Finite Group Databasebeta

← #14790007

Subgroups — #14790007

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082426C211yesmaximal, characteristic, complemented
2#13078413C212yesmaximal
3#13069966C212yesmaximal, complemented
4#13069772C212yesmaximal
5#13069593C212yesmaximal, complemented
6#13069020C212yesmaximal
7#13068830C212yesmaximal, complemented
8#13068612C211yesmaximal, characteristic, complemented
9C4×C11×#124C211yesmaximal, characteristic
10C2×C11×#124C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623343C2212yes—
14#10623101—22no—
15#10623100—24no—
16Q8×Dic22—22no—
17#10623031—22no—
18#10623031C2212yes—
19#10623001—22no—
20#10623001C2212yes—
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#388—22no—
24C11×#382C2211yescharacteristic
25C4×C11×C22⋊C4—22no—
26C43×C11C2211yescharacteristic
27C2×#66900C2212yes—
28#10622828C2214yes—
29#10622622—24no—
30#10622621—22no—
31#10622620—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C11×#124—22no—
41C11×#124Q814yescomplemented
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×D4×C11—22no—
45C4×D4×C11—22no—
46C2×C11×C4⋊C4D412yes—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C2×C42×C11—21no—
54C2×C42×C11D412yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58Q8×Dic11—24no—
59Q8×Dic11—24no—
60#66979—24no—
61#66979C2314yes—
62#66977—22no—
63#66977—24no—
64#66977—22no—
65C2×#4318C2314yes—
66#66943—28no—
67#66943—24no—
68#66941—28no—
69#66941—24no—
70#66923—24no—
71#66923D414yes—
72#66922—22no—
73#66922—22no—
74#66922D412yes—
75#66922D412yes—
76C4×Dic22—24no—
77C4×Dic22—24no—
78C4×Dic22—22no—
79C4×Dic22—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66900—24no—
83#66896—24no—
84#66896—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24313—111nomaximal, Sylow
90C24×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C2×Q812yes—
94C2×Q8×C11#4112yes—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11C2×Q812yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—44no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×Dic22—24no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—44no—
118C11×C22⋊C4—42no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—21no—
122C42×C11—22no—
123C42×C11—42no—
124C42×C11—42no—
125C42×C11C2×D412yes—
126C42×C11C2×D412yes—
127C42×C11C2×Q812yes—
128C22⋊Dic11—24no—
129C4⋊Dic11—24no—
130C4⋊Dic11—24no—
131C4⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11C2×D414yes—
135C4⋊Dic11C2×D414yes—
136Dic11⋊C4—28no—
137Dic11⋊C4—24no—
138Dic11⋊C4—24no—
139C4×Dic11—28no—
140C4×Dic11—24no—
141#4318—24no—
142#4318—24no—
143C2×C11⋊C8—24no—
144#3502—111no—
145#3077—112no—
146C4×#124D1111yescharacteristic
147#2061—112no—
148#2027—112no—
149#1994—112no—
150#1888—112no—
151#1857—112no—
152#1801—111no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11C22×D411yescharacteristic
159Q8×C11—24no—
160Q8×C11—24no—
161D4×C11—24no—
162D4×C11—42no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
178C2×C4×C11—82no—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12012yes—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11C22⋊Q814yes—
183C2×C4×C11C22×D412yes—
184C2×C4×C11C22×Q811yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C112−1+412yes—
187C2×Dic11—24no—
188C2×Dic11—24no—
189Dic22—44no—
190Dic22—82no—
191Dic22—84no—
192C11⋊C8—44no—
193Q82—222no—
194#557—224no—
195#557—222no—
196#544—112no—
197#544—222no—
198#533—112no—
199#533—222no—
200C2×#124C2×D1111yescharacteristic
201#519—112no—
202C2×C4×Q8C2×D1111yescharacteristic
203C2×C4×D4C2×D1111yescharacteristic
204#478—224no—
205#476—222no—
206#474—222no—
207#428—114no—
208#423—112no—
209#418—114no—
210C2×#101—112no—
211#391C2×D1111yescharacteristic
212#390C2×D1111yescharacteristic
213#388—22no—
214#382C2×D1111yescharacteristic
215C4×C22⋊C4—22no—
216C43C2×D1111yescharacteristic
217#343—112no—
218#339—114no—
219#339—114no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—44no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11C2×#12011yescharacteristic
228C22×C11C2×C22⋊Q811yescharacteristic
229C22×C11#53611yescharacteristic
230C4×C11—24no—
231C4×C11—21no—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—81no—
237C4×C11#45412yes—
238C4×C11#54812yes—
239C4×C11D4×Q812yes—
240Dic11—44no—
241Dic11—44no—
242C22×Q8C22×D1111yescharacteristic
243C22×D4C22×D1111yescharacteristic
244C23×C4—21no—
245C2×M16—114no—
246C4⋊Q8—112no—
247C4⋊Q8—112no—
248C4⋊Q8—222no—
249C4⋊Q8—222no—
250C4⋊Q8—224no—
251C4⋊Q8—228no—
252#125—114no—
253#125—224no—
254#125—224no—
255#125—228no—
256#124—22no—
257#124Dic2214yescomplemented
258C22⋊Q8—222no—
259C22⋊Q8—222no—
260C22⋊Q8—224no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×Q8—224no—
264C4×Q8—224no—
265C4×Q8—224no—
266C4×Q8—224no—
267C4×Q8—222no—
268C4×Q8—222no—
269C4×D4—22no—
270C4×D4—22no—
271#117—114no—
272#117—224no—
273C2×C4⋊C4C22⋊D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C4⋊C4C22×D1111yescharacteristic
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42C22⋊D1112yes—
282C2×C42C22×D1111yescharacteristic
283C2×C42C22×D1111yescharacteristic
284C2×C42C22×D1111yescharacteristic
285#107—224no—
286#106—224no—
287C4⋊C8—222no—
288C4⋊C8—222no—
289#102—224no—
290#102—224no—
291#101—224no—
292#95—22no—
293#95—22no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—82no—
297C2×C11#240911yescharacteristic
298C2×C11C2×#45411yescharacteristic
299C2×C11#301811yescharacteristic
300C24—21no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—224no—
304C2×Q8—222no—
305C2×Q8—222no—
306C2×Q8C2×Dic2212yes—
307C2×Q8#433912yes—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4C2×Dic2212yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—44no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×C22⋊D1112yes—
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C2×C22⋊D1112yes—
321C22×C4C2×C22⋊D1111yescharacteristic
322C22×C4C23×D1111yescharacteristic
323M16—224no—
324M16—224no—
325C2×C8—224no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—114no—
330C4⋊C4—114no—
331C4⋊C4—224no—
332C4⋊C4—224no—
333C4⋊C4—224no—
334C4⋊C4—228no—
335C4⋊C4—224no—
336C4⋊C4—222no—
337C4⋊C4—224no—
338C4⋊C4—222no—
339C22⋊C4—28no—
340C22⋊C4—44no—
341C22⋊C4—42no—
342C22⋊C4—224no—
343C42—22no—
344C42—22no—
345C42—21no—
346C42—22no—
347C42—42no—
348C42—42no—
349C42—228no—
350C42—224no—
351C42C2×Dic2212yes—
352C42D4×D1112yes—
353C42D4×D1112yes—
354C11#2431311yescharacteristic, complemented, Sylow
355C23—22no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23C22×C22⋊D1111yescharacteristic
361Q8—24no—
362Q8—24no—
363Q8—444no—
364Q8—882no—
365Q8—884no—
366D4—24no—
367D4—42no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—224no—
385C2×C4—224no—
386C2×C4#6697714yes—
387C2×C4#6699011yescharacteristic
388C2×C4#6699012yes—
389C2×C4#6699011yescharacteristic
390C2×C4C22×Dic2211yescharacteristic
391C2×C4C2×#433911yescharacteristic
392C2×C4C2×D4×D1112yes—
393C2×C4#6704312yes—
394C8—444no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22—42no—
399C22—82no—
400C22—81no—
401C22—81no—
402C22C2×#6697711yescharacteristic
403C22C2×#6699011yescharacteristic
404C22#1062335611yescharacteristic
405C4—24no—
406C4—21no—
407C4—22no—
408C4—42no—
409C4—42no—
410C4—42no—
411C4—81no—
412C4—444no—
413C4—444no—
414C4#1062267512yes—
415C4D4×Dic2212yes—
416C4#1062308312yes—
417C2—21no—
418C2—21no—
419C2—82no—
420C2#1307198111yescharacteristic
421C2C2×#1062267511yescharacteristic
422C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#124C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenterC4×#124D11
hypocenterC11#24313
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #13082426C2semidirect
3. #13069966C2semidirect
5. #13069593C2semidirect
7. #13068830C2semidirect
8. #13068612C2semidirect
41. C11×#124Q8semidirect
257. #124Dic22semidirect
354. C11#24313semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130784132
#130699662
#130697722
#130695932
#130690202
#130688302
#130686122
C4×C11×#1242
#2431311