Finite Group Databasebeta

← #14908261

Subgroups — #14908261

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622522C211yesmaximal, characteristic, complemented
2#13078197C211yesmaximal, characteristic
3C2×#10622729C211yesmaximal, characteristic, complemented
4#13070729C212yesmaximal, complemented
5#13070724C212yesmaximal, complemented
6#13070712C212yesmaximal, complemented
7#13070707C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070337C211yesmaximal, characteristic, complemented
10#13070329C211yesmaximal, characteristic, complemented
11C22×C11×M32C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13#10623322—21no—
14C2×#66977—21no—
15C22×Dic44C2211yescharacteristic
16C2×#66957C2211yescharacteristic
17C2×C11×M32—24no—
18C2×C11×M32C2211yescharacteristic
19C2×C11×M32C2212yes—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2212yes—
22#10622729—21no—
23#10622729—21no—
24#10622729C2211yescharacteristic
25#10622729C2212yes—
26#10622729C2211yescharacteristic
27#10622729C2212yes—
28#10622728C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622727—21no—
31#10622727—21no—
32#10622726—21no—
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66880—21no—
36#10622522—24no—
37C2×Dic88C2212yescomplemented
38C2×#66864C2212yescomplemented
39#10622147C2212yescomplemented
40#10622143C2212yescomplemented
41#10622142C2212yescomplemented
42#10622141C2212yescomplemented
43#10622141C2212yescomplemented
44#10622141C2212yescomplemented
45C23×C4×C11D411yescharacteristic
46C2×#4339—21no—
47C22×Dic22—21no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56#67006—41no—
57C2×C22⋊Dic11—41no—
58#66983—21no—
59#66983—21no—
60#66982—41no—
61C4×C22⋊D11—41no—
62C4×C22⋊D11—41no—
63#66979—21no—
64C2×C4⋊Dic11—21no—
65#66977—21no—
66#66977—21no—
67#66977—22no—
68#66977—22no—
69#66977—41no—
70#66977—41no—
71C2×Dic11⋊C4—41no—
72C2×Dic44—22no—
73C2×Dic44—22no—
74C2×Dic44—21no—
75C2×Dic44C2311yescharacteristic
76C2×Dic44C2312yes—
77#66957—22no—
78#66957—22no—
79C2×D88C2311yescharacteristic
80C2×#4314—21no—
81C11×M32—22no—
82C11×M32—24no—
83C11×M32D414yescomplemented
84C2×C11×C16—24no—
85C2×C11×C16C2312yes—
86C2×C11×C16C2312yes—
87#66885—21no—
88#66885—21no—
89#66882—21no—
90#66882C2311yescharacteristic
91#66882C2311yescharacteristic
92#66882C2312yes—
93#66881—21no—
94#66880—21no—
95#66880—21no—
96#66880—22no—
97#66880—22no—
98Dic88—24no—
99#66864—24no—
100#33606—111nomaximal, Sylow
101C24×C11D811yescharacteristic
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11D811yescharacteristic
105C22×C4×C11D811yescharacteristic
106C22×C4×C11D811yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C2×C22⋊D11—41no—
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115#4339—42no—
116#4339—42no—
117C2×D44—21no—
118C2×C4×D11—41no—
119C2×Dic22—21no—
120C2×Dic22—22no—
121C2×Dic22—42no—
122C2×Dic22—41no—
123C2×Dic22—42no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11C2×D412yes—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11#4112yes—
136C2×C8×C11C2411yescharacteristic
137C22⋊Dic11—42no—
138C22⋊Dic11—42no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148Dic11⋊C4—42no—
149Dic11⋊C4—42no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152C4×Dic11—41no—
153Dic44—22no—
154Dic44—21no—
155Dic44—21no—
156Dic44—22no—
157Dic44—42no—
158D88—21no—
159D88—21no—
160#4314—42no—
161C11×C16—22no—
162C11×C16C2×D414yes—
163C2×#510—111no—
164C22×M32D1111yescharacteristic, complemented
165#3050—111no—
166C2×#467—111no—
167#2220—112no—
168#2219—112no—
169#2217—112no—
170#2216—112no—
171#2159—111no—
172#2141—111no—
173#2139—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—41no—
177C23×C11C2×D811yescharacteristic
178C23×C11C2×D811yescharacteristic
179C23×C11C2×D811yescharacteristic
180C22×D11—41no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11#12112yes—
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11#13512yes—
193C2×C4×C11C22×D411yescharacteristic
194C22⋊D11—82no—
195C22⋊D11—82no—
196C22⋊D11—82no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—82no—
203C2×Dic11—82no—
204D44—41no—
205D44—41no—
206C4×D11—82no—
207Dic22—41no—
208Dic22—42no—
209Dic22—42no—
210Dic22—41no—
211Dic22—82no—
212C8×C11—21no—
213C8×C11—21no—
214C8×C11#12112yes—
215C8×C11C22×D411yescharacteristic
216C8×C11C2×#4111yescharacteristic
217C2×#135—111no—
218C22×Q16—111no—
219C23×C8C2×D1111yescharacteristic
220#525—221no—
221C2×C22⋊Q8—221no—
222#510—224no—
223C2×Q32—112no—
224C2×SD32—112no—
225C2×M32—24no—
226C2×M32C2×D1111yescharacteristic
227C2×M32C2×D1112yes—
228C2×M32C2×D1111yescharacteristic
229C22×C16C2×D1112yes—
230#467—111no—
231#467—112no—
232#467—111no—
233#467—112no—
234#467—221no—
235#467—221no—
236#466—111no—
237#466—111no—
238#465—221no—
239#465—221no—
240#427—111no—
241C2×#107—111no—
242#416—221no—
243C2×#103—221no—
244#367—112no—
245#366—112no—
246#358—112no—
247#358—112no—
248#358—112no—
249#357—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—44no—
258C22×C11#46612yes—
259C22×C11#51012yescomplemented
260C22×C11C22×D811yescharacteristic
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11#46612yes—
267C4×C11C2×#12111yescharacteristic
268C4×C11C2×#13511yescharacteristic
269Dic11—81no—
270Dic11—82no—
271Dic11—81no—
272Dic11—82no—
273Dic11—81no—
274C2×#41—221no—
275C22×Q8—221no—
276C23×C4D4411yescharacteristic
277#135—222no—
278#135—222no—
279C2×Q16—112no—
280C2×Q16—111no—
281C2×Q16—221no—
282C2×Q16—222no—
283C2×Q16—222no—
284C2×SD16—221no—
285C2×D8—111no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8D4411yescharacteristic
289C22×C8D4411yescharacteristic
290C22×C8D4411yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
293C22×C8C22×D1111yescharacteristic
294#123—441no—
295C22⋊Q8—222no—
296C22⋊Q8—222no—
297C22⋊Q8—221no—
298C22⋊Q8—221no—
299C22⋊Q8—441no—
300C22⋊Q8—441no—
301#121—221no—
302#121—221no—
303#120—441no—
304C4×D4—441no—
305C4×D4—441no—
306#117—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—441no—
309C2×C22⋊C4—441no—
310Q32—224no—
311SD32—224no—
312M32—22no—
313M32—24no—
314M32C22⋊D1114yescomplemented
315C2×C16—24no—
316C2×C16C22×D1112yes—
317C2×C16C22×D1112yes—
318#107—112no—
319#107—111no—
320#107—111no—
321#107—221no—
322#106—221no—
323#103—222no—
324#103—222no—
325#103—221no—
326#103—221no—
327#102—221no—
328#102—221no—
329C2×C11—22no—
330C2×C11—22no—
331C2×C11—41no—
332C2×C11C2×#46611yescharacteristic
333C2×C11C2×#51011yescharacteristic
334C2×C11#341411yescharacteristic
335D11—161no—
336C24D8811yescharacteristic
337#41—442no—
338#41—442no—
339C2×Q8—221no—
340C2×Q8—222no—
341C2×Q8—441no—
342C2×Q8—442no—
343C2×Q8—442no—
344C2×D4—221no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4D8811yescharacteristic
354C22×C4D8811yescharacteristic
355C22×C4D8811yescharacteristic
356C22×C4C2×D4411yescharacteristic
357C22×C4C2×D4411yescharacteristic
358C22×C4C2×D4411yescharacteristic
359Q16—222no—
360Q16—221no—
361Q16—222no—
362Q16—221no—
363Q16—442no—
364SD16—442no—
365D8—221no—
366D8—221no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8C2×D4411yescharacteristic
375C2×C8C2×D4411yescharacteristic
376C2×C8C2×D4411yescharacteristic
377C2×C8#433912yes—
378C2×C8C2×C22⋊D1112yes—
379C2×C8C23×D1111yescharacteristic
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—441no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—441no—
396C16—22no—
397C16C2×C22⋊D1114yes—
398C11#3360611yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—41no—
402C23—441no—
403C23C2×D8811yescharacteristic
404C23C2×D8811yescharacteristic
405C23C2×D8811yescharacteristic
406Q8—442no—
407Q8—441no—
408Q8—441no—
409Q8—442no—
410Q8—882no—
411D4—441no—
412D4—441no—
413D4—882no—
414D4—882no—
415D4—882no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—882no—
429C2×C4—882no—
430C2×C4—882no—
431C2×C4C2×D8811yescharacteristic
432C2×C4C2×D8811yescharacteristic
433C2×C4C2×D8811yescharacteristic
434C2×C4#6695712yes—
435C2×C4#6698312yes—
436C2×C4C22×D4411yescharacteristic
437C8—21no—
438C8—21no—
439C8#6698312yes—
440C8C2×#433911yescharacteristic
441C8C22×C22⋊D1111yescharacteristic
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22#1062252212yescomplemented
454C22#1062272812yes—
455C22C22×D8811yescharacteristic
456C4—21no—
457C4—21no—
458C4—881no—
459C4—882no—
460C4—881no—
461C4—881no—
462C4—882no—
463C4#1062272812yes—
464C4C2×#6695711yescharacteristic
465C4C2×#6698311yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—1761no—
470C2C2×#1062272811yescharacteristic
471C2C2×#1062252211yescharacteristic
472C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×M32C2
socleC22×C11C22×D8
prime radical#13078197C2
hypercenterC22×M32D11
hypocenterC11#33606
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

Complements

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

NH ≅ G/Ntype
1. C2×#10622522C2semidirect
3. C2×#10622729C2semidirect
4. #13070729C2semidirect
5. #13070724C2semidirect
6. #13070712C2semidirect
7. #13070707C2semidirect
8. #13070404C2semidirect
9. #13070337C2semidirect
10. #13070329C2semidirect
11. C22×C11×M32C2semidirect
37. C2×Dic88C22semidirect
38. C2×#66864C22semidirect
39. #10622147C22semidirect
40. #10622143C22semidirect
41. #10622142C22semidirect
42. #10622141C22semidirect
43. #10622141C22semidirect
44. #10622141C22semidirect
83. C11×M32D4semidirect
164. C22×M32D11semidirect
259. C22×C11#510semidirect
314. M32C22⋊D11semidirect
398. C11#33606semidirect
453. C22#10622522semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
#130781972
C2×#106227292
#130707292
#130707242
#130707122
#130707072
#130704042
#130703372
#130703292
C22×C11×M322
#3360611