Finite Group Databasebeta

← #14648643

Subgroups — #14648643

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078398C211yesmaximal, characteristic
2#13077185C211yesmaximal, characteristic
3#13067019C211yesmaximal, characteristic, complemented
4#13066999C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C11×#1493C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66960—21no—
10C4×#4339C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13#10622732—21no—
14#10622707C411yescharacteristic
15#10622704C411yescharacteristic
16#10622700C411yescharacteristic
17#10622697C411yescharacteristic
18#10622679—21no—
19#10622676—21no—
20#10622615—21no—
21#10622611—21no—
22#10622538C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622452—22no—
26#10622450—21no—
27D11×C4⋊C8—21no—
28C11×Q8⋊C8—22no—
29Q8⋊(C11⋊C8)—21no—
30Q8⋊(C11⋊C8)—21no—
31#10622097—21no—
32#10622094—21no—
33C2×#4339D411yescharacteristic
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8C2×C411yescharacteristic
37C11×C4⋊Q8C2×C411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C42×C11C2311yescharacteristic
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47#66979D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66960—42no—
51#66960—42no—
52C2×#4313—22no—
53C2×C8×D11—22no—
54C4×D44C2×C411yescharacteristic
55C4×D44D411yescharacteristic
56#66925—21no—
57C42×D11—21no—
58C4×Dic22C2×C411yescharacteristic
59C4×Dic22D411yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64C22⋊(C11⋊C8)—21no—
65Dic11⋊C8—22no—
66Dic11⋊C8—22no—
67#66874—21no—
68#66874—21no—
69#66873—21no—
70#66873—21no—
71#66872—21no—
72#66872—21no—
73#66871—21no—
74#66871—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2×C411yescharacteristic
79C4⋊(C11⋊C8)C2×C411yescharacteristic
80C4⋊(C11⋊C8)D411yescharacteristic
81C4⋊(C11⋊C8)D411yescharacteristic
82C4×C11⋊C8—21no—
83#8993—111nomaximal, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—21no—
90#4339—21no—
91#4339—21no—
92#4339SD1612yes—
93#4339Q1612yes—
94C2×D44C22⋊C411yescharacteristic
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×Dic22C22⋊C411yescharacteristic
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C22⋊Dic11—21no—
118(C2×D11)⋊C4—21no—
119(C2×D11)⋊C4—21no—
120C4⋊Dic11C22⋊C411yescharacteristic
121C4⋊Dic11C22⋊C411yescharacteristic
122Dic11⋊C4—21no—
123Dic11⋊C4—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136#4313—44no—
137C8×D11—44no—
138#3076—111no—
139#2906—111no—
140#1493D1111yescharacteristic, complemented
141#1481—111no—
142#1476—111no—
143#1301—111no—
144#1277—111no—
145C23×C11#12311yescharacteristic
146C22×D11—21no—
147Q8×C11—42no—
148Q8×C11—41no—
149Q8×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11C2×SD1611yescharacteristic
162C2×C4×C11C2×Q1611yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C22⋊D11—22no—
166C22⋊D11—22no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170D44—21no—
171D44#10312yes—
172C4×D11—22no—
173C4×D11—22no—
174C4×D11—41no—
175C4×D11—41no—
176C4×D11—81no—
177Dic22—21no—
178Dic22#10312yes—
179C8×C11—42no—
180C8×C11—42no—
181C11⋊C8—41no—
182C11⋊C8—41no—
183C11⋊C8—41no—
184C11⋊C8—41no—
185C11⋊C8—81no—
186C2×#131—221no—
187#533C2×D1111yescharacteristic
188C4×#41—111no—
189#479—221no—
190#478—221no—
191#477—111no—
192#476—111no—
193#475—111no—
194#474—111no—
195#431—111no—
196#427—221no—
197#424—221no—
198#424—222no—
199#423—221no—
200#423C2×D1111yescharacteristic
201C2×C4⋊C8—111no—
202C2×C4⋊C8—111no—
203C2×C4⋊C8—221no—
204#416—221no—
205C2×C4×C8C2×D1111yescharacteristic
206Q8⋊C8—22no—
207Q8⋊C8—221no—
208Q8⋊C8—221no—
209Q8⋊C8—221no—
210D4⋊C8—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11#38611yescharacteristic
214C22×C11#48311yescharacteristic
215C22×C11#48411yescharacteristic
216C2×D11—22no—
217C2×D11—41no—
218C2×D11—41no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11C2×#10311yescharacteristic
225C4×C11#41711yescharacteristic
226C4×C11#44311yescharacteristic
227C4×C11#44411yescharacteristic
228C4×C11#45011yescharacteristic
229C4×C11#45111yescharacteristic
230Dic11—22no—
231Dic11—41no—
232Dic11—41no—
233C2×#41—111no—
234#131—442no—
235#131—442no—
236C2×M16—21no—
237C2×M16—222no—
238C22×C8—21no—
239C22×C8—222no—
240C22×C8—221no—
241C22×C8—221no—
242C4⋊Q8C4×D1111yescharacteristic
243C4⋊Q8C4×D1111yescharacteristic
244#125—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—111no—
250C4×Q8—111no—
251C4×D4—111no—
252C4×D4—111no—
253C4×D4—221no—
254C4×D4—221no—
255#117—21no—
256#117—111no—
257#117—221no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260#107—221no—
261#107—221no—
262#106—221no—
263#106—221no—
264C4⋊C8—21no—
265C4⋊C8—111no—
266C4⋊C8—111no—
267C4⋊C8—111no—
268C4⋊C8—111no—
269C4⋊C8—222no—
270C4⋊C8—222no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8—221no—
274C4⋊C8C22⋊D1112yes—
275#103—221no—
276#103—221no—
277#102—221no—
278#102—221no—
279C22⋊C8—221no—
280C4×C8—21no—
281C4×C8—21no—
282C4×C8—221no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11#187211yescharacteristic
286C2×C11#187611yescharacteristic
287C2×C11#188111yescharacteristic
288D11—42no—
289#41—112no—
290#41—112no—
291#41—221no—
292#41—221no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—111no—
296C2×D4—111no—
297C2×D4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4#433911yescharacteristic
302C22×C4D4×D1111yescharacteristic
303C22×C4#434111yescharacteristic
304M16—41no—
305M16—41no—
306M16—444no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—221no—
312C2×C8—221no—
313C2×C8—221no—
314C2×C8—221no—
315C2×C8—444no—
316C2×C8—441no—
317C2×C8—441no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—441no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—111no—
328C4⋊C4—111no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C22⋊C4—41no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C42—41no—
336C42—221no—
337C42—221no—
338C42—221no—
339C42C2×C4×D1111yescharacteristic
340C42D4×D1111yescharacteristic
341C42D4×D1111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C11#899311yescharacteristic, complemented, Sylow
344C23—221no—
345C23#6693611yescharacteristic
346Q8—42no—
347Q8—41no—
348Q8—41no—
349Q8—112no—
350Q8—221no—
351D4—112no—
352D4—222no—
353D4—222no—
354D4—221no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—221no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—881no—
368C2×C4C22⋊C4×D1111yescharacteristic
369C2×C4(C22⋊D11)⋊C411yescharacteristic
370C2×C4#6693711yescharacteristic
371C2×C4SD16×D1111yescharacteristic
372C2×C4#6696711yescharacteristic
373C2×C4Q16×D1111yescharacteristic
374C2×C4#6697111yescharacteristic
375C2×C4C4×C22⋊D1111yescharacteristic
376C2×C4#6699011yescharacteristic
377C2×C4#6699111yescharacteristic
378C8—42no—
379C8—42no—
380C8—441no—
381C8—441no—
382C8—441no—
383C8—441no—
384C8—881no—
385C22—21no—
386C22—21no—
387C22—222no—
388C22—441no—
389C22—441no—
390C22#1062241811yescharacteristic
391C22#1062242211yescharacteristic
392C22#1062256911yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—222no—
399C4—441no—
400C4—441no—
401C4D11×#10311yescharacteristic
402C4#1062241611yescharacteristic
403C4#1062243611yescharacteristic
404C4#1062243711yescharacteristic
405C4#1062278211yescharacteristic
406C4#1062279911yescharacteristic
407C2—21no—
408C2—21no—
409C2—442no—
410C2#1306892011yescharacteristic
411C2#1306894011yescharacteristic
412C2#1306898111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1493D11
hypocenterC11#8993
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #13067019C2semidirect
5. #13066511C2semidirect
6. #13066451C2semidirect
7. C11×#1493C2semidirect
140. #1493D11semidirect
343. C11#8993semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130771852
#130670192
#130669992
#130665112
#130664512
C11×#14932
#899311