Finite Group Databasebeta

← #14779875

Subgroups — #14779875

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071875C211yesmaximal, characteristic
2#13069331C212yesmaximal, complemented
3#13069225C212yesmaximal, complemented
4#13069219C212yesmaximal, complemented
5#13069180C212yesmaximal, complemented
6#13068909C211yesmaximal, characteristic
7#13068793C212yesmaximal, complemented
8#13068598C212yesmaximal, complemented
9C11×#1955C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C23×C11⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C22⋊C8C2212yes—
15C2×C11×C22⋊C8C2212yes—
16C2×C11×#97C2211yescharacteristic
17#10622835C412yes—
18C4×C22⋊Dic11C2212yes—
19C4×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×Dic11⋊C8C2212yes—
25C2×C8×Dic11C2212yes—
26#10622599C411yescharacteristic
27#10622596C411yescharacteristic
28#10622566C411yescharacteristic
29#10622565C412yes—
30#10622562C411yescharacteristic
31C4×Dic11⋊C4C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C8×C11C2312yes—
41C22×C8×C11C2312yes—
42C4×D4×C11—41no—
43C4×D4×C11—41no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11C2×C412yes—
49C2×C22⋊Dic11C2×C412yes—
50C2×C22⋊Dic11C2×C412yes—
51C2×C22⋊Dic11C2×C412yes—
52#66979—41no—
53#66979—41no—
54C2×C4⋊Dic11C2×C411yescharacteristic
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×C4×Dic11C2312yes—
59C2×C4×Dic11C2312yes—
60C22×C11⋊C8—41no—
61C22×C11⋊C8—42no—
62C22×C11⋊C8C2312yes—
63C22×C11⋊C8C2312yes—
64C11×C4⋊C8—41no—
65C11×C22⋊C8—42no—
66C11×C22⋊C8—42no—
67C11×#97—41no—
68C11⋊#95C2×C412yes—
69C11⋊#95C2×C412yes—
70C11⋊#95C2×C411yescharacteristic
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C411yescharacteristic
74C22⋊(C11⋊C8)—42no—
75C22⋊(C11⋊C8)—41no—
76Dic11⋊C8—42no—
77Dic11⋊C8—42no—
78Dic11⋊C8—42no—
79C8×Dic11—42no—
80#23315—111nomaximal, Sylow
81C24×C11C22×C411yescharacteristic
82C24×C11C22×C411yescharacteristic
83C2×D4×C11—22no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11C22×C412yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—21no—
113C42×C11—21no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C22⋊Dic11—24no—
117C22⋊Dic11—42no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—24no—
121Dic11⋊C4—42no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—44no—
133#2395—111no—
134#1955D1111yescharacteristic
135#1939—112no—
136#1923—112no—
137#1923—112no—
138#1917—112no—
139#1869—111no—
140#1850—112no—
141#1798—112no—
142C23×C11—21no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11#13112yes—
152C23×C11C23×C411yescharacteristic
153D4×C11—44no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11H(5,𝔽2)12yes—
170C2×C4×C11H(5,𝔽2)11yescharacteristic
171C2×C4×C11H(5,𝔽2)11yescharacteristic
172C2×C4×C112−1+412yes—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11#13114yes—
185C8×C11—42no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C23×C8—111no—
190C2×C4×D4C2×D1111yescharacteristic
191C2×#117—111no—
192C2×C4⋊C8—112no—
193C2×C4⋊C8—112no—
194C2×C4⋊C8—112no—
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×C22⋊C8—112no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1112yes—
199C2×C22⋊C8C2×D1112yes—
200C2×#97C2×D1111yescharacteristic
201C2×C4×C8—112no—
202#400—111no—
203#399—111no—
204#398—111no—
205#397—112no—
206#397—111no—
207#394—112no—
208C4×C4⋊C4—112no—
209C4×C22⋊C4—112no—
210C4×C22⋊C4—111no—
211#336—112no—
212#336—112no—
213#336—112no—
214#336—112no—
215#336—112no—
216C22×C11—22no—
217C22×C11—24no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—42no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11#51811yescharacteristic
227C22×C11#52012yes—
228C22×C11C2×#13111yescharacteristic
229C22×C11C2×#13112yes—
230C22×C11#56811yescharacteristic
231C4×C11—41no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11#56011yescharacteristic
236C4×C11#56212yes—
237C4×C11#56311yescharacteristic
238Dic11—24no—
239Dic11—42no—
240Dic11—42no—
241Dic11—42no—
242C22×D4C4×D1111yescharacteristic
243C23×C4C22×D1111yescharacteristic
244C23×C4C22×D1111yescharacteristic
245C22×C8—112no—
246C22×C8—112no—
247C22×C8—442no—
248C22×C8—441no—
249C22×C8C22×D1112yes—
250C22×C8C22×D1112yes—
251C4×D4—41no—
252C4×D4—41no—
253#117—441no—
254#117—441no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4C4×D1111yescharacteristic
260C2×C22⋊C4—112no—
261C2×C22⋊C4—112no—
262C2×C22⋊C4—112no—
263C2×C22⋊C4—112no—
264C2×C22⋊C4C4×D1111yescharacteristic
265C2×C22⋊C4C4×D1111yescharacteristic
266C2×C42—112no—
267C2×C42—112no—
268C2×C42C22×D1111yescharacteristic
269C4⋊C8—41no—
270C4⋊C8—442no—
271C4⋊C8—442no—
272C4⋊C8—442no—
273C22⋊C8—42no—
274C22⋊C8—42no—
275C22⋊C8—442no—
276C22⋊C8—441no—
277#97—41no—
278C4×C8—442no—
279#95—112no—
280#95—111no—
281#95—112no—
282#95—111no—
283#95—112no—
284#95—112no—
285C2×C11—42no—
286C2×C11—81no—
287C2×C11#237611yescharacteristic
288C2×C11#297611yescharacteristic
289C2×C11#297911yescharacteristic
290C2×C11#299212yes—
291C2×C11#299412yes—
292C24C2×C4×D1111yescharacteristic
293C24C2×C4×D1111yescharacteristic
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—112no—
306C22×C4—112no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4C2×C4×D1111yescharacteristic
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—444no—
327C4⋊C4—41no—
328C4⋊C4—224no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—442no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—224no—
335C22⋊C4—224no—
336C22⋊C4—224no—
337C22⋊C4—442no—
338C42—21no—
339C42—21no—
340C42—222no—
341C42—222no—
342C42—222no—
343C42—222no—
344C11#2331511yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—22no—
348C23—22no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—22no—
353C23—22no—
354C23#6696012yes—
355C23C22×C4×D1111yescharacteristic
356D4—44no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—114no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4#6703712yes—
385C2×C4#6703711yescharacteristic
386C2×C4#6703711yescharacteristic
387C2×C4#6704312yes—
388C8—42no—
389C8—42no—
390C8—442no—
391C8—442no—
392C22—24no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22#1062301711yescharacteristic
403C22#1062307712yes—
404C22C2×#6696011yescharacteristic
405C22#1062327611yescharacteristic
406C22D11×#13112yes—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—224no—
412C4—442no—
413C4—442no—
414C4—442no—
415C4#1062315212yes—
416C4#1062320311yescharacteristic
417C4#1062325111yescharacteristic
418C2—42no—
419C2—81no—
420C2#1307176611yescharacteristic
421C2#1307766611yescharacteristic
422C2#1307768011yescharacteristic
423C2#1307775112yes—
424C2#1307776912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#23315
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #13069331C2semidirect
3. #13069225C2semidirect
4. #13069219C2semidirect
5. #13069180C2semidirect
7. #13068793C2semidirect
8. #13068598C2semidirect
344. C11#23315semidirect

Maximal subgroups

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

subgroupindex
#130718752
#130693312
#130692252
#130692192
#130691802
#130689092
#130687932
#130685982
C11×#19552
#2331511