Finite Group Databasebeta

← #14908250

Subgroups — #14908250

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2#13078197C211yesmaximal, characteristic, complemented
3C2×#10622728C211yesmaximal, characteristic, complemented
4#13070729C212yesmaximal, complemented
5#13070719C212yesmaximal, complemented
6#13070712C212yesmaximal, complemented
7#13070702C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070333C211yesmaximal, characteristic, complemented
10#13070329C211yesmaximal, characteristic, complemented
11C22×C11×M32C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13#10623322—21no—
14C2×#66983—21no—
15C2×#66957C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C2×C11×M32—24no—
18C2×C11×M32C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C2×C11×M32C2212yescomplemented
21C22×C11×C16C2212yescomplemented
22#10622729C2211yescharacteristic, complemented
23#10622729C2211yescharacteristic, complemented
24#10622728—21no—
25#10622728—21no—
26#10622728C2212yes—
27#10622728C2212yes—
28#10622728C2211yescharacteristic, complemented
29#10622728C2211yescharacteristic, complemented
30#10622727—21no—
31#10622727—21no—
32#10622726—21no—
33C2×#66885—21no—
34#10622719C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36#10622521—24no—
37C2×#66864C2212yescomplemented
38C2×D176C2212yescomplemented
39#10622147C2212yescomplemented
40#10622147C2212yescomplemented
41#10622147C2212yescomplemented
42#10622143C2212yescomplemented
43#10622142C2212yescomplemented
44#10622141C2212yescomplemented
45C23×C4×C11D411yescharacteristic
46C22×C22⋊D11—41no—
47C2×#4339—21no—
48C22×D44—21no—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57#67006—41no—
58#66983—21no—
59#66983—21no—
60#66983—22no—
61#66983—22no—
62#66983—41no—
63#66983—41no—
64#66982—41no—
65C4×C22⋊D11—41no—
66C4×C22⋊D11—41no—
67C2×(C2×D11)⋊C4—41no—
68#66979—21no—
69C2×C4⋊Dic11—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73#66957—22no—
74#66957—22no—
75C2×D88—22no—
76C2×D88—22no—
77C2×D88—21no—
78C2×D88C2312yes—
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—22no—
88#66885—22no—
89#66885—21no—
90#66885—21no—
91#66882—21no—
92#66882C2312yes—
93#66882C2311yescharacteristic
94#66882C2311yescharacteristic
95#66881—21no—
96#66880—21no—
97#66880—21no—
98#66864—24no—
99D176—24no—
100#33605—111nomaximal, Sylow
101C24×C11D811yescharacteristic
102C23×D11—41no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11D811yescharacteristic
106C22×C4×C11D811yescharacteristic
107C22×C4×C11D811yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—42no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—84no—
117C22×Dic11—41no—
118#4339—42no—
119#4339—42no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—42no—
123C2×D44—41no—
124C2×D44—42no—
125C2×C4×D11—41no—
126C2×Dic22—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11#4112yes—
139C2×C8×C11C2411yescharacteristic
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143(C2×D11)⋊C4—42no—
144(C2×D11)⋊C4—42no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153C4×Dic11—41no—
154Dic44—21no—
155Dic44—21no—
156D88—21no—
157D88—22no—
158D88—22no—
159D88—21no—
160D88—42no—
161#4314—42no—
162C11×C16—22no—
163C11×C16C2×D414yescomplemented
164C2×#509—111no—
165C22×M32D1111yescharacteristic, complemented
166#3050—111no—
167C2×#466—111no—
168#2220—112no—
169#2218—112no—
170#2217—112no—
171#2215—112no—
172#2159—111no—
173#2140—111no—
174#2139—111no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11C2×D811yescharacteristic
179C23×C11C2×D811yescharacteristic
180C23×C11C2×D811yescharacteristic
181C22×D11—41no—
182C22×D11—42no—
183C22×D11—82no—
184C22×D11—82no—
185C22×D11—82no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11#12112yes—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11#13512yes—
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—82no—
200C22⋊D11—84no—
201C22⋊D11—82no—
202C22⋊D11—82no—
203C22⋊D11—84no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—82no—
209D44—41no—
210D44—42no—
211D44—42no—
212D44—41no—
213D44—82no—
214C4×D11—82no—
215Dic22—41no—
216Dic22—41no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11#12112yes—
220C8×C11C22×D411yescharacteristic
221C8×C11C2×#4111yescharacteristic
222C2×#135—111no—
223C22×D8—111no—
224C23×C8C2×D1111yescharacteristic
225#525—221no—
226C2×#121—221no—
227#509—224no—
228C2×SD32—112no—
229C2×D16—112no—
230C2×M32—24no—
231C2×M32C2×D1111yescharacteristic
232C2×M32C2×D1111yescharacteristic
233C2×M32C2×D1112yescomplemented
234C22×C16C2×D1112yescomplemented
235#467—111no—
236#467—111no—
237#466—112no—
238#466—112no—
239#466—111no—
240#466—111no—
241#466—221no—
242#466—221no—
243#465—221no—
244#465—221no—
245#427—111no—
246C2×#107—111no—
247#416—221no—
248C2×#102—221no—
249#367—112no—
250#366—112no—
251#358—112no—
252#357—112no—
253#357—112no—
254#357—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—44no—
263C22×C11#46612yes—
264C22×C11#50912yescomplemented
265C22×C11C22×D811yescharacteristic
266C2×D11—82no—
267C2×D11—81no—
268C2×D11—82no—
269C2×D11—81no—
270C2×D11—82no—
271C2×D11—81no—
272C2×D11—164no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11#46612yes—
276C4×C11C2×#12111yescharacteristic
277C4×C11C2×#13511yescharacteristic
278Dic11—82no—
279Dic11—81no—
280Dic11—81no—
281Dic11—81no—
282C2×#41—221no—
283C22×D4—221no—
284C22×D4—441no—
285C23×C4D4411yescharacteristic
286#135—222no—
287#135—222no—
288C2×Q16—111no—
289C2×SD16—221no—
290C2×D8—112no—
291C2×D8—111no—
292C2×D8—221no—
293C2×D8—222no—
294C2×D8—222no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8D4411yescharacteristic
298C22×C8D4411yescharacteristic
299C22×C8D4411yescharacteristic
300C22×C8C22×D1111yescharacteristic
301C22×C8C22×D1111yescharacteristic
302C22×C8C22×D1111yescharacteristic
303#123—441no—
304C22⋊Q8—221no—
305C22⋊Q8—221no—
306#121—222no—
307#121—222no—
308#121—221no—
309#121—221no—
310#121—441no—
311#121—441no—
312#120—441no—
313C4×D4—441no—
314C4×D4—441no—
315#117—221no—
316C2×C4⋊C4—221no—
317C2×C22⋊C4—441no—
318SD32—224no—
319D16—224no—
320M32—22no—
321M32—24no—
322M32C22⋊D1114yescomplemented
323C2×C16—24no—
324C2×C16C22×D1112yes—
325C2×C16C22×D1112yes—
326#107—111no—
327#107—111no—
328#107—112no—
329#107—221no—
330#106—221no—
331#103—221no—
332#103—221no—
333#102—222no—
334#102—222no—
335#102—221no—
336#102—221no—
337C2×C11—22no—
338C2×C11—22no—
339C2×C11—41no—
340C2×C11C2×#46611yescharacteristic
341C2×C11C2×#50911yescharacteristic
342C2×C11#341411yescharacteristic
343D11—161no—
344D11—162no—
345C24—441no—
346C24D8811yescharacteristic
347#41—442no—
348#41—442no—
349C2×Q8—221no—
350C2×D4—222no—
351C2×D4—221no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—442no—
356C2×D4—442no—
357C2×D4—441no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—884no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4D8811yescharacteristic
366C22×C4D8811yescharacteristic
367C22×C4D8811yescharacteristic
368C22×C4C2×D4411yescharacteristic
369C22×C4C2×D4411yescharacteristic
370C22×C4C2×D4411yescharacteristic
371Q16—221no—
372Q16—221no—
373SD16—442no—
374D8—222no—
375D8—221no—
376D8—221no—
377D8—222no—
378D8—442no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8C2×D4411yescharacteristic
387C2×C8C2×D4411yescharacteristic
388C2×C8C2×D4411yescharacteristic
389C2×C8#433912yes—
390C2×C8C2×C22⋊D1112yes—
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—222no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—442no—
402C22⋊C4—442no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C42—441no—
406C16—22no—
407C16C2×C22⋊D1114yescomplemented
408C11#3360511yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—41no—
412C23—441no—
413C23—442no—
414C23—882no—
415C23—882no—
416C23—882no—
417C23C2×D8811yescharacteristic
418C23C2×D8811yescharacteristic
419C23C2×D8811yescharacteristic
420Q8—441no—
421Q8—441no—
422D4—442no—
423D4—441no—
424D4—442no—
425D4—441no—
426D4—884no—
427D4—882no—
428D4—882no—
429D4—884no—
430D4—882no—
431D4—882no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—882no—
444C2×C4—882no—
445C2×C4C2×D8811yescharacteristic
446C2×C4C2×D8811yescharacteristic
447C2×C4C2×D8811yescharacteristic
448C2×C4#6695712yes—
449C2×C4#6698312yes—
450C2×C4C22×D4411yescharacteristic
451C8—21no—
452C8—21no—
453C8#6698312yes—
454C8C2×#433911yescharacteristic
455C8C22×C22⋊D1111yescharacteristic
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—882no—
465C22—881no—
466C22—881no—
467C22—882no—
468C22—881no—
469C22—882no—
470C22—1764no—
471C22#1062252112yescomplemented
472C22#1062272812yes—
473C22C22×D8811yescharacteristic
474C4—21no—
475C4—21no—
476C4—882no—
477C4—881no—
478C4—881no—
479C4—881no—
480C4#1062272812yes—
481C4C2×#6695711yescharacteristic
482C4C2×#6698311yescharacteristic
483C2—22no—
484C2—22no—
485C2—41no—
486C2—1762no—
487C2—1761no—
488C2C2×#1062272811yescharacteristic
489C2C2×#1062252111yescharacteristic
490C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×M32C2
socleC22×C11C22×D8
hypercenterC22×M32D11
hypocenterC11#33605
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×#10622521C2semidirect
2. #13078197C2semidirect
3. C2×#10622728C2semidirect
4. #13070729C2semidirect
5. #13070719C2semidirect
6. #13070712C2semidirect
7. #13070702C2semidirect
8. #13070404C2semidirect
9. #13070333C2semidirect
10. #13070329C2semidirect
11. C22×C11×M32C2semidirect
20. C2×C11×M32C22semidirect
21. C22×C11×C16C22semidirect
22. #10622729C22semidirect
23. #10622729C22semidirect
28. #10622728C22semidirect
29. #10622728C22semidirect
37. C2×#66864C22semidirect
38. C2×D176C22semidirect
39. #10622147C22semidirect
40. #10622147C22semidirect
41. #10622147C22semidirect
42. #10622143C22semidirect
43. #10622142C22semidirect
44. #10622141C22semidirect
83. C11×M32D4semidirect
163. C11×C16C2×D4semidirect
165. C22×M32D11semidirect
233. C2×M32C2×D11semidirect
234. C22×C16C2×D11semidirect
264. C22×C11#509semidirect
322. M32C22⋊D11semidirect
407. C16C2×C22⋊D11semidirect
408. C11#33605semidirect
471. C22#10622521semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
#130781972
C2×#106227282
#130707292
#130707192
#130707122
#130707022
#130704042
#130703332
#130703292
C22×C11×M322
#3360511