Finite Group Databasebeta

← #14771440

Subgroups — #14771440

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622493C211yesmaximal, characteristic
2#13071508C212yesmaximal
3#13069350C211yesmaximal, characteristic, complemented
4#13069197C212yesmaximal, complemented
5#13069191C212yesmaximal, complemented
6#13068709C212yesmaximal
7#13068642C211yesmaximal, characteristic
8#107×Dic11C211yesmaximal, characteristic, complemented
9C4×#66882C211yesmaximal, characteristic, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic
11C11×#1942C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C2×#66945C2212yes—
14C2×C11×#107C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#389C2212yes—
18C2×(C2×D11)⋊C8C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21C2×C8×Dic11C2211yescharacteristic
22#10622603—22no—
23#10622600C2212yes—
24#10622598C2212yes—
25C4⋊C4×Dic11—22no—
26C4⋊C4×Dic11C2212yes—
27C2×#66872C2212yes—
28C4×(C2×D11)⋊C4C2211yescharacteristic
29C4×C4⋊Dic11C2212yes—
30#10622493C418yescomplemented
31#10622283—22no—
32#10622264—22no—
33C11×#340C2212yes—
34#10622189C2212yes—
35#10622188C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622162C2211yescharacteristic
40C22×C4×D11C2311yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4D411yescharacteristic
50C2×(C2×D11)⋊C4D411yescharacteristic
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11C2312yes—
53C2×C4⋊Dic11C2312yes—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11C2311yescharacteristic
58C22×C11⋊C8C2311yescharacteristic
59C22×C11⋊C8C2311yescharacteristic
60C2×C8×D11—22no—
61C2×C8×D11—22no—
62C2×C8×D11C2×C414yes—
63#66945—24no—
64#66945C2×C418yes—
65C11×#107—22no—
66C11×#107C2×C414yes—
67C4×C8×C11—22no—
68C11×#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95D411yescharacteristic
74C11⋊#95D411yescharacteristic
75(C2×D11)⋊C8—22no—
76#66882—22no—
77#66882C2×C414yes—
78C8×Dic11—22no—
79#66872C2×C418yes—
80#22614—111nomaximal, Sylow
81C23×D11C2×D411yescharacteristic
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11C2×D411yescharacteristic
90C22×Dic11C2×D411yescharacteristic
91C22×Dic11C2×D411yescharacteristic
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11C22×C412yes—
97C2×C4×D11#4112yes—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11C22×C412yes—
102C2×C8×C11#4112yes—
103C2×C8×C11#4112yes—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—44no—
108C11×C4⋊C4C22×C414yes—
109C42×C11—21no—
110C42×C11—21no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—28no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—82no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—44no—
119C4⋊Dic11C22×C414yes—
120C4×Dic11—28no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C4×Dic11—82no—
124C4×Dic11—82no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8C22×C412yes—
131C8×D11—28no—
132C2×#427—111no—
133#2347—112no—
134#1942—111no—
135#1942D1111yescharacteristic, complemented
136#1919—112no—
137#1919—112no—
138#1825—112no—
139#1808—111no—
140C4×#107—111no—
141C4×#107—111no—
142C8×C22⋊C4—111no—
143C23×C11C22×D411yescharacteristic
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11C4×D412yes—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—24no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11#13512yes—
163C2×C4×C11C23×C411yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C112−1+411yescharacteristic
168C2×C4×C112−1+411yescharacteristic
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—24no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11C4×D412yes—
183C2×Dic11#13512yes—
184C4×D11—22no—
185C4×D11—22no—
186C4×D11—22no—
187C4×D11—22no—
188C8×C11—41no—
189C8×C11#11714yes—
190C11⋊C8—22no—
191C11⋊C8—41no—
192C23×C8—111no—
193C2×#117—112no—
194#427—118no—
195C2×#107—111no—
196C2×#107—111no—
197C2×#107C2×D1111yescharacteristic
198C2×#107C2×D1111yescharacteristic
199C2×#106—112no—
200C2×C22⋊C8—111no—
201C2×C4×C8—111no—
202C2×C4×C8C2×D1111yescharacteristic
203#389—112no—
204#389C2×D1112yes—
205#388—222no—
206#388—222no—
207#383—222no—
208#380—112no—
209C4×C4⋊C4—112no—
210C4×C4⋊C4—112no—
211C4×C4⋊C4—222no—
212C4×C22⋊C4—111no—
213#340—112no—
214#340—112no—
215#340—112no—
216#340—112no—
217#340C2×D1112yes—
218#336—111no—
219#336—111no—
220C22×C11C2×C4×D411yescharacteristic
221C22×C11#54711yescharacteristic
222C22×C11#54711yescharacteristic
223C22×C11C2×#13511yescharacteristic
224C22×C11C2×#13511yescharacteristic
225C22×C11#57611yescharacteristic
226C22×C11#57811yescharacteristic
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C4×C11—22no—
235C4×C11—41no—
236C4×C11—44no—
237C4×C11—82no—
238C4×C11C2×#11711yescharacteristic
239C4×C11#51911yescharacteristic
240C4×C11#55211yescharacteristic
241C4×C11#55211yescharacteristic
242Dic11—22no—
243Dic11—22no—
244Dic11—41no—
245Dic11—44no—
246Dic11—82no—
247C23×C4—111no—
248C22×C8—111no—
249C22×C8—114no—
250C22×C8—111no—
251C22×C8—222no—
252C22×C8—222no—
253C22×C8C22×D1111yescharacteristic
254C22×C8C22×D1111yescharacteristic
255#117—118no—
256#117—224no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4C22×D1112yes—
262C2×C4⋊C4C22×D1112yes—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—222no—
266C2×C22⋊C4—222no—
267C2×C42—111no—
268C2×C42—222no—
269C2×C42—222no—
270C2×C42—222no—
271C2×C42C22×D1111yescharacteristic
272#107—22no—
273#107—114no—
274#107—222no—
275#107C4×D1114yes—
276#106—118no—
277C22⋊C8—222no—
278C4×C8—22no—
279C4×C8—222no—
280#95—22no—
281#95—111no—
282#95—111no—
283#95—222no—
284#95—222no—
285#95—222no—
286#95—222no—
287C2×C11#234411yescharacteristic
288C2×C11C4×#13511yescharacteristic
289C2×C11#295111yescharacteristic
290C2×C11#333911yescharacteristic
291C2×C11#333911yescharacteristic
292C2×C11#334211yescharacteristic
293C2×C11#334211yescharacteristic
294D11—42no—
295C24—111no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—111no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4C23×D1111yescharacteristic
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—112no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—228no—
319C2×C8—221no—
320C2×C8—221no—
321C2×C8—221no—
322C2×C8C2×C4×D1112yes—
323C2×C8#434112yes—
324C2×C8#434312yes—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—44no—
329C4⋊C4—114no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—444no—
334C4⋊C4C2×C4×D1114yes—
335C22⋊C4—222no—
336C22⋊C4—228no—
337C22⋊C4—222no—
338C22⋊C4—882no—
339C42—21no—
340C42—21no—
341C42—228no—
342C42—221no—
343C42—221no—
344C42—882no—
345C42—882no—
346C11#2261411yescharacteristic, complemented, Sylow
347C23—112no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23C2×D4×D1111yescharacteristic
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—112no—
367C2×C4—112no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—224no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4#6696512yes—
386C2×C4C22×C4×D1111yescharacteristic
387C2×C4C2×#434111yescharacteristic
388C2×C4C2×#434311yescharacteristic
389C2×C4#6704011yescharacteristic
390C2×C4#41×D1111yescharacteristic
391C2×C4#6704311yescharacteristic
392C8—41no—
393C8—222no—
394C8—441no—
395C8#6694514yes—
396C22—222no—
397C22—222no—
398C22—222no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22C4×D4×D1111yescharacteristic
404C22#1062314211yescharacteristic
405C22#1062325711yescharacteristic
406C22C2×#6696511yescharacteristic
407C22#1062329711yescharacteristic
408C22D11×#13511yescharacteristic
409C22#1062330011yescharacteristic
410C4—22no—
411C4—44no—
412C4—41no—
413C4—82no—
414C4—222no—
415C4—222no—
416C4—441no—
417C4—444no—
418C4—882no—
419C4C2×#6694511yescharacteristic
420C4#1062310311yescharacteristic
421C4#1062317011yescharacteristic
422C4#1062322511yescharacteristic
423C2—442no—
424C2#1307148411yescharacteristic
425C2C4×#6696511yescharacteristic
426C2#1307749111yescharacteristic
427C2#1308101711yescharacteristic
428C2#1308102111yescharacteristic
429C2#1308104311yescharacteristic
430C2#1308104611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1942C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1942D11
hypocenterC11#22614
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
3. #13069350C2semidirect
4. #13069197C2semidirect
5. #13069191C2semidirect
8. #107×Dic11C2semidirect
9. C4×#66882C2semidirect
11. C11×#1942C2semidirect
30. #10622493C4semidirect
135. #1942D11semidirect
346. C11#22614semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
#130715082
#130693502
#130691972
#130691912
#130687092
#130686422
#107×Dic112
C4×#668822
C8×(C2×D11)⋊C42
C11×#19422
#2261411