Finite Group Databasebeta

← #14758049

Subgroups — #14758049

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic, complemented
3#13069481C212yesmaximal
4#13069346C212yesmaximal, complemented
5#13069316C212yesmaximal, complemented
6#13069312C212yesmaximal, complemented
7C4×#66871C211yesmaximal, characteristic, complemented
8#13068444C211yesmaximal, characteristic, complemented
9#13068441C211yesmaximal, characteristic, complemented
10#13068303C211yesmaximal, characteristic, complemented
11C11×#2319C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#390C2212yes—
16C11×#389C2212yes—
17C11×#388—22no—
18C11×#381—21no—
19C11×#380—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C11×#376C2211yescharacteristic
22C2×#66896C2212yes—
23C2×#66896C2211yescharacteristic
24C4×#4323C418yescomplemented
25C2×#66873C2212yes—
26C2×#66873C2211yescharacteristic
27C2×#66871C2212yes—
28C2×#66871C2211yescharacteristic
29#10622552C2212yes—
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541C2212yes—
32C2×#66867C2212yes—
33C2×#66867C2211yescharacteristic
34C2×C4×C11⋊C8C2212yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622282—22no—
37#10622280—21no—
38#10622277—21no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C4×D4×C11—22no—
47C4×D4×C11C2×C414yes—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11—21no—
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×#4323—24no—
58C2×#4323C2×C414yes—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C22×C11⋊C8C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C4×D44—22no—
70C4×D44C2×C414yes—
71C11×#95—21no—
72C11×#95—22no—
73C11×#95D411yescharacteristic
74C11×#95D411yescharacteristic
75C11×#95D412yes—
76#66896—24no—
77#66896C2×C414yes—
78C11⋊#95—21no—
79C11⋊#95—22no—
80#66873—24no—
81#66873C2×C414yes—
82#66871—24no—
83#66871C2×C414yes—
84#66867—22no—
85#66867—24no—
86C4×C11⋊C8—24no—
87C4×C11⋊C8C2×C414yes—
88#21282—111nomaximal, Sylow
89C24×C11—21no—
90C23×D11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11C22×C412yes—
95C22×C4×C11—21no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—22no—
106C2×D44—21no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44C22×C412yes—
110C2×C4×D11—24no—
111C2×C4×D11—82no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—82no—
116C11×C4⋊C4C22×C412yes—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—82no—
119C11×C22⋊C4—82no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—81no—
123C42×C11C22×C412yes—
124C42×C11#4112yes—
125#4323—28no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—82no—
128(C2×D11)⋊C4—82no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11C22×C412yes—
133Dic11⋊C4—82no—
134C4×Dic11—81no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8C22×C412yes—
139C2×C11⋊C8C22×C412yes—
140C2×C11⋊C8#4114yes—
141C2×C11⋊C8#4114yes—
142C2×C4×D8—111no—
143#2319—111no—
144#2319D1111yescharacteristic, complemented
145#1970—112no—
146#1942—112no—
147#1936—112no—
148#1936—112no—
149C4×#107—111no—
150#1762—111no—
151#1762—111no—
152#1726—111no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11C22×D411yescharacteristic
159C22×D11—22no—
160C22×D11—42no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—41no—
164D4×C11—22no—
165D4×C11—22no—
166D4×C11—42no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—84no—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C4×D412yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4112yes—
187C2×C4×C11C2×#4112yes—
188C2×Dic11—22no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193D44—22no—
194D44—22no—
195D44—42no—
196C4×D11—84no—
197C11⋊C8—22no—
198C11⋊C8—24no—
199C11⋊C8#11714yes—
200C22×D8—111no—
201C2×C4×D4—111no—
202C2×C4×D4C2×D1111yescharacteristic
203C4×D8—118no—
204C2×#107—111no—
205C2×#107—112no—
206C2×#102—111no—
207C2×#102—111no—
208C2×#102—112no—
209C2×#102—112no—
210C2×#97—112no—
211C2×#97—111no—
212C2×C4×C8—111no—
213C2×C4×C8—112no—
214#390—112no—
215#390C2×D1112yes—
216#389—112no—
217#389C2×D1112yes—
218#388—22no—
219#388—222no—
220#381—21no—
221#381—221no—
222#380—21no—
223#380—221no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4C2×D1111yescharacteristic
226#376C2×D1111yescharacteristic
227#340—112no—
228#340—112no—
229#340—112no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11C2×C4×D411yescharacteristic
236C22×C11#53212yes—
237C22×C11#57612yes—
238C22×C11#57611yescharacteristic
239C22×C11#57811yescharacteristic
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—82no—
244C2×D11—82no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—82no—
251C4×C11C2×#11711yescharacteristic
252C4×C11C4×#4111yescharacteristic
253C4×C11#52912yes—
254Dic11—42no—
255Dic11—82no—
256C22×D4—111no—
257C22×D4C22×D1111yescharacteristic
258C23×C4—21no—
259C23×C4—221no—
260C2×D8—114no—
261C2×D8—224no—
262C22×C8—111no—
263C22×C8—111no—
264C22×C8—112no—
265C4×D4—22no—
266C4×D4—114no—
267C4×D4—222no—
268C4×D4C4×D1114yes—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4C22×D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C42—21no—
282C2×C42—221no—
283C2×C42C22×D1112yes—
284C2×C42C22×D1111yescharacteristic
285#107—114no—
286#107—224no—
287#102—114no—
288#102—114no—
289#102—224no—
290#102—224no—
291#97—224no—
292#97—222no—
293C4×C8—114no—
294C4×C8—224no—
295#95—21no—
296#95—22no—
297#95—221no—
298#95—222no—
299#95C22⋊D1111yescharacteristic
300#95C22⋊D1111yescharacteristic
301#95C22⋊D1112yes—
302C2×C11—82no—
303C2×C11#229311yescharacteristic
304C2×C11#294811yescharacteristic
305C2×C11#295111yescharacteristic
306C2×C11#317512yes—
307C2×C11#317612yes—
308D11—82no—
309C24—21no—
310C24—221no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—112no—
315C2×D4—221no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4C2×C4×D1112yes—
319C22×C4—21no—
320C22×C4—24no—
321C22×C4—22no—
322C22×C4—82no—
323C22×C4—221no—
324C22×C4—224no—
325C22×C4—222no—
326C22×C4—882no—
327C22×C4C2×C22⋊D1112yes—
328C22×C4C2×C22⋊D1112yes—
329C22×C4C2×C22⋊D1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332D8—228no—
333C2×C8—112no—
334C2×C8—114no—
335C2×C8—112no—
336C2×C8—114no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—82no—
344C4⋊C4—112no—
345C4⋊C4—221no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—882no—
349C4⋊C4C2×C4×D1112yes—
350C22⋊C4—24no—
351C22⋊C4—82no—
352C22⋊C4—82no—
353C22⋊C4—224no—
354C22⋊C4—882no—
355C22⋊C4—882no—
356C42—22no—
357C42—22no—
358C42—81no—
359C42—881no—
360C42C2×C4×D1112yes—
361C42#433912yes—
362C11#2128211yescharacteristic, complemented, Sylow
363C23—22no—
364C23—42no—
365C23—41no—
366C23—42no—
367C23—41no—
368C23—222no—
369C23—442no—
370C23—441no—
371C23—442no—
372C23—441no—
373C23C22×C22⋊D1111yescharacteristic
374D4—22no—
375D4—22no—
376D4—42no—
377D4—222no—
378D4—222no—
379D4—442no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—84no—
395C2×C4—222no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—884no—
401C2×C4C4×C22⋊D1112yes—
402C2×C4C4×C22⋊D1112yes—
403C2×C4C22×C4×D1111yescharacteristic
404C2×C4C2×#433911yescharacteristic
405C2×C4#41×D1112yes—
406C2×C4#41×D1112yes—
407C8—114no—
408C8—222no—
409C8—224no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—82no—
414C22—82no—
415C22—442no—
416C22—442no—
417C22—442no—
418C22—882no—
419C22—882no—
420C22C2×C4×C22⋊D1111yescharacteristic
421C22#1062336312yes—
422C22#1062336612yes—
423C22#1062336611yescharacteristic
424C22#1062336911yescharacteristic
425C4—22no—
426C4—22no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—82no—
431C4—442no—
432C4—882no—
433C4D11×#11711yescharacteristic
434C4#1062305311yescharacteristic
435C4#1062305912yes—
436C2—82no—
437C2—882no—
438C2#1307107511yescharacteristic
439C2#1307746611yescharacteristic
440C2#1307748911yescharacteristic
441C2#1307924912yes—
442C2#1307926012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2319C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#2319D11
hypocenterC11#21282
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #13071260C2semidirect
4. #13069346C2semidirect
5. #13069316C2semidirect
6. #13069312C2semidirect
7. C4×#66871C2semidirect
8. #13068444C2semidirect
9. #13068441C2semidirect
10. #13068303C2semidirect
11. C11×#2319C2semidirect
24. C4×#4323C4semidirect
144. #2319D11semidirect
362. C11#21282semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
#130712602
#130694812
#130693462
#130693162
#130693122
C4×#668712
#130684442
#130684412
#130683032
C11×#23192
#2128211