Finite Group Databasebeta

← #14754141

Subgroups — #14754141

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077044C211yesmaximal, characteristic
2#13068762C212yesmaximal, complemented
3#13068738C212yesmaximal, complemented
4#13068720C211yesmaximal, characteristic
5#13068664C211yesmaximal, characteristic
6#13068660C211yesmaximal, characteristic
7#13068499C212yesmaximal, complemented
8#13068419C211yesmaximal, characteristic
9#13068418C211yesmaximal, characteristic
10#13068370C212yesmaximal, complemented
11C11×#1827C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13C2×#67001C2211yescharacteristic
14C2×#67001C2211yescharacteristic
15C11×#413C2211yescharacteristic
16C11×#410C2211yescharacteristic
17#10622853C2211yescharacteristic
18#10622850C2211yescharacteristic
19C2×#66886C2212yes—
20#10622735C2212yes—
21#10622611C2212yes—
22#10622610C412yescomplemented
23#10622610C412yescomplemented
24#10622610C2212yes—
25#10622610C2211yescharacteristic
26#10622610C2211yescharacteristic
27C4×#4318C412yescomplemented
28C4×#4318C2211yescharacteristic
29C2×#66867C412yescomplemented
30C2×#66867C2211yescharacteristic
31C11×#339C2212yes—
32C11×H(3,ℤ/4)C2212yes—
33C11⋊#338C2212yes—
34#10622197C2212yes—
35#10622171C2212yes—
36#10622169C2212yes—
37#10622169C2212yes—
38#10622161C2212yes—
39C2×C11×#41C2311yescharacteristic
40C2×C11×M16C2312yes—
41C4×Q8×C11—21no—
42C4×D4×C11—22no—
43C4×D4×C11—21no—
44C11×#117C2×C412yes—
45C11×#117C2312yes—
46C11×#117C2311yescharacteristic
47C2×C42×C11C2×C412yes—
48C2×C42×C11C2311yescharacteristic
49#67001—22no—
50#67001—22no—
51#67001—22no—
52#67001—22no—
53#66979C2312yes—
54C2×#4318C2×C412yes—
55C2×#4318C2×C412yes—
56C2×#4318C2312yes—
57C2×#4318C2311yescharacteristic
58C2×#4318C2311yescharacteristic
59C22×C11⋊C8C2×C412yes—
60C22×C11⋊C8C2×C412yes—
61C22×C11⋊C8C2311yescharacteristic
62C22×C11⋊C8C2311yescharacteristic
63C11×#101—21no—
64C11×#100—21no—
65C11×#99—22no—
66#66900—21no—
67#66898—22no—
68#66897—21no—
69#66886—22no—
70#66886—22no—
71#66879—22no—
72C8×Dic11—22no—
73#66872—22no—
74#66871—22no—
75#66867—22no—
76#66867C2×C411yescharacteristic
77#66867C2×C412yes—
78#66867C2×C412yes—
79#66867C2×C412yes—
80#66867C2×C411yescharacteristic
81#66867C2×C411yescharacteristic
82#66867C2×C411yescharacteristic
83C4×C11⋊C8—22no—
84C4×C11⋊C8C2×C412yes—
85C4×C11⋊C8C2×C412yes—
86C4×C11⋊C8C2×C412yes—
87#20788—111nomaximal, Sylow
88C11×#41—22no—
89C11×#41—22no—
90C2×Q8×C11#4111yescharacteristic
91C2×D4×C11#4112yes—
92C2×D4×C11#4111yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2411yescharacteristic
97C11×M16—22no—
98C11×M16—22no—
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—21no—
105C11×C22⋊C4—22no—
106C42×C11—22no—
107C42×C11—21no—
108C42×C11—22no—
109C42×C11C22×C412yes—
110C42×C11C22×C411yescharacteristic
111C42×C11C22×C411yescharacteristic
112C22⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4×Dic11—22no—
115#4318—24no—
116#4318—24no—
117#4318—22no—
118#4318—22no—
119#4318—22no—
120#4318—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8C22×C412yes—
127C2×C11⋊C8C22×C412yes—
128C2×C11⋊C8C22×C411yescharacteristic
129C2×C11⋊C8C22×C411yescharacteristic
130C2×C11⋊C8C22×C411yescharacteristic
131C2×C11⋊C8C22×C411yescharacteristic
132C2×C11⋊C8#4112yes—
133C2×C11⋊C8#4112yes—
134C2×C11⋊C8#4112yes—
135C2×C11⋊C8#4112yes—
136#2875—111no—
137#1841—112no—
138#1833—112no—
139#1827—111no—
140#1827D1111yescharacteristic
141#1813—111no—
142#1812—111no—
143#1773—112no—
144#1757—111no—
145#1757—111no—
146#1747—112no—
147C23×C11#11712yes—
148C23×C11C2×#4111yescharacteristic
149Q8×C11—22no—
150D4×C11—24no—
151D4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—81no—
159C2×C4×C11—82no—
160C2×C4×C11#11712yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C2×C4×C11C2×#4112yes—
164C2×C4×C11C2×#4112yes—
165C2×Dic11—42no—
166C8×C11—42no—
167C11⋊C8—22no—
168C11⋊C8—22no—
169C11⋊C8—42no—
170C11⋊C8#11711yescharacteristic
171C11⋊C8#11711yescharacteristic
172C11⋊C8#11711yescharacteristic
173C11⋊C8#11711yescharacteristic
174C11⋊C8#11712yes—
175C11⋊C8#11712yes—
176C2×#131—111no—
177C2×#131—111no—
178C4×#41C2×D1111yescharacteristic
179C2×#108—112no—
180#427—112no—
181#413—111no—
182#413C2×D1111yescharacteristic
183#410—111no—
184#410C2×D1111yescharacteristic
185#405—111no—
186#405—111no—
187#405—112no—
188#405—112no—
189#405—112no—
190#405—112no—
191C4×M16—111no—
192C4×M16—112no—
193C2×#97—111no—
194C2×#97—112no—
195#344—112no—
196#344—112no—
197#339—112no—
198#339C2×D1112yes—
199#338—112no—
200H(3,ℤ/4)—112no—
201H(3,ℤ/4)—112no—
202H(3,ℤ/4)C2×D1112yes—
203C22×C11—22no—
204C22×C11—41no—
205C22×C11—42no—
206C22×C11C2×#11711yescharacteristic
207C22×C11#52912yes—
208C4×C11—22no—
209C4×C11—42no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—82no—
213C4×C11C2×#11711yescharacteristic
214C4×C11C2×#11711yescharacteristic
215C4×C11#52912yes—
216Dic11—82no—
217C2×#41C22×D1111yescharacteristic
218#131—222no—
219#131—222no—
220#131—222no—
221#131—222no—
222C2×M16—112no—
223C2×M16—112no—
224C2×M16—111no—
225C2×M16—111no—
226C2×M16—112no—
227C2×M16C22×D1112yes—
228C22×C8—111no—
229C22×C8—111no—
230C22×C8—112no—
231C22×C8—112no—
232C4×Q8—21no—
233C4×D4—22no—
234C4×D4—21no—
235#117—112no—
236#117C4×D1112yes—
237#117C22×D1112yes—
238#117C22×D1111yescharacteristic
239C2×C42C4×D1112yes—
240C2×C42C22×D1111yescharacteristic
241#108—222no—
242#108—222no—
243#107—222no—
244#106—222no—
245#101—21no—
246#101—221no—
247#100—21no—
248#100—221no—
249#99—22no—
250#99—222no—
251#97—111no—
252#97—111no—
253#97—112no—
254#97—111no—
255#97—111no—
256#97—112no—
257#97—112no—
258#97—222no—
259#97—222no—
260C4×C8—112no—
261C4×C8—112no—
262C4×C8—112no—
263C4×C8—222no—
264C4×C8—222no—
265C2×C11—22no—
266C2×C11—21no—
267C2×C11—42no—
268C2×C11#228311yescharacteristic
269#41—22no—
270#41—22no—
271C2×Q8#434111yescharacteristic
272C2×D4#434112yes—
273C2×D4#434111yescharacteristic
274C22×C4—22no—
275C22×C4—21no—
276C22×C4C2×C4×D1112yes—
277C22×C4C23×D1111yescharacteristic
278M16—22no—
279M16—22no—
280M16—224no—
281M16—224no—
282M16—222no—
283M16—222no—
284M16—222no—
285M16—222no—
286C2×C8—22no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8—111no—
291C2×C8—112no—
292C2×C8—112no—
293C2×C8—112no—
294C2×C8—112no—
295C2×C8—112no—
296C2×C8—112no—
297C2×C8—222no—
298C2×C8—222no—
299C2×C8—222no—
300C2×C8—222no—
301C2×C8—222no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—222no—
306C22⋊C4—22no—
307C22⋊C4—21no—
308C22⋊C4—22no—
309C22⋊C4—222no—
310C42—22no—
311C42—21no—
312C42—22no—
313C42—222no—
314C42C2×C4×D1111yescharacteristic
315C42C2×C4×D1112yes—
316C42C2×C4×D1111yescharacteristic
317C11#2078811yescharacteristic, complemented, Sylow
318C23#6693012yes—
319C23C2×#434111yescharacteristic
320Q8—22no—
321D4—24no—
322D4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—442no—
332C2×C4#6693012yes—
333C2×C4C22×C4×D1111yescharacteristic
334C2×C4C2×#434111yescharacteristic
335C2×C4#41×D1112yes—
336C2×C4#41×D1112yes—
337C8—42no—
338C8—111no—
339C8—111no—
340C8—112no—
341C8—111no—
342C8—111no—
343C8—112no—
344C8—222no—
345C8—222no—
346C8—442no—
347C22—22no—
348C22—41no—
349C22—42no—
350C22C2×#6693011yescharacteristic
351C22#1062318012yes—
352C4—22no—
353C4—41no—
354C4—42no—
355C4—41no—
356C4—82no—
357C4—882no—
358C4D11×#11711yescharacteristic
359C4D11×#11711yescharacteristic
360C4#1062318012yes—
361C2—21no—
362C2—22no—
363C2—42no—
364C2#1307100711yescharacteristic
subgroupG/H
centerC4D11×#117
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1827C2
socleC2×C11#2283
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#1827D11
hypocenterC11#20788
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ #117 ◁ #1827

Complements

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

NH ≅ G/Ntype
2. #13068762C2semidirect
3. #13068738C2semidirect
7. #13068499C2semidirect
10. #13068370C2semidirect
22. #10622610C4semidirect
23. #10622610C4semidirect
27. C4×#4318C4semidirect
29. C2×#66867C4semidirect
317. C11#20788semidirect

Maximal subgroups

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

subgroupindex
#130770442
#130687622
#130687382
#130687202
#130686642
#130686602
#130684992
#130684192
#130684182
#130683702
C11×#18272
#2078811