Finite Group Databasebeta

← #14908593

Subgroups — #14908593

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078198C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic, complemented
3#13070827C212yesmaximal, complemented
4#13070826C212yesmaximal, complemented
5#13070810C212yesmaximal, complemented
6#13070809C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070329C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10#13070226C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14#10623055—21no—
15C2×#66945—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66872—21no—
23#10622500C2211yescharacteristic
24#10622500C2211yescharacteristic
25#10622496C2211yescharacteristic
26#10622496C2211yescharacteristic
27#10622493—21no—
28#10622493—21no—
29#10622493C2212yes—
30#10622493C2212yes—
31#10622477—21no—
32#10622477—21no—
33C11×#367C2212yescomplemented
34C11×#366C2212yescomplemented
35#10622147C2212yescomplemented
36(C2×D11)⋊C16C2212yes—
37(C2×D11)⋊C16C2212yes—
38#10622141C2212yescomplemented
39#10622130C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×#4339—21no—
44C22×C4×D11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×(C2×D11)⋊C4—41no—
49C2×C4⋊Dic11—21no—
50C2×C4×Dic11—41no—
51C22×C11⋊C8D411yescharacteristic
52C2×Dic44C2311yescharacteristic
53#66957—22no—
54#66957—22no—
55C2×D88C2311yescharacteristic
56C2×#4314—21no—
57C2×C8×D11—22no—
58C2×C8×D11—22no—
59C2×C8×D11D411yescharacteristic
60C2×C8×D11D411yescharacteristic
61C2×C8×D11C2311yescharacteristic
62C2×C8×D11C2311yescharacteristic
63#66950—21no—
64#66950—21no—
65#66948—21no—
66#66948—21no—
67#66945—22no—
68#66945—22no—
69#66945—41no—
70#66945—41no—
71#66939—41no—
72#66935—41no—
73C4×D44—41no—
74C4×D44—41no—
75C11×M32—22no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2312yes—
79C11×#107C2311yescharacteristic
80C11×#107C2311yescharacteristic
81C11×#106—21no—
82#66882—21no—
83#66882C2312yes—
84#66876—22no—
85C2×C11⋊C16C2312yes—
86#66874—21no—
87#66874—21no—
88#66873—21no—
89#66873—21no—
90#66872—22no—
91#66872—22no—
92#33647—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—41no—
97C22×Dic11—41no—
98C22×Dic11D811yescharacteristic
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—41no—
103C2×D44—41no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—41no—
107C2×C4×D11D811yescharacteristic
108C2×C4×D11D811yescharacteristic
109C2×C4×D11C2×D411yescharacteristic
110C2×C4×D11C2×D411yescharacteristic
111C2×Dic22—21no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11#4112yes—
114C2×C8×C11#4112yes—
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C4×Dic11—42no—
133C4×Dic11—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137Dic44—21no—
138Dic44—21no—
139D88—21no—
140D88—21no—
141#4314—42no—
142C8×D11—22no—
143C8×D11—22no—
144C8×D11—21no—
145C8×D11—21no—
146C8×D11—21no—
147C8×D11—21no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3050—111no—
151C2×#427—111no—
152#2237—112no—
153#2237—112no—
154#2234—112no—
155#2234—112no—
156#2159—111no—
157#2159D1111yescharacteristic, complemented
158#2139—111no—
159#2139—111no—
160#2112—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11C2×D811yescharacteristic
167C22×D11C2×D811yescharacteristic
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—82no—
172C2×C4×C11#12312yes—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11#13712yes—
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—82no—
177C2×Dic11—22no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—82no—
181C2×Dic11C2×D811yescharacteristic
182C2×Dic11C2×D811yescharacteristic
183D44—41no—
184D44—41no—
185D44—82no—
186D44—82no—
187C4×D11—21no—
188C4×D11—21no—
189C4×D11—21no—
190C4×D11—21no—
191C4×D11—22no—
192C4×D11—22no—
193C4×D11—82no—
194Dic22—41no—
195Dic22—41no—
196C8×C11#12312yes—
197C8×C11C2×#4111yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—21no—
200C11⋊C8—21no—
201C2×#135—111no—
202C23×C8—111no—
203#525—221no—
204C2×#117—221no—
205C2×M32—111no—
206C2×M32C2×D1111yescharacteristic
207#467—111no—
208#467—111no—
209#466—111no—
210#466—111no—
211#465—221no—
212#465—221no—
213#427—112no—
214#427—112no—
215#427—221no—
216#427—221no—
217#427C2×D1111yescharacteristic
218C2×#107—111no—
219C2×#107C2×D1111yescharacteristic
220C2×#106—221no—
221#416—221no—
222#367—112no—
223#367C2×D1112yescomplemented
224#366—112no—
225#366C2×D1112yescomplemented
226#358—112no—
227#358—112no—
228#357—112no—
229#357—112no—
230C22⋊C16—112no—
231C22⋊C16—112no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11#48012yes—
235C22×C11C22×D811yescharacteristic
236C2×D11—21no—
237C2×D11—21no—
238C2×D11—21no—
239C2×D11—21no—
240C2×D11—21no—
241C2×D11—21no—
242C2×D11—44no—
243C2×D11—81no—
244C2×D11—81no—
245C2×D11—81no—
246C4×C11—82no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11#48012yes—
250C4×C11C2×#12311yescharacteristic
251C4×C11C2×#13711yescharacteristic
252Dic11—21no—
253Dic11—21no—
254Dic11—81no—
255Dic11—82no—
256C2×#41—221no—
257C23×C4—111no—
258#135—222no—
259#135—222no—
260C2×Q16—111no—
261C2×SD16—221no—
262C2×D8—111no—
263C22×C8—111no—
264C22×C8—111no—
265C22×C8—111no—
266C22×C8—111no—
267C22×C8—111no—
268C22×C8—222no—
269C22×C8—222no—
270C22×C8C22×D1111yescharacteristic
271#123—441no—
272C22⋊Q8—221no—
273C22⋊Q8—221no—
274#121—221no—
275#121—221no—
276#120—441no—
277C4×D4—441no—
278C4×D4—441no—
279#117—21no—
280#117—222no—
281#117—222no—
282#117—441no—
283#117—441no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—221no—
286C2×C22⋊C4—441no—
287C2×C42—441no—
288M32—22no—
289M32—222no—
290C2×C16—112no—
291C2×C16C22×D1112yes—
292#107—21no—
293#107—112no—
294#107—221no—
295#107C22×D1112yes—
296#107C22×D1111yescharacteristic
297#107C22×D1111yescharacteristic
298#106—21no—
299#106—222no—
300#106—222no—
301#103—221no—
302#103—221no—
303#102—221no—
304#102—221no—
305C2×C11—22no—
306C2×C11C2×#48011yescharacteristic
307C2×C11#341411yescharacteristic
308C2×C11#341411yescharacteristic
309D11—41no—
310D11—41no—
311D11—161no—
312C24—111no—
313#41—442no—
314#41—442no—
315C2×Q8—221no—
316C2×D4—221no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—441no—
320C22×C4—41no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331Q16—221no—
332Q16—221no—
333SD16—442no—
334D8—221no—
335D8—221no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8—221no—
344C2×C8—221no—
345C2×C8#433912yes—
346C2×C8D4×D1111yescharacteristic
347C2×C8#434312yes—
348C2×C8C23×D1111yescharacteristic
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—41no—
353C4⋊C4—222no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C22⋊C4—41no—
358C22⋊C4—441no—
359C22⋊C4—441no—
360C22⋊C4—442no—
361C22⋊C4—442no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C42—41no—
365C42—442no—
366C42—442no—
367C16—22no—
368C16—222no—
369C11#3364711yescharacteristic, complemented, Sylow
370C23—111no—
371C23—111no—
372C23—222no—
373C23—441no—
374C23—441no—
375C23—441no—
376C23D8×D1111yescharacteristic
377Q8—441no—
378Q8—441no—
379D4—441no—
380D4—441no—
381D4—882no—
382D4—882no—
383D4—882no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4#6694712yes—
402C2×C4D8×D1111yescharacteristic
403C2×C4#6697112yes—
404C2×C4C2×D4×D1111yescharacteristic
405C8—221no—
406C8—221no—
407C8#6694712yes—
408C8C2×#433911yescharacteristic
409C8C2×#434311yescharacteristic
410C22—21no—
411C22—21no—
412C22—221no—
413C22—221no—
414C22—221no—
415C22—221no—
416C22—221no—
417C22—221no—
418C22—444no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22#1062249512yes—
423C22C2×D8×D1111yescharacteristic
424C4—82no—
425C4—81no—
426C4—81no—
427C4—221no—
428C4—221no—
429C4—882no—
430C4—881no—
431C4#1062249512yes—
432C4C2×#6694711yescharacteristic
433C4C2×#6697111yescharacteristic
434C2—22no—
435C2—441no—
436C2—441no—
437C2—1761no—
438C2C2×#1062249511yescharacteristic
439C2#1308174811yescharacteristic
440C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radical#13078198C2
hypercenter#2159D11
hypocenterC11#33647
LCSG ▷ C2×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. C2×#10622493C2semidirect
3. #13070827C2semidirect
4. #13070826C2semidirect
5. #13070810C2semidirect
6. #13070809C2semidirect
7. #13070405C2semidirect
8. #13070329C2semidirect
9. #13070326C2semidirect
10. #13070226C2semidirect
11. C11×#2159C2semidirect
33. C11×#367C22semidirect
34. C11×#366C22semidirect
35. #10622147C22semidirect
38. #10622141C22semidirect
39. #10622130C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
157. #2159D11semidirect
223. #367C2×D11semidirect
225. #366C2×D11semidirect
369. C11#33647semidirect

Maximal subgroups

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

subgroupindex
#130781982
C2×#106224932
#130708272
#130708262
#130708102
#130708092
#130704052
#130703292
#130703262
#130702262
C11×#21592
#3364711