Finite Group Databasebeta

← #14908601

Subgroups — #14908601

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622496C211yesmaximal, characteristic
2D11×#427C211yesmaximal, characteristic, complemented
3#13070810C212yesmaximal, complemented
4#13070809C212yesmaximal, complemented
5#13070803C212yesmaximal, complemented
6#13070798C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070333C211yesmaximal, characteristic, complemented
9#13070331C211yesmaximal, characteristic, complemented
10#13070226C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14D11×#117—21no—
15C2×#66948—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622719C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622611—21no—
22C2×#66873—21no—
23#10622496—21no—
24#10622496—21no—
25#10622496C2212yes—
26#10622496C2212yes—
27#10622493C2211yescharacteristic, complemented
28#10622493C2211yescharacteristic, complemented
29D11×#107C2211yescharacteristic, complemented
30D11×#107C2211yescharacteristic, complemented
31#10622473—21no—
32D11×#106—21no—
33C11×#367C2212yescomplemented
34C11×#366C2212yescomplemented
35#10622147C2212yescomplemented
36#10622147C2212yescomplemented
37(C2×D11)⋊C16C2212yescomplemented
38(C2×D11)⋊C16C2212yescomplemented
39#10622129C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C22×D44—21no—
44C22×D44—41no—
45C22×C4×D11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49C2×(C2×D11)⋊C4—41no—
50#66979—21no—
51C22×C11⋊C8D411yescharacteristic
52C2×D88—22no—
53C2×D88—22no—
54C2×D88—21no—
55C2×D88C2312yes—
56C2×C8×D11—22no—
57C2×C8×D11—22no—
58C2×C8×D11D411yescharacteristic
59C2×C8×D11D411yescharacteristic
60C2×C8×D11C2311yescharacteristic
61C2×C8×D11C2311yescharacteristic
62#66948—22no—
63#66948—22no—
64#66948—41no—
65#66948—41no—
66#66945—21no—
67#66945—21no—
68C4⋊C4×D11—21no—
69C4⋊C4×D11—21no—
70C22⋊C4×D11—41no—
71#66930—41no—
72#66925—41no—
73C42×D11—41no—
74C11×M32—22no—
75C2×C11×C16C2312yes—
76C11×#107—21no—
77C11×#107C2311yescharacteristic
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#106—21no—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84#66876—22no—
85C2×C11⋊C16C2312yes—
86#66873—22no—
87#66873—22no—
88#66872—21no—
89#66872—21no—
90#66871—21no—
91#66871—21no—
92#33648—111nomaximal, Sylow
93C23×D11—41no—
94C23×D11D811yescharacteristic
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11D811yescharacteristic
98C2×D44—22no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—42no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—84no—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11D811yescharacteristic
110C2×C4×D11D811yescharacteristic
111C2×C4×D11C2×D411yescharacteristic
112C2×C4×D11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11#4112yes—
115C2×C8×C11#4112yes—
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C22⋊Dic11—41no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138D88—22no—
139D88—22no—
140D88—42no—
141C8×D11—22no—
142C8×D11—22no—
143C8×D11—21no—
144C8×D11—21no—
145C8×D11—21no—
146C8×D11—21no—
147C11×C16—22no—
148C11⋊C16—22no—
149C2×#466—111no—
150C2×#427—111no—
151#2234—112no—
152#2234—112no—
153#2233—112no—
154#2232—112no—
155#2159—111no—
156#2159D1111yescharacteristic, complemented
157#2140—111no—
158#2140—111no—
159#2112—111no—
160C23×C11C2×D811yescharacteristic
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—42no—
165C22×D11—82no—
166C22×D11—82no—
167C22×D11—82no—
168C22×D11C2×D811yescharacteristic
169C22×D11C2×D811yescharacteristic
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—82no—
174C2×C4×C11#12312yes—
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11#13712yes—
177C2×C4×C11C22×D411yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11C2×D811yescharacteristic
182C2×Dic11C2×D811yescharacteristic
183D44—42no—
184D44—42no—
185D44—84no—
186D44—84no—
187D44—82no—
188C4×D11—21no—
189C4×D11—21no—
190C4×D11—21no—
191C4×D11—21no—
192C4×D11—22no—
193C4×D11—22no—
194C4×D11—82no—
195C4×D11—82no—
196C8×C11#12312yes—
197C8×C11C2×#4111yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—21no—
200C11⋊C8—21no—
201C22×D8—111no—
202C23×C8—111no—
203C2×#121—221no—
204C2×#117—221no—
205C2×M32—111no—
206C2×M32C2×D1111yescharacteristic
207#466—112no—
208#466—112no—
209#466—221no—
210#466—221no—
211#427—111no—
212#427—111no—
213#427—111no—
214#427—221no—
215#427—221no—
216#427C2×D1111yescharacteristic
217C2×#107—111no—
218C2×#107—111no—
219C2×#107C2×D1111yescharacteristic
220C2×#106—221no—
221C2×#102—221no—
222#367—112no—
223#367C2×D1112yescomplemented
224#366—112no—
225#366C2×D1112yescomplemented
226#357—112no—
227#357—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—44no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—164no—
246C2×D11#50912yes—
247C4×C11—82no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11#48012yes—
251C4×C11C2×#12311yescharacteristic
252C4×C11C2×#13711yescharacteristic
253Dic11—21no—
254Dic11—21no—
255Dic11—81no—
256Dic11—81no—
257C22×D4—221no—
258C22×D4—441no—
259C23×C4—111no—
260C2×D8—112no—
261C2×D8—222no—
262C2×D8—221no—
263C2×D8—222no—
264C22×C8—111no—
265C22×C8—111no—
266C22×C8—111no—
267C22×C8—111no—
268C22×C8—111no—
269C22×C8—222no—
270C22×C8—222no—
271C22×C8C22×D1111yescharacteristic
272#121—222no—
273#121—222no—
274#121—441no—
275#121—441no—
276#117—21no—
277#117—221no—
278#117—221no—
279#117—221no—
280#117—441no—
281#117—441no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C22⋊C4—441no—
286C2×C22⋊C4—441no—
287C2×C42—441no—
288M32—22no—
289M32—222no—
290C2×C16—112no—
291C2×C16C22×D1112yes—
292#107—21no—
293#107—111no—
294#107—111no—
295#107—221no—
296#107—221no—
297#107C22×D1111yescharacteristic
298#107C22×D1111yescharacteristic
299#107C22×D1112yes—
300#106—21no—
301#106—221no—
302#106—221no—
303#106—221no—
304#102—222no—
305#102—222no—
306C2×C11—22no—
307C2×C11C2×#48011yescharacteristic
308C2×C11C2×#50911yescharacteristic
309C2×C11#341411yescharacteristic
310D11—22no—
311D11—41no—
312D11—162no—
313C24—111no—
314C24—441no—
315C2×D4—222no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—442no—
319C2×D4—441no—
320C2×D4—442no—
321C2×D4—884no—
322C22×C4—41no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4D4×D1111yescharacteristic
333D8—222no—
334D8—222no—
335D8—442no—
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—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—41no—
353C4⋊C4—221no—
354C4⋊C4—221no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C22⋊C4—41no—
358C22⋊C4—442no—
359C22⋊C4—442no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C42—41no—
364C42—441no—
365C42—441no—
366C42—441no—
367C16—22no—
368C16—222no—
369C11#3364811yescharacteristic, complemented, Sylow
370C23—111no—
371C23—111no—
372C23—222no—
373C23—222no—
374C23—441no—
375C23—442no—
376C23—882no—
377C23—882no—
378C23—882no—
379C23D8×D1111yescharacteristic
380D4—442no—
381D4—442no—
382D4—884no—
383D4—884no—
384D4—882no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—111no—
390C2×C4—111no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—882no—
401C2×C4—882no—
402C2×C4#6694712yes—
403C2×C4D8×D1111yescharacteristic
404C2×C4#6697112yes—
405C2×C4C2×D4×D1111yescharacteristic
406C8—221no—
407C8—221no—
408C8#6694712yes—
409C8C2×#433911yescharacteristic
410C8C2×#434311yescharacteristic
411C22—21no—
412C22—21no—
413C22—112no—
414C22—221no—
415C22—221no—
416C22—221no—
417C22—221no—
418C22—221no—
419C22—444no—
420C22—882no—
421C22—882no—
422C22—882no—
423C22—1764no—
424C22#1062249512yes—
425C22C2×D8×D1111yescharacteristic
426C4—82no—
427C4—81no—
428C4—81no—
429C4—221no—
430C4—221no—
431C4—881no—
432C4—881no—
433C4#1062249512yes—
434C4C2×#6694711yescharacteristic
435C4C2×#6697111yescharacteristic
436C2—22no—
437C2—222no—
438C2—441no—
439C2—1762no—
440C2C2×#1062249511yescharacteristic
441C2D11×#50911yescharacteristic
442C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#10622496C2
hypercenter#2159D11
hypocenterC11#33648
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. D11×#427C2semidirect
3. #13070810C2semidirect
4. #13070809C2semidirect
5. #13070803C2semidirect
6. #13070798C2semidirect
7. #13070402C2semidirect
8. #13070333C2semidirect
9. #13070331C2semidirect
10. #13070226C2semidirect
11. C11×#2159C2semidirect
27. #10622493C22semidirect
28. #10622493C22semidirect
29. D11×#107C22semidirect
30. D11×#107C22semidirect
33. C11×#367C22semidirect
34. C11×#366C22semidirect
35. #10622147C22semidirect
36. #10622147C22semidirect
37. (C2×D11)⋊C16C22semidirect
38. (C2×D11)⋊C16C22semidirect
39. #10622129C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
156. #2159D11semidirect
223. #367C2×D11semidirect
225. #366C2×D11semidirect
369. C11#33648semidirect

Maximal subgroups

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

subgroupindex
C2×#106224962
D11×#4272
#130708102
#130708092
#130708032
#130707982
#130704022
#130703332
#130703312
#130702262
C11×#21592
#3364811