Finite Group Databasebeta

← #14783690

Subgroups — #14783690

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071098C211yesmaximal, characteristic
2#13071019C211yesmaximal, characteristic
3#13070188C212yesmaximal, complemented
4#13070186C212yesmaximal, complemented
5#13070181C212yesmaximal, complemented
6#13070176C212yesmaximal, complemented
7#13068333C211yesmaximal, characteristic
8#13068332C211yesmaximal, characteristic
9#13068332C211yesmaximal, characteristic
10C2×#10622188C211yesmaximal, characteristic
11C11×#1735C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10622590C2211yescharacteristic
20#10622590C2211yescharacteristic
21#10622589C2211yescharacteristic
22#10622589C2211yescharacteristic
23#10622586C2212yes—
24#10622586C2212yes—
25#10622559—22no—
26#10622555—22no—
27C4×Dic11⋊C4—22no—
28C4×Dic11⋊C4—22no—
29C11×#340C2212yes—
30C11×#340C2212yes—
31#10622189C2212yes—
32#10622189C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11D412yes—
41C22×C8×C11—22no—
42C22×C8×C11—22no—
43C22×C8×C11—22no—
44C22×C8×C11C2312yes—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58#66979—22no—
59#66979—22no—
60#66979—22no—
61#66979Q814yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11D412yes—
74C2×C4×Dic11C2311yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8—22no—
79C22×C11⋊C8C2312yes—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#23744—111nomaximal, Sylow
85C24×C11C2×D411yescharacteristic
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×Q812yes—
91C22×C4×C11#4112yes—
92C22×C4×C11#4112yes—
93C22×C4×C11#4112yes—
94C22×C4×C11#4112yes—
95C22×C4×C11#4112yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—22no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—42no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—44no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—42no—
117C42×C11—42no—
118C42×C11—42no—
119C22⋊Dic11—24no—
120C22⋊Dic11—42no—
121C4⋊Dic11—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11C2×Q814yes—
127Dic11⋊C4—44no—
128Dic11⋊C4—44no—
129Dic11⋊C4—44no—
130Dic11⋊C4—44no—
131C4×Dic11—24no—
132C4×Dic11—24no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—42no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—44no—
142#2296—111no—
143#2285—111no—
144#2101—112no—
145#2101—112no—
146#2100—112no—
147#2099—112no—
148#1735—111no—
149#1735—111no—
150#1735—111no—
151#1735D1111yescharacteristic
152C2×#336—111no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11C22⋊Q812yes—
156C23×C11#12312yes—
157C23×C11#12412yes—
158C23×C11C22×D411yescharacteristic
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11C22⋊Q812yes—
167C2×C4×C11#12312yes—
168C2×C4×C11#12412yes—
169C2×C4×C11#12514yes—
170C2×C4×C11#12514yes—
171C2×C4×C11#12614yes—
172C2×C4×C11#12614yes—
173C2×C4×C11C22×Q811yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—48no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11#13514yes—
193C8×C11—42no—
194C11⋊C8—42no—
195C23×C8—111no—
196C23×C8C2×D1111yescharacteristic
197C2×#117—111no—
198C2×#117—111no—
199C2×#117C2×D1111yescharacteristic
200C2×#117C2×D1111yescharacteristic
201C22×C42—111no—
202#389—112no—
203#389—112no—
204#385—222no—
205#384—111no—
206#384—111no—
207#382—111no—
208#382—111no—
209#380—222no—
210C4×C4⋊C4—222no—
211C4×C4⋊C4—222no—
212#340—112no—
213#340—112no—
214#340—112no—
215#340—112no—
216#340—112no—
217#340—112no—
218#340C2×D1112yes—
219#340C2×D1112yes—
220#336—112no—
221#336—112no—
222C22×C11—24no—
223C22×C11—24no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#40014yes—
227C22×C11C2×C22⋊Q811yescharacteristic
228C22×C11C2×#12311yescharacteristic
229C22×C11C2×#12411yescharacteristic
230C22×C11C2×#13512yes—
231C22×C11#57512yes—
232C4×C11—82no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11#40014yes—
236C4×C11C2×#12511yescharacteristic
237C4×C11C2×#12511yescharacteristic
238C4×C11C2×#12611yescharacteristic
239C4×C11C2×#12611yescharacteristic
240Dic11—24no—
241Dic11—44no—
242Dic11—42no—
243Dic11—81no—
244Dic11—81no—
245C23×C4—112no—
246C23×C4C22×D1111yescharacteristic
247C22×C8—22no—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—112no—
251C22×C8—222no—
252C22×C8—222no—
253C22×C8—222no—
254C22×C8C22×D1112yes—
255#117—22no—
256#117—22no—
257#117—22no—
258#117—22no—
259#117—114no—
260#117—222no—
261#117—222no—
262#117—222no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4C22×D1111yescharacteristic
271C2×C4⋊C4C22×D1111yescharacteristic
272C2×C4⋊C4C22×D1112yes—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—112no—
280C2×C42—111no—
281C2×C42—111no—
282C2×C42—222no—
283C2×C42—221no—
284C2×C42—222no—
285C2×C42—221no—
286#95—222no—
287#95—222no—
288#95—222no—
289#95—222no—
290C2×C11—24no—
291C2×C11C2×#40011yescharacteristic
292C2×C11#307612yes—
293C2×C11#309112yes—
294C2×C11#313111yescharacteristic
295C2×C11#313511yescharacteristic
296C24D4×D1111yescharacteristic
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—224no—
303C22×C4—224no—
304C22×C4—222no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—442no—
308C22×C4#433912yes—
309C22×C4#433912yes—
310C22×C4#433912yes—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434112yes—
313C22×C4#434112yes—
314C22×C4Q8×D1112yes—
315C22×C4C23×D1111yescharacteristic
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—44no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—444no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—114no—
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—444no—
337C4⋊C4—444no—
338C4⋊C4—444no—
339C4⋊C4—444no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—224no—
343C22⋊C4—442no—
344C42—42no—
345C42—42no—
346C42—224no—
347C42—224no—
348C42—221no—
349C42—221no—
350C42—221no—
351C42—221no—
352C42—442no—
353C11#2374411yescharacteristic, complemented, Sylow
354C23—22no—
355C23—22no—
356C23#6693612yes—
357C23#6693812yes—
358C23#6694912yes—
359C23C2×D4×D1111yescharacteristic
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—114no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—224no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—448no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4#6692914yes—
382C2×C4#6693214yes—
383C2×C4#6693612yes—
384C2×C4#6693812yes—
385C2×C4#6694214yes—
386C2×C4#6694214yes—
387C2×C4#6694912yes—
388C2×C4C2×#433911yescharacteristic
389C2×C4C2×#433911yescharacteristic
390C2×C4C2×#433911yescharacteristic
391C2×C4C2×#434111yescharacteristic
392C2×C4C2×#434111yescharacteristic
393C2×C4C2×Q8×D1111yescharacteristic
394C8—42no—
395C8—442no—
396C22—24no—
397C22—22no—
398C22—22no—
399C22—24no—
400C22#1062227114yes—
401C22C2×#6693611yescharacteristic
402C22C2×#6693811yescharacteristic
403C22C2×#6694911yescharacteristic
404C22D11×#13512yes—
405C22#1062329912yes—
406C4—81no—
407C4—81no—
408C4—82no—
409C4—224no—
410C4—444no—
411C4—442no—
412C4—881no—
413C4—881no—
414C4#1062227114yes—
415C4C2×#6692911yescharacteristic
416C4C2×#6693211yescharacteristic
417C4C2×#6694211yescharacteristic
418C4C2×#6694211yescharacteristic
419C2—24no—
420C2C2×#1062227111yescharacteristic
421C2#1307840212yes—
422C2#1307852712yes—
423C2#1307893611yescharacteristic
424C2#1307895911yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1735D11
hypocenterC11#23744
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
3. #13070188C2semidirect
4. #13070186C2semidirect
5. #13070181C2semidirect
6. #13070176C2semidirect
353. C11#23744semidirect

Maximal subgroups

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

subgroupindex
#130710982
#130710192
#130701882
#130701862
#130701812
#130701762
#130683332
#130683322
C2×#106221882
C11×#17352
#2374411