Finite Group Databasebeta

← #14779962

Subgroups — #14779962

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66988C211yesmaximal, characteristic
2#13069336C212yesmaximal, complemented
3#13069232C212yesmaximal, complemented
4#13069226C212yesmaximal, complemented
5#13069173C212yesmaximal, complemented
6#13068909C211yesmaximal, characteristic
7#13068793C212yesmaximal, complemented
8#13068594C212yesmaximal, complemented
9C11×#1954C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66988C411yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C23×C11⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2212yes—
16C2×C11×C22⋊C8C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18#10622833C411yescharacteristic
19C4×C22⋊Dic11C2212yes—
20C4×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66879C2212yes—
24C2×Dic11⋊C8C2212yes—
25C2×Dic11⋊C8C2212yes—
26C2×Dic11⋊C8C2212yes—
27#10622591C412yes—
28#10622559C411yescharacteristic
29#10622557C412yes—
30#10622556C411yescharacteristic
31C4×Dic11⋊C4C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C23×Dic11C2×C411yescharacteristic
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C4×D4×C11—41no—
45C4×D4×C11—41no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11C2×C412yes—
51C2×C22⋊Dic11C2×C412yes—
52C2×C22⋊Dic11C2×C411yescharacteristic
53C2×C22⋊Dic11C2×C411yescharacteristic
54#66988—24no—
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×C4×Dic11—41no—
58C2×C4×Dic11—41no—
59C2×C4×Dic11C2×C412yes—
60C2×C4×Dic11C2312yes—
61C2×C4×Dic11C2312yes—
62C22×C11⋊C8—41no—
63C22×C11⋊C8—42no—
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2312yes—
66C11×C4⋊C8—41no—
67C11×C22⋊C8—42no—
68C11×C22⋊C8—42no—
69C4×C8×C11—41no—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C412yes—
74C11⋊#95C2×C412yes—
75C22⋊(C11⋊C8)—41no—
76C22⋊(C11⋊C8)—42no—
77#66879—42no—
78Dic11⋊C8—42no—
79Dic11⋊C8—42no—
80Dic11⋊C8—42no—
81#23322—111nomaximal, Sylow
82C24×C11C22×C411yescharacteristic
83C24×C11C22×C411yescharacteristic
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11M1614yes—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—24no—
101C22×Dic11—22no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11C22×C412yes—
106C22×Dic11C22×C412yes—
107C22×Dic11C22×C412yes—
108C22×Dic11C22×C412yes—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11—21no—
119C42×C11—21no—
120C22⋊Dic11—24no—
121C22⋊Dic11—24no—
122C22⋊Dic11—22no—
123C22⋊Dic11—41no—
124Dic11⋊C4—24no—
125Dic11⋊C4—24no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130C4×Dic11—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—44no—
138C4×#123—111no—
139#1954D1111yescharacteristic
140#1940—112no—
141#1924—112no—
142#1924—112no—
143#1916—112no—
144#1869—111no—
145#1850—112no—
146#1797—112no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11C2×M1612yes—
156C23×C11C2×M1612yes—
157C23×C11C23×C411yescharacteristic
158D4×C11—44no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11C2×M1612yes—
174C2×C4×C11H(5,𝔽2)12yes—
175C2×C4×C11H(5,𝔽2)11yescharacteristic
176C2×C4×C11H(5,𝔽2)11yescharacteristic
177C2×C4×C112−1+412yes—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—44no—
190C2×Dic11—44no—
191C2×Dic11#13114yes—
192C8×C11—42no—
193C8×C11—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C23×C8—111no—
197C2×#123—111no—
198C2×C4×D4C2×D1111yescharacteristic
199C22×C42—111no—
200C2×C4⋊C8—112no—
201C2×C4⋊C8—112no—
202C2×C4⋊C8—112no—
203C2×C4⋊C8C2×D1111yescharacteristic
204C2×C22⋊C8—112no—
205C2×C22⋊C8—111no—
206C2×C22⋊C8C2×D1112yes—
207C2×C22⋊C8C2×D1112yes—
208C2×#97—112no—
209C2×C4×C8C2×D1111yescharacteristic
210#388—112no—
211#387—112no—
212#386—111no—
213#385—111no—
214#381—111no—
215C4×C4⋊C4—112no—
216C4×C22⋊C4—112no—
217C4×C22⋊C4—111no—
218#336—112no—
219#336—112no—
220#336—112no—
221#336—112no—
222#336—112no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—24no—
226C22×C11—24no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11#51811yescharacteristic
234C22×C11#52012yes—
235C22×C11C22×M1611yescharacteristic
236C22×C11C2×#13112yes—
237C22×C11#56811yescharacteristic
238C4×C11—22no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11#56011yescharacteristic
243C4×C11#56212yes—
244C4×C11#56311yescharacteristic
245Dic11—24no—
246Dic11—42no—
247Dic11—42no—
248Dic11—42no—
249C22×D4C4×D1111yescharacteristic
250C23×C4—111no—
251C23×C4—111no—
252C23×C4C22×D1111yescharacteristic
253C23×C4C22×D1111yescharacteristic
254C22×C8—112no—
255C22×C8—112no—
256C22×C8—442no—
257C22×C8—441no—
258C22×C8C22×D1112yes—
259C22×C8C22×D1112yes—
260#123—224no—
261C4×D4—41no—
262C4×D4—41no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4C4×D1111yescharacteristic
266C2×C22⋊C4—111no—
267C2×C22⋊C4—112no—
268C2×C22⋊C4—112no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4C4×D1111yescharacteristic
271C2×C22⋊C4C4×D1111yescharacteristic
272C2×C42—112no—
273C2×C42—112no—
274C2×C42—112no—
275C2×C42—441no—
276C2×C42—441no—
277C2×C42C22×D1111yescharacteristic
278C4⋊C8—41no—
279C4⋊C8—442no—
280C4⋊C8—442no—
281C4⋊C8—442no—
282C22⋊C8—42no—
283C22⋊C8—42no—
284C22⋊C8—442no—
285C22⋊C8—441no—
286#97—442no—
287C4×C8—41no—
288#95—112no—
289#95—112no—
290#95—112no—
291#95—112no—
292#95—112no—
293C2×C11—42no—
294C2×C11—42no—
295C2×C11#237611yescharacteristic
296C2×C11#297311yescharacteristic
297C2×C11#297711yescharacteristic
298C2×C11#299012yes—
299C2×C11#299312yes—
300C24C2×C4×D1111yescharacteristic
301C24C2×C4×D1111yescharacteristic
302C2×D4—41no—
303C2×D4—41no—
304C2×D4#431314yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—112no—
314C22×C4—112no—
315C22×C4—112no—
316C22×C4—112no—
317C22×C4—224no—
318C22×C4—222no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4C2×C4×D1111yescharacteristic
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4C23×D1111yescharacteristic
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—444no—
340C4⋊C4—41no—
341C4⋊C4—224no—
342C4⋊C4—224no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—224no—
346C22⋊C4—222no—
347C22⋊C4—224no—
348C22⋊C4—441no—
349C42—21no—
350C42—21no—
351C42—222no—
352C42—222no—
353C42—222no—
354C42—222no—
355C42—442no—
356C11#2332211yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—22no—
365C23C2×#431312yes—
366C23C2×#431312yes—
367C23C22×C4×D1111yescharacteristic
368D4—44no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—114no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—444no—
396C2×C4—444no—
397C2×C4C2×#431312yes—
398C2×C4#6703712yes—
399C2×C4#6703711yescharacteristic
400C2×C4#6703711yescharacteristic
401C2×C4#6704312yes—
402C8—42no—
403C8—42no—
404C8—442no—
405C8—442no—
406C22—22no—
407C22—22no—
408C22—24no—
409C22—24no—
410C22—42no—
411C22—42no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22#1062301711yescharacteristic
417C22#1062307712yes—
418C22C22×#431311yescharacteristic
419C22#1062327611yescharacteristic
420C22D11×#13112yes—
421C4—22no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—224no—
426C4—442no—
427C4—442no—
428C4—442no—
429C4#1062315212yes—
430C4#1062320311yescharacteristic
431C4#1062325111yescharacteristic
432C2—42no—
433C2—42no—
434C2#1307176611yescharacteristic
435C2#1307764211yescharacteristic
436C2#1307766811yescharacteristic
437C2#1307773912yes—
438C2#1307776212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1954C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1954D11
hypocenterC11#23322
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #13069336C2semidirect
3. #13069232C2semidirect
4. #13069226C2semidirect
5. #13069173C2semidirect
7. #13068793C2semidirect
8. #13068594C2semidirect
356. C11#23322semidirect

Maximal subgroups

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

subgroupindex
C4×#669882
#130693362
#130692322
#130692262
#130691732
#130689092
#130687932
#130685942
C11×#19542
#2332211