Finite Group Databasebeta

← #14908412

Subgroups — #14908412

Order 2816.

546 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#13079127C211yesmaximal, characteristic, complemented
2C4×#66965C211yesmaximal, characteristic
3#13070779C212yesmaximal, complemented
4#13070771C212yesmaximal, complemented
5#13070769C211yesmaximal, characteristic, complemented
6#13070763C211yesmaximal, characteristic, complemented
7#13070755C211yesmaximal, characteristic, complemented
8#13070397C212yesmaximal, complemented
9D11×C4⋊C16C211yesmaximal, characteristic, complemented
10#13070320C212yesmaximal
11C11×#2224C211yesmaximal, characteristic, complemented
12C2×#66965C2211yescharacteristic
13#10623259—21no—
14C4×#4341—21no—
15C11×#500C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17D8×Dic11C2211yescharacteristic
18#10622692—21no—
19C4×#4324—21no—
20C2×C16×D11C2212yes—
21#10622493—21no—
22#10622493C2211yescharacteristic
23#10622493C2212yes—
24#10622491—21no—
25#10622491C2212yes—
26#10622486C2211yescharacteristic
27#10622385—21no—
28#10622371—21no—
29C4×Dic44C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#366C2212yes—
33C11×C4⋊C16C2211yescharacteristic
34C11×#357C2212yes—
35#10622200C2212yes—
36#10622142C2212yes—
37#10622141C2212yes—
38Dic11⋊C16C2212yes—
39#10622130C2212yes—
40#10622128C2212yes—
41#10622128C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×#4341—21no—
44C2×C11×D8C2311yescharacteristic
45C11×C4⋊Q8—21no—
46C4×D4×C11—21no—
47#66999—41no—
48Q8×Dic11—41no—
49D4×Dic11—21no—
50C2×#4324—21no—
51C4×C22⋊D11—41no—
52C2×C4×Dic11—41no—
53#66965—22no—
54#66965Q814yescomplemented
55C2×Dic44C2311yescharacteristic
56C2×C8×D11D411yescharacteristic
57C2×C8×D11C2311yescharacteristic
58#66950—41no—
59#66945—22no—
60#66945—21no—
61#66943—22no—
62#66940—21no—
63#66940—41no—
64(C22⋊D11)⋊C4—41no—
65#66930—41no—
66C42×D11D411yescharacteristic
67#66922—21no—
68C4×Dic22—21no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#102—21no—
74C4×C8×C11C2311yescharacteristic
75#66896—21no—
76#66882—21no—
77#66882C2312yes—
78#66882C2311yescharacteristic
79#66880—21no—
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83#66874—21no—
84#66872—22no—
85#66872—22no—
86#66872—21no—
87C4×C11⋊C8D411yescharacteristic
88C16×D11—24no—
89#33626—111nomaximal, Sylow
90C2×Q8×C11—41no—
91C2×D4×C11—21no—
92C22×C4×C11—41no—
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96#4341—24no—
97#4341—42no—
98C2×C4×D11D811yescharacteristic
99C2×C4×D11D811yescharacteristic
100C2×C4×D11C2×D411yescharacteristic
101C2×Dic22—21no—
102C2×Dic22—41no—
103C11×D8—21no—
104C11×D8C2×Q812yes—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C22⋊Dic11—41no—
113#4324—24no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—42no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125C4×Dic11—42no—
126C4×Dic11—41no—
127C4×Dic11D811yescharacteristic
128C4×Dic11D811yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C2×C11⋊C8C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132Dic44—21no—
133Dic44C2×Q812yes—
134C8×D11—22no—
135C8×D11C2×Q812yes—
136C8×D11#4112yes—
137C11×C16—22no—
138C11⋊C16—22no—
139#3160—111no—
140C4×#135—111no—
141#2229—112no—
142#2228—112no—
143#2227—111no—
144#2226—111no—
145#2225—111no—
146#2224D1111yescharacteristic, complemented
147#2158—112no—
148C2×C4⋊C16—111no—
149#2138—112no—
150C23×C11—41no—
151C22×D11C2×D811yescharacteristic
152Q8×C11—82no—
153D4×C11—22no—
154D4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—44no—
162C2×Dic11—41no—
163C2×Dic11—44no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—82no—
167C2×Dic11C2×D811yescharacteristic
168C2×Dic11C2×D811yescharacteristic
169C2×Dic11C2×D811yescharacteristic
170C4×D11—22no—
171C4×D11—41no—
172C4×D11C22⋊Q812yes—
173C4×D11#13712yes—
174Dic22—22no—
175Dic22—41no—
176Dic22—82no—
177C8×C11—21no—
178C8×C11C22×Q811yescharacteristic
179C8×C11C2×#4111yescharacteristic
180C11⋊C8—21no—
181C11⋊C8C22⋊Q812yes—
182C2×#135—111no—
183#533—221no—
184C4×#41—221no—
185C22×C16—112no—
186#500—111no—
187#500C2×D1111yescharacteristic
188#499—112no—
189#499—221no—
190#498—221no—
191C4×Q16—111no—
192C4×Q16—111no—
193C4×SD16—221no—
194C4×SD16—221no—
195C4×D8—111no—
196C4×D8C2×D1111yescharacteristic
197#427—112no—
198#427—111no—
199#427—221no—
200#416—221no—
201C2×C4×C8—111no—
202#367—112no—
203#367—112no—
204#366—112no—
205#366C2×D1112yes—
206C4⋊C16—112no—
207C4⋊C16—111no—
208C4⋊C16C2×D1111yescharacteristic
209#358—112no—
210#358—112no—
211#357—112no—
212#357C2×D1112yes—
213C22×C11—42no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11C22×D811yescharacteristic
217C2×D11—21no—
218C2×D11—21no—
219C2×D11#47412yes—
220C4×C11—21no—
221C4×C11—81no—
222C4×C11—82no—
223C4×C11#50812yes—
224C4×C11C2×C22⋊Q811yescharacteristic
225C4×C11C2×#13711yescharacteristic
226Dic11—21no—
227Dic11—21no—
228Dic11—42no—
229Dic11—82no—
230Dic11—81no—
231Dic11#47412yes—
232C2×#41—221no—
233#135—114no—
234#135—222no—
235C2×Q16—111no—
236C2×SD16—221no—
237C2×D8C22×D1111yescharacteristic
238C22×C8—111no—
239C22×C8—111no—
240C4⋊Q8—21no—
241C4⋊Q8—221no—
242#125—222no—
243C22⋊Q8—441no—
244C22⋊Q8—441no—
245C4×Q8—221no—
246C4×Q8—221no—
247C4×Q8—441no—
248C4×Q8—441no—
249C4×D4—21no—
250C4×D4—221no—
251C4×D4—441no—
252C4×D4—441no—
253#117—221no—
254#117—222no—
255#117—441no—
256C2×C42—111no—
257C2×C42—441no—
258C2×C16—112no—
259C2×C16—224no—
260C2×C16C22×D1112yes—
261#107—21no—
262#107—112no—
263#107—111no—
264#107—221no—
265#107C22×D1112yes—
266#107C22×D1111yescharacteristic
267#106—221no—
268#106—222no—
269#106—222no—
270#103—221no—
271#103—221no—
272#102—21no—
273#102—221no—
274C4×C8—111no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8C22×D1111yescharacteristic
278C2×C11—82no—
279C2×C11C2×#47411yescharacteristic
280C2×C11C2×#50811yescharacteristic
281C2×C11#341411yescharacteristic
282D11—22no—
283#41—224no—
284#41—442no—
285C2×Q8—41no—
286C2×Q8—221no—
287C2×Q8—441no—
288C2×D4—21no—
289C2×D4—441no—
290C22×C4—41no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—441no—
295C22×C4—441no—
296Q16—112no—
297Q16—221no—
298SD16—224no—
299D8—21no—
300D8Q8×D1112yes—
301C2×C8—111no—
302C2×C8—112no—
303C2×C8—112no—
304C2×C8—111no—
305C2×C8—222no—
306C2×C8D4×D1111yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—221no—
312C4⋊C4—222no—
313C4⋊C4—441no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—41no—
319C22⋊C4—441no—
320C22⋊C4—442no—
321C22⋊C4—441no—
322C42—111no—
323C42—111no—
324C42—111no—
325C42—441no—
326C42—441no—
327C42—442no—
328C42—441no—
329C42D4×D1111yescharacteristic
330C16—22no—
331C16—222no—
332C11#3362611yescharacteristic, complemented, Sylow
333C23—41no—
334C23—111no—
335Q8—82no—
336Q8—222no—
337Q8—441no—
338Q8—882no—
339D4—22no—
340D4—41no—
341D4—444no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—82no—
345C2×C4—111no—
346C2×C4—112no—
347C2×C4—112no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—222no—
351C2×C4—441no—
352C2×C4—444no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—882no—
357C2×C4D8×D1111yescharacteristic
358C2×C4D8×D1111yescharacteristic
359C2×C4C2×D4×D1111yescharacteristic
360C8—21no—
361C8—112no—
362C8—221no—
363C8C2×Q8×D1111yescharacteristic
364C8#41×D1111yescharacteristic
365C22—42no—
366C22—81no—
367C22—81no—
368C22—112no—
369C22—221no—
370C22—221no—
371C22C2×D8×D1111yescharacteristic
372C4—21no—
373C4—81no—
374C4—82no—
375C4—112no—
376C4—221no—
377C4—221no—
378C4—442no—
379C4—881no—
380C4—882no—
381C4#1062252512yes—
382C4D11×C22⋊Q811yescharacteristic
383C4D11×#13711yescharacteristic
384C2—82no—
385C2—222no—
386C2D11×#47411yescharacteristic
387C2C2×#1062252511yescharacteristic
388C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
prime radicalC2×#66965C22
hypercenter#2224D11
hypocenterC11#33626
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13079127C2semidirect
3. #13070779C2semidirect
4. #13070771C2semidirect
5. #13070769C2semidirect
6. #13070763C2semidirect
7. #13070755C2semidirect
8. #13070397C2semidirect
9. D11×C4⋊C16C2semidirect
11. C11×#2224C2semidirect
54. #66965Q8semidirect
146. #2224D11semidirect
332. C11#33626semidirect

Maximal subgroups

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

subgroupindex
#130791272
C4×#669652
#130707792
#130707712
#130707692
#130707632
#130707552
#130703972
D11×C4⋊C162
#130703202
C11×#22242
#3362611