Finite Group Databasebeta

← #28373218

Subgroups — #28373218

Order 13952.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295647C211yesmaximal, characteristic, complemented
2#20295500C211yesmaximal, characteristic, complemented
3#20295368C211yesmaximal, characteristic, complemented
4#20295351C211yesmaximal, characteristic, complemented
5#20295317C211yesmaximal, characteristic, complemented
6#20295307C211yesmaximal, characteristic, complemented
7#20295242C211yesmaximal, characteristic, complemented
8#20295242C211yesmaximal, characteristic, complemented
9#20295179C211yesmaximal, characteristic, complemented
10#20295162C211yesmaximal, characteristic
11#20295139C211yesmaximal, characteristic, complemented
12#20295128C211yesmaximal, characteristic, complemented
13C4×#13182018C211yesmaximal, characteristic, complemented
14C4×D872C211yesmaximal, characteristic, complemented
15#433×C109C211yesmaximal, characteristic, complemented
16C22×D436C2211yescharacteristic
17C2×#13182018C2211yescharacteristic
18C2×#13182018C2211yescharacteristic
19C2×D872C2211yescharacteristic
20C2×D872C2211yescharacteristic
21#16812699C2211yescharacteristic, complemented
22#16812694—21no—
23#16812687C2211yescharacteristic, complemented
24#16812685—21no—
25#16812681—21no—
26#16812678C2211yescharacteristic
27#16812677—21no—
28#16812673C2211yescharacteristic
29C4×Dic218C2211yescharacteristic, complemented
30C4×D436C2211yescharacteristic
31C4×D436C2211yescharacteristic
32C4×D436C2211yescharacteristic
33C4×D436C2211yescharacteristic
34C4×D436C2211yescharacteristic, complemented
35#16812661—21no—
36#16812661—21no—
37#16812658C2211yescharacteristic
38C22⋊C4×D109—21no—
39C22⋊C4×D109—21no—
40#16812633C2211yescharacteristic, complemented
41#16812633C2211yescharacteristic, complemented
42#16812631C2211yescharacteristic, complemented
43#16812631C2211yescharacteristic, complemented
44#16812624C2211yescharacteristic, complemented
45#16812624C2211yescharacteristic, complemented
46#16812621C2211yescharacteristic
47#16812621C2211yescharacteristic
48#16812621C2211yescharacteristic
49#16812621C2211yescharacteristic
50#16812621C2211yescharacteristic, complemented
51#16812621C2211yescharacteristic, complemented
52#117×C109C2211yescharacteristic
53C4⋊C8×C109C2211yescharacteristic, complemented
54C4⋊C8×C109C2211yescharacteristic, complemented
55C22⋊C8×C109C2211yescharacteristic
56C22⋊C8×C109C2211yescharacteristic
57#97×C109C2211yescharacteristic, complemented
58C4×C8×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60C2×Dic218—21no—
61C2×Dic218C2311yescharacteristic
62C2×D436—21no—
63C2×D436—22no—
64C2×D436—22no—
65C2×D436C2311yescharacteristic
66C2×D436C2311yescharacteristic
67C2×D436C2311yescharacteristic
68C2×C22⋊D109—21no—
69C2×C4×D109—21no—
70C2×C4×D109—21no—
71C2×C4×D109—21no—
72C2×C4×D109—21no—
73C2×C4×D109—21no—
74#13182018—22no—
75#13182018—22no—
76D872—22no—
77D872—22no—
78C4⋊Dic109—21no—
79C4⋊Dic109C2311yescharacteristic
80C4⋊Dic109C2311yescharacteristic
81C4⋊Dic109C2311yescharacteristic
82C4⋊Dic109C2311yescharacteristic
83#13182008—21no—
84#13182008—21no—
85C22⋊Dic109—21no—
86C22⋊Dic109—21no—
87#13182006—21no—
88#13182006—21no—
89#13182006—21no—
90#13182006—21no—
91#13182006—21no—
92#13182006—21no—
93#13182006—21no—
94#13182006—21no—
95C4×Dic109—21no—
96C4×Dic109—21no—
97C22×C4×C109C2311yescharacteristic
98C2×C8×C109C2311yescharacteristic
99C2×C8×C109C2311yescharacteristic
100C2×C8×C109C2311yescharacteristic
101C2×C8×C109C2311yescharacteristic
102C4⋊C4×C109D411yescharacteristic
103C4⋊C4×C109D411yescharacteristic
104C22⋊C4×C109D411yescharacteristic
105C22⋊C4×C109D411yescharacteristic
106C42×C109C2311yescharacteristic
107C42×C109C2311yescharacteristic
108C23×C109C2×D411yescharacteristic
109C22×D109—21no—
110C22×D109—21no—
111C22×D109—24no—
112C22×D109—21no—
113C22×D109—81no—
114C22×D109—81no—
115C2×C4×C109—21no—
116C2×C4×C109—21no—
117C2×C4×C109C2×D411yescharacteristic
118C2×C4×C109C2×D411yescharacteristic
119C2×C4×C109C2×D411yescharacteristic
120C2×C4×C109C2×D411yescharacteristic
121C2×C4×C109C2×D411yescharacteristic
122C2×C4×C109C2411yescharacteristic
123C22⋊D109—81no—
124C2×Dic109—21no—
125C2×Dic109—21no—
126C2×Dic109—21no—
127C2×Dic109—21no—
128C2×Dic109—21no—
129D436—24no—
130D436—21no—
131D436—21no—
132D436—21no—
133D436—21no—
134D436#4112yes—
135D436#4112yes—
136C4×D109—81no—
137C4×D109—81no—
138C4×D109—81no—
139C4×D109—81no—
140C4×D109—81no—
141Dic218—21no—
142Dic218—21no—
143Dic218—81no—
144C8×C109—21no—
145C8×C109—21no—
146C8×C109—21no—
147C8×C109—21no—
148C22×C109—21no—
149C22×C109—21no—
150C22×C109—21no—
151C22×C109C22×D411yescharacteristic
152C2×D109—22no—
153C2×D109—22no—
154C2×D109—41no—
155C2×D109—41no—
156C2×D109—41no—
157C2×D109—41no—
158C2×D109—41no—
159C2×D109—41no—
160C2×D109—41no—
161C2×D109—84no—
162C4×C109—21no—
163C4×C109—21no—
164C4×C109—21no—
165C4×C109—21no—
166C4×C109—21no—
167C4×C109C2×#4111yescharacteristic
168C4×C109C2×#4111yescharacteristic
169Dic109—41no—
170Dic109—41no—
171Dic109—41no—
172Dic109—41no—
173Dic109—41no—
174C2×C109—41no—
175C2×C109#52511yescharacteristic
176C2×C109#57611yescharacteristic
177C2×C109#57711yescharacteristic
178D109—42no—
179D109—42no—
180D109—81no—
181#3118—1091nomaximal, Sylow
182C109#311811yescharacteristic, complemented, Sylow
183#542—1091no—
184#518—1091no—
185#485—1091no—
186#482—1091no—
187#476—1091no—
188#474—1091no—
189#463—1091no—
190#463—1091no—
191#450—1091no—
192#447—1091no—
193#442—1091no—
194#440—1091no—
195C4×SD16—1091no—
196C4×D8—1091no—
197#433D10911yescharacteristic, complemented
198C22×D4—1091no—
199C2×SD16—1091no—
200C2×SD16—1091no—
201C2×D8—1091no—
202C2×D8—1091no—
203C4⋊Q8—1091no—
204#126—2181no—
205#124—1091no—
206#124—2181no—
207#123—2181no—
208C22⋊Q8—1091no—
209C22⋊Q8—2181no—
210#121—1091no—
211C4×Q8—1091no—
212C4×D4—1091no—
213C4×D4—1091no—
214C4×D4—1091no—
215C4×D4—1091no—
216C4×D4—1091no—
217C4×D4—2181no—
218C4×D4—2181no—
219#117—1091no—
220#117C2×D10911yescharacteristic
221C2×C22⋊C4—2181no—
222C2×C22⋊C4—2181no—
223#107—1091no—
224#107—1091no—
225#106—1091no—
226#106—1091no—
227C4⋊C8C2×D10911yescharacteristic, complemented
228C4⋊C8C2×D10911yescharacteristic, complemented
229#103—1091no—
230#103—1091no—
231#102—1091no—
232#102—1091no—
233#102—1091no—
234#102—1091no—
235#102—1091no—
236#102—1091no—
237C22⋊C8C2×D10911yescharacteristic
238C22⋊C8C2×D10911yescharacteristic
239#97C2×D10911yescharacteristic, complemented
240C4×C8C2×D10911yescharacteristic, complemented
241C24—2181no—
242C2×Q8—1091no—
243C2×Q8—2181no—
244C2×D4—1091no—
245C2×D4—1091no—
246C2×D4—1091no—
247C2×D4—2182no—
248C2×D4—2182no—
249C2×D4—2181no—
250C2×D4—2181no—
251C22×C4—2181no—
252C22×C4—2181no—
253C22×C4—2181no—
254C22×C4—2181no—
255C22×C4—2181no—
256C22×C4C22×D10911yescharacteristic
257SD16—2182no—
258SD16—2182no—
259D8—2182no—
260D8—2182no—
261C2×C8C22×D10911yescharacteristic
262C2×C8C22×D10911yescharacteristic
263C2×C8C22×D10911yescharacteristic
264C2×C8C22×D10911yescharacteristic
265C4⋊C4—1091no—
266C4⋊C4—1091no—
267C4⋊C4—1091no—
268C4⋊C4—1091no—
269C4⋊C4—2181no—
270C4⋊C4—2181no—
271C4⋊C4—2181no—
272C4⋊C4D43611yescharacteristic
273C4⋊C4D43611yescharacteristic
274C22⋊C4—2181no—
275C22⋊C4—2181no—
276C22⋊C4—2181no—
277C22⋊C4—2181no—
278C22⋊C4—2181no—
279C22⋊C4—2181no—
280C22⋊C4—2181no—
281C22⋊C4—2181no—
282C22⋊C4—2181no—
283C22⋊C4—2181no—
284C22⋊C4D43611yescharacteristic
285C22⋊C4D43611yescharacteristic
286C42—2181no—
287C42—2181no—
288C42C22×D10911yescharacteristic
289C42C22×D10911yescharacteristic
290C23—8721no—
291C23—8721no—
292C23—2184no—
293C23—2181no—
294C23—2181no—
295C23—2181no—
296C23C2×D43611yescharacteristic
297Q8—8721no—
298Q8—2181no—
299Q8—2181no—
300D4—8721no—
301D4—1092no—
302D4—1092no—
303D4—2184no—
304D4—2181no—
305D4—2181no—
306D4—2181no—
307D4—2181no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—8721no—
311C2×C4—8721no—
312C2×C4—8721no—
313C2×C4—8721no—
314C2×C4—8721no—
315C2×C4—2181no—
316C2×C4—2181no—
317C2×C4—2181no—
318C2×C4—2181no—
319C2×C4—2181no—
320C2×C4C2×D43611yescharacteristic
321C2×C4C2×D43611yescharacteristic
322C2×C4C2×D43611yescharacteristic
323C2×C4C2×D43611yescharacteristic
324C2×C4C2×D43611yescharacteristic
325C2×C4C23×D10911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—8724no—
334C22—4361no—
335C22—4361no—
336C22—4361no—
337C22—4361no—
338C22—4361no—
339C22—4361no—
340C22—4361no—
341C22—2182no—
342C22—2182no—
343C22C22×D43611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—4361no—
350C4—4361no—
351C4—4361no—
352C4—4361no—
353C4—4361no—
354C4#41×D10911yescharacteristic
355C4#41×D10911yescharacteristic
356C2—41no—
357C2—8721no—
358C2—4362no—
359C2—4362no—
360C2#2029553811yescharacteristic
361C2#2029583111yescharacteristic
362C2#2029583811yescharacteristic
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#433×C109C2
socleC22×C109C22×D4
prime radical#20295162C2
hypercenter#433D109
hypocenterC109#3118
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20295647C2semidirect
2. #20295500C2semidirect
3. #20295368C2semidirect
4. #20295351C2semidirect
5. #20295317C2semidirect
6. #20295307C2semidirect
7. #20295242C2semidirect
8. #20295242C2semidirect
9. #20295179C2semidirect
11. #20295139C2semidirect
12. #20295128C2semidirect
13. C4×#13182018C2semidirect
14. C4×D872C2semidirect
15. #433×C109C2semidirect
21. #16812699C22semidirect
23. #16812687C22semidirect
29. C4×Dic218C22semidirect
34. C4×D436C22semidirect
40. #16812633C22semidirect
41. #16812633C22semidirect
42. #16812631C22semidirect
43. #16812631C22semidirect
44. #16812624C22semidirect
45. #16812624C22semidirect
50. #16812621C22semidirect
51. #16812621C22semidirect
53. C4⋊C8×C109C22semidirect
54. C4⋊C8×C109C22semidirect
57. #97×C109C22semidirect
58. C4×C8×C109C22semidirect
182. C109#3118semidirect
197. #433D109semidirect
227. C4⋊C8C2×D109semidirect
228. C4⋊C8C2×D109semidirect
239. #97C2×D109semidirect
240. C4×C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956472
#202955002
#202953682
#202953512
#202953172
#202953072
#202952422
#202951792
#202951622
#202951392
#202951282
C4×#131820182
C4×D8722
#433×C1092
#3118109