Finite Group Databasebeta

← #14756931

Subgroups — #14756931

Order 2816.

862 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
1C2×C4×#4325C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic
3#13069243C212yesmaximal
4#13069201C212yesmaximal, complemented
5#13068971C212yesmaximal
6#13068884C212yesmaximal, complemented
7C4×#66872C211yesmaximal, characteristic, complemented
8#13068446C211yesmaximal, characteristic, complemented
9#13068444C211yesmaximal, characteristic
10#13068368C211yesmaximal, characteristic, complemented
11C11×#2276C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C4×C11×C4⋊C4—21no—
17C4×C11×C4⋊C4—22no—
18C4×C11×C4⋊C4C2212yes—
19C4×C11×C4⋊C4C2211yescharacteristic
20C11×#376—21no—
21C11×#376C2211yescharacteristic
22C2×#66899C2212yes—
23C2×#66899C2211yescharacteristic
24C4×#4325C418yescomplemented
25C2×#66873C2212yes—
26C2×#66873C2211yescharacteristic
27C2×#66872C2212yes—
28C2×#66872C2211yescharacteristic
29#10622552C2212yes—
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541C2212yes—
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622282—22no—
35#10622280—21no—
36#10622277—21no—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C4×Q8×C11—24no—
46C4×Q8×C11—24no—
47C4×Q8×C11—22no—
48C4×Q8×C11C2×C414yes—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C42×C11—22no—
54C2×C42×C11—21no—
55C2×C42×C11—22no—
56C2×C42×C11—21no—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×#4325—24no—
60C2×#4325C2×C414yes—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C22×C11⋊C8C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C4×D44—22no—
72C4×D44C2×C414yes—
73C11×#95—22no—
74C11×#95—21no—
75C11×#95D411yescharacteristic
76C11×#95D411yescharacteristic
77C11×#95D412yes—
78#66899—24no—
79#66899C2×C414yes—
80C11⋊#95—21no—
81C11⋊#95—22no—
82#66873—24no—
83#66873C2×C414yes—
84#66872—24no—
85#66872C2×C414yes—
86#66867—22no—
87C4×C11⋊C8C2×C414yes—
88#21131—111nomaximal, Sylow
89C23×D11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22×C412yes—
93C2×Q8×C11#4114yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—22no—
104C2×D44—21no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44C22×C412yes—
108C2×C4×D11—24no—
109C2×C4×D11—82no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4C22×C412yes—
115C11×C4⋊C4#4114yes—
116C42×C11—28no—
117C42×C11—24no—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—81no—
121C42×C11—82no—
122C42×C11C22×C412yes—
123C42×C11#4112yes—
124#4325—28no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—82no—
127(C2×D11)⋊C4—82no—
128C4⋊Dic11—21no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11C22×C412yes—
132Dic11⋊C4—82no—
133C4×Dic11—81no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C412yes—
140C2×C11⋊C8C22×C412yes—
141C2×C4×SD16—111no—
142#2319—111no—
143#2276D1111yescharacteristic, complemented
144#1926—112no—
145#1920—112no—
146#1880—112no—
147#1865—112no—
148C4×#106—111no—
149#1763—111no—
150#1762—111no—
151#1746—111no—
152C23×C11C22×D411yescharacteristic
153C22×D11—22no—
154C22×D11—42no—
155C22×D11—41no—
156C22×D11—42no—
157C22×D11—41no—
158Q8×C11—22no—
159Q8×C11—24no—
160Q8×C11#11714yes—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11C4×D412yes—
179C2×C4×C11C4×D412yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11C2×#4112yes—
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189D44—22no—
190D44—22no—
191D44—42no—
192C4×D11—84no—
193C11⋊C8—22no—
194C11⋊C8—22no—
195C11⋊C8—42no—
196C22×SD16—111no—
197C2×C4×Q8C2×D1112yes—
198C2×C4×Q8C2×D1111yescharacteristic
199C2×C4×D4—111no—
200C4×SD16—118no—
201C2×#106—111no—
202C2×#106—112no—
203C2×#103—111no—
204C2×#103—112no—
205C2×#102—111no—
206C2×#102—112no—
207C2×#97—111no—
208C2×C4×C8—111no—
209#390—112no—
210#389—112no—
211#388—222no—
212#381—221no—
213#380—221no—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—22no—
216C4×C4⋊C4—111no—
217C4×C4⋊C4C2×D1112yes—
218C4×C4⋊C4C2×D1111yescharacteristic
219#376—21no—
220#376C2×D1111yescharacteristic
221#340—112no—
222#340—112no—
223#340—112no—
224#336—112no—
225#336—112no—
226C22×C11C2×C4×D411yescharacteristic
227C22×C11#52512yes—
228C22×C11#57711yescharacteristic
229C22×C11#57712yes—
230C22×C11#57711yescharacteristic
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—82no—
235C2×D11—82no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—24no—
239C4×C11—42no—
240C4×C11—44no—
241C4×C11—42no—
242C4×C11—42no—
243C4×C11C2×#11711yescharacteristic
244C4×C11C4×#4111yescharacteristic
245C4×C11#52912yes—
246Dic11—42no—
247Dic11—82no—
248C22×Q8C22×D1111yescharacteristic
249C22×D4—111no—
250C23×C4—221no—
251C2×SD16—114no—
252C2×SD16—224no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—112no—
256C4×Q8—24no—
257C4×Q8—24no—
258C4×Q8—22no—
259C4×Q8C4×D1114yes—
260C4×D4—114no—
261C4×D4—222no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C22×D1111yescharacteristic
268C2×C4⋊C4C22×D1112yes—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C42—22no—
273C2×C42—21no—
274C2×C42—22no—
275C2×C42—21no—
276C2×C42—221no—
277C2×C42C22×D1112yes—
278C2×C42C22×D1111yescharacteristic
279#106—114no—
280#106—224no—
281#103—114no—
282#103—224no—
283#102—114no—
284#102—224no—
285#97—222no—
286C4×C8—114no—
287#95—22no—
288#95—21no—
289#95—221no—
290#95—222no—
291#95C22⋊D1111yescharacteristic
292#95C22⋊D1111yescharacteristic
293#95C22⋊D1112yes—
294C2×C11#229011yescharacteristic
295C2×C11#294911yescharacteristic
296C2×C11#295211yescharacteristic
297C2×C11#312512yes—
298C2×C11#312612yes—
299D11—82no—
300C24—221no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8C2×C4×D1112yes—
304C2×Q8#433914yes—
305C2×D4—112no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—221no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—221no—
313C22×C4—224no—
314C22×C4—222no—
315C22×C4—882no—
316C22×C4C2×C22⋊D1112yes—
317C22×C4C2×C22⋊D1112yes—
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321SD16—228no—
322C2×C8—112no—
323C2×C8—112no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C4⋊C4—28no—
330C4⋊C4—24no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—112no—
334C4⋊C4—221no—
335C4⋊C4—222no—
336C4⋊C4—222no—
337C4⋊C4—882no—
338C4⋊C4C2×C4×D1112yes—
339C4⋊C4#433914yes—
340C22⋊C4—224no—
341C22⋊C4—882no—
342C22⋊C4—882no—
343C42—28no—
344C42—24no—
345C42—22no—
346C42—22no—
347C42—81no—
348C42—82no—
349C42—881no—
350C42C2×C4×D1112yes—
351C42#433912yes—
352C11#2113111yescharacteristic, complemented, Sylow
353C23—222no—
354C23—442no—
355C23—441no—
356C23—441no—
357C23—442no—
358C23C22×C22⋊D1111yescharacteristic
359Q8—22no—
360Q8—24no—
361Q8#6692514yes—
362D4—222no—
363D4—222no—
364D4—442no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—222no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—884no—
388C2×C4C4×C22⋊D1112yes—
389C2×C4C4×C22⋊D1112yes—
390C2×C4C22×C4×D1111yescharacteristic
391C2×C4C2×#433912yes—
392C2×C4C2×#433912yes—
393C2×C4C2×#433911yescharacteristic
394C8—222no—
395C8—222no—
396C8—442no—
397C22—442no—
398C22—442no—
399C22—442no—
400C22—882no—
401C22—882no—
402C22C2×C4×C22⋊D1111yescharacteristic
403C22#1062332212yes—
404C22#1062336711yescharacteristic
405C22#1062336812yes—
406C22#1062336811yescharacteristic
407C4—24no—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—42no—
413C4—42no—
414C4—442no—
415C4—882no—
416C4C2×#6692511yescharacteristic
417C4C4×#433911yescharacteristic
418C4#1062301012yes—
419C2—882no—
420C2#1307105911yescharacteristic
421C2#1307747511yescharacteristic
422C2#1307749711yescharacteristic
423C2#1307889312yes—
424C2#1307890712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2276C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2276D11
hypocenterC11#21131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2276

Complements

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

NH ≅ G/Ntype
4. #13069201C2semidirect
6. #13068884C2semidirect
7. C4×#66872C2semidirect
8. #13068446C2semidirect
10. #13068368C2semidirect
11. C11×#2276C2semidirect
24. C4×#4325C4semidirect
143. #2276D11semidirect
352. C11#21131semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130712602
#130692432
#130692012
#130689712
#130688842
C4×#668722
#130684462
#130684442
#130683682
C11×#22762
#2113111