Finite Group Databasebeta

← #14757137

Subgroups — #14757137

Order 2816.

982 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×#10622473C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic
3C2×#10622321C211yesmaximal, characteristic
4#13071238C212yesmaximal
5#13069360C211yesmaximal, characteristic, complemented
6#13069359C211yesmaximal, characteristic, complemented
7#13069357C211yesmaximal, characteristic, complemented
8#13069348C212yesmaximal, complemented
9#13069346C212yesmaximal, complemented
10#13068334C212yesmaximal
11C11×#1944C211yesmaximal, characteristic, complemented
12C22×#4313C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C2×#66945C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×#66925C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C11×#389C2212yes—
21C2×#66882C2211yescharacteristic
22C2×#66881C2211yescharacteristic
23C2×#66879C2211yescharacteristic
24C2×C8×Dic11C2211yescharacteristic
25#10622602—22no—
26#10622598C2212yes—
27#10622589—22no—
28#10622586C2212yes—
29C2×#66871C2212yes—
30C2×#66871C2212yes—
31#10622541C2212yes—
32C2×C4×C11⋊C8C2211yescharacteristic
33D11×#107—24no—
34#10622473C418yescomplemented
35#10622321—24no—
36#10622281—22no—
37#10622263—22no—
38C11×#340C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×C4×D11—22no—
43C22×C4×D11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4D411yescharacteristic
52C2×(C2×D11)⋊C4D411yescharacteristic
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4D411yescharacteristic
60C2×Dic11⋊C4D411yescharacteristic
61C2×C4×Dic11—22no—
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65C2×#4313—22no—
66C2×#4313—22no—
67C2×#4313Q814yes—
68C2×C8×D11C2×C414yes—
69C2×C8×D11D414yes—
70C2×C8×D11Q814yes—
71#66945—24no—
72#66945C2×C418yes—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—24no—
75#66925—22no—
76#66925—22no—
77C11×#107—22no—
78C11×#106C2×C414yescomplemented
79C11×#97—22no—
80C11×#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66882—22no—
85#66881C2×C414yescomplemented
86#66879—22no—
87C8×Dic11—22no—
88#66871—24no—
89#66871C2×C418yescomplemented
90C4×C11⋊C8—22no—
91#21156—111nomaximal, Sylow
92C23×D11C2×D411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C2×C4×D11—44no—
104C2×C4×D11—82no—
105C2×C4×D11—82no—
106C2×C4×D11C22×C412yes—
107C2×C4×D11C2×D412yes—
108C2×C4×D11C2×Q812yes—
109C2×C4×D11C2×Q812yes—
110C2×C4×D11#4112yes—
111C2×C4×D11#4112yes—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11C22×C412yes—
115C2×C8×C11C2×D412yes—
116C2×C8×C11C2×Q812yes—
117C2×C8×C11C2×Q812yes—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4C22×C414yes—
123C42×C11—21no—
124C42×C11—21no—
125(C2×D11)⋊C4—28no—
126(C2×D11)⋊C4—22no—
127(C2×D11)⋊C4—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—82no—
132C4⋊Dic11C22×C414yes—
133Dic11⋊C4—22no—
134Dic11⋊C4—22no—
135Dic11⋊C4—44no—
136Dic11⋊C4—82no—
137Dic11⋊C4—82no—
138C4×Dic11—28no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8C22×C412yes—
144C2×C11⋊C8C2×D412yes—
145C2×C11⋊C8C2×Q812yes—
146C2×C11⋊C8C2×Q812yes—
147#4313—28no—
148C8×D11C4⋊C4116yescomplemented
149C2×#427—111no—
150C22×#107—111no—
151C2×#405—111no—
152#2317—112no—
153#1944—111no—
154#1944—111no—
155#1944—111no—
156#1944D1111yescharacteristic, complemented
157#1942—112no—
158#1942—112no—
159#1736—112no—
160C23×C11C22×D411yescharacteristic
161C22×D11—22no—
162C22×D11—22no—
163C22×D11C4×D412yes—
164C22×D11#12112yes—
165C22×D11C4⋊Q812yes—
166C2×C4×C11—24no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C23×C411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C22×Q811yescharacteristic
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×Dic11—24no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11C4×D412yes—
193C2×Dic11#12112yes—
194C2×Dic11C4⋊Q812yes—
195C4×D11—88no—
196C4×D11C2×C4⋊C414yes—
197C4×D11C4×Q814yes—
198C4×D11C22⋊Q814yes—
199C4×D11#12514yes—
200C8×C11—22no—
201C8×C11C2×C4⋊C414yes—
202C11⋊C8—22no—
203C11⋊C8C2×C4⋊C414yes—
204C22×M16—111no—
205C23×C8—111no—
206C2×#117—111no—
207C2×#117—112no—
208C22×C4⋊C4—112no—
209#427—118no—
210C2×#107—112no—
211C2×#107—111no—
212C2×#107—112no—
213C2×#107—224no—
214C2×#107C2×D1111yescharacteristic
215C2×#106—111no—
216C2×#106C2×D1111yescharacteristic
217#405—224no—
218C2×#97—111no—
219C2×#97C2×D1111yescharacteristic
220C2×C4×C8—111no—
221C2×C4×C8—111no—
222#389—112no—
223#389—112no—
224#389—112no—
225#389C2×D1112yes—
226#385—222no—
227#385—222no—
228#384—222no—
229#382—222no—
230#340—112no—
231#340—112no—
232#340—112no—
233#340C2×D1112yes—
234C22×C11C2×C4×D411yescharacteristic
235C22×C11C2×#12111yescharacteristic
236C22×C11C2×C4⋊Q811yescharacteristic
237C22×C11#57612yes—
238C22×C11#57812yes—
239C2×D11—24no—
240C2×D11—24no—
241C2×D11—22no—
242C2×D11—22no—
243C2×D11#38914yes—
244C4×C11—44no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—82no—
248C4×C11C22×C4⋊C411yescharacteristic
249C4×C11C2×C4×Q811yescharacteristic
250C4×C11C2×C22⋊Q811yescharacteristic
251C4×C11C2×#12511yescharacteristic
252Dic11—44no—
253Dic11—41no—
254Dic11—41no—
255Dic11—82no—
256Dic11#38914yes—
257C23×C4—111no—
258C23×C4—222no—
259C2×M16—114no—
260C2×M16—222no—
261C2×M16—222no—
262C22×C8—111no—
263C22×C8—114no—
264C22×C8—114no—
265C22×C8—114no—
266C22×C8—111no—
267C22×C8C22×D1111yescharacteristic
268C22×C8C22×D1111yescharacteristic
269#117—118no—
270#117—222no—
271#117—222no—
272#117—224no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—224no—
279C2×C4⋊C4—224no—
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×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—222no—
289C2×C42—111no—
290C2×C42—222no—
291C2×C42C22×D1111yescharacteristic
292#107—22no—
293#107—118no—
294#107—224no—
295#107—222no—
296#106—114no—
297#106C4×D1114yescomplemented
298#97—22no—
299#97—222no—
300C4×C8—222no—
301C4×C8—222no—
302#95—22no—
303#95—222no—
304#95—222no—
305#95—222no—
306C2×C11C2×#38911yescharacteristic
307C2×C11#295112yes—
308C2×C11#305811yescharacteristic
309C2×C11#305911yescharacteristic
310C2×C11#316412yes—
311D11—24no—
312C24—111no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—111no—
316C22×C4—112no—
317C22×C4—112no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—112no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—444no—
327C22×C4—882no—
328C22×C4—882no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332M16—228no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—112no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—1116no—
339C2×C8—112no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8C2×C4×D1112yes—
343C2×C8D4×D1112yes—
344C2×C8Q8×D1112yes—
345C2×C8Q8×D1112yes—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—82no—
350C4⋊C4—114no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—222no—
356C4⋊C4—444no—
357C4⋊C4—882no—
358C4⋊C4—882no—
359C4⋊C4—882no—
360C4⋊C4C2×C4×D1114yes—
361C22⋊C4—222no—
362C22⋊C4—222no—
363C22⋊C4—228no—
364C42—21no—
365C42—21no—
366C42—228no—
367C42—221no—
368C42—221no—
369C11#2115611yescharacteristic, complemented, Sylow
370C23—112no—
371C23—112no—
372C23—112no—
373C23—222no—
374C23—222no—
375C23C2×D4×D1111yescharacteristic
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—112no—
389C2×C4—114no—
390C2×C4—114no—
391C2×C4—114no—
392C2×C4—114no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—224no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—888no—
404C2×C4C22×C4×D1111yescharacteristic
405C2×C4C2×D4×D1111yescharacteristic
406C2×C4C2×Q8×D1111yescharacteristic
407C2×C4C2×Q8×D1111yescharacteristic
408C2×C4#41×D1111yescharacteristic
409C2×C4#41×D1111yescharacteristic
410C8—22no—
411C8—114no—
412C8—222no—
413C8C4⋊C4×D1114yes—
414C22—114no—
415C22—224no—
416C22—224no—
417C22—222no—
418C22—222no—
419C22C4×D4×D1111yescharacteristic
420C22D11×#12111yescharacteristic
421C22D11×C4⋊Q811yescharacteristic
422C22#1062330512yes—
423C22#1062331012yes—
424C4—44no—
425C4—41no—
426C4—41no—
427C4—82no—
428C4—114no—
429C4—444no—
430C4—441no—
431C4—441no—
432C4—882no—
433C4C2×C4⋊C4×D1111yescharacteristic
434C4C4×Q8×D1111yescharacteristic
435C4D11×C22⋊Q811yescharacteristic
436C4D11×#12511yescharacteristic
437C2—224no—
438C2D11×#38911yescharacteristic
439C2#1307748812yes—
440C2#1307826211yescharacteristic
441C2#1307826911yescharacteristic
442C2#1307915112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#21156
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
5. #13069360C2semidirect
6. #13069359C2semidirect
7. #13069357C2semidirect
8. #13069348C2semidirect
9. #13069346C2semidirect
11. C11×#1944C2semidirect
34. #10622473C4semidirect
78. C11×#106C2×C4semidirect
85. #66881C2×C4semidirect
89. #66871C2×C4semidirect
148. C8×D11C4⋊C4semidirect
156. #1944D11semidirect
297. #106C4×D11semidirect
369. C11#21156semidirect

Maximal subgroups

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

subgroupindex
C2×#106224732
C2×D11×#1072
C2×#106223212
#130712382
#130693602
#130693592
#130693572
#130693482
#130693462
#130683342
C11×#19442
#2115611