Finite Group Databasebeta

← #14805653

Subgroups — #14805653

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic
3#13073986C211yesmaximal, characteristic
4#13070117C212yesmaximal
5#13069994C212yesmaximal
6#13069578C211yesmaximal, characteristic
7#13069379C211yesmaximal, characteristic
8#13069341C212yesmaximal
9#13069291C212yesmaximal
10C4×#66874C211yesmaximal, characteristic
11C11×#2546C211yesmaximal, characteristic
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C11×#398—22no—
17C11×#391—21no—
18C11×#389C2212yes—
19C11×#389C2212yes—
20C4×C11×C4⋊C4C2211yescharacteristic
21#10622843—21no—
22#10622707—24no—
23Q8×C11⋊C8—24no—
24#10622597—22no—
25#10622586—21no—
26C2×#66874C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66874C2211yescharacteristic
29C2×#66872C2212yes—
30C2×#66872C2212yes—
31#10622548C2211yescharacteristic
32#10622542C2212yes—
33#10622541C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×Dic22C2311yescharacteristic
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—44no—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C22×C11⋊C8C2311yescharacteristic
72C4×Dic22—22no—
73C4×Dic22—22no—
74C11×#95—21no—
75C11×#95—22no—
76C11×#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66874—22no—
81#66874—24no—
82#66874Q814yescomplemented
83#66872—24no—
84#66872—24no—
85C4⋊(C11⋊C8)—24no—
86C4⋊(C11⋊C8)D414yes—
87C4×C11⋊C8—22no—
88C4×C11⋊C8—24no—
89#25472—111nomaximal, Sylow
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C2×Q8×C11SD1614yes—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22C2×Q812yes—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—44no—
121C11×C4⋊C4—44no—
122C11×C4⋊C4C2×Q812yes—
123C11×C4⋊C4#4112yes—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—42no—
127C42×C11C2×D412yes—
128C42×C11#4112yes—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134C4⋊Dic11—81no—
135Dic11⋊C4—42no—
136Dic11⋊C4—82no—
137C4×Dic11—42no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8C2×D414yes—
146C2×C11⋊C8C2×Q812yes—
147C2×#475—111no—
148C2×C8×Q8—111no—
149#2582—111no—
150#2546D1111yescharacteristic
151#2088—112no—
152#2066—112no—
153#1990—111no—
154#1948—111no—
155#1941—112no—
156#1933—112no—
157C4×#103—111no—
158C23×C11C22×D411yescharacteristic
159Q8×C11—28no—
160Q8×C11—84no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11#12112yes—
178C2×C4×C11#12112yes—
179C2×C4×C11C2×SD1614yes—
180C2×C4×C11C2×SD1612yes—
181C2×C4×C11#13512yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C112−1+411yescharacteristic
187C2×C4×C112−1+411yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197Dic22—22no—
198Dic22—22no—
199Dic22—41no—
200Dic22—41no—
201C11⋊C8—24no—
202C11⋊C8—22no—
203C11⋊C8—41no—
204C2×C4⋊Q8—21no—
205C2×C4⋊Q8C2×D1111yescharacteristic
206C2×C4×Q8—111no—
207C2×C4×Q8C2×D1111yescharacteristic
208#475—224no—
209C8×Q8—224no—
210C2×#106—112no—
211C2×#106—112no—
212C2×C4⋊C8—111no—
213C2×C4⋊C8—112no—
214C2×#103—111no—
215C2×#103—112no—
216C2×#103—111no—
217C2×C4×C8—112no—
218C2×C4×C8—111no—
219#398—22no—
220#398—222no—
221#391—21no—
222#391—112no—
223#391—221no—
224#389—112no—
225#389—221no—
226#389C2×D1112yes—
227#389C2×D1112yes—
228#384—111no—
229C4×C4⋊C4C2×D1111yescharacteristic
230#340—112no—
231#340—111no—
232#340—112no—
233#340—112no—
234#340—111no—
235C22×C11C2×#12111yescharacteristic
236C22×C11#54811yescharacteristic
237C22×C11D4×Q811yescharacteristic
238C22×C11C22×SD1611yescharacteristic
239C22×C11C2×#13511yescharacteristic
240C22×C11#57711yescharacteristic
241C22×C11#57811yescharacteristic
242C4×C11—24no—
243C4×C11—22no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—82no—
248C4×C11#46514yes—
249C4×C11#53311yescharacteristic
250C4×C11#54111yescharacteristic
251C4×C11#54711yescharacteristic
252C4×C11D4×Q811yescharacteristic
253Dic11—42no—
254Dic11—82no—
255Dic11—81no—
256C22×Q8—21no—
257C22×Q8—111no—
258C22×Q8C22⋊D1111yescharacteristic
259C22×C8—111no—
260C22×C8—112no—
261C22×C8—111no—
262C4⋊Q8—22no—
263C4⋊Q8—22no—
264C4⋊Q8—44no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×Q8—222no—
268C4×Q8—222no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C4⋊C4C22⋊D1112yes—
280C2×C4⋊C4C22×D1112yes—
281C2×C4⋊C4C22×D1111yescharacteristic
282C2×C4⋊C4C22×D1111yescharacteristic
283C2×C42—21no—
284C2×C42—221no—
285C2×C42C22×D1112yes—
286C2×C42C22×D1111yescharacteristic
287#106—224no—
288#106—224no—
289C4⋊C8—114no—
290C4⋊C8—224no—
291#103—114no—
292#103—224no—
293#103—222no—
294C4×C8—224no—
295C4×C8—222no—
296#95—21no—
297#95—22no—
298#95—22no—
299#95—222no—
300#95—222no—
301#95—222no—
302C2×C11#242911yescharacteristic
303C2×C11C2×#46511yescharacteristic
304C2×C11#306311yescharacteristic
305C2×C11#335911yescharacteristic
306C2×C11#336511yescharacteristic
307C2×C11Q8×SD1611yescharacteristic
308C2×C11#338311yescharacteristic
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8—112no—
315C2×Q8—221no—
316C2×Q8—221no—
317C2×Q8—221no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×Q8#432414yes—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—221no—
327C22×C4C2×C22⋊D1112yes—
328C22×C4C2×C22⋊D1112yes—
329C22×C4C2×C22⋊D1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332C2×C8—114no—
333C2×C8—112no—
334C2×C8—221no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C4⋊C4—24no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—44no—
348C4⋊C4—44no—
349C4⋊C4—42no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—442no—
355C4⋊C4—442no—
356C4⋊C4—882no—
357C4⋊C4—881no—
358C4⋊C4Q8×D1112yes—
359C4⋊C4#434312yes—
360C42—22no—
361C42—22no—
362C42—42no—
363C42—442no—
364C42D4×D1112yes—
365C42#434112yes—
366C11#2547211yescharacteristic, complemented, Sylow
367C23C22×C22⋊D1111yescharacteristic
368Q8—28no—
369Q8—84no—
370Q8—222no—
371Q8—222no—
372Q8—441no—
373Q8—441no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—222no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4C2×#432414yes—
400C2×C4C2×#432412yes—
401C2×C4#6699212yes—
402C2×C4#6699212yes—
403C2×C4#6700312yes—
404C2×C4C2×D4×D1111yescharacteristic
405C2×C4C2×#434111yescharacteristic
406C2×C4C2×Q8×D1111yescharacteristic
407C2×C4C2×#434311yescharacteristic
408C2×C4#6704011yescharacteristic
409C2×C4#6704011yescharacteristic
410C8—224no—
411C8—222no—
412C8—441no—
413C22C22×#432411yescharacteristic
414C22C2×#6699211yescharacteristic
415C22Q8×C22⋊D1111yescharacteristic
416C22#1062334811yescharacteristic
417C22C2×#6700311yescharacteristic
418C22#1062336811yescharacteristic
419C22#1062336911yescharacteristic
420C4—22no—
421C4—24no—
422C4—42no—
423C4—42no—
424C4—42no—
425C4—82no—
426C4—442no—
427C4—881no—
428C4—882no—
429C4#1062265414yes—
430C4#1062325711yescharacteristic
431C4#1062325811yescharacteristic
432C4#1062325911yescharacteristic
433C4#1062326211yescharacteristic
434C2#1307221811yescharacteristic
435C2C2×#1062265411yescharacteristic
436C2#1307830311yescharacteristic
437C2#1308125811yescharacteristic
438C2#1308131211yescharacteristic
439C2Q8×#432411yescharacteristic
440C2#1308150311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2546C2
socle, prime radicalC23×C11C22×D4
hypercenter#2546D11
hypocenterC11#25472
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
82. #66874Q8semidirect
366. C11#25472semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×Q8×C11⋊C82
#130739862
#130701172
#130699942
#130695782
#130693792
#130693412
#130692912
C4×#668742
C11×#25462
#2547211