Finite Group Databasebeta

← #14812745

Subgroups — #14812745

Order 2816.

714 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
1#13073855C211yesmaximal, characteristic, complemented
2#13071565C211yesmaximal, characteristic
3#13070135C212yesmaximal
4#13070002C212yesmaximal
5#13069387C212yesmaximal, complemented
6#13069379C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13069207C212yesmaximal, complemented
9#13068776C211yesmaximal, characteristic, complemented
10#13068616C211yesmaximal, characteristic
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66979—21no—
14C2×C11×#102C2211yescharacteristic
15C2×C11×#102C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C4×C11×C4⋊C4C2211yescharacteristic
18#10622834C2212yes—
19C2×#66896C2212yes—
20#10622825—21no—
21C2×#66882C2212yes—
22C2×#66882C2212yes—
23C2×Dic11⋊C8C2212yes—
24#10622590C2212yes—
25C4⋊C4×Dic11C2212yes—
26#10622586C2212yes—
27C2×#66872C2212yes—
28#10622564—22no—
29#10622549—21no—
30#10622548C2211yescharacteristic
31#10622548C2211yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33#10622541—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622273—22no—
36C11×#340C2211yescharacteristic
37C11×#340C2211yescharacteristic
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C4×D4×C11—22no—
46C4×D4×C11Q814yes—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55#66979—44no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2312yes—
68C11×#102—22no—
69C11×#102—22no—
70C4×C8×C11—22no—
71C11×#95—21no—
72#66896—42no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95D412yes—
78#66882—24no—
79#66882—42no—
80Dic11⋊C8—24no—
81#66872—42no—
82C4⋊(C11⋊C8)—22no—
83#26087—111nomaximal, Sylow
84C24×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11C2×Q812yes—
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D412yes—
103C22×Dic11C2×D412yes—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11#4112yes—
109C2×C8×C11#4112yes—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4C2×Q812yes—
116C11×C22⋊C4—24no—
117C42×C11—42no—
118C42×C11C2×Q812yes—
119C42×C11#4112yes—
120C22⋊Dic11—44no—
121C22⋊Dic11—82no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—42no—
129C4⋊Dic11—42no—
130C4⋊Dic11—81no—
131C4⋊Dic11—81no—
132Dic11⋊C4—82no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—44no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139#2571—111no—
140#2354—111no—
141#2092—112no—
142#2067—112no—
143#1949—112no—
144#1948—111no—
145#1939—111no—
146#1921—112no—
147#1845—111no—
148#1802—111no—
149C4×#102D1111yescharacteristic
150C23×C11—22no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—41no—
161D4×C11—41no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—48no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11C22⋊Q812yes—
175C2×C4×C11C22⋊Q812yes—
176C2×C4×C11#13512yes—
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11C22×Q811yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C8×C11—22no—
197C8×C11—22no—
198C11⋊C8—42no—
199C2×C4×D4C2×D1111yescharacteristic
200C2×#117—221no—
201C2×#107—112no—
202C2×#107—112no—
203C2×#106—112no—
204C2×C4⋊C8—112no—
205C2×C4⋊C8—111no—
206C2×#102—112no—
207C2×#102C2×D1111yescharacteristic
208C2×#102C2×D1111yescharacteristic
209C2×C4×C8C2×D1111yescharacteristic
210#400—222no—
211#390—112no—
212#389—112no—
213#389—221no—
214#388—222no—
215#384—111no—
216#384—111no—
217#382—112no—
218#382—221no—
219#380—221no—
220C4×C4⋊C4—111no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4C2×D1111yescharacteristic
223#340—112no—
224#340—112no—
225#340C2×D1111yescharacteristic
226#340C2×D1111yescharacteristic
227#336—112no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11C2×C22⋊Q811yescharacteristic
236C22×C11#54711yescharacteristic
237C22×C11#55011yescharacteristic
238C22×C11C2×#13511yescharacteristic
239C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C22×C11#57611yescharacteristic
241C22×C11#57811yescharacteristic
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11#47814yes—
247C4×C11#53311yescharacteristic
248C4×C11#54411yescharacteristic
249C4×C11#55211yescharacteristic
250C4×C11#55311yescharacteristic
251Dic11—42no—
252Dic11—42no—
253Dic11—82no—
254Dic11—82no—
255C22×D4C22×D1111yescharacteristic
256C23×C4—21no—
257C22×C8—112no—
258C22×C8C22×D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260C4×D4—22no—
261C4×D4Dic2214yes—
262#117—444no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4C22×D1111yescharacteristic
273C2×C4⋊C4C22×D1111yescharacteristic
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—21no—
279C2×C42—112no—
280C2×C42—222no—
281C2×C42C22×D1111yescharacteristic
282#107—224no—
283#107—442no—
284#106—442no—
285C4⋊C8—224no—
286C4⋊C8—222no—
287#102—22no—
288#102—22no—
289#102—442no—
290C4×C8—22no—
291#95—21no—
292#95—112no—
293#95—222no—
294#95—222no—
295#95—222no—
296#95—222no—
297C2×C11—82no—
298C2×C11#244111yescharacteristic
299C2×C11C2×#47811yescharacteristic
300C2×C11#308311yescharacteristic
301C2×C11#334111yescharacteristic
302C2×C11#335311yescharacteristic
303C2×C11#339311yescharacteristic
304C2×C11#339911yescharacteristic
305C24—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4C2×Dic2212yes—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—222no—
321C22×C4—222no—
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8#433912yes—
333C2×C8#433912yes—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C4⋊C4—881no—
348C4⋊C4—881no—
349C4⋊C4—882no—
350C4⋊C4C2×Dic2212yes—
351C22⋊C4—24no—
352C22⋊C4—444no—
353C22⋊C4—882no—
354C42—42no—
355C42—222no—
356C42—222no—
357C42—444no—
358C42C2×Dic2212yes—
359C42#434112yes—
360C11#2608711yescharacteristic, complemented, Sylow
361C23—22no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23C2×D4×D1111yescharacteristic
369D4—22no—
370D4—22no—
371D4—41no—
372D4—41no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—48no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4#6693112yes—
398C2×C4#6693112yes—
399C2×C4#6696512yes—
400C2×C4#6696712yes—
401C2×C4C22×Dic2211yescharacteristic
402C2×C4C2×#433911yescharacteristic
403C2×C4C2×#433911yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4#6704211yescharacteristic
406C2×C4#6704311yescharacteristic
407C8—22no—
408C8—22no—
409C8—442no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C2×#6693111yescharacteristic
418C22#1062308211yescharacteristic
419C22#1062308411yescharacteristic
420C22C2×#6696511yescharacteristic
421C22C2×#6696711yescharacteristic
422C22#1062330011yescharacteristic
423C22#1062330211yescharacteristic
424C4—22no—
425C4—42no—
426C4—81no—
427C4—81no—
428C4—442no—
429C4—442no—
430C4—882no—
431C4—882no—
432C4#1062237914yes—
433C4#1062300111yescharacteristic
434C4#1062305011yescharacteristic
435C4#1062307211yescharacteristic
436C4#1062309611yescharacteristic
437C2—82no—
438C2#1307232911yescharacteristic
439C2C2×#1062237911yescharacteristic
440C2#1307846511yescharacteristic
441C2#1308104011yescharacteristic
442C2#1308120211yescharacteristic
443C2#1308160211yescharacteristic
444C2#1308165611yescharacteristic
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#26087
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. #13073855C2semidirect
5. #13069387C2semidirect
6. #13069379C2semidirect
7. #13069334C2semidirect
8. #13069207C2semidirect
9. #13068776C2semidirect
360. C11#26087semidirect

Maximal subgroups

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

subgroupindex
#130738552
#130715652
#130701352
#130700022
#130693872
#130693792
#130693342
#130692072
#130687762
#130686162
C4×C11×#1022
#2608711