Finite Group Databasebeta

← #14812728

Subgroups — #14812728

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#13070144C212yesmaximal
3#13070004C212yesmaximal
4#13069374C212yesmaximal, complemented
5#13069372C211yesmaximal, characteristic, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069187C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068616C211yesmaximal, characteristic
10C4×#66896C211yesmaximal, characteristic
11C11×#2354C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×C11×#117—21no—
14C2×#66943—21no—
15C11×#390C2212yes—
16C11×#388—22no—
17C11×#384C2211yescharacteristic
18C11×#380—21no—
19C4×C11×C4⋊C4C2212yes—
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66896C2211yescharacteristic
22C2×#66896C2211yescharacteristic
23C2×#66896C2212yes—
24#10622598—21no—
25C2×#66871C2212yes—
26C2×#66871C2212yes—
27C2×#66871C2212yes—
28#10622548C2212yes—
29#10622548C2211yescharacteristic
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622274—22no—
36#10622167C2212yes—
37#10622167C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2211yescharacteristic
40#10622162C2212yes—
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C4×D4×C11—22no—
44C4×D4×C11Q814yes—
45C11×#117—44no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11—22no—
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—21no—
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70#66943—44no—
71C11×#95—22no—
72C11×#95D412yes—
73#66896—22no—
74#66896—22no—
75#66896—42no—
76C11⋊#95—21no—
77C11⋊#95—22no—
78#66871—24no—
79#66871—42no—
80#66871—42no—
81C4⋊(C11⋊C8)—22no—
82C4⋊(C11⋊C8)—24no—
83C4×C11⋊C8—22no—
84#26086—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—24no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—81no—
111C11×C4⋊C4D814yes—
112C11×C4⋊C4C2×Q812yes—
113C11×C22⋊C4—24no—
114C11×C22⋊C4—44no—
115C11×C22⋊C4—82no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—44no—
119C42×C11C2×Q812yes—
120C42×C11#4112yes—
121C4⋊Dic11—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—44no—
128C4⋊Dic11—42no—
129C4⋊Dic11—81no—
130C4⋊Dic11—82no—
131Dic11⋊C4—44no—
132C4×Dic11—42no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8#4112yes—
141C2×C11⋊C8#4112yes—
142#2552—111no—
143#2354D1111yescharacteristic
144#2093—112no—
145#2067—112no—
146#1947—111no—
147#1947—112no—
148#1939—111no—
149#1918—112no—
150#1845—111no—
151#1802—111no—
152C4×#102—111no—
153C23×C11—22no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11C22×D411yescharacteristic
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—41no—
164D4×C11—41no—
165C2×C4×C11—22no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—48no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11C22⋊Q812yes—
180C2×C4×C11C22⋊Q812yes—
181C2×C4×C11C2×D814yes—
182C2×C4×C11C2×D812yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C22×Q811yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11H(5,𝔽2)11yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C11⋊C8—22no—
200C11⋊C8—22no—
201C11⋊C8—42no—
202C2×#125—221no—
203C2×C4×D4C2×D1111yescharacteristic
204C2×#117—21no—
205C2×#107—112no—
206C2×#107—112no—
207C2×#107—112no—
208C2×C4⋊C8—111no—
209C2×C4⋊C8—112no—
210C2×#102—111no—
211C2×#102—111no—
212C2×#102—112no—
213C2×C4×C8—111no—
214#398—222no—
215#390C2×D1112yes—
216#389—112no—
217#389—221no—
218#388—22no—
219#384—111no—
220#384—112no—
221#384C2×D1111yescharacteristic
222#380—21no—
223C4×C4⋊C4—111no—
224C4×C4⋊C4C2×D1112yes—
225C4×C4⋊C4C2×D1111yescharacteristic
226#340—112no—
227#340—112no—
228#340—111no—
229#340—111no—
230#336—112no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11C2×C22⋊Q811yescharacteristic
239C22×C11#54711yescharacteristic
240C22×C11#55011yescharacteristic
241C22×C11C22×D811yescharacteristic
242C22×C11C2×#13711yescharacteristic
243C22×C11#57611yescharacteristic
244C22×C11#57811yescharacteristic
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—82no—
250C4×C11#47414yes—
251C4×C11#53311yescharacteristic
252C4×C11#54411yescharacteristic
253C4×C11#55211yescharacteristic
254C4×C11#55311yescharacteristic
255Dic11—81no—
256Dic11—81no—
257Dic11—82no—
258C22×D4C22×D1111yescharacteristic
259C23×C4—21no—
260C22×C8—111no—
261C22×C8—111no—
262C22×C8—112no—
263#125—444no—
264C4×D4—22no—
265C4×D4Dic2214yes—
266#117—44no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C4⋊C4C22×D1112yes—
280C2×C4⋊C4C22×D1111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C42—22no—
285C2×C42—221no—
286C2×C42C22×D1112yes—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289#107—442no—
290#107—442no—
291C4⋊C8—224no—
292C4⋊C8—222no—
293#102—222no—
294#102—222no—
295#102—442no—
296C4×C8—222no—
297#95—22no—
298#95—221no—
299#95—222no—
300#95C22⋊D1112yes—
301C2×C11—82no—
302C2×C11#244111yescharacteristic
303C2×C11C2×#47411yescharacteristic
304C2×C11#308311yescharacteristic
305C2×C11#333411yescharacteristic
306C2×C11#335711yescharacteristic
307C2×C11#339111yescharacteristic
308C2×C11#339811yescharacteristic
309C24—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4C2×Dic2212yes—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—222no—
324C22×C4C2×C22⋊D1112yes—
325C22×C4C2×C22⋊D1111yescharacteristic
326C22×C4C2×C22⋊D1112yes—
327C22×C4C2×C22⋊D1111yescharacteristic
328C22×C4C23×D1111yescharacteristic
329C2×C8—112no—
330C2×C8—112no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C4⋊C4—22no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—81no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—444no—
351C4⋊C4—444no—
352C4⋊C4—442no—
353C4⋊C4—881no—
354C4⋊C4—882no—
355C4⋊C4#432314yes—
356C4⋊C4C2×Dic2212yes—
357C22⋊C4—24no—
358C22⋊C4—44no—
359C22⋊C4—82no—
360C42—22no—
361C42—22no—
362C42—44no—
363C42—442no—
364C42C2×Dic2212yes—
365C42#433912yes—
366C11#2608611yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23C22×C22⋊D1111yescharacteristic
375D4—22no—
376D4—22no—
377D4—41no—
378D4—41no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—48no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—442no—
401C2×C4—441no—
402C2×C4#6697712yes—
403C2×C4#6697712yes—
404C2×C4C2×#432314yes—
405C2×C4C2×#432312yes—
406C2×C4#6700412yes—
407C2×C4C22×Dic2211yescharacteristic
408C2×C4C2×#433911yescharacteristic
409C2×C4#41×D1111yescharacteristic
410C2×C4#41×D1111yescharacteristic
411C2×C4#6704211yescharacteristic
412C2×C4#6704311yescharacteristic
413C8—222no—
414C8—222no—
415C8—442no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22C2×#6697711yescharacteristic
424C22C22×#432311yescharacteristic
425C22C2×#6700411yescharacteristic
426C22#1062335511yescharacteristic
427C22#1062336511yescharacteristic
428C22#1062336611yescharacteristic
429C22#1062336911yescharacteristic
430C4—24no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—82no—
435C4—881no—
436C4—881no—
437C4—882no—
438C4#1062262014yes—
439C4#1062304811yescharacteristic
440C4#1062305011yescharacteristic
441C4#1062306011yescharacteristic
442C4#1062306111yescharacteristic
443C2—82no—
444C2#1307232311yescharacteristic
445C2C2×#1062262011yescharacteristic
446C2#1307846711yescharacteristic
447C2#1308095911yescharacteristic
448C2#1308123611yescharacteristic
449C2#1308158811yescharacteristic
450C2#1308164711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2354D11
hypocenterC11#26086
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. #13073647C2semidirect
4. #13069374C2semidirect
5. #13069372C2semidirect
6. #13069335C2semidirect
7. #13069187C2semidirect
8. #13068775C2semidirect
366. C11#26086semidirect

Maximal subgroups

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

subgroupindex
#130736472
#130701442
#130700042
#130693742
#130693722
#130693352
#130691872
#130687752
#130686162
C4×#668962
C11×#23542
#2608611