Finite Group Databasebeta

← #14808168

Subgroups — #14808168

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×#10622677C211yesmaximal, characteristic, complemented
3C2×#10622682C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal
5#13069812C212yesmaximal
6#13069584C211yesmaximal, characteristic, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13068883C212yesmaximal, complemented
9#13068869C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic
11C11×#2629C211yesmaximal, characteristic
12C2×C11×#125C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66977C2212yes—
15#10623049—24no—
16#10623049—24no—
17C2×#66942—22no—
18C2×#66932—22no—
19C2×#66923C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2212yes—
22C11×#398—22no—
23C11×#396—22no—
24C11×#389C2212yes—
25C11×#384C2211yescharacteristic
26C11×#380C2212yes—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622682—24no—
30#10622677—24no—
31C2×#66874C2212yes—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66872C2212yes—
36C2×#66871C2212yes—
37C2×#66867C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2211yescharacteristic
42#10622162C2211yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×Dic22C2312yes—
45C11×#125—22no—
46C11×#125—22no—
47C11×#117—22no—
48C11×#117—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11C2312yes—
62#66977—24no—
63#66977—24no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72#66942—216no—
73#66932—216no—
74#66923—22no—
75#66923D414yes—
76#66922—22no—
77#66922D414yes—
78C4×Dic22—24no—
79C4×Dic22—24no—
80C11×#95—22no—
81C11×#95—22no—
82C22⋊(C11⋊C8)—22no—
83C22⋊(C11⋊C8)—22no—
84#66874—24no—
85#66874—24no—
86#66874—24no—
87#66874—24no—
88#66872—24no—
89#66871—24no—
90#66867—22no—
91C4×C11⋊C8—22no—
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×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—22no—
107C22×Dic11—22no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22C2×D414yes—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—44no—
120C11×C4⋊C4—82no—
121C11×C4⋊C4—82no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—82no—
124C42×C11—21no—
125C42×C11—21no—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128C22⋊Dic11—28no—
129C4⋊Dic11—28no—
130C4⋊Dic11—22no—
131C4⋊Dic11C2×D414yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—28no—
134Dic11⋊C4—28no—
135C4×Dic11—28no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8#4112yes—
147C2×C11⋊C8#4112yes—
148C2×#541—111no—
149C2×#499—111no—
150C2×#491—111no—
151#2629D1111yescharacteristic
152#2036—112no—
153#2035—112no—
154#1992—111no—
155#1956—111no—
156#1865—112no—
157#1863—112no—
158#1750—111no—
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—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11#12014yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196Dic22—24no—
197Dic22—24no—
198Dic22—42no—
199Dic22—42no—
200C11⋊C8—22no—
201C11⋊C8—22no—
202C11⋊C8—41no—
203C11⋊C8—41no—
204#541—224no—
205#541—224no—
206C2×C4⋊Q8—111no—
207C2×#126—222no—
208C2×#125—111no—
209C2×#125—222no—
210C2×#125C2×D1111yescharacteristic
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⋊C8—111no—
223C2×C22⋊C8—111no—
224C2×#97—111no—
225C2×C4×C8—111no—
226#398—22no—
227#396—22no—
228#389C2×D1112yes—
229#384C2×D1111yescharacteristic
230#380C2×D1112yes—
231#340—112no—
232#340—112no—
233#336—111no—
234#336—111no—
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—82no—
249C4×C11—82no—
250C4×C11#54711yescharacteristic
251C4×C11#54711yescharacteristic
252C4×C11#54811yescharacteristic
253C4×C11#54811yescharacteristic
254Dic11—44no—
255Dic11—44no—
256C22×Q8—112no—
257C23×C4C22×D1111yescharacteristic
258C22×C8—111no—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8—111no—
262C4⋊Q8—114no—
263C4⋊Q8—222no—
264#126—2216no—
265#125—22no—
266#125—22no—
267#125—114no—
268#125—2216no—
269#125—222no—
270C22⋊Q8—224no—
271C22⋊Q8—224no—
272C4×Q8—224no—
273C4×Q8—224no—
274#117—22no—
275#117—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—112no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4C22⋊D1112yes—
285C2×C4⋊C4C22×D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4C22⋊D1112yes—
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—222no—
300C22⋊C8—222no—
301#97—222no—
302C4×C8—222no—
303#95—22no—
304#95—22no—
305C2×C11—81no—
306C2×C11#243211yescharacteristic
307C2×C11#301312yes—
308C2×C11#317411yescharacteristic
309C2×C11#317711yescharacteristic
310C2×C11#324212yes—
311C24C2×C22⋊D1111yescharacteristic
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—22no—
325C22×C4—22no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4C2×C22⋊D1111yescharacteristic
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C23×D1111yescharacteristic
332C2×C8—112no—
333C2×C8—112no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8—221no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—44no—
350C4⋊C4—82no—
351C4⋊C4—82no—
352C4⋊C4—114no—
353C4⋊C4—228no—
354C4⋊C4—228no—
355C4⋊C4—228no—
356C4⋊C4—228no—
357C4⋊C4—222no—
358C22⋊C4—24no—
359C22⋊C4—82no—
360C22⋊C4—228no—
361C42—21no—
362C42—21no—
363C42—228no—
364C42D4×D1112yes—
365C42D4×D1112yes—
366C11#2568311yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—21no—
370C23—22no—
371C23—22no—
372C23C22×C22⋊D1111yescharacteristic
373Q8—224no—
374Q8—224no—
375Q8—442no—
376Q8—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—224no—
396C2×C4—224no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6699014yes—
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4#6704011yescharacteristic
405C2×C4#6704011yescharacteristic
406C2×C4#41×D1111yescharacteristic
407C2×C4#41×D1111yescharacteristic
408C8—222no—
409C8—222no—
410C8—441no—
411C8—441no—
412C22—42no—
413C22—41no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22C2×#6699011yescharacteristic
418C22#1062334711yescharacteristic
419C22#1062336311yescharacteristic
420C22#1062336712yes—
421C22#1062336912yes—
422C4—24no—
423C4—41no—
424C4—42no—
425C4—82no—
426C4—82no—
427C4—444no—
428C4—444no—
429C4#1062316211yescharacteristic
430C4#1062316211yescharacteristic
431C4#1062316411yescharacteristic
432C4#1062316411yescharacteristic
433C2—81no—
434C2#1307224511yescharacteristic
435C2#1307792812yes—
436C2#1307923811yescharacteristic
437C2#1307926911yescharacteristic
438C2#1307988412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2629C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2629D11
hypocenterC11#25683
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2629

Complements

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

NH ≅ G/Ntype
2. C2×#10622677C2semidirect
3. C2×#10622682C2semidirect
6. #13069584C2semidirect
7. #13069417C2semidirect
8. #13068883C2semidirect
9. #13068869C2semidirect
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×#106226772
C2×#106226822
#130698192
#130698122
#130695842
#130694172
#130688832
#130688692
#130683822
C11×#26292
#2568311