Finite Group Databasebeta

← #14773557

Subgroups — #14773557

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2#13071591C211yesmaximal, characteristic
3#13071581C211yesmaximal, characteristic, complemented
4#13069494C212yesmaximal
5#13069253C212yesmaximal, complemented
6#13069241C212yesmaximal
7#13068778C211yesmaximal, characteristic, complemented
8#13068627C211yesmaximal, characteristic
9#13068512C212yesmaximal, complemented
10#13068486C211yesmaximal, characteristic, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103C2212yes—
17C11×#382C2211yescharacteristic
18#10622843C2212yes—
19C2×#66899C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66879C2212yes—
22C4×#4325C418yescomplemented
23#10622601C2212yes—
24#10622594—22no—
25C4⋊C4×Dic11C2212yes—
26C4⋊C4×Dic11C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66872C2212yes—
29C2×#66872C2211yescharacteristic
30C2×#66871C2212yes—
31#10622550—21no—
32#10622549C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34#10622545—21no—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622283—22no—
37#10622279—21no—
38#10622277—21no—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622188C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C8×C11C2312yes—
46C4×Q8×C11—22no—
47C4×Q8×C11C2×C414yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—22no—
54C2×#4325—22no—
55C2×#4325C2×C414yes—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11D412yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4×Dic11—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66C22×C11⋊C8C2311yescharacteristic
67C4×D44—22no—
68C4×D44C2×C414yes—
69C11×C4⋊C8—22no—
70C11×#103—42no—
71C11×#95—21no—
72C11×#95—21no—
73#66899C2×C414yes—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D411yescharacteristic
81C11⋊#95D411yescharacteristic
82#66885—42no—
83#66879—24no—
84#66873C2×C414yes—
85#66872—42no—
86#66872C2×C414yes—
87#66871—24no—
88C4×C11⋊C8C2×C414yes—
89#22812—111nomaximal, Sylow
90C23×D11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11C22×C412yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11C2×D412yes—
106C22×Dic11C2×D412yes—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44C22×C412yes—
113C2×C4×D11—24no—
114C2×C4×D11—82no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4C22×C412yes—
123C42×C11—24no—
124C42×C11C22×C412yes—
125C42×C11#4112yes—
126#4325—28no—
127(C2×D11)⋊C4—24no—
128(C2×D11)⋊C4—44no—
129(C2×D11)⋊C4—82no—
130C4⋊Dic11—21no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134C4⋊Dic11C22×C412yes—
135C4×Dic11—22no—
136C4×Dic11—22no—
137C4×Dic11—44no—
138C4×Dic11—82no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8C22×C412yes—
142C2×C11⋊C8C22×C412yes—
143C2×C11⋊C8#4112yes—
144C2×C11⋊C8#4112yes—
145C2×C4×SD16—111no—
146#2357—111no—
147#2356—111no—
148#1973—112no—
149#1927—112no—
150#1926—112no—
151#1846—111no—
152#1805D1111yescharacteristic, complemented
153#1804—111no—
154#1776—112no—
155#1770—111no—
156C23×C11C22×D411yescharacteristic
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—42no—
161C22×D11—42no—
162Q8×C11—22no—
163Q8×C11—22no—
164Q8×C11—41no—
165Q8×C11—41no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195D44—22no—
196D44—22no—
197D44—41no—
198D44—41no—
199C4×D11—84no—
200C8×C11—42no—
201C11⋊C8—22no—
202C11⋊C8#11714yes—
203C22×SD16—111no—
204C2×C4×Q8C2×D1111yescharacteristic
205C2×C4×D4—111no—
206C4×SD16—118no—
207C2×#107—112no—
208C2×#106—111no—
209C2×#106—112no—
210C2×C4⋊C8C2×D1111yescharacteristic
211C2×#103—111no—
212C2×#103C2×D1112yes—
213C2×#102—111no—
214C2×#102—112no—
215C2×#97—112no—
216C2×C4×C8—111no—
217#391—112no—
218#390—112no—
219#388—222no—
220#387—222no—
221#383—221no—
222#382—111no—
223#382C2×D1111yescharacteristic
224#381—221no—
225C4×C4⋊C4—111no—
226C4×C4⋊C4—112no—
227C4×C4⋊C4—112no—
228C4×C22⋊C4—221no—
229#376—221no—
230#340—112no—
231#340C2×D1112yes—
232#336—112no—
233C22×C11C2×C4×D411yescharacteristic
234C22×C11#54711yescharacteristic
235C22×C11#55011yescharacteristic
236C22×C11#57512yes—
237C22×C11#57712yes—
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—82no—
242C2×D11—82no—
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—82no—
248C4×C11C2×#11711yescharacteristic
249C4×C11#52011yescharacteristic
250C4×C11#55511yescharacteristic
251C4×C11#55611yescharacteristic
252Dic11—42no—
253Dic11—42no—
254Dic11—42no—
255Dic11—82no—
256C22×Q8C22×D1111yescharacteristic
257C22×D4—111no—
258C23×C4—221no—
259C2×SD16—114no—
260C2×SD16—222no—
261C2×SD16—222no—
262C22×C8—111no—
263C22×C8—111no—
264C22×C8C22×D1112yes—
265C4×Q8—22no—
266C4×Q8C4×D1114yes—
267C4×D4—114no—
268C4×D4—222no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4C22×D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—221no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—21no—
279C2×C42—112no—
280C2×C42—222no—
281C2×C42—222no—
282C2×C42C22×D1111yescharacteristic
283#107—224no—
284#106—114no—
285#106—442no—
286C4⋊C8—22no—
287#103—42no—
288#103—114no—
289#102—114no—
290#102—442no—
291#97—224no—
292C4×C8—114no—
293#95—21no—
294#95—21no—
295#95—111no—
296#95—111no—
297#95—222no—
298#95—222no—
299#95—222no—
300#95—222no—
301#95—221no—
302#95—221no—
303C2×C11#235411yescharacteristic
304C2×C11#294311yescharacteristic
305C2×C11#294911yescharacteristic
306C2×C11#335112yes—
307C2×C11#340112yes—
308D11—82no—
309C24—221no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8C2×C4×D1112yes—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—112no—
326C22×C4—112no—
327C22×C4—221no—
328C22×C4—224no—
329C22×C4—222no—
330C22×C4—882no—
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1111yescharacteristic
333C22×C4C23×D1111yescharacteristic
334SD16—228no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—112no—
341C2×C8—112no—
342C2×C8—221no—
343C2×C8—221no—
344C4⋊C4—24no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—112no—
349C4⋊C4—221no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—442no—
353C4⋊C4C2×C4×D1112yes—
354C22⋊C4—224no—
355C22⋊C4—444no—
356C22⋊C4—882no—
357C42—24no—
358C42—222no—
359C42—222no—
360C42—444no—
361C42—882no—
362C42C2×C4×D1112yes—
363C42#434112yes—
364C11#2281211yescharacteristic, complemented, Sylow
365C23—222no—
366C23—442no—
367C23—442no—
368C23—441no—
369C23—441no—
370C23C2×D4×D1111yescharacteristic
371Q8—22no—
372Q8—22no—
373Q8—41no—
374Q8—41no—
375D4—222no—
376D4—222no—
377D4—441no—
378D4—441no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—884no—
401C2×C4(C22⋊D11)⋊C412yes—
402C2×C4(C22⋊D11)⋊C412yes—
403C2×C4C22×C4×D1111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4#6703711yescharacteristic
406C2×C4#6704011yescharacteristic
407C2×C4#41×D1111yescharacteristic
408C2×C4#41×D1111yescharacteristic
409C8—42no—
410C8—114no—
411C8—222no—
412C22—442no—
413C22—442no—
414C22—442no—
415C22—882no—
416C22—882no—
417C22C2×(C22⋊D11)⋊C411yescharacteristic
418C22#1062313011yescharacteristic
419C22#1062316211yescharacteristic
420C22#1062329912yes—
421C22#1062330912yes—
422C4—22no—
423C4—22no—
424C4—42no—
425C4—42no—
426C4—82no—
427C4—442no—
428C4—442no—
429C4—442no—
430C4—882no—
431C4#1062303511yescharacteristic
432C4D11×#11711yescharacteristic
433C4#1062314711yescharacteristic
434C4#1062317211yescharacteristic
435C2—882no—
436C2#1307156011yescharacteristic
437C2#1307741211yescharacteristic
438C2#1307747111yescharacteristic
439C2#1308117312yes—
440C2#1308168612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1805D11
hypocenterC11#22812
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
3. #13071581C2semidirect
5. #13069253C2semidirect
7. #13068778C2semidirect
9. #13068512C2semidirect
10. #13068486C2semidirect
11. C11×#1805C2semidirect
22. C4×#4325C4semidirect
152. #1805D11semidirect
364. C11#22812semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130715912
#130715812
#130694942
#130692532
#130692412
#130687782
#130686272
#130685122
#130684862
C11×#18052
#2281211