Finite Group Databasebeta

← #14908452

Subgroups — #14908452

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622491C211yesmaximal, characteristic, complemented
2#13077387C211yesmaximal, characteristic
3#13070783C212yesmaximal, complemented
4#13070779C212yesmaximal, complemented
5#13070776C212yesmaximal, complemented
6#13070772C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070371C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic
10#13070326C211yesmaximal, characteristic
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13#10623053—21no—
14C2×#66943—21no—
15C2×C11×M32C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×#66882C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66872—21no—
23#10622491—21no—
24#10622491—21no—
25#10622491C2212yes—
26#10622491C2212yes—
27#10622486C2211yescharacteristic
28#10622486C2211yescharacteristic
29#10622485C2211yescharacteristic
30#10622485C2211yescharacteristic
31#10622465—21no—
32#10622465—21no—
33C11×#367C2212yes—
34C11×#366C2212yes—
35#10622147C2212yes—
36#10622141C2212yes—
37Dic11⋊C16C2212yes—
38Dic11⋊C16C2212yes—
39#10622130C2212yes—
40#10622129C2212yes—
41#10622128C2212yes—
42#10622127C2212yes—
43C2×#4339—21no—
44C22×C8×C11C2311yescharacteristic
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—41no—
49C2×Dic11⋊C4—41no—
50C2×C4×Dic11D411yescharacteristic
51C22×C11⋊C8D411yescharacteristic
52C2×Dic44C2311yescharacteristic
53#66957—22no—
54#66957Q814yes—
55C2×D88C2311yescharacteristic
56C2×#4314—21no—
57#66946—21no—
58#66946—21no—
59#66943—22no—
60#66943—22no—
61#66943—41no—
62#66943—41no—
63#66940—21no—
64#66940—21no—
65(C22⋊D11)⋊C4—41no—
66(C22⋊D11)⋊C4—41no—
67#66925—41no—
68C42×D11—41no—
69C11×M32—22no—
70C2×C11×C16C2312yes—
71C11×#107—21no—
72C11×#107C2311yescharacteristic
73C11×#107C2311yescharacteristic
74C11×#107C2312yes—
75C11×#106—21no—
76#66882—21no—
77#66882C2312yes—
78C8×Dic11D411yescharacteristic
79C8×Dic11D411yescharacteristic
80C8×Dic11C2311yescharacteristic
81C8×Dic11C2311yescharacteristic
82#66876—22no—
83C2×C11⋊C16C2312yes—
84#66874—21no—
85#66874—21no—
86#66873—21no—
87#66873—21no—
88#66872—22no—
89#66872—22no—
90#33630—111nomaximal, Sylow
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C22×Dic11D811yescharacteristic
96C22×Dic11D811yescharacteristic
97#4339—24no—
98#4339—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×Q812yes—
106C2×C8×C11#4112yes—
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—22no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C4×Dic11D811yescharacteristic
127C4×Dic11D811yescharacteristic
128C4×Dic11C2×D411yescharacteristic
129C4×Dic11C2×D411yescharacteristic
130C2×C11⋊C8—22no—
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133Dic44—21no—
134Dic44C2×Q812yes—
135D88—21no—
136D88C2×Q812yes—
137#4314—24no—
138C11×C16—22no—
139C11⋊C16—22no—
140C2×#499—111no—
141C4×#135—111no—
142#2229—112no—
143#2229—112no—
144#2228—112no—
145#2228—112no—
146#2159—111no—
147#2159D1111yescharacteristic, complemented
148#2150—111no—
149#2139—111no—
150#2139—111no—
151C23×C11C2×D811yescharacteristic
152C22×D11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11C22⋊Q812yes—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11#13712yes—
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—44no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—82no—
167C2×Dic11C2×D811yescharacteristic
168C2×Dic11C2×D811yescharacteristic
169C2×Dic11C2×D811yescharacteristic
170C2×Dic11C2×D811yescharacteristic
171D44—22no—
172D44—41no—
173C4×D11—44no—
174C4×D11—82no—
175C4×D11—82no—
176Dic22—22no—
177Dic22—41no—
178C8×C11C22⋊Q812yes—
179C8×C11C22×Q811yescharacteristic
180C8×C11C2×#4111yescharacteristic
181C11⋊C8—21no—
182C11⋊C8—21no—
183C2×#135—111no—
184C2×#125—221no—
185C4×#41—221no—
186C2×M32—111no—
187C2×M32C2×D1111yescharacteristic
188#499—112no—
189#499—112no—
190#499—221no—
191#499—221no—
192C4×Q16—111no—
193C4×Q16—111no—
194C4×SD16—221no—
195C4×SD16—221no—
196C4×D8—111no—
197C4×D8—111no—
198#427C2×D1111yescharacteristic
199C2×#107—111no—
200C2×#107C2×D1111yescharacteristic
201C2×#106—221no—
202#416—221no—
203C2×C4×C8—111no—
204#367—112no—
205#367C2×D1112yes—
206#366—112no—
207#366C2×D1112yes—
208C4⋊C16—112no—
209C4⋊C16—112no—
210#358—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11#47412yes—
217C22×C11C22×D811yescharacteristic
218C2×D11—42no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11#47412yes—
225C4×C11C2×C22⋊Q811yescharacteristic
226C4×C11C2×#13711yescharacteristic
227Dic11—21no—
228Dic11—21no—
229Dic11—21no—
230Dic11—21no—
231Dic11—42no—
232Dic11—82no—
233C2×#41—221no—
234#135—114no—
235#135—222no—
236C2×Q16—111no—
237C2×SD16—221no—
238C2×D8—111no—
239C22×C8—111no—
240C22×C8C22×D1111yescharacteristic
241#125—222no—
242#125—222no—
243#125—441no—
244#125—441no—
245C4×Q8—221no—
246C4×Q8—221no—
247C4×D4—221no—
248C4×D4—221no—
249C4×D4—441no—
250C4×D4—441no—
251#117—21no—
252#117—441no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—441no—
256C2×C4⋊C4—441no—
257C2×C42—111no—
258C2×C42—441no—
259M32—22no—
260M32—222no—
261C2×C16—112no—
262C2×C16C22×D1112yes—
263#107—21no—
264#107—112no—
265#107—221no—
266#107C22×D1112yes—
267#107C22×D1111yescharacteristic
268#107C22×D1111yescharacteristic
269#106—21no—
270#106—222no—
271#106—222no—
272#103—221no—
273#103—221no—
274#102—221no—
275#102—221no—
276C4×C8—111no—
277C4×C8—111no—
278C4×C8—111no—
279C4×C8—111no—
280C2×C11—22no—
281C2×C11C2×#47411yescharacteristic
282C2×C11#341411yescharacteristic
283C2×C11#341411yescharacteristic
284D11—82no—
285#41—224no—
286#41—442no—
287C2×Q8—221no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—41no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4D4×D1111yescharacteristic
298Q16—112no—
299Q16—221no—
300SD16—224no—
301D8—112no—
302D8—221no—
303C2×C8—111no—
304C2×C8—111no—
305C2×C8—222no—
306C2×C8#433912yes—
307C2×C8D4×D1111yescharacteristic
308C2×C8Q8×D1112yes—
309C2×C8C23×D1111yescharacteristic
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—222no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—41no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C42—41no—
326C42—111no—
327C42—111no—
328C42—111no—
329C42—111no—
330C42—441no—
331C42—441no—
332C16—22no—
333C16—222no—
334C11#3363011yescharacteristic, complemented, Sylow
335C23—441no—
336C23D8×D1111yescharacteristic
337Q8—222no—
338Q8—441no—
339D4—222no—
340D4—444no—
341D4—441no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—444no—
354C2×C4—442no—
355C2×C4—882no—
356C2×C4—882no—
357C2×C4—882no—
358C2×C4#6694912yes—
359C2×C4D8×D1111yescharacteristic
360C2×C4#6697112yes—
361C2×C4C2×D4×D1111yescharacteristic
362C8—221no—
363C8—221no—
364C8#6694912yes—
365C8C2×#433911yescharacteristic
366C8C2×Q8×D1111yescharacteristic
367C22—21no—
368C22—21no—
369C22—442no—
370C22—881no—
371C22—881no—
372C22#1062250312yes—
373C22C2×D8×D1111yescharacteristic
374C4—82no—
375C4—81no—
376C4—81no—
377C4—221no—
378C4—221no—
379C4—221no—
380C4—221no—
381C4—442no—
382C4—882no—
383C4#1062250312yes—
384C4C2×#6694911yescharacteristic
385C4C2×#6697111yescharacteristic
386C2—22no—
387C2—882no—
388C2C2×#1062250311yescharacteristic
389C2#1308174811yescharacteristic
390C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2159D11
hypocenterC11#33630
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. C2×#10622491C2semidirect
3. #13070783C2semidirect
4. #13070779C2semidirect
5. #13070776C2semidirect
6. #13070772C2semidirect
7. #13070405C2semidirect
8. #13070371C2semidirect
11. C11×#2159C2semidirect
147. #2159D11semidirect
334. C11#33630semidirect

Maximal subgroups

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

subgroupindex
C2×#106224912
#130773872
#130707832
#130707792
#130707762
#130707722
#130704052
#130703712
#130703292
#130703262
C11×#21592
#3363011