Finite Group Databasebeta

← #14811856

Subgroups — #14811856

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073642C211yesmaximal, characteristic, complemented
2#13071565C211yesmaximal, characteristic
3#13070000C212yesmaximal
4#13069750C212yesmaximal
5#13069566C212yesmaximal, complemented
6#13069374C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13069190C212yesmaximal, complemented
9#13068744C211yesmaximal, characteristic, complemented
10#13068616C211yesmaximal, characteristic
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66979—21no—
14C2×#66941C2212yes—
15C2×#66922—21no—
16C2×C11×#102C2211yescharacteristic
17C2×C11×#102C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20#10622834C2212yes—
21C2×#66896C2212yes—
22#10622825—21no—
23C2×Dic11⋊C8C2212yes—
24#10622598C2212yes—
25C4⋊C4×Dic11C2212yes—
26C2×#66871C2212yes—
27#10622564—22no—
28#10622548C2211yescharacteristic
29#10622548C2211yescharacteristic
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541—21no—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622269—22no—
34C11×#340C2211yescharacteristic
35C11×#340C2211yescharacteristic
36#10622189C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C22×Dic22—22no—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C4×D4×C11—22no—
47C4×D4×C11Q814yescomplemented
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56#66979—44no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2312yes—
69C22×C11⋊C8C2312yes—
70#66941—24no—
71#66941—42no—
72#66922—44no—
73C11×#102—22no—
74C11×#102—22no—
75C4×C8×C11—22no—
76C11×#95—21no—
77#66896—42no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D412yes—
81Dic11⋊C8—42no—
82#66871—24no—
83C4⋊(C11⋊C8)—22no—
84#26020—111nomaximal, Sylow
85C24×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11C2×Q812yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—24no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×Dic22—44no—
106C2×Dic22—44no—
107C2×Dic22—82no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4C2×Q812yes—
118C11×C4⋊C4#4112yes—
119C11×C4⋊C4#4112yes—
120C11×C22⋊C4—24no—
121C42×C11—42no—
122C42×C11C2×Q812yes—
123C42×C11#4112yes—
124C22⋊Dic11—44no—
125C22⋊Dic11—82no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—44no—
132C4⋊Dic11—42no—
133C4⋊Dic11—42no—
134C4⋊Dic11—81no—
135C4⋊Dic11—81no—
136C4⋊Dic11D814yes—
137Dic11⋊C4—44no—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—44no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144#2551—111no—
145#2354—111no—
146#2067—112no—
147#2023—112no—
148#1988—112no—
149#1947—111no—
150#1939—111no—
151#1918—112no—
152#1834—111no—
153#1802—111no—
154C4×#102D1111yescharacteristic
155C23×C11—22no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C22×D411yescharacteristic
163D4×C11—22no—
164D4×C11—22no—
165D4×C11—41no—
166D4×C11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—48no—
179C2×C4×C11C22⋊Q812yes—
180C2×C4×C11C22⋊Q812yes—
181C2×C4×C11C2×D812yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11C2×D814yes—
201Dic22—88no—
202C8×C11—41no—
203C8×C11—41no—
204C11⋊C8—42no—
205C2×C4⋊Q8—112no—
206C2×C4⋊Q8—221no—
207C2×C4×D4C2×D1111yescharacteristic
208C2×#117—221no—
209C2×#107—112no—
210C2×C4⋊C8—111no—
211C2×C4⋊C8—112no—
212C2×#102—112no—
213C2×#102C2×D1111yescharacteristic
214C2×#102C2×D1111yescharacteristic
215C2×C4×C8C2×D1111yescharacteristic
216#395—222no—
217#390—112no—
218#389—112no—
219#389—221no—
220#388—222no—
221#384—111no—
222#384—111no—
223#380—221no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4—112no—
226C4×C4⋊C4C2×D1111yescharacteristic
227#340—112no—
228#340—112no—
229#340—112no—
230#340—112no—
231#340C2×D1111yescharacteristic
232#340C2×D1111yescharacteristic
233#336—112no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11C2×C22⋊Q811yescharacteristic
242C22×C11#54611yescharacteristic
243C22×C11#54811yescharacteristic
244C22×C11C22×D811yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C22×C11#57711yescharacteristic
247C22×C11#57711yescharacteristic
248C4×C11—22no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11#47414yes—
253C4×C11#53311yescharacteristic
254C4×C11#54411yescharacteristic
255C4×C11#55511yescharacteristic
256C4×C11#55611yescharacteristic
257Dic11—24no—
258Dic11—42no—
259Dic11—82no—
260Dic11—82no—
261C22×Q8—222no—
262C22×D4C22×D1111yescharacteristic
263C23×C4—21no—
264C22×C8—112no—
265C22×C8C22×D1111yescharacteristic
266C22×C8C22×D1111yescharacteristic
267C4⋊Q8—224no—
268C4⋊Q8—444no—
269C4⋊Q8—442no—
270C4×D4—22no—
271C4×D4Dic2214yescomplemented
272#117—444no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4C22×D1111yescharacteristic
284C2×C4⋊C4C22×D1111yescharacteristic
285C2×C4⋊C4C22×D1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C42—21no—
290C2×C42—112no—
291C2×C42—222no—
292C2×C42C22×D1111yescharacteristic
293#107—224no—
294C4⋊C8—222no—
295C4⋊C8—442no—
296#102—22no—
297#102—22no—
298#102—442no—
299C4×C8—22no—
300#95—21no—
301#95—112no—
302#95—222no—
303#95—222no—
304C2×C11—82no—
305C2×C11#243911yescharacteristic
306C2×C11C2×#47411yescharacteristic
307C2×C11#308411yescharacteristic
308C2×C11#329411yescharacteristic
309C2×C11#332911yescharacteristic
310C2×C11#335811yescharacteristic
311C2×C11#336911yescharacteristic
312C24—21no—
313C2×Q8—444no—
314C2×Q8—444no—
315C2×Q8—882no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4C2×Dic2212yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—24no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—112no—
329C22×C4—112no—
330C22×C4—222no—
331C22×C4—222no—
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4C23×D1111yescharacteristic
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—114no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—444no—
354C4⋊C4—444no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—881no—
358C4⋊C4—881no—
359C4⋊C4C2×Dic2212yes—
360C4⋊C4#433912yes—
361C4⋊C4#433912yes—
362C22⋊C4—24no—
363C22⋊C4—444no—
364C22⋊C4—882no—
365C42—42no—
366C42—222no—
367C42—222no—
368C42—444no—
369C42C2×Dic2212yes—
370C42#434112yes—
371C11#2602011yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C2×D4×D1111yescharacteristic
380Q8—888no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—48no—
397C2×C4—114no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4#6693112yes—
410C2×C4#6693112yes—
411C2×C4D8×D1112yes—
412C2×C4#6696812yes—
413C2×C4C22×Dic2211yescharacteristic
414C2×C4C2×#433911yescharacteristic
415C2×C4C2×#433911yescharacteristic
416C2×C4C2×#434111yescharacteristic
417C2×C4#6704211yescharacteristic
418C2×C4#6704311yescharacteristic
419C8—41no—
420C8—41no—
421C8—442no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22C2×#6693111yescharacteristic
430C22#1062308111yescharacteristic
431C22#1062308311yescharacteristic
432C22C2×D8×D1111yescharacteristic
433C22C2×#6696811yescharacteristic
434C22#1062330111yescharacteristic
435C22#1062330111yescharacteristic
436C4—22no—
437C4—42no—
438C4—42no—
439C4—42no—
440C4—224no—
441C4—442no—
442C4—882no—
443C4—882no—
444C4#1062237214yes—
445C4#1062300111yescharacteristic
446C4#1062305011yescharacteristic
447C4#1062307311yescharacteristic
448C4#1062309411yescharacteristic
449C2—82no—
450C2#1307230711yescharacteristic
451C2C2×#1062237211yescharacteristic
452C2#1307847611yescharacteristic
453C2#1308043111yescharacteristic
454C2#1308091211yescharacteristic
455C2#1308124911yescharacteristic
456C2#1308135411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC4×#102D11
hypocenterC11#26020
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #13073642C2semidirect
5. #13069566C2semidirect
6. #13069374C2semidirect
7. #13069334C2semidirect
8. #13069190C2semidirect
9. #13068744C2semidirect
47. C4×D4×C11Q8semidirect
271. C4×D4Dic22semidirect
371. C11#26020semidirect

Maximal subgroups

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

subgroupindex
#130736422
#130715652
#130700002
#130697502
#130695662
#130693742
#130693342
#130691902
#130687442
#130686162
C4×C11×#1022
#2602011