Finite Group Databasebeta

← #14737409

Subgroups — #14737409

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079764C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic
4#13068198C212yesmaximal, complemented
5#13068156C212yesmaximal, complemented
6#13068074C212yesmaximal, complemented
7#13068032C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9C2×#10622119C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623008C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#446—22no—
16C11×#446C2212yes—
17C8×Q8×C11C2212yes—
18C11×#424—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#405—21no—
21C4×C11×M16C2211yescharacteristic
22#10622746—21no—
23#10622746—21no—
24#10622697—21no—
25#10622696—21no—
26#10622694—21no—
27#10622691—21no—
28#10622661—22no—
29#10622657—22no—
30#10622640C2212yes—
31#10622634C2212yes—
32#10622634C2212yes—
33#10622633C2212yes—
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622327—22no—
37#10622307C2212yes—
38#10622294C2212yes—
39#10622123C2211yescharacteristic
40#10622123C2211yescharacteristic
41#10622120C2211yescharacteristic
42#10622120C2211yescharacteristic
43#10622119C2212yes—
44#10622119C2212yes—
45#10622096C2212yes—
46#10622095C2212yes—
47C2×#4339—21no—
48C22×Dic22—21no—
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C22×C8×C11—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8D412yes—
57C4×Q8×C11—21no—
58C4×Q8×C11C2312yes—
59C11×#117—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4325—22no—
62#66983—21no—
63#66983—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C22×C11⋊C8—21no—
67#66928—21no—
68#66927C2311yescharacteristic
69C4×D44—21no—
70C4×D44—21no—
71#66922—21no—
72#66922—21no—
73#66922—21no—
74#66922C2312yes—
75#66922C2311yescharacteristic
76C11×C4⋊C8—22no—
77C11×C4⋊C8—22no—
78C11×C4⋊C8—21no—
79C11×C4⋊C8C2311yescharacteristic
80C11×C4⋊C8C2311yescharacteristic
81C11×#97—22no—
82C11×#97D412yes—
83C4×C8×C11—22no—
84C4×C8×C11C2312yes—
85#66899—22no—
86#66899—22no—
87#66899—22no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66885—22no—
91#66880—22no—
92#66880—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96#66871—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4×C11⋊C8—21no—
102#19244—111nomaximal, Sylow
103C2×Q8×C11—21no—
104C2×Q8×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—41no—
109C22×Dic11—41no—
110#4339—42no—
111#4339—42no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C2×Dic22—22no—
118C2×Dic22—41no—
119C2×Dic22—82no—
120C11×M16—22no—
121C11×M16—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—42no—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D412yes—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C2×D412yes—
133C11×C22⋊C4—22no—
134C42×C11—22no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139#4325—82no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—81no—
152#3246—111no—
153#3230—111no—
154#3141—111no—
155#2962D1111yescharacteristic, complemented
156#1704—112no—
157#1698—112no—
158#1684—112no—
159#1678—112no—
160#1565—111no—
161C2×#333—111no—
162#1540—111no—
163C23×C11#12111yescharacteristic
164C22×D11—41no—
165Q8×C11—22no—
166Q8×C11—22no—
167Q8×C11—81no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#13512yes—
177C2×C4×C11#13712yes—
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C22⋊D11—82no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—82no—
185D44—41no—
186D44—41no—
187D44—41no—
188D44—41no—
189D44—81no—
190C4×D11—82no—
191Dic22—41no—
192Dic22—41no—
193Dic22—82no—
194Dic22—82no—
195C8×C11—22no—
196C8×C11—22no—
197C8×C11—41no—
198C8×C11—41no—
199C11⋊C8—41no—
200C11⋊C8—42no—
201C11⋊C8—41no—
202#533C2×D1111yescharacteristic
203#532—111no—
204C2×C4⋊Q8—111no—
205#500—221no—
206#489—222no—
207#487—112no—
208#487—221no—
209#486—112no—
210#484—222no—
211#477—112no—
212#477—112no—
213#476—221no—
214#475—112no—
215#465—222no—
216#461—221no—
217#460—112no—
218#446—22no—
219#446C2×D1112yes—
220C8×Q8C2×D1112yes—
221#431—111no—
222#424—21no—
223C2×C4⋊C8—111no—
224C2×C4⋊C8C2×D1111yescharacteristic
225#417—221no—
226#417—221no—
227#405—21no—
228C4×M16C2×D1111yescharacteristic
229#335—112no—
230#334—112no—
231#333—112no—
232#333—112no—
233#332—111no—
234#332—111no—
235#331—111no—
236#331—111no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11#46412yes—
240C22×C11C2×#12111yescharacteristic
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11#46412yes—
250C4×C11C2×#13511yescharacteristic
251C4×C11C2×#13711yescharacteristic
252C4×C11#57711yescharacteristic
253C4×C11#57811yescharacteristic
254Dic11—81no—
255Dic11—82no—
256C2×#41—221no—
257C22×Q8—221no—
258C2×SD16—222no—
259C2×M16C22⋊D1111yescharacteristic
260C2×M16C22⋊D1111yescharacteristic
261C22×C8—21no—
262C22×C8—221no—
263C4⋊Q8—112no—
264C4⋊Q8—111no—
265C4⋊Q8—221no—
266C4⋊Q8—221no—
267C4⋊Q8—221no—
268C4⋊Q8D4411yescharacteristic
269C4⋊Q8D4411yescharacteristic
270#127—111no—
271#125—21no—
272#124—221no—
273C22⋊Q8—21no—
274C22⋊Q8D4412yes—
275#121—221no—
276#121—221no—
277C4×Q8—21no—
278C4×Q8C22×D1112yes—
279C4×D4—221no—
280C4×D4—221no—
281#117—21no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C42C22×D1111yescharacteristic
285#107—222no—
286#107—222no—
287#106—222no—
288C4⋊C8—22no—
289C4⋊C8—22no—
290C4⋊C8—21no—
291C4⋊C8—111no—
292C4⋊C8—111no—
293C4⋊C8—112no—
294C4⋊C8—221no—
295C4⋊C8C22×D1111yescharacteristic
296C4⋊C8C22×D1111yescharacteristic
297#103—222no—
298#103—222no—
299#103—222no—
300#103—222no—
301#103—222no—
302#102—222no—
303#102—222no—
304#102—222no—
305C22⋊C8—221no—
306#97—22no—
307#97C22⋊D1112yes—
308C4×C8—22no—
309C4×C8—221no—
310C4×C8C22×D1112yes—
311C2×C11—22no—
312C2×C11C2×#46411yescharacteristic
313C2×C11#306311yescharacteristic
314C2×C11#306811yescharacteristic
315D11—161no—
316#41—442no—
317#41—442no—
318C2×Q8—21no—
319C2×Q8—222no—
320C2×Q8—221no—
321C2×Q8—441no—
322C2×Q8—882no—
323C2×Q8C2×D4412yes—
324C2×D4—221no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—441no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4C2×D4411yescharacteristic
331C22×C4#433911yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—882no—
334M16—22no—
335M16—22no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—42no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—222no—
342C2×C8—881no—
343C2×C8C2×C22⋊D1112yes—
344C2×C8C2×C22⋊D1112yes—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—221no—
351C4⋊C4—222no—
352C4⋊C4—221no—
353C4⋊C4—222no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4C2×D4412yes—
357C22⋊C4—22no—
358C22⋊C4—441no—
359C22⋊C4—441no—
360C42—22no—
361C42C2×D4411yescharacteristic
362C42#433911yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C42C23×D1111yescharacteristic
365C11#1924411yescharacteristic, complemented, Sylow
366C23—441no—
367C23#6698311yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—81no—
371Q8—441no—
372Q8—441no—
373Q8—882no—
374Q8—882no—
375D4—441no—
376D4—441no—
377D4—441no—
378D4—441no—
379D4—881no—
380D4—882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—882no—
389C2×C4—882no—
390C2×C4#6698311yescharacteristic
391C2×C4#6698311yescharacteristic
392C2×C4#6698311yescharacteristic
393C2×C4#6699512yes—
394C2×C4#6700312yes—
395C2×C4C22×D4411yescharacteristic
396C2×C4C2×#433911yescharacteristic
397C2×C4C22×C22⋊D1111yescharacteristic
398C8—22no—
399C8—22no—
400C8—41no—
401C8—41no—
402C8—442no—
403C8—441no—
404C8—441no—
405C22—21no—
406C22—21no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22#1062264112yes—
411C22C2×#6698311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—42no—
417C4—881no—
418C4—882no—
419C4#1062264112yes—
420C4#1062328211yescharacteristic
421C4#1062328411yescharacteristic
422C4C2×#6699511yescharacteristic
423C4C2×#6700311yescharacteristic
424C2—22no—
425C2—1761no—
426C2C2×#1062264111yescharacteristic
427C2#1307830711yescharacteristic
428C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2962D11
hypocenterC11#19244
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
2. #13079764C2semidirect
4. #13068198C2semidirect
5. #13068156C2semidirect
6. #13068074C2semidirect
7. #13068032C2semidirect
8. #13067368C2semidirect
9. C2×#10622119C2semidirect
11. C11×#2962C2semidirect
155. #2962D11semidirect
365. C11#19244semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797642
#130790102
#130681982
#130681562
#130680742
#130680322
#130673682
C2×#106221192
#130672662
C11×#29622
#1924411