Finite Group Databasebeta

← #14781064

Subgroups — #14781064

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622615C212yesmaximal
2#13071106C211yesmaximal, characteristic
3#13069764C212yesmaximal, complemented
4#13069759C212yesmaximal, complemented
5#13069754C212yesmaximal, complemented
6#13069749C212yesmaximal, complemented
7#13068332C212yesmaximal, complemented
8C2×#10622162C211yesmaximal, characteristic, complemented
9C2×C11×#533C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C11×#533—28no—
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×#125C2212yes—
14C2×C11×C22⋊Q8—22no—
15C2×C4×Q8×C11—22no—
16C2×C11×#117C2212yes—
17C22×C42×C11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C23×C11⋊C8C2212yes—
20#10622826—22no—
21#10622615—28no—
22C2×#66874C2214yes—
23C2×#66873C2214yes—
24#10622552C2211yescharacteristic
25#10622552C2211yescharacteristic
26C4×(C2×D11)⋊C4—22no—
27#10622542C2211yescharacteristic
28#10622542C2211yescharacteristic
29#10622167C2214yes—
30#10622167C2214yes—
31#10622162C2212yes—
32#10622162C2212yes—
33C22×Q8×C11—22no—
34C23×C4×C11D412yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C2×#4339—22no—
38C2×#4339—24no—
39C2×#4339—24no—
40C2×#4339Q814yescomplemented
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×Dic22C2311yescharacteristic
44C11×C4⋊Q8—28no—
45C11×#125—28no—
46C11×C22⋊Q8—216no—
47C4×Q8×C11—216no—
48C11×#117—24no—
49C11×#117D418yes—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11—24no—
55C2×C42×C11—22no—
56C2×C42×C11D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62#66979—24no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4×Dic11—21no—
66C22×C11⋊C8—24no—
67C22×C11⋊C8—24no—
68C22×C11⋊C8—24no—
69C22×C11⋊C8C2314yes—
70C11⋊#95—22no—
71C11⋊#95—22no—
72#66874—28no—
73#66873—28no—
74#23451—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C2×Q8×C11—28no—
78C2×Q8×C11—44no—
79C2×Q8×C11—44no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—42no—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D414yes—
88C22×C4×C11C2×Q812yes—
89C22×C4×C11#4114yes—
90C22×C4×C11#4112yes—
91C22×C4×C11C2411yescharacteristic
92C2×C22⋊D11—24no—
93C2×C22⋊D11—42no—
94C2×C22⋊D11—42no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98#4339—216no—
99#4339—48no—
100C2×D44—22no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44C2×Q812yes—
104C2×C4×D11—24no—
105C2×C4×D11—42no—
106C2×C4×D11—42no—
107C2×Dic22—22no—
108C2×Dic22—22no—
109C2×Dic22—21no—
110C2×Dic22C2×Q812yes—
111C11×C4⋊C4—216no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4C2×D418yes—
115C11×C22⋊C4—28no—
116C42×C11—24no—
117C42×C11—28no—
118C42×C11—22no—
119C42×C11—22no—
120C22⋊Dic11—42no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—44no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4×Dic11—42no—
126C2×C11⋊C8—24no—
127C2×C11⋊C8—24no—
128C2×C11⋊C8—24no—
129C2×C11⋊C8—48no—
130C2×#533D1111yescharacteristic, complemented
131C2×#416—112no—
132#2297—111no—
133#2026—112no—
134#2025—112no—
135#2024—112no—
136#2023—112no—
137#1735—112no—
138C2×#336—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11#12012yes—
142C23×C11C22⋊Q812yes—
143C23×C11#12412yes—
144C23×C11C22×D411yescharacteristic
145C22×D11—22no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—42no—
149C22×D11—42no—
150Q8×C11—416no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—28no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—48no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11#12012yes—
161C2×C4×C11C22⋊Q818yes—
162C2×C4×C11C22⋊Q812yes—
163C2×C4×C11#12418yes—
164C2×C4×C11#12412yes—
165C2×C4×C11#13514yes—
166C2×C4×C11C22×D412yes—
167C2×C4×C11C22×Q811yescharacteristic
168C2×C4×C11C2×#4112yes—
169C2×C4×C11C2×#4111yescharacteristic
170C22⋊D11—48no—
171C2×Dic11—22no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178D44—24no—
179D44—42no—
180C4×D11—48no—
181Dic22—24no—
182Dic22—42no—
183C11⋊C8—44no—
184C22×#41—111no—
185C23×C8—112no—
186#533—28no—
187C2×C4⋊Q8C2×D1112yes—
188C2×#125C2×D1112yes—
189C2×C22⋊Q8—22no—
190C2×C4×Q8—22no—
191C2×#117—111no—
192C2×#117C2×D1112yes—
193C22×C42C2×D1111yescharacteristic
194#416—228no—
195C2×#103—114no—
196C2×#102—114no—
197#391—111no—
198#391—111no—
199#390—111no—
200#390—111no—
201#386—222no—
202C4×C22⋊C4—222no—
203#340—114no—
204#340—114no—
205#336—112no—
206#336—112no—
207C22×C11—24no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—24no—
211C22×C11#39314yes—
212C22×C11C2×#12011yescharacteristic
213C22×C11C2×C22⋊Q811yescharacteristic
214C22×C11C2×#12411yescharacteristic
215C22×C11C2×#13512yes—
216C22×C11#57512yes—
217C2×D11—44no—
218C2×D11—42no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—82no—
222C4×C11—24no—
223C4×C11—42no—
224C4×C11—48no—
225C4×C11#39314yes—
226C4×C11C2×C22⋊Q812yes—
227C4×C11C2×#12412yes—
228Dic11—42no—
229Dic11—81no—
230Dic11—81no—
231C2×#41—114no—
232C2×#41—222no—
233C2×#41—224no—
234C2×#41—224no—
235C22×Q8—22no—
236C22×Q8—111no—
237C22×D4—111no—
238C22×D4—221no—
239C23×C4—221no—
240C23×C4C22⋊D1112yes—
241C23×C4C22×D1111yescharacteristic
242C22×C8—114no—
243C22×C8—224no—
244C22×C8—224no—
245C22×C8—224no—
246C4⋊Q8—28no—
247#125—28no—
248C22⋊Q8—216no—
249C4×Q8—216no—
250#117—24no—
251#117—224no—
252#117C22⋊D1118yes—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4C22×D1114yes—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—222no—
261C2×C22⋊C4—222no—
262C2×C42—24no—
263C2×C42—22no—
264C2×C42—221no—
265C2×C42C22⋊D1112yes—
266C2×C42C22×D1111yescharacteristic
267C2×C42C22×D1111yescharacteristic
268#103—228no—
269#102—228no—
270#95—222no—
271#95—222no—
272C2×C11—24no—
273C2×C11C2×#39311yescharacteristic
274C2×C11#300212yes—
275C2×C11#307612yes—
276C2×C11#313111yescharacteristic
277C2×C11#313511yescharacteristic
278D11—82no—
279C24—221no—
280C24C2×C22⋊D1111yescharacteristic
281#41—2216no—
282#41—448no—
283C2×Q8—28no—
284C2×Q8—44no—
285C2×Q8—44no—
286C2×Q8—112no—
287C2×Q8—221no—
288C2×Q8—222no—
289C2×Q8—222no—
290C2×D4—112no—
291C2×D4—224no—
292C2×D4—222no—
293C2×D4—221no—
294C2×D4—222no—
295C2×D4—442no—
296C2×D4—442no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—42no—
301C22×C4—221no—
302C22×C4—224no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—442no—
306C22×C4—442no—
307C22×C4Q8×D1112yes—
308C22×C4#434314yes—
309C22×C4#434312yes—
310C22×C4C2×C22⋊D1112yes—
311C22×C4C2×C22⋊D1112yes—
312C22×C4C2×C22⋊D1114yes—
313C22×C4C2×C22⋊D1111yescharacteristic
314C22×C4C23×D1111yescharacteristic
315C2×C8—224no—
316C2×C8—224no—
317C2×C8—224no—
318C2×C8—448no—
319C4⋊C4—216no—
320C4⋊C4—28no—
321C4⋊C4—24no—
322C4⋊C4—222no—
323C4⋊C4—222no—
324C4⋊C4C2×C22⋊D1118yes—
325C22⋊C4—28no—
326C22⋊C4—444no—
327C22⋊C4—442no—
328C22⋊C4—444no—
329C42—24no—
330C42—28no—
331C42—22no—
332C42—22no—
333C42—442no—
334C11#2345111yescharacteristic, complemented, Sylow
335C23—22no—
336C23—22no—
337C23—222no—
338C23—441no—
339C23—442no—
340C23—442no—
341C23—441no—
342C23#6699912yes—
343C23#6700012yes—
344C23#6700612yes—
345C23C22×C22⋊D1111yescharacteristic
346Q8—416no—
347Q8—224no—
348Q8—442no—
349D4—224no—
350D4—448no—
351D4—442no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—28no—
358C2×C4—48no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—222no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—448no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4#6699918yes—
370C2×C4#6699912yes—
371C2×C4#6700018yes—
372C2×C4#6700012yes—
373C2×C4#6700314yes—
374C2×C4#6700612yes—
375C2×C4C2×Q8×D1111yescharacteristic
376C2×C4C2×#434312yes—
377C2×C4C2×#434311yescharacteristic
378C2×C4C22×C22⋊D1112yes—
379C8—444no—
380C22—24no—
381C22—24no—
382C22—22no—
383C22—22no—
384C22—444no—
385C22—442no—
386C22—882no—
387C22—881no—
388C22—881no—
389C22#1062284414yes—
390C22C2×#6699911yescharacteristic
391C22C2×#6700011yescharacteristic
392C22C2×#6700312yes—
393C22#1062335312yes—
394C22C2×#6700611yescharacteristic
395C4—24no—
396C4—42no—
397C4—48no—
398C4—442no—
399C4—881no—
400C4—881no—
401C4#1062284414yes—
402C4C2×#6699912yes—
403C4C2×#6700012yes—
404C2—24no—
405C2—882no—
406C2C2×#1062284411yescharacteristic
407C2#1307783412yes—
408C2#1307839812yes—
409C2#1307894111yescharacteristic
410C2#1307896411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#533D11
hypocenterC11#23451
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #13069764C2semidirect
4. #13069759C2semidirect
5. #13069754C2semidirect
6. #13069749C2semidirect
7. #13068332C2semidirect
8. C2×#10622162C2semidirect
9. C2×C11×#533C2semidirect
40. C2×#4339Q8semidirect
130. C2×#533D11semidirect
334. C11#23451semidirect

Maximal subgroups

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

subgroupindex
C2×#106226152
#130711062
#130697642
#130697592
#130697542
#130697492
#130683322
C2×#106221622
C2×C11×#5332
#2345111