Finite Group Databasebeta

← #14907090

Subgroups — #14907090

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic
2#13077387C211yesmaximal, characteristic, complemented
3C2×#10622485C211yesmaximal, characteristic, complemented
4#13070491C212yesmaximal, complemented
5#13070479C212yesmaximal, complemented
6#13070467C212yesmaximal, complemented
7#13070462C212yesmaximal, complemented
8#13070331C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C22×D88C2211yescharacteristic
14#10623053—21no—
15C2×#66946—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66873—21no—
23#10622521C418yescomplemented
24C2×#66864C2212yes—
25C2×D176C2212yes—
26#10622486C2211yescharacteristic, complemented
27#10622486C2211yescharacteristic, complemented
28#10622485—21no—
29#10622485—21no—
30#10622485C2212yes—
31#10622485C2212yes—
32#10622485C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic, complemented
34#10622465—21no—
35#10622465—21no—
36C11×#367C2212yescomplemented
37C11×#366C2212yescomplemented
38#10622140C2212yescomplemented
39C16×Dic11C2212yescomplemented
40#10622130C2212yescomplemented
41#10622129C2212yes—
42#10622129C2212yes—
43#10622129C2212yescomplemented
44C2×#4339—21no—
45C22×D44—21no—
46C22×C4×D11—41no—
47C22×C8×C11C2311yescharacteristic
48C11×#117—21no—
49C2×C11×C4⋊C4—21no—
50C2×(C2×D11)⋊C4—41no—
51C2×C4×Dic11D411yescharacteristic
52C22×C11⋊C8D411yescharacteristic
53C2×Dic44C2311yescharacteristic
54#66957—22no—
55#66957C2×C414yescomplemented
56C2×D88—21no—
57C2×D88—22no—
58C2×D88C2×C414yescomplemented
59C2×D88C2312yes—
60C2×D88C2311yescharacteristic
61C2×#4314—21no—
62#66946—21no—
63#66946—21no—
64#66946—22no—
65#66946—22no—
66#66946—41no—
67#66946—41no—
68#66940—21no—
69#66940—21no—
70(C22⋊D11)⋊C4—41no—
71(C22⋊D11)⋊C4—41no—
72#66925—41no—
73C42×D11—41no—
74C11×M32C2×C414yescomplemented
75C2×C11×C16C2312yes—
76C11×#107—21no—
77C11×#107C2312yes—
78C11×#107C2311yescharacteristic
79C11×#107C2311yescharacteristic
80C11×#106—21no—
81C8×Dic11D411yescharacteristic
82C8×Dic11D411yescharacteristic
83C8×Dic11C2311yescharacteristic
84C8×Dic11C2311yescharacteristic
85#66876—22no—
86C2×C11⋊C16C2312yes—
87#66874—21no—
88#66874—21no—
89#66873—21no—
90#66873—21no—
91#66873—22no—
92#66873—22no—
93#66864C2×C418yescomplemented
94D176C2×C418yescomplemented
95C4×#509—111nomaximal, Sylow
96C23×D11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C22×Dic11D811yescharacteristic
101C22×Dic11D811yescharacteristic
102#4339—24no—
103#4339—42no—
104C2×D44—24no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—42no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—41no—
114C2×C4×D11—84no—
115C2×Dic22—21no—
116C2×C8×C11C22×C412yes—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11#4112yes—
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C4×Dic11D811yescharacteristic
135C4×Dic11D811yescharacteristic
136C4×Dic11C2×D411yescharacteristic
137C4×Dic11C2×D411yescharacteristic
138C2×C11⋊C8—22no—
139C2×C11⋊C8C2×D411yescharacteristic
140C2×C11⋊C8C2×D411yescharacteristic
141Dic44—21no—
142Dic44C22×C412yescomplemented
143D88—24no—
144D88—22no—
145D88—21no—
146D88C22×C414yes—
147D88C22×C412yescomplemented
148#4314—24no—
149C11×C16C22×C414yescomplemented
150C11⋊C16—22no—
151C2×#509—111no—
152C4×#135—111no—
153C2×C4×D8—111no—
154#2177—112no—
155#2175—112no—
156C4×SD32—112no—
157C4×D16—112no—
158#2159D1111yescharacteristic, complemented
159#2140—111no—
160#2139—111no—
161C4×M32—111no—
162C23×C11C2×D811yescharacteristic
163C22×D11—41no—
164C22×D11—42no—
165C22×D11—44no—
166C22×D11—82no—
167C22×D11—82no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—44no—
177C2×Dic11—22no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11C2×D811yescharacteristic
181C2×Dic11C2×D811yescharacteristic
182C2×Dic11C2×D811yescharacteristic
183C2×Dic11C2×D811yescharacteristic
184D44—22no—
185D44—24no—
186D44—42no—
187D44—41no—
188D44—44no—
189C4×D11—44no—
190C4×D11—82no—
191C4×D11—84no—
192C4×D11—82no—
193C4×D11—84no—
194Dic22—22no—
195Dic22—41no—
196C8×C11C4×D412yes—
197C8×C11C23×C411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—21no—
200C11⋊C8—21no—
201C2×#135—111no—
202C22×D8—111no—
203C4×#41—221no—
204C2×C4×D4—221no—
205#509—118no—
206C2×SD32—112no—
207C2×D16—112no—
208C2×M32—111no—
209C2×M32C2×D1111yescharacteristic
210C4×Q16—111no—
211C4×Q16—111no—
212C4×SD16—221no—
213C4×SD16—221no—
214C4×D8—112no—
215C4×D8—112no—
216C4×D8—111no—
217C4×D8—111no—
218C4×D8—221no—
219C4×D8—221no—
220#427C2×D1111yescharacteristic
221C2×#107C2×D1111yescharacteristic
222#416—221no—
223C2×#102—221no—
224C2×C4×C8—111no—
225#367C2×D1112yescomplemented
226#366C2×D1112yescomplemented
227#358—112no—
228#357—112no—
229#357—112no—
230#357—112no—
231#346—112no—
232C4×C16—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11C4×D812yes—
236C22×C11C22×D811yescharacteristic
237C2×D11—44no—
238C2×D11—42no—
239C2×D11—88no—
240C2×D11—82no—
241C2×D11—81no—
242C2×D11—82no—
243C2×D11—81no—
244C4×C11—82no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11C4×D812yes—
248C4×C11C2×C4×D411yescharacteristic
249C4×C11C2×#13511yescharacteristic
250Dic11—21no—
251Dic11—21no—
252Dic11—21no—
253Dic11—42no—
254Dic11#50912yescomplemented
255C2×#41—221no—
256C22×D4—221no—
257C23×C4—441no—
258#135—114no—
259#135—222no—
260C2×Q16—111no—
261C2×SD16—221no—
262C2×D8—114no—
263C2×D8—112no—
264C2×D8—111no—
265C2×D8—221no—
266C2×D8—222no—
267C22×C8—111no—
268C22×C8C22×D1111yescharacteristic
269C4×Q8—221no—
270C4×Q8—221no—
271C4×D4—222no—
272C4×D4—222no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4—441no—
276C4×D4—441no—
277C4×D4—441no—
278C4×D4—441no—
279#117—21no—
280#117—441no—
281C2×C4⋊C4—21no—
282C2×C22⋊C4—441no—
283C2×C42—111no—
284C2×C42—441no—
285SD32—118no—
286D16—118no—
287M32—222no—
288M32C4×D1114yescomplemented
289C2×C16—112no—
290C2×C16C22×D1112yes—
291#107—21no—
292#107C22×D1111yescharacteristic
293#107C22×D1111yescharacteristic
294#107C22×D1112yes—
295#106—21no—
296#103—221no—
297#103—221no—
298#102—222no—
299#102—222no—
300#102—221no—
301#102—221no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—111no—
306C2×C11—22no—
307C2×C11C2×C4×D811yescharacteristic
308C2×C11C2×#50911yescharacteristic
309C2×C11#341411yescharacteristic
310D11—82no—
311D11—84no—
312C24—441no—
313#41—224no—
314#41—442no—
315C2×Q8—221no—
316C2×D4—224no—
317C2×D4—222no—
318C2×D4—221no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—442no—
322C22×C4—41no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4—442no—
328C22×C4—442no—
329C22×C4—441no—
330C22×C4—884no—
331C22×C4D4×D1111yescharacteristic
332Q16—112no—
333Q16—221no—
334SD16—224no—
335D8—112no—
336D8—114no—
337D8—224no—
338D8—222no—
339D8—221no—
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—222no—
343C2×C8C2×C4×D1112yes—
344C2×C8D4×D1111yescharacteristic
345C2×C8#434312yes—
346C2×C8C23×D1111yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—41no—
354C22⋊C4—442no—
355C22⋊C4—442no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—41no—
359C42—111no—
360C42—111no—
361C42—111no—
362C42—111no—
363C42—441no—
364C42—441no—
365C16—222no—
366C16C2×C4×D1114yescomplemented
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—444no—
369C23—441no—
370C23—442no—
371C23—882no—
372C23—882no—
373C23D8×D1111yescharacteristic
374Q8—222no—
375Q8—441no—
376D4—224no—
377D4—222no—
378D4—444no—
379D4—444no—
380D4—442no—
381D4—441no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—82no—
386C2×C4—111no—
387C2×C4—111no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—222no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—444no—
394C2×C4—884no—
395C2×C4—882no—
396C2×C4—884no—
397C2×C4—882no—
398C2×C4#6694612yes—
399C2×C4D8×D1111yescharacteristic
400C2×C4#6697212yes—
401C2×C4C2×D4×D1111yescharacteristic
402C8—221no—
403C8—221no—
404C8#6694612yes—
405C8C22×C4×D1111yescharacteristic
406C8C2×#434311yescharacteristic
407C22—21no—
408C22—21no—
409C22—442no—
410C22—444no—
411C22—888no—
412C22—882no—
413C22—881no—
414C22—881no—
415C22—882no—
416C22#1062248512yes—
417C22C2×D8×D1111yescharacteristic
418C4—82no—
419C4—81no—
420C4—81no—
421C4—112no—
422C4—221no—
423C4—221no—
424C4—221no—
425C4—442no—
426C4#1062248512yes—
427C4C2×#6694611yescharacteristic
428C4C2×#6697211yescharacteristic
429C2—22no—
430C2—884no—
431C2—882no—
432C2C2×#1062248511yescharacteristic
433C2D11×#50911yescharacteristic
434C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#10622521C2
cosocleC2×C8×C11C24
hypercenter#2159D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
2. #13077387C2semidirect
3. C2×#10622485C2semidirect
4. #13070491C2semidirect
5. #13070479C2semidirect
6. #13070467C2semidirect
7. #13070462C2semidirect
8. #13070331C2semidirect
9. #13070326C2semidirect
10. M32×Dic11C2semidirect
11. C11×#2159C2semidirect
23. #10622521C4semidirect
26. #10622486C22semidirect
27. #10622486C22semidirect
32. #10622485C22semidirect
33. #10622485C22semidirect
36. C11×#367C22semidirect
37. C11×#366C22semidirect
38. #10622140C22semidirect
39. C16×Dic11C22semidirect
40. #10622130C22semidirect
43. #10622129C22semidirect
55. #66957C2×C4semidirect
58. C2×D88C2×C4semidirect
74. C11×M32C2×C4semidirect
93. #66864C2×C4semidirect
94. D176C2×C4semidirect
142. Dic44C22×C4semidirect
147. D88C22×C4semidirect
149. C11×C16C22×C4semidirect
158. #2159D11semidirect
225. #367C2×D11semidirect
226. #366C2×D11semidirect
254. Dic11#509semidirect
288. M32C4×D11semidirect
366. C16C2×C4×D11semidirect
367. C11C4×#509semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
#130773872
C2×#106224852
#130704912
#130704792
#130704672
#130704622
#130703312
#130703262
M32×Dic112
C11×#21592
C4×#50911