Finite Group Databasebeta

← #14649334

Subgroups — #14649334

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622538C211yesmaximal, characteristic
2C2×#10622176C212yesmaximal
3#13066843C211yesmaximal, characteristic
4#13066494C212yesmaximal
5C11×#2855C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C11×#391C411yescharacteristic, complemented
9C11×#391C411yescharacteristic, complemented
10C11×#389C411yescharacteristic, complemented
11C11×#389C411yescharacteristic, complemented
12C11×#387—21no—
13C11×#387—21no—
14C11×#385—21no—
15C11×#381—21no—
16C11×#380C2211yescharacteristic
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21#10622538—24no—
22C2×C4⋊(C11⋊C8)—21no—
23C2×C4×C11⋊C8—21no—
24#10622176—24no—
25C22×Q8×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—22no—
30C11×C22⋊Q8—22no—
31C11×C22⋊Q8—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—22no—
41C2×C42×C11—22no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C22×C11⋊C8—22no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—24no—
55C11⋊#95—22no—
56C11⋊#95—22no—
57C11⋊#95—42no—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)D414yes—
60C4⋊(C11⋊C8)—24no—
61C4×C11⋊C8—24no—
62#9112—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11SD1612yes—
83C22×C4×C11Q1612yes—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C22×C4×C11#4112yes—
88C22×Dic11—24no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11—21no—
109C42×C11—21no—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—42no—
113C2×#431—111no—
114#2855D1111yescharacteristic
115C2×#328—112no—
116#1434—111no—
117#1294—112no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11#12112yes—
124C23×C11C2×SD1611yescharacteristic
125C23×C11C2×Q1611yescharacteristic
126C23×C11#13512yes—
127Q8×C11—82no—
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—24no—
139C2×C4×C11—24no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11#10312yes—
159C2×C4×C11#10312yes—
160C2×C4×C11#10412yes—
161C2×C4×C11C4×D412yes—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12311yescharacteristic
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—82no—
168C2×Dic11—82no—
169C2×Dic11—82no—
170C2×Dic11—82no—
171C11⋊C8—44no—
172C2×C22⋊Q8C2×D1111yescharacteristic
173C22×C42C2×D1111yescharacteristic
174#431—224no—
175C2×C4⋊C8—221no—
176C2×C22⋊C8—112no—
177C2×C4×C8—221no—
178#391Dic1111yescharacteristic, complemented
179#391Dic1111yescharacteristic, complemented
180#389Dic1111yescharacteristic, complemented
181#389Dic1111yescharacteristic, complemented
182#387—21no—
183#387—21no—
184#385—21no—
185#381—21no—
186#380C2×D1111yescharacteristic
187C2×#95—112no—
188C2×#95—221no—
189C2×#95—221no—
190#328—224no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—22no—
199C22×C11#38611yescharacteristic
200C22×C11#41011yescharacteristic
201C22×C11#41011yescharacteristic
202C22×C11C2×#10311yescharacteristic
203C22×C11#41611yescharacteristic
204C22×C11C2×#10411yescharacteristic
205C22×C11#42111yescharacteristic
206C22×C11#46512yes—
207C22×C11#46712yes—
208C4×C11—22no—
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—41no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11—81no—
219Dic11—84no—
220C22×Q8C2×Dic1111yescharacteristic
221C23×C4—222no—
222C23×C4C22⋊D1111yescharacteristic
223C23×C4C22⋊D1111yescharacteristic
224C23×C4C22×D1111yescharacteristic
225C22×C8—222no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C2×Dic1111yescharacteristic
232C2×C4⋊C4C2×Dic1111yescharacteristic
233C2×C4⋊C4C2×Dic1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42C2×Dic1111yescharacteristic
239C2×C42C2×Dic1111yescharacteristic
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22⋊D1111yescharacteristic
242C4⋊C8—224no—
243C22⋊C8—114no—
244C22⋊C8—222no—
245C4×C8—224no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—224no—
254#95—222no—
255#95—222no—
256#95—442no—
257C2×C11—22no—
258C2×C11—22no—
259C2×C11#150011yescharacteristic
260C2×C11#150311yescharacteristic
261C2×C11#151811yescharacteristic
262C2×C11#152111yescharacteristic
263C2×C11#187111yescharacteristic
264C2×C11#189211yescharacteristic
265C2×C11#189911yescharacteristic
266C24C2×C22⋊D1111yescharacteristic
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—41no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—224no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4#432512yes—
289C22×C4#432612yes—
290C22×C4C22⋊Dic1111yescharacteristic
291C22×C4C22⋊Dic1111yescharacteristic
292C22×C4C22⋊Dic1111yescharacteristic
293C22×C4C22⋊Dic1111yescharacteristic
294C22×C4D4×D1112yes—
295C22×C4#434112yes—
296C22×C4C22×Dic1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C2×C8—224no—
299C2×C8—442no—
300C2×C8—442no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C42—22no—
311C42—22no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—21no—
316C11#911211yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23#6699212yes—
322C23C2×#432511yescharacteristic
323C23C2×#432611yescharacteristic
324C23#6700312yes—
325C23C2×C22⋊Dic1111yescharacteristic
326Q8—82no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4#6689912yes—
365C2×C4#6689912yes—
366C2×C4#6690112yes—
367C2×C4D4×Dic1112yes—
368C2×C4#6698811yescharacteristic
369C2×C4#6699011yescharacteristic
370C8—444no—
371C22—22no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22#1062266112yes—
380C22#1062266412yes—
381C22#1062283311yescharacteristic
382C22C2×#6689911yescharacteristic
383C22#1062284611yescharacteristic
384C22C2×#6690111yescharacteristic
385C22#1062284911yescharacteristic
386C22#1062285311yescharacteristic
387C22#1062285311yescharacteristic
388C4—21no—
389C4—22no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—884no—
400C2—22no—
401C2—22no—
402C2#1306710211yescharacteristic
403C2#1306711511yescharacteristic
404C2#1306718011yescharacteristic
405C2#1306719311yescharacteristic
406C2#1306891911yescharacteristic
407C2#1306904011yescharacteristic
408C2#1306907511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2855C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2855D11
hypocenterC11#9112
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
8. C11×#391C4semidirect
9. C11×#391C4semidirect
10. C11×#389C4semidirect
11. C11×#389C4semidirect
178. #391Dic11semidirect
179. #391Dic11semidirect
180. #389Dic11semidirect
181. #389Dic11semidirect
316. C11#9112semidirect

Maximal subgroups

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

subgroupindex
C2×#106225382
C2×#106221762
#130668432
#130664942
C11×#28552
#911211