Finite Group Databasebeta

← #14773539

Subgroups — #14773539

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622485C211yesmaximal, characteristic
2#13071585C212yesmaximal, complemented
3#13069482C211yesmaximal, characteristic
4#13069480C211yesmaximal, characteristic
5#13069243C212yesmaximal, complemented
6#13069241C212yesmaximal, complemented
7#13068779C211yesmaximal, characteristic, complemented
8#13068625C212yesmaximal, complemented
9#107×Dic11C211yesmaximal, characteristic, complemented
10C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
11C4×C11×#107C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13C2×#66946C2212yes—
14C2×C11×#107C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C4×C11×C4⋊C4C2212yes—
18C2×#66885C2212yes—
19C2×#66882C2211yescharacteristic
20C2×Dic11⋊C8C2211yescharacteristic
21C2×C8×Dic11C2211yescharacteristic
22C2×C8×Dic11C2211yescharacteristic
23#10622601C2212yes—
24#10622590C2212yes—
25C4⋊C4×Dic11C2212yes—
26C2×#66873C2212yes—
27C2×#66873C2212yes—
28C2×#66872C2212yes—
29#10622553—22no—
30#10622552C2212yes—
31C4×(C2×D11)⋊C4—22no—
32C4×Dic11⋊C4C2211yescharacteristic
33#10622485C418yescomplemented
34#10622282—22no—
35#10622277—22no—
36C11×#340C2212yes—
37#10622188C2211yescharacteristic
38#10622167C2212yes—
39#10622162C2211yescharacteristic
40C22×D44C2312yes—
41C22×C4×D11—22no—
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11—22no—
47C2×C42×C11C2311yescharacteristic
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11C2312yes—
54C2×Dic11⋊C4D411yescharacteristic
55C2×Dic11⋊C4D411yescharacteristic
56C2×C4×Dic11—22no—
57C2×C4×Dic11C2311yescharacteristic
58C2×C4×Dic11C2311yescharacteristic
59C22×C11⋊C8C2311yescharacteristic
60C22×C11⋊C8C2311yescharacteristic
61C2×D88—22no—
62C2×D88—22no—
63C2×D88C2×C414yes—
64#66946—24no—
65#66946C2×C418yes—
66C11×#107—22no—
67C11×#107C2×C414yes—
68C4×C8×C11—22no—
69C11×#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95D411yescharacteristic
74C11⋊#95D411yescharacteristic
75#66885—42no—
76#66882—22no—
77Dic11⋊C8—22no—
78C8×Dic11—22no—
79C8×Dic11C2×C414yes—
80#66873—42no—
81#66873C2×C418yes—
82#66872—42no—
83#22810—111nomaximal, Sylow
84C23×D11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—22no—
91C22×Dic11C2×D411yescharacteristic
92C22×Dic11C2×D411yescharacteristic
93C22×Dic11C2×D411yescharacteristic
94C22×Dic11C2×D411yescharacteristic
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44C22×C414yes—
101C2×C4×D11—28no—
102C2×C4×D11—82no—
103C2×C4×D11—82no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11C22×C412yes—
108C2×C8×C11#4112yes—
109C2×C8×C11#4112yes—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4C22×C414yes—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—82no—
117(C2×D11)⋊C4—28no—
118(C2×D11)⋊C4—44no—
119(C2×D11)⋊C4—44no—
120(C2×D11)⋊C4—82no—
121(C2×D11)⋊C4—82no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124Dic11⋊C4—22no—
125Dic11⋊C4—22no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—82no—
129C4×Dic11C22×C412yes—
130C4×Dic11#4112yes—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8C22×C412yes—
137D88—28no—
138C2×C4×D8—111no—
139#2357—112no—
140#1970—111no—
141#1970—111no—
142#1926—112no—
143#1926—112no—
144#1846—111no—
145#1804—112no—
146C4×#107—111no—
147C4×#107D1111yescharacteristic, complemented
148C8×C4⋊C4—111no—
149C23×C11C22×D411yescharacteristic
150C22×D11—24no—
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—42no—
156C22×D11—42no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—24no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11#13512yes—
169C2×C4×C11C23×C411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C11H(5,𝔽2)11yescharacteristic
174C2×C4×C112−1+411yescharacteristic
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11C4×D412yes—
188C2×Dic11C4×D412yes—
189C2×Dic11#13512yes—
190D44—24no—
191D44—24no—
192D44—42no—
193D44—42no—
194C4×D11—88no—
195C8×C11—41no—
196C8×C11#11714yes—
197C11⋊C8—22no—
198C11⋊C8—41no—
199C22×D8—111no—
200C2×C4×D4—112no—
201C4×D8—118no—
202C2×#107—111no—
203C2×#107C2×D1111yescharacteristic
204C2×#107C2×D1111yescharacteristic
205C2×#106—112no—
206C2×C4⋊C8—111no—
207C2×#102—112no—
208C2×#102—112no—
209C2×#102—112no—
210C2×C4×C8—111no—
211C2×C4×C8—111no—
212C2×C4×C8C2×D1111yescharacteristic
213#390—112no—
214#390—112no—
215#388—222no—
216#388—222no—
217#382—112no—
218#381—222no—
219C4×C4⋊C4—111no—
220C4×C4⋊C4—112no—
221C4×C4⋊C4C2×D1112yes—
222C4×C22⋊C4—222no—
223#340—112no—
224#340C2×D1112yes—
225#336—111no—
226#336—111no—
227C22×C11C2×C4×D411yescharacteristic
228C22×C11#54711yescharacteristic
229C22×C11#55011yescharacteristic
230C22×C11C2×#13511yescharacteristic
231C22×C11C2×#13511yescharacteristic
232C22×C11#57611yescharacteristic
233C22×C11#57611yescharacteristic
234C2×D11—44no—
235C2×D11—44no—
236C2×D11—44no—
237C2×D11—82no—
238C2×D11—82no—
239C2×D11—82no—
240C2×D11—82no—
241C4×C11—22no—
242C4×C11—41no—
243C4×C11—44no—
244C4×C11—82no—
245C4×C11C2×#11711yescharacteristic
246C4×C11#52011yescharacteristic
247C4×C11#55511yescharacteristic
248C4×C11#55611yescharacteristic
249Dic11—22no—
250Dic11—22no—
251Dic11—22no—
252Dic11—41no—
253Dic11—82no—
254C22×D4—112no—
255C23×C4—222no—
256C2×D8—114no—
257C2×D8—222no—
258C2×D8—222no—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8C22×D1111yescharacteristic
262C22×C8C22×D1111yescharacteristic
263C4×D4—118no—
264C4×D4—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4C22×D1112yes—
269C2×C4⋊C4C22×D1112yes—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—222no—
273C2×C22⋊C4—222no—
274C2×C22⋊C4—222no—
275C2×C42—22no—
276C2×C42—111no—
277C2×C42—111no—
278C2×C42—222no—
279C2×C42C22×D1111yescharacteristic
280#107—22no—
281#107—222no—
282#107C4×D1114yes—
283#106—442no—
284C4⋊C8—222no—
285#102—118no—
286#102—442no—
287#102—442no—
288C4×C8—22no—
289C4×C8—114no—
290C4×C8—222no—
291#95—22no—
292#95—111no—
293#95—111no—
294#95—222no—
295#95—222no—
296#95—222no—
297C2×C11#235411yescharacteristic
298C2×C11C4×#13511yescharacteristic
299C2×C11#294811yescharacteristic
300C2×C11#333911yescharacteristic
301C2×C11#333911yescharacteristic
302C2×C11#339611yescharacteristic
303C2×C11#339611yescharacteristic
304D11—84no—
305C24—222no—
306C2×D4—114no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—222no—
311C2×D4—222no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—228no—
319C22×C4—222no—
320C22×C4—882no—
321C22×C4—882no—
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325D8—228no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—112no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8C2×C4×D1112yes—
336C2×C8#433912yes—
337C2×C8#433912yes—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4C2×C4×D1114yes—
346C22⋊C4—228no—
347C22⋊C4—444no—
348C22⋊C4—444no—
349C22⋊C4—882no—
350C22⋊C4—882no—
351C42—21no—
352C42—21no—
353C42—82no—
354C42—112no—
355C42—112no—
356C42—221no—
357C42—221no—
358C42—882no—
359C11#2281011yescharacteristic, complemented, Sylow
360C23—224no—
361C23—442no—
362C23—442no—
363C23—442no—
364C23—442no—
365C23—442no—
366C23—442no—
367C23C2×D4×D1111yescharacteristic
368D4—224no—
369D4—224no—
370D4—442no—
371D4—442no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—112no—
384C2×C4—112no—
385C2×C4—112no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—888no—
399C2×C4#6697212yes—
400C2×C4C22×C4×D1111yescharacteristic
401C2×C4C2×#433911yescharacteristic
402C2×C4C2×#433911yescharacteristic
403C2×C4#6704011yescharacteristic
404C2×C4#41×D1111yescharacteristic
405C2×C4#6704211yescharacteristic
406C8—41no—
407C8—222no—
408C8—441no—
409C8#6692514yes—
410C22—444no—
411C22—444no—
412C22—444no—
413C22—882no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22#1062303811yescharacteristic
418C22C4×D4×D1111yescharacteristic
419C22#1062308411yescharacteristic
420C22#1062328811yescharacteristic
421C22C2×#6697211yescharacteristic
422C22D11×#13511yescharacteristic
423C22#1062330011yescharacteristic
424C4—22no—
425C4—41no—
426C4—44no—
427C4—82no—
428C4—222no—
429C4—222no—
430C4—222no—
431C4—441no—
432C4—882no—
433C4C2×#6692511yescharacteristic
434C4#1062306311yescharacteristic
435C4#1062309911yescharacteristic
436C4#1062310511yescharacteristic
437C2—884no—
438C2#1307156111yescharacteristic
439C2C4×#6697211yescharacteristic
440C2#1307746311yescharacteristic
441C2#1308101411yescharacteristic
442C2#1308101811yescharacteristic
443C2#1308162611yescharacteristic
444C2#1308162811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#107C2
socleC23×C11C22×D4
prime radicalC22×D88C22
cosocleC22×C4×C11C24
hypercenterC4×#107D11
hypocenterC11#22810
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #13071585C2semidirect
5. #13069243C2semidirect
6. #13069241C2semidirect
7. #13068779C2semidirect
8. #13068625C2semidirect
9. #107×Dic11C2semidirect
10. C8×Dic11⋊C4C2semidirect
11. C4×C11×#107C2semidirect
33. #10622485C4semidirect
147. C4×#107D11semidirect
359. C11#22810semidirect

Maximal subgroups

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

subgroupindex
C2×#106224852
#130715852
#130694822
#130694802
#130692432
#130692412
#130687792
#130686252
#107×Dic112
C8×Dic11⋊C42
C4×C11×#1072
#2281011