Finite Group Databasebeta

← #14653850

Subgroups — #14653850

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076926C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066495C212yesmaximal
4#13066495C212yesmaximal
5C11×C4⋊#95C211yesmaximal, characteristic
6C22×C11×C4⋊C4—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66923C411yescharacteristic, complemented
9C2×C11×#95—21no—
10C2×C11×#95C2212yes—
11#10622825C2211yescharacteristic
12#10622825C2211yescharacteristic
13#10622823—21no—
14#10622823—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622549C411yescharacteristic, complemented
17#10622546—21no—
18#10622546—21no—
19#10622541C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×#66867—21no—
22#10622162—21no—
23C23×C4×C11—22no—
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C2×C11×C4⋊C4—24no—
28C2×C11×C4⋊C4—42no—
29C2×C11×C4⋊C4—42no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8—22no—
46#66923—42no—
47C11×#95—24no—
48C11×#95—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)Q814yes—
57#66867—42no—
58#9887—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—24no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4112yes—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C11×C4⋊C4—48no—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—41no—
93C42×C11—41no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—42no—
108C2×C11⋊C8—42no—
109#2851—111no—
110#1749—111no—
111C4⋊#95D1111yescharacteristic
112#1294—112no—
113#1294—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11C2×C22⋊C411yescharacteristic
119C23×C11#12411yescharacteristic
120C23×C11C4⋊Q811yescharacteristic
121C23×C11AGL(1,ℤ/8)11yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C23×C11#13711yescharacteristic
124C23×C11#13711yescharacteristic
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11#9912yes—
153C2×C4×C11#10412yes—
154C2×C4×C11C4×Q812yes—
155C2×C4×C11C22⋊Q812yes—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C11⋊C8—44no—
169C2×#125—111no—
170C22×C4⋊C4—21no—
171C22×C42C2×D1111yescharacteristic
172C2×C22⋊C8—112no—
173C2×#97—221no—
174#389—111no—
175#389—111no—
176#387—221no—
177#387—221no—
178#385—221no—
179#385—221no—
180#382—111no—
181#380—111no—
182#380—111no—
183C2×#95—21no—
184C2×#95C2×D1112yes—
185#336—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#39111yescharacteristic
199C22×C11C2×#9911yescharacteristic
200C22×C11#41011yescharacteristic
201C22×C11#41711yescharacteristic
202C22×C11#41711yescharacteristic
203C22×C11C2×#10411yescharacteristic
204C22×C11#42111yescharacteristic
205C22×C11#49011yescharacteristic
206C22×C11#49111yescharacteristic
207C22×C11#50111yescharacteristic
208C22×C11#50111yescharacteristic
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—41no—
214C4×C11—41no—
215C4×C11—84no—
216Dic11—81no—
217Dic11—81no—
218Dic11—81no—
219Dic11—81no—
220C23×C4—22no—
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22×D1111yescharacteristic
224C22×C8—222no—
225#125—442no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—42no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C42—42no—
240C2×C42C4×D1111yescharacteristic
241C2×C42C4×D1111yescharacteristic
242C2×C42D4411yescharacteristic
243C2×C42D4411yescharacteristic
244C22⋊C8—114no—
245C22⋊C8—222no—
246#97—442no—
247#95—24no—
248#95—42no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11#150411yescharacteristic
260C2×C11#150911yescharacteristic
261C2×C11#151211yescharacteristic
262C2×C11#151311yescharacteristic
263C2×C11#198611yescharacteristic
264C2×C11#199211yescharacteristic
265C2×C11#199611yescharacteristic
266C24C2×C22⋊D1111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—24no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4C2×C4×D1111yescharacteristic
293C22×C4C2×D4411yescharacteristic
294C22×C4#434112yes—
295C22×C4Q8×D1112yes—
296C2×C8—224no—
297C2×C8—442no—
298C2×C8—442no—
299C4⋊C4—48no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—442no—
305C4⋊C4—442no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C42—22no—
313C42—22no—
314C42—41no—
315C42—41no—
316C11#988711yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×(C2×D11)⋊C411yescharacteristic
322C23#6698511yescharacteristic
323C23#6698511yescharacteristic
324C23#6698911yescharacteristic
325C23#6699511yescharacteristic
326C23#6699511yescharacteristic
327C23#6699711yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4#6686912yes—
368C2×C4#6687012yes—
369C2×C4#6694012yes—
370C2×C4#6695012yes—
371C8—444no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22C2×#6686911yescharacteristic
385C22C2×#6687011yescharacteristic
386C22#1062257911yescharacteristic
387C22#1062257911yescharacteristic
388C22#1062258711yescharacteristic
389C22#1062261811yescharacteristic
390C22#1062261911yescharacteristic
391C22#1062268411yescharacteristic
392C22#1062269311yescharacteristic
393C22#1062269311yescharacteristic
394C22#1062269511yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—84no—
402C4—881no—
403C4—881no—
404C4—881no—
405C4—881no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2#1306711811yescharacteristic
411C2#1306713911yescharacteristic
412C2#1306715211yescharacteristic
413C2#1306715711yescharacteristic
414C2#1306955911yescharacteristic
415C2#1306958411yescharacteristic
416C2#1306960011yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×C4⋊#95C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4⋊#95D11
hypocenterC11#9887
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
8. C2×#66923C4semidirect
16. #10622549C4semidirect
19. #10622541C4semidirect
20. #10622541C4semidirect
316. C11#9887semidirect

Maximal subgroups

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

subgroupindex
#130769262
#130683782
#130664952
C11×C4⋊#952
#988711