Finite Group Databasebeta

← #14737420

Subgroups — #14737420

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079561C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic
4#13068184C212yesmaximal, complemented
5#13068170C212yesmaximal, complemented
6#13068060C212yesmaximal, complemented
7#13068046C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067266C211yesmaximal, characteristic
10C2×#10622124C211yesmaximal, characteristic, complemented
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#10622706—21no—
25#10622705—21no—
26#10622697—21no—
27#10622696—21no—
28#10622663—22no—
29#10622661—22no—
30#10622644C2212yes—
31#10622644C2212yes—
32#10622640C2212yes—
33#10622633C2212yes—
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622327—22no—
37#10622307C2212yes—
38#10622294C2212yes—
39#10622124C2212yes—
40#10622124C2212yes—
41#10622123C2211yescharacteristic
42#10622123C2211yescharacteristic
43#10622120C2211yescharacteristic
44#10622120C2211yescharacteristic
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×#4326—22no—
62C2×#4326—22no—
63C2×#4325—22no—
64#66983—21no—
65#66983—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C22×C11⋊C8—21no—
69#66928—21no—
70#66927C2311yescharacteristic
71C4×D44—21no—
72C4×D44—21no—
73#66922—21no—
74#66922—21no—
75#66922—21no—
76#66922C2312yes—
77#66922C2311yescharacteristic
78C11×C4⋊C8—22no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—21no—
81C11×C4⋊C8C2311yescharacteristic
82C11×C4⋊C8C2311yescharacteristic
83C11×#97—22no—
84C11×#97D412yes—
85C4×C8×C11—22no—
86C4×C8×C11C2312yes—
87#66899—22no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90#66885—22no—
91#66880—22no—
92#66880—22no—
93#66874—22no—
94#66874—22no—
95#66873—22no—
96#66872—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4×C11⋊C8—21no—
102#19245—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—22no—
117C2×Dic22—21no—
118C2×Dic22—41no—
119C2×Dic22—81no—
120C2×Dic22—81no—
121C11×M16—22no—
122C11×M16—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—42no—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C2×D412yes—
134C11×C22⋊C4—22no—
135C42×C11—22no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140#4326—82no—
141#4326—82no—
142#4325—82no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—81no—
155#3246—111no—
156#3209—111no—
157#3141—111no—
158#2962D1111yescharacteristic, complemented
159#1702—112no—
160#1700—112no—
161#1682—112no—
162#1680—112no—
163#1565—111no—
164#1540—111no—
165C2×#332—111no—
166C23×C11#12111yescharacteristic
167C22×D11—41no—
168Q8×C11—22no—
169Q8×C11—22no—
170Q8×C11—81no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#13512yes—
180C2×C4×C11#13712yes—
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C22⋊D11—82no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—82no—
188D44—41no—
189D44—41no—
190D44—41no—
191D44—41no—
192D44—81no—
193C4×D11—82no—
194Dic22—41no—
195Dic22—41no—
196Dic22—42no—
197Dic22—42no—
198Dic22—82no—
199C8×C11—22no—
200C8×C11—22no—
201C8×C11—41no—
202C8×C11—41no—
203C11⋊C8—42no—
204C11⋊C8—41no—
205C11⋊C8—41no—
206#533C2×D1111yescharacteristic
207#532—111no—
208C2×C4⋊Q8—111no—
209#494—221no—
210#489—222no—
211#487—112no—
212#487—221no—
213#486—112no—
214#476—221no—
215#475—112no—
216#465—222no—
217#462—112no—
218#462—112no—
219#461—221no—
220#460—112no—
221#451—222no—
222#446—22no—
223#446C2×D1112yes—
224C8×Q8C2×D1112yes—
225#431—111no—
226#424—21no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8C2×D1111yescharacteristic
229#417—221no—
230#417—221no—
231#405—21no—
232C4×M16C2×D1111yescharacteristic
233#335—112no—
234#334—112no—
235#332—112no—
236#332—112no—
237#332—111no—
238#332—111no—
239#331—111no—
240#331—111no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11#46412yes—
244C22×C11C2×#12111yescharacteristic
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11#46412yes—
254C4×C11C2×#13511yescharacteristic
255C4×C11C2×#13711yescharacteristic
256C4×C11#57611yescharacteristic
257C4×C11#57711yescharacteristic
258Dic11—81no—
259Dic11—82no—
260C2×#41—221no—
261C22×Q8—221no—
262C2×Q16—222no—
263C2×Q16—222no—
264C2×SD16—222no—
265C2×M16C22⋊D1111yescharacteristic
266C2×M16C22⋊D1111yescharacteristic
267C22×C8—21no—
268C22×C8—221no—
269C4⋊Q8—112no—
270C4⋊Q8—111no—
271C4⋊Q8—221no—
272C4⋊Q8—221no—
273C4⋊Q8—221no—
274C4⋊Q8D4411yescharacteristic
275C4⋊Q8D4411yescharacteristic
276#127—111no—
277#125—21no—
278#124—221no—
279C22⋊Q8—21no—
280C22⋊Q8D4412yes—
281#121—221no—
282#121—221no—
283C4×Q8—21no—
284C4×Q8C22×D1112yes—
285C4×D4—221no—
286C4×D4—221no—
287#117—21no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C42C22×D1111yescharacteristic
291#106—222no—
292C4⋊C8—22no—
293C4⋊C8—22no—
294C4⋊C8—21no—
295C4⋊C8—111no—
296C4⋊C8—111no—
297C4⋊C8—112no—
298C4⋊C8—221no—
299C4⋊C8C22×D1111yescharacteristic
300C4⋊C8C22×D1111yescharacteristic
301#103—222no—
302#103—222no—
303#103—222no—
304#103—222no—
305#103—222no—
306#102—222no—
307#102—222no—
308#102—222no—
309C22⋊C8—221no—
310#97—22no—
311#97C22⋊D1112yes—
312C4×C8—22no—
313C4×C8—221no—
314C4×C8C22×D1112yes—
315C2×C11—22no—
316C2×C11C2×#46411yescharacteristic
317C2×C11#306211yescharacteristic
318C2×C11#306911yescharacteristic
319D11—161no—
320#41—442no—
321#41—442no—
322C2×Q8—21no—
323C2×Q8—222no—
324C2×Q8—221no—
325C2×Q8—441no—
326C2×Q8—881no—
327C2×Q8—881no—
328C2×Q8C2×D4412yes—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—441no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4C2×D4411yescharacteristic
336C22×C4#433911yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338Q16—882no—
339Q16—882no—
340SD16—882no—
341M16—22no—
342M16—22no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—42no—
346C2×C8—221no—
347C2×C8—221no—
348C2×C8—222no—
349C2×C8—881no—
350C2×C8C2×C22⋊D1112yes—
351C2×C8C2×C22⋊D1112yes—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—221no—
358C4⋊C4—222no—
359C4⋊C4—221no—
360C4⋊C4—222no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C4⋊C4C2×D4412yes—
364C22⋊C4—22no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C42—22no—
368C42C2×D4411yescharacteristic
369C42#433911yescharacteristic
370C42C2×C22⋊D1111yescharacteristic
371C42C23×D1111yescharacteristic
372C11#1924511yescharacteristic, complemented, Sylow
373C23—441no—
374C23#6698311yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—81no—
378Q8—442no—
379Q8—442no—
380Q8—441no—
381Q8—441no—
382Q8—882no—
383D4—441no—
384D4—441no—
385D4—441no—
386D4—441no—
387D4—881no—
388D4—882no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—882no—
397C2×C4—882no—
398C2×C4#6698311yescharacteristic
399C2×C4#6698311yescharacteristic
400C2×C4#6698311yescharacteristic
401C2×C4#6699512yes—
402C2×C4#6700312yes—
403C2×C4C22×D4411yescharacteristic
404C2×C4C2×#433911yescharacteristic
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—22no—
407C8—22no—
408C8—41no—
409C8—41no—
410C8—441no—
411C8—442no—
412C8—441no—
413C22—21no—
414C22—21no—
415C22—881no—
416C22—881no—
417C22—881no—
418C22#1062264112yes—
419C22C2×#6698311yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—882no—
426C4—881no—
427C4#1062264112yes—
428C4#1062328211yescharacteristic
429C4#1062328311yescharacteristic
430C4C2×#6699511yescharacteristic
431C4C2×#6700311yescharacteristic
432C2—22no—
433C2—1761no—
434C2C2×#1062264111yescharacteristic
435C2#1307829611yescharacteristic
436C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2962D11
hypocenterC11#19245
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. #13079561C2semidirect
4. #13068184C2semidirect
5. #13068170C2semidirect
6. #13068060C2semidirect
7. #13068046C2semidirect
8. #13067368C2semidirect
10. C2×#10622124C2semidirect
11. C11×#2962C2semidirect
158. #2962D11semidirect
372. C11#19245semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795612
#130790102
#130681842
#130681702
#130680602
#130680462
#130673682
#130672662
C2×#106221242
C11×#29622
#1924511