C2×Dic11—44no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—82no—
170D44—41no—
171D44—41no—
172C4×D11—82no—
173Dic22—24no—
174Dic22—44no—
175Dic22—42no—
176Dic22—41no—
177Dic22—41no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11C2×#4112yes—
182C22×Q16—111no—
183#529—221no—
184C2×C4×Q8—221no—
185C2×Q32—112no—
186C2×SD32—112no—
187#499—111no—
188#495—111no—
189#488—221no—
190#467—111no—
191#466—111no—
192#465—221no—
193C4×Q16—111no—
194C4×Q16—112no—
195C4×Q16—112no—
196C4×Q16—221no—
197C4×Q16—221no—
198C4×SD16—221no—
199C4×D8—111no—
200C2×#107—111no—
201C2×#103—221no—
202C2×C4×C8C2×D1111yescharacteristic
203#367—112no—
204#366—112no—
205C4⋊C16C2×D1112yes—
206#358—112no—
207#358—112no—
208#358—112no—
209#357—112no—
210C22⋊C16C2×D1111yescharacteristic
211C22⋊C16C2×D1111yescharacteristic
212#346C2×D1112yes—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11#51012yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11#52511yescharacteristic
226C4×C11#57511yescharacteristic
227Dic11—44no—
228Dic11—81no—
229Dic11—81no—
230Dic11—81no—
231Dic11—82no—
232C22×Q8—221no—
233C2×Q16—112no—
234C2×Q16—111no—
235C2×Q16—224no—
236C2×Q16—221no—
237C2×SD16—221no—
238C2×D8—111no—
239C22×C8D4411yescharacteristic
240C22×C8C22×D1111yescharacteristic
241#126—441no—
242#125—221no—
243#124—221no—
244#123—441no—
245C22⋊Q8—221no—
246#121—221no—
247C4×Q8—222no—
248C4×Q8—222no—
249C4×Q8—221no—
250C4×Q8—441no—
251C4×Q8—441no—
252C4×D4—221no—
253C4×D4—441no—
254#117—441no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—441no—
257C2×C42—441no—
258C2×C42D4411yescharacteristic
259Q32—224no—
260SD32—224no—
261C2×C16C22×D1112yes—
262C2×C16C22×D1112yes—
263#107—112no—
264#107—111no—
265#107—111no—
266#107—221no—
267#106—221no—
268#103—222no—
269#103—222no—
270#103—221no—
271#103—221no—
272#102—221no—
273#102—221no—
274C4×C8D4411yescharacteristic
275C4×C8D4411yescharacteristic
276C4×C8C22×D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C2×C11—22no—
279C2×C11#310011yescharacteristic
280C2×C11C2×#51011yescharacteristic
281C2×C11#341411yescharacteristic
282D11—161no—
283C2×Q8—224no—
284C2×Q8—222no—
285C2×Q8—221no—
286C2×Q8—442no—
287C2×Q8—441no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4D8811yescharacteristic
294C22×C4D8811yescharacteristic
295C22×C4C2×D4411yescharacteristic
296Q16—114no—
297Q16—224no—
298Q16—222no—
299Q16—222no—
300SD16—442no—
301D8—222no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8C2×D4411yescharacteristic
305C2×C8C2×D4411yescharacteristic
306C2×C8C2×D4411yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—441no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C42—442no—
324C42—442no—
325C42—441no—
326C42D8811yescharacteristic
327C42D8811yescharacteristic
328C42C2×D4411yescharacteristic
329C42C2×D4411yescharacteristic
330C16—22no—
331C16—22no—
332C11#3367711yescharacteristic, complemented, Sylow
333C23—441no—
334C23C2×D8811yescharacteristic
335Q8—224no—
336Q8—444no—
337Q8—442no—
338Q8—441no—
339Q8—441no—
340D4—441no—
341D4—441no—
342D4—882no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—444no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—882no—
354C2×C4—882no—
355C2×C4C2×D8811yescharacteristic
356C2×C4C2×D8811yescharacteristic
357C2×C4C2×D8811yescharacteristic
358C2×C4C2×D8811yescharacteristic
359C2×C4C2×D8811yescharacteristic
360C2×C4C22×D4411yescharacteristic
361C8—21no—
362C8—21no—
363C8—21no—
364C8#41×D1112yes—
365C22—21no—
366C22—21no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22#1062252212yes—
371C22C22×D8811yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—444no—
378C4—881no—
379C4—881no—
380C4—882no—
381C4—881no—
382C4#1062305511yescharacteristic
383C4#1062327911yescharacteristic
384C2—22no—
385C2—1761no—
386C2#1307861711yescharacteristic
387C2C2×#1062252211yescharacteristic
388C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#2163D11
hypocenterC11#33677
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic44C2semidirect
3. #13070819C2semidirect
5. #13070781C2semidirect
6. #13070679C2semidirect
7. #13070552C2semidirect
9. #13070488C2semidirect
10. #13070482C2semidirect
11. C11×#2163C2semidirect
149. #2163D11semidirect
332. C11#33677semidirect

Maximal subgroups

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

subgroupindex
#130791862
C2×C4×Dic442
#130708192
#130708022
#130707812
#130706792
#130705522
#130705352
#130704882
#130704822
C11×#21632
#3367711