Finite Group Databasebeta

← #14808167

Subgroups — #14808167

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic
2C2×#10622296C211yesmaximal, characteristic, complemented
3C2×#10622316C211yesmaximal, characteristic, complemented
4#13074446C211yesmaximal, characteristic
5#13069820C212yesmaximal
6#13069813C212yesmaximal
7#13069585C211yesmaximal, characteristic, complemented
8#13069418C211yesmaximal, characteristic, complemented
9#13068887C212yesmaximal, complemented
10#13068873C212yesmaximal, complemented
11C11×#1750C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66977C2212yes—
14#10623049—24no—
15#10623049—24no—
16C2×#66942—22no—
17C2×#66932—22no—
18C2×#66923C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2212yes—
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26#10622825C2212yes—
27C2×#66882C2212yes—
28C2×#66881C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33#10622597—22no—
34#10622561—22no—
35#10622548C2211yescharacteristic
36#10622541C2212yes—
37#10622316—24no—
38#10622296—24no—
39C11×#336C2211yescharacteristic
40C11×#336C2211yescharacteristic
41#10622189C2212yes—
42#10622189C2212yes—
43C23×C4×C11C2311yescharacteristic
44C22×Dic22C2312yes—
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#117—22no—
50C11×#117—22no—
51C2×C11×C4⋊C4D412yes—
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62#66977—24no—
63#66977—24no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70#66942—216no—
71#66932—216no—
72#66923—22no—
73#66923—22no—
74#66923—22no—
75#66923D414yes—
76#66922—22no—
77#66922D414yes—
78C4×Dic22—24no—
79C4×Dic22—24no—
80C11×C22⋊C8—22no—
81C11×C22⋊C8—22no—
82C11×#97—22no—
83C4×C8×C11—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66882—24no—
87#66881—24no—
88#66880—24no—
89#66880—24no—
90#66880—24no—
91#66880—24no—
92#25683—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22C2×D414yes—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11#4112yes—
125C2×C8×C11#4112yes—
126C11×C4⋊C4—24no—
127C11×C22⋊C4—24no—
128C42×C11—21no—
129C42×C11—21no—
130C42×C11C2×D412yes—
131C42×C11C2×D412yes—
132C22⋊Dic11—28no—
133C22⋊Dic11—82no—
134C4⋊Dic11—28no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—82no—
141C4⋊Dic11C2×D414yes—
142Dic11⋊C4—28no—
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145Dic11⋊C4—44no—
146Dic11⋊C4—82no—
147C4×Dic11—28no—
148C2×#541—111no—
149C2×#499—111no—
150C2×#491—111no—
151#2629—111no—
152#2036—112no—
153#2035—112no—
154#1992—111no—
155#1956—111no—
156#1865—112no—
157#1863—112no—
158#1750D1111yescharacteristic
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C22×D411yescharacteristic
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11#12014yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C112−1+411yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196Dic22—24no—
197Dic22—24no—
198Dic22—42no—
199Dic22—42no—
200C8×C11—22no—
201C8×C11—22no—
202C8×C11—41no—
203C8×C11—41no—
204#541—224no—
205#541—224no—
206C2×C4⋊Q8—111no—
207C2×#126—222no—
208C2×#125—111no—
209C2×#125—111no—
210C2×#125—222no—
211C2×C22⋊Q8—112no—
212C2×C4×Q8—112no—
213C2×#117C2×D1111yescharacteristic
214#499—224no—
215#491—224no—
216C2×#107—112no—
217C2×#106—112no—
218C2×#103—112no—
219C2×#103—112no—
220C2×#103—112no—
221C2×#103—112no—
222C2×C22⋊C8C2×D1111yescharacteristic
223C2×C22⋊C8C2×D1111yescharacteristic
224C2×#97C2×D1111yescharacteristic
225C2×C4×C8C2×D1111yescharacteristic
226#398—222no—
227#396—222no—
228#389—112no—
229#384—111no—
230#380—112no—
231#340—112no—
232#340—112no—
233#336C2×D1111yescharacteristic
234#336C2×D1111yescharacteristic
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11C2×#12011yescharacteristic
241C22×C11#53211yescharacteristic
242C22×C11#53611yescharacteristic
243C22×C11#57712yes—
244C22×C11#57812yes—
245C4×C11—24no—
246C4×C11—41no—
247C4×C11—42no—
248C4×C11#54711yescharacteristic
249C4×C11#54711yescharacteristic
250C4×C11#54811yescharacteristic
251C4×C11#54811yescharacteristic
252Dic11—44no—
253Dic11—44no—
254Dic11—82no—
255Dic11—82no—
256C22×Q8—112no—
257C23×C4C22×D1111yescharacteristic
258C22×C8C22×D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260C22×C8C22×D1111yescharacteristic
261C22×C8C22×D1111yescharacteristic
262C4⋊Q8—114no—
263C4⋊Q8—222no—
264#126—2216no—
265#125—114no—
266#125—2216no—
267#125—222no—
268#125—222no—
269#125—222no—
270C22⋊Q8—224no—
271C22⋊Q8—224no—
272C4×Q8—224no—
273C4×Q8—224no—
274#117—22no—
275#117—22no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4D4412yes—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4D4412yes—
290C2×C42—222no—
291C2×C42C22×D1111yescharacteristic
292C2×C42C22×D1111yescharacteristic
293#107—224no—
294#106—224no—
295#103—224no—
296#103—224no—
297#103—224no—
298#103—224no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301#97—22no—
302C4×C8—22no—
303#95—222no—
304#95—222no—
305C2×C11—81no—
306C2×C11#243211yescharacteristic
307C2×C11#301312yes—
308C2×C11#317411yescharacteristic
309C2×C11#317711yescharacteristic
310C2×C11#324212yes—
311C24C2×D4411yescharacteristic
312C2×Q8—114no—
313C2×Q8—222no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×Q8—222no—
317C2×Q8—222no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4C2×D4411yescharacteristic
329C22×C4C2×D4412yes—
330C22×C4C2×D4412yes—
331C22×C4C23×D1111yescharacteristic
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8#433912yes—
343C2×C8#433912yes—
344C4⋊C4—24no—
345C4⋊C4—114no—
346C4⋊C4—228no—
347C4⋊C4—228no—
348C4⋊C4—228no—
349C4⋊C4—228no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—444no—
356C4⋊C4—882no—
357C4⋊C4—882no—
358C22⋊C4—24no—
359C22⋊C4—228no—
360C22⋊C4—882no—
361C42—21no—
362C42—21no—
363C42—228no—
364C42D4×D1112yes—
365C42D4×D1112yes—
366C11#2568311yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23—21no—
372C23C22×D4411yescharacteristic
373Q8—224no—
374Q8—224no—
375Q8—442no—
376Q8—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—224no—
390C2×C4—224no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6693514yes—
402C2×C4C2×#433911yescharacteristic
403C2×C4C2×#433911yescharacteristic
404C2×C4C2×D4×D1111yescharacteristic
405C2×C4C2×D4×D1111yescharacteristic
406C2×C4#6704311yescharacteristic
407C2×C4#6704311yescharacteristic
408C8—22no—
409C8—22no—
410C8—41no—
411C8—41no—
412C22—42no—
413C22—41no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22#1062300811yescharacteristic
418C22C2×#6693511yescharacteristic
419C22#1062305711yescharacteristic
420C22#1062328212yes—
421C22#1062328412yes—
422C4—24no—
423C4—41no—
424C4—42no—
425C4—444no—
426C4—444no—
427C4—882no—
428C4—882no—
429C4#1062308211yescharacteristic
430C4#1062308211yescharacteristic
431C4#1062308311yescharacteristic
432C4#1062308311yescharacteristic
433C2—81no—
434C2#1307224411yescharacteristic
435C2#1307793412yes—
436C2#1307924411yescharacteristic
437C2#1307927511yescharacteristic
438C2#1307988612yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1750C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1750D11
hypocenterC11#25683
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#10622296C2semidirect
3. C2×#10622316C2semidirect
7. #13069585C2semidirect
8. #13069418C2semidirect
9. #13068887C2semidirect
10. #13068873C2semidirect
366. C11#25683semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106222962
C2×#106223162
#130744462
#130698202
#130698132
#130695852
#130694182
#130688872
#130688732
C11×#17502
#2568311