Finite Group Databasebeta

← #14812732

Subgroups — #14812732

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073647C211yesmaximal, characteristic, complemented
2#13071563C211yesmaximal, characteristic
3#13070143C212yesmaximal
4#13070003C212yesmaximal
5#13069375C212yesmaximal, complemented
6#13069375C211yesmaximal, characteristic, complemented
7#13069188C212yesmaximal, complemented
8#13068776C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×#66943—21no—
14C2×C4×D44C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C2×#66885C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×#66885C2212yes—
22C2×#66882C2212yes—
23C2×#66882C2212yes—
24C2×#66882C2212yes—
25#10622600—21no—
26#10622598—21no—
27#10622552C2212yes—
28#10622548C2212yes—
29#10622548C2211yescharacteristic
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622541C2212yes—
34#10622283—22no—
35#10622274—22no—
36C11×#336C2212yes—
37#10622189C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2211yescharacteristic
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×C8×C11C2312yes—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67#66945—44no—
68#66943—44no—
69C4×D44—22no—
70C4×D44Q814yes—
71C11×C4⋊C8—24no—
72C11×C4⋊C8—22no—
73C4×C8×C11—22no—
74C11×#95D412yes—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78#66885—22no—
79#66885—22no—
80#66885—42no—
81#66882—24no—
82#66882—42no—
83#66882—42no—
84#26086—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44C2×Q812yes—
102C2×C4×D11—24no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—21no—
110C2×C8×C11—22no—
111C2×C8×C11—21no—
112C2×C8×C11#4112yes—
113C2×C8×C11#4112yes—
114C11×C4⋊C4—22no—
115C11×C4⋊C4D814yes—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11C2×Q812yes—
119C42×C11#4112yes—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—82no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—44no—
133C4⋊Dic11—42no—
134C4⋊Dic11—42no—
135C4⋊Dic11—81no—
136C4⋊Dic11—81no—
137C4⋊Dic11—82no—
138C4⋊Dic11C2×Q812yes—
139Dic11⋊C4—44no—
140C4×Dic11—42no—
141C4×Dic11—44no—
142#2552—111no—
143#2354—111no—
144#2093—112no—
145#2067—112no—
146#1947—112no—
147#1947—111no—
148#1939D1111yescharacteristic, complemented
149#1918—112no—
150#1845—111no—
151#1802—111no—
152C4×#102—111no—
153C23×C11C22×D411yescharacteristic
154C22×D11—22no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C2×C4×C11—22no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11C22⋊Q812yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11C2×D814yes—
171C2×C4×C11C2×D812yes—
172C2×C4×C11#13712yes—
173C2×C4×C11C22×Q811yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11H(5,𝔽2)11yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194D44—22no—
195D44—22no—
196D44—41no—
197D44—41no—
198C4×D11—48no—
199C8×C11—22no—
200C8×C11—22no—
201C8×C11—42no—
202C2×#125—221no—
203C2×C4×D4—111no—
204C2×#117—221no—
205C2×#107—112no—
206C2×#107—112no—
207C2×#107—112no—
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×C4⋊C8C2×D1112yes—
210C2×#102—111no—
211C2×#102—111no—
212C2×#102—112no—
213C2×C4×C8C2×D1111yescharacteristic
214#398—222no—
215#390—112no—
216#389—112no—
217#389—221no—
218#388—222no—
219#384—111no—
220#384—112no—
221#384—111no—
222#380—221no—
223C4×C4⋊C4—112no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4C2×D1111yescharacteristic
226#340—112no—
227#340—112no—
228#340—111no—
229#340—111no—
230#336C2×D1112yes—
231C22×C11C2×C22⋊Q811yescharacteristic
232C22×C11#54711yescharacteristic
233C22×C11#55011yescharacteristic
234C22×C11C22×D811yescharacteristic
235C22×C11C2×#13711yescharacteristic
236C22×C11#57611yescharacteristic
237C22×C11#57811yescharacteristic
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11#47414yes—
249C4×C11#53311yescharacteristic
250C4×C11#54411yescharacteristic
251C4×C11#55211yescharacteristic
252C4×C11#55311yescharacteristic
253Dic11—42no—
254Dic11—81no—
255Dic11—81no—
256Dic11—82no—
257Dic11—82no—
258C22×D4—111no—
259C23×C4—221no—
260C22×C8C22×D1112yes—
261C22×C8C22×D1111yescharacteristic
262C22×C8C22×D1111yescharacteristic
263#125—444no—
264C4×D4—114no—
265C4×D4—222no—
266#117—444no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4D4411yescharacteristic
280C2×C4⋊C4D4411yescharacteristic
281C2×C22⋊C4—221no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C42—222no—
285C2×C42—221no—
286C2×C42C22×D1112yes—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289#107—442no—
290#107—442no—
291C4⋊C8—24no—
292C4⋊C8—22no—
293#102—222no—
294#102—222no—
295#102—442no—
296C4×C8—22no—
297#95—222no—
298#95—221no—
299#95—222no—
300#95D4412yes—
301C2×C11#244111yescharacteristic
302C2×C11C2×#47411yescharacteristic
303C2×C11#308311yescharacteristic
304C2×C11#333411yescharacteristic
305C2×C11#335711yescharacteristic
306C2×C11#339111yescharacteristic
307C2×C11#339811yescharacteristic
308D11—82no—
309C24—221no—
310C2×D4—112no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—221no—
316C22×C4—221no—
317C22×C4—224no—
318C22×C4—221no—
319C22×C4—222no—
320C22×C4—221no—
321C22×C4—222no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4C2×D4412yes—
325C22×C4C2×D4411yescharacteristic
326C22×C4C2×D4412yes—
327C22×C4C2×D4411yescharacteristic
328C22×C4C23×D1111yescharacteristic
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8#434112yes—
337C2×C8#434312yes—
338C4⋊C4—22no—
339C4⋊C4—112no—
340C4⋊C4—221no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—221no—
347C4⋊C4—222no—
348C4⋊C4—221no—
349C4⋊C4—442no—
350C4⋊C4—444no—
351C4⋊C4—444no—
352C4⋊C4—442no—
353C4⋊C4—881no—
354C4⋊C4—881no—
355C4⋊C4—882no—
356C4⋊C4D8814yes—
357C22⋊C4—224no—
358C22⋊C4—444no—
359C22⋊C4—882no—
360C42—22no—
361C42—22no—
362C42—444no—
363C42—442no—
364C42#434112yes—
365C42Q8×D1112yes—
366C11#2608611yescharacteristic, complemented, Sylow
367C23—222no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23C22×D4411yescharacteristic
375D4—222no—
376D4—222no—
377D4—441no—
378D4—441no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—222no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—448no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4#6695012yes—
403C2×C4#6695012yes—
404C2×C4C2×D8814yes—
405C2×C4C2×D8812yes—
406C2×C4#6696212yes—
407C2×C4C2×#434111yescharacteristic
408C2×C4C2×#434111yescharacteristic
409C2×C4C2×Q8×D1111yescharacteristic
410C2×C4C2×#434311yescharacteristic
411C2×C4#6704211yescharacteristic
412C2×C4#6704311yescharacteristic
413C8—22no—
414C8—22no—
415C8—42no—
416C22—442no—
417C22—442no—
418C22—442no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22C2×#6695011yescharacteristic
424C22#1062308611yescharacteristic
425C22#1062310811yescharacteristic
426C22C22×D8811yescharacteristic
427C22C2×#6696211yescharacteristic
428C22#1062328311yescharacteristic
429C22#1062328411yescharacteristic
430C4—24no—
431C4—22no—
432C4—42no—
433C4—442no—
434C4—881no—
435C4—882no—
436C4—881no—
437C4—882no—
438C4#1062245914yes—
439C4#1062314911yescharacteristic
440C4#1062317311yescharacteristic
441C4#1062322011yescharacteristic
442C4#1062325911yescharacteristic
443C2—882no—
444C2#1307232711yescharacteristic
445C2C2×#1062245911yescharacteristic
446C2#1307846911yescharacteristic
447C2#1308096411yescharacteristic
448C2#1308124311yescharacteristic
449C2#1308159111yescharacteristic
450C2#1308164911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#26086
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #13073647C2semidirect
5. #13069375C2semidirect
6. #13069375C2semidirect
7. #13069188C2semidirect
8. #13068776C2semidirect
11. C11×#1939C2semidirect
148. #1939D11semidirect
366. C11#26086semidirect

Maximal subgroups

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

subgroupindex
#130736472
#130715632
#130701432
#130700032
#130693752
#130691882
#130687762
#130686172
C4×#668852
C11×#19392
#2608611