Finite Group Databasebeta

← #28373214

Subgroups — #28373214

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#20295641C211yesmaximal, characteristic, complemented
2#20295498C211yesmaximal, characteristic, complemented
3#20295370C211yesmaximal, characteristic, complemented
4#20295348C211yesmaximal, characteristic, complemented
5#20295315C211yesmaximal, characteristic, complemented
6#20295304C211yesmaximal, characteristic, complemented
7#20295240C211yesmaximal, characteristic, complemented
8#20295239C211yesmaximal, characteristic, complemented
9#20295178C211yesmaximal, characteristic, complemented
10#20295158C211yesmaximal, characteristic
11#20295128C211yesmaximal, characteristic, complemented
12C4×#13182017C211yesmaximal, characteristic, complemented
13C4×#13182014C211yesmaximal, characteristic, complemented
14#20295088C211yesmaximal, characteristic, complemented
15#442×C109C211yesmaximal, characteristic, complemented
16C2×D4×D109C2211yescharacteristic
17C2×#13182018C2211yescharacteristic
18C2×#13182017C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20#16812698C2211yescharacteristic, complemented
21#16812692—21no—
22#16812686C2211yescharacteristic, complemented
23#16812685—21no—
24#16812682—21no—
25#16812679C2211yescharacteristic
26#16812678—21no—
27#16812670C2211yescharacteristic
28C4×Dic218C2211yescharacteristic, complemented
29C4×D436C2211yescharacteristic
30D4×Dic109C2211yescharacteristic
31#16812661C2211yescharacteristic
32C4×C22⋊D109—21no—
33#16812659—21no—
34#16812657C2211yescharacteristic
35#16812656C2211yescharacteristic
36C2×#13182006—21no—
37C22⋊C4×D109—21no—
38#16812633C2211yescharacteristic, complemented
39#16812632C2211yescharacteristic, complemented
40#16812630C2211yescharacteristic, complemented
41#16812628C2211yescharacteristic, complemented
42#16812628C2211yescharacteristic, complemented
43#16812624C2211yescharacteristic, complemented
44#16812622C2211yescharacteristic, complemented
45#16812621C2211yescharacteristic
46#16812620C2211yescharacteristic
47#16812620C2211yescharacteristic, complemented
48#16812619C2211yescharacteristic
49#16812611C2211yescharacteristic
50#16812611C2211yescharacteristic
51C4×#11724784C2211yescharacteristic, complemented
52C2×D8×C109C2211yescharacteristic
53C4×D4×C109C2211yescharacteristic
54C4×D4×C109C2211yescharacteristic, complemented
55#106×C109C2211yescharacteristic, complemented
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic, complemented
58#97×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60C2×Dic218—21no—
61C2×Dic218C2311yescharacteristic
62C2×D436C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65D4×D109—22no—
66D4×D109—22no—
67C22×Dic109—21no—
68C2×C4×D109—21no—
69C2×C4×D109—21no—
70C2×C4×D109C2311yescharacteristic
71#13182018—22no—
72#13182017—22no—
73#13182014—22no—
74C2×#11724784C2311yescharacteristic
75C2×#11724784C2311yescharacteristic
76C4⋊Dic109—21no—
77C4⋊Dic109C2311yescharacteristic
78C4⋊Dic109C2311yescharacteristic
79#13182008—21no—
80#13182008—21no—
81#13182008D411yescharacteristic
82#13182008D411yescharacteristic
83C22⋊Dic109—21no—
84C22⋊Dic109—21no—
85C22⋊Dic109—21no—
86C22⋊Dic109—21no—
87#13182006—21no—
88#13182006—21no—
89#13182006—21no—
90#13182006—21no—
91#13182006D411yescharacteristic
92#13182006D411yescharacteristic
93C4×Dic109—21no—
94C4×Dic109—21no—
95C4×Dic109C2311yescharacteristic
96C2×D4×C109C2311yescharacteristic
97C2×D4×C109C2311yescharacteristic
98C22×C4×C109—21no—
99C22×C4×C109—21no—
100D8×C109—22no—
101C2×C8×C109C2311yescharacteristic
102C2×C8×C109C2311yescharacteristic
103C4⋊C4×C109C2311yescharacteristic
104C4⋊C4×C109C2311yescharacteristic
105C22⋊C4×C109—21no—
106C22⋊C4×C109—21no—
107C42×C109C2311yescharacteristic
108C23×C109—21no—
109C23×C109—21no—
110C22×D109—21no—
111C22×D109—24no—
112C22×D109—81no—
113C22×D109—81no—
114C22×D109C2×D411yescharacteristic
115D4×C109—21no—
116D4×C109—21no—
117D4×C109—21no—
118D4×C109#4112yes—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—81no—
122C2×C4×C109—81no—
123C2×C4×C109C2×D411yescharacteristic
124C2×C4×C109C2×D411yescharacteristic
125C2×C4×C109C2411yescharacteristic
126C22⋊D109—24no—
127C22⋊D109—81no—
128C2×Dic109—21no—
129C2×Dic109—21no—
130C2×Dic109—21no—
131C2×Dic109—81no—
132C2×Dic109C2×D411yescharacteristic
133C2×Dic109C2×D411yescharacteristic
134C2×Dic109C2×D411yescharacteristic
135D436—21no—
136D436#4112yes—
137C4×D109—21no—
138C4×D109—21no—
139C4×D109—81no—
140C4×D109—81no—
141Dic218—21no—
142Dic218—21no—
143Dic218—81no—
144C8×C109—21no—
145C8×C109—21no—
146#11724784—21no—
147#11724784—21no—
148C22×C109—22no—
149C22×C109—41no—
150C22×C109—41no—
151C22×C109—41no—
152C22×C109—41no—
153C22×C109—41no—
154C22×C109C22×D411yescharacteristic
155C2×D109—21no—
156C2×D109—22no—
157C2×D109—21no—
158C2×D109—21no—
159C2×D109—41no—
160C2×D109—41no—
161C2×D109—84no—
162C4×C109—21no—
163C4×C109—21no—
164C4×C109—41no—
165C4×C109—41no—
166C4×C109C2×#4111yescharacteristic
167C4×C109C2×#4111yescharacteristic
168Dic109—21no—
169Dic109—21no—
170Dic109—21no—
171Dic109—41no—
172Dic109—41no—
173Dic109—41no—
174C2×C109—42no—
175C2×C109—81no—
176C2×C109#52511yescharacteristic
177C2×C109#57611yescharacteristic
178C2×C109#57711yescharacteristic
179D109—41no—
180D109—42no—
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#442D10911yescharacteristic, complemented
194#440—1091no—
195C4×SD16—1091no—
196C4×D8—1091no—
197#433—1091no—
198C22×D4—1091no—
199C2×SD16—1091no—
200C2×SD16—1091no—
201C2×D8—1091no—
202C2×D8C2×D10911yescharacteristic
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—2181no—
216C4×D4—2181no—
217C4×D4C2×D10911yescharacteristic
218C4×D4C2×D10911yescharacteristic, complemented
219#117—1091no—
220#117—1091no—
221C2×C22⋊C4—2181no—
222C2×C22⋊C4—2181no—
223#107—1091no—
224#107—1091no—
225#106—1091no—
226#106C2×D10911yescharacteristic, complemented
227C4⋊C8—1091no—
228C4⋊C8—1091no—
229#103—1091no—
230#103—1091no—
231#102—1091no—
232#102—1091no—
233#102—1091no—
234#102—1091no—
235#102C2×D10911yescharacteristic
236#102C2×D10911yescharacteristic, complemented
237C22⋊C8—1091no—
238C22⋊C8—1091no—
239#97C2×D10911yescharacteristic, complemented
240C4×C8—1091no—
241C24—2181no—
242C2×Q8—1091no—
243C2×Q8—2181no—
244C2×D4—1091no—
245C2×D4—2181no—
246C2×D4—2182no—
247C2×D4—2181no—
248C2×D4—2182no—
249C2×D4C22×D10911yescharacteristic
250C2×D4C22×D10911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1091no—
254C22×C4—2181no—
255C22×C4—2181no—
256C22×C4—2181no—
257SD16—2182no—
258SD16—2182no—
259D8—22no—
260D8—2182no—
261C2×C8—1091no—
262C2×C8—1091no—
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⋊C4C22×D10911yescharacteristic
273C4⋊C4C22×D10911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—1091no—
277C22⋊C4—1091no—
278C22⋊C4—2181no—
279C22⋊C4—2181no—
280C22⋊C4—2181no—
281C22⋊C4—2181no—
282C22⋊C4—2181no—
283C22⋊C4—2181no—
284C22⋊C4—2181no—
285C22⋊C4—2181no—
286C42—1091no—
287C42—2181no—
288C42—2181no—
289C42C22×D10911yescharacteristic
290C23—21no—
291C23—21no—
292C23—8721no—
293C23—8721no—
294C23—1091no—
295C23—2184no—
296C23—2181no—
297Q8—8721no—
298Q8—2181no—
299Q8—2181no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—8721no—
304D4—1092no—
305D4—2184no—
306D4—2181no—
307D4#1318202912yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—8721no—
313C2×C4—8721no—
314C2×C4—8721no—
315C2×C4—1091no—
316C2×C4—1091no—
317C2×C4—1091no—
318C2×C4—2181no—
319C2×C4—2181no—
320C2×C4—2181no—
321C2×C4—2181no—
322C2×C4—2181no—
323C2×C4D4×D10911yescharacteristic
324C2×C4D4×D10911yescharacteristic
325C2×C4C23×D10911yescharacteristic
326C8—21no—
327C8—21no—
328C8—2181no—
329C8—2181no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—8724no—
337C22—4361no—
338C22—4361no—
339C22—2181no—
340C22—2182no—
341C22—2181no—
342C22—2181no—
343C22C2×D4×D10911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—4361no—
349C4—4361no—
350C4—4361no—
351C4—2181no—
352C4—2181no—
353C4—2181no—
354C4#41×D10911yescharacteristic
355C4C2×#1318202911yescharacteristic
356C2—42no—
357C2—81no—
358C2—4361no—
359C2—4362no—
360C2#2029553511yescharacteristic
361C2#2029583011yescharacteristic
362C2#2029583611yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#442×C109C2
socleC22×C109C22×D4
prime radical#20295158C2
hypercenter#442D109
hypocenterC109#3118
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #20295641C2semidirect
2. #20295498C2semidirect
3. #20295370C2semidirect
4. #20295348C2semidirect
5. #20295315C2semidirect
6. #20295304C2semidirect
7. #20295240C2semidirect
8. #20295239C2semidirect
9. #20295178C2semidirect
11. #20295128C2semidirect
12. C4×#13182017C2semidirect
13. C4×#13182014C2semidirect
14. #20295088C2semidirect
15. #442×C109C2semidirect
20. #16812698C22semidirect
22. #16812686C22semidirect
28. C4×Dic218C22semidirect
38. #16812633C22semidirect
39. #16812632C22semidirect
40. #16812630C22semidirect
41. #16812628C22semidirect
42. #16812628C22semidirect
43. #16812624C22semidirect
44. #16812622C22semidirect
47. #16812620C22semidirect
51. C4×#11724784C22semidirect
54. C4×D4×C109C22semidirect
55. #106×C109C22semidirect
57. #102×C109C22semidirect
58. #97×C109C22semidirect
182. C109#3118semidirect
193. #442D109semidirect
218. C4×D4C2×D109semidirect
226. #106C2×D109semidirect
236. #102C2×D109semidirect
239. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956412
#202954982
#202953702
#202953482
#202953152
#202953042
#202952402
#202952392
#202951782
#202951582
#202951282
C4×#131820172
C4×#131820142
#202950882
#442×C1092
#3118109