Finite Group Databasebeta

← #28373274

Subgroups — #28373274

Order 13952.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295627C211yesmaximal, characteristic, complemented
2#20295498C211yesmaximal, characteristic, complemented
3#20295352C211yesmaximal, characteristic, complemented
4#20295349C211yesmaximal, characteristic, complemented
5#20295328C211yesmaximal, characteristic, complemented
6#20295325C211yesmaximal, characteristic, complemented
7#20295220C211yesmaximal, characteristic, complemented
8#20295219C211yesmaximal, characteristic, complemented
9#20295161C211yesmaximal, characteristic, complemented
10#20295158C211yesmaximal, characteristic, complemented
11#20295139C211yesmaximal, characteristic, complemented
12C4×#13182014C211yesmaximal, characteristic, complemented
13C4×#13182014C211yesmaximal, characteristic, complemented
14#20295088C211yesmaximal, characteristic, complemented
15#442×C109C211yesmaximal, characteristic, complemented
16C2×D4×D109C2211yescharacteristic
17C2×D872C2211yescharacteristic
18C2×#13182014C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20#16812695C2211yescharacteristic, complemented
21#16812690C2211yescharacteristic, complemented
22#16812682—21no—
23#16812681—21no—
24#16812674C2211yescharacteristic
25#16812673—21no—
26#16812672—21no—
27#16812670C2211yescharacteristic
28C4×D436C2211yescharacteristic
29C4×D436C2211yescharacteristic, complemented
30D4×Dic109C2211yescharacteristic
31#16812661C2211yescharacteristic
32C4×C22⋊D109—21no—
33#16812659—21no—
34#16812657C2211yescharacteristic
35#16812656C2211yescharacteristic
36C2×#13182006—21no—
37C22⋊C4×D109—21no—
38#16812632C2211yescharacteristic, complemented
39#16812632C2211yescharacteristic, complemented
40#16812631C2211yescharacteristic, complemented
41#16812628C2211yescharacteristic, complemented
42#16812628C2211yescharacteristic, complemented
43#16812621C2211yescharacteristic
44#16812621C2211yescharacteristic, complemented
45#16812620C2211yescharacteristic
46#16812620C2211yescharacteristic, complemented
47#16812619C2211yescharacteristic
48#16812619C2211yescharacteristic, complemented
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×D436—21no—
61C2×D436C2311yescharacteristic
62C2×D436C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C22⋊D109—21no—
66C2×C22⋊D109—21no—
67D4×D109—22no—
68D4×D109—22no—
69C22×Dic109—21no—
70C2×C4×D109—21no—
71C2×C4×D109—21no—
72C2×C4×D109—21no—
73C2×C4×D109C2311yescharacteristic
74D872—22no—
75#13182014—22no—
76#13182014—22no—
77C2×#11724784C2311yescharacteristic
78C2×#11724784C2311yescharacteristic
79C4⋊Dic109—21no—
80C4⋊Dic109C2311yescharacteristic
81C4⋊Dic109C2311yescharacteristic
82#13182008—21no—
83#13182008D411yescharacteristic
84#13182008D411yescharacteristic
85C22⋊Dic109—21no—
86C22⋊Dic109—21no—
87#13182006—21no—
88#13182006—21no—
89#13182006—21no—
90#13182006—21no—
91#13182006—21no—
92#13182006D411yescharacteristic
93#13182006D411yescharacteristic
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—21no—
113C22×D109—81no—
114C22×D109—81no—
115C22×D109C2×D411yescharacteristic
116D4×C109—21no—
117D4×C109—21no—
118D4×C109—21no—
119D4×C109#4112yes—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—81no—
123C2×C4×C109—81no—
124C2×C4×C109C2×D411yescharacteristic
125C2×C4×C109C2×D411yescharacteristic
126C2×C4×C109C2411yescharacteristic
127C22⋊D109—24no—
128C22⋊D109—81no—
129C22⋊D109—81no—
130C22⋊D109—81no—
131C2×Dic109—21no—
132C2×Dic109—21no—
133C2×Dic109—81no—
134C2×Dic109C2×D411yescharacteristic
135C2×Dic109C2×D411yescharacteristic
136C2×Dic109C2×D411yescharacteristic
137D436—21no—
138D436—21no—
139D436—21no—
140D436—81no—
141D436#4112yes—
142C4×D109—21no—
143C4×D109—21no—
144C4×D109—81no—
145C4×D109—81no—
146C4×D109—81no—
147C8×C109—21no—
148C8×C109—21no—
149#11724784—21no—
150#11724784—21no—
151C22×C109—22no—
152C22×C109—41no—
153C22×C109—41no—
154C22×C109—41no—
155C22×C109—41no—
156C22×C109—41no—
157C22×C109C22×D411yescharacteristic
158C2×D109—21no—
159C2×D109—22no—
160C2×D109—21no—
161C2×D109—21no—
162C2×D109—41no—
163C2×D109—41no—
164C2×D109—41no—
165C2×D109—41no—
166C2×D109—41no—
167C2×D109—84no—
168C4×C109—21no—
169C4×C109—21no—
170C4×C109—41no—
171C4×C109—41no—
172C4×C109C2×#4111yescharacteristic
173C4×C109C2×#4111yescharacteristic
174Dic109—21no—
175Dic109—21no—
176Dic109—21no—
177Dic109—41no—
178Dic109—41no—
179C2×C109—42no—
180C2×C109—81no—
181C2×C109#52511yescharacteristic
182C2×C109#57611yescharacteristic
183C2×C109#57611yescharacteristic
184D109—41no—
185D109—42no—
186D109—81no—
187#3122—1091nomaximal, Sylow
188C109#312211yescharacteristic, complemented, Sylow
189#540—1091no—
190#518—1091no—
191#482—1091no—
192#482—1091no—
193#478—1091no—
194#478—1091no—
195#459—1091no—
196#459—1091no—
197#447—1091no—
198#447—1091no—
199#442—1091no—
200#442D10911yescharacteristic, complemented
201C4×D8—1091no—
202C4×D8—1091no—
203#433—1091no—
204C22×D4—1091no—
205C2×D8—1091no—
206C2×D8—1091no—
207C2×D8—1091no—
208C2×D8C2×D10911yescharacteristic
209#127—1091no—
210#125—1091no—
211#123—2181no—
212#123—2181no—
213#121—1091no—
214#121—1091no—
215#121—2181no—
216#121—2181no—
217C4×D4—1091no—
218C4×D4—1091no—
219C4×D4—1091no—
220C4×D4—1091no—
221C4×D4—2181no—
222C4×D4—2181no—
223C4×D4C2×D10911yescharacteristic
224C4×D4C2×D10911yescharacteristic, complemented
225#117—1091no—
226#117—1091no—
227C2×C22⋊C4—2181no—
228C2×C22⋊C4—2181no—
229#107—1091no—
230#107—1091no—
231#106—1091no—
232#106C2×D10911yescharacteristic, complemented
233C4⋊C8—1091no—
234C4⋊C8—1091no—
235#102—1091no—
236#102—1091no—
237#102—1091no—
238#102—1091no—
239#102—1091no—
240#102—1091no—
241#102C2×D10911yescharacteristic
242#102C2×D10911yescharacteristic, complemented
243C22⋊C8—1091no—
244C22⋊C8—1091no—
245#97C2×D10911yescharacteristic, complemented
246C4×C8—1091no—
247C24—2181no—
248C2×D4—1091no—
249C2×D4—1091no—
250C2×D4—2181no—
251C2×D4—2181no—
252C2×D4—2181no—
253C2×D4—2181no—
254C2×D4—2182no—
255C2×D4—2181no—
256C2×D4—2182no—
257C2×D4C22×D10911yescharacteristic
258C2×D4C22×D10911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1091no—
262C22×C4—2181no—
263C22×C4—2181no—
264C22×C4—2181no—
265C22×C4—2181no—
266D8—22no—
267D8—2182no—
268D8—2182no—
269D8—2182no—
270C2×C8—1091no—
271C2×C8—1091no—
272C2×C8C22×D10911yescharacteristic
273C2×C8C22×D10911yescharacteristic
274C4⋊C4—1091no—
275C4⋊C4—1091no—
276C4⋊C4—1091no—
277C4⋊C4—1091no—
278C4⋊C4—2181no—
279C4⋊C4—2181no—
280C4⋊C4C22×D10911yescharacteristic
281C4⋊C4C22×D10911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1091no—
285C22⋊C4—1091no—
286C22⋊C4—2181no—
287C22⋊C4—2181no—
288C22⋊C4—2181no—
289C22⋊C4—2181no—
290C22⋊C4—2181no—
291C22⋊C4—2181no—
292C22⋊C4—2181no—
293C42—1091no—
294C42—2181no—
295C42C22×D10911yescharacteristic
296C23—21no—
297C23—21no—
298C23—8721no—
299C23—8721no—
300C23—1091no—
301C23—2184no—
302C23—2181no—
303C23—2181no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—8721no—
308D4—8721no—
309D4—8721no—
310D4—8721no—
311D4—1092no—
312D4—2184no—
313D4—2181no—
314D4—2181no—
315D4—2181no—
316D4#1318202912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—8721no—
322C2×C4—8721no—
323C2×C4—8721no—
324C2×C4—8721no—
325C2×C4—1091no—
326C2×C4—1091no—
327C2×C4—1091no—
328C2×C4—2181no—
329C2×C4—2181no—
330C2×C4—2181no—
331C2×C4—2181no—
332C2×C4D4×D10911yescharacteristic
333C2×C4D4×D10911yescharacteristic
334C2×C4C23×D10911yescharacteristic
335C8—21no—
336C8—21no—
337C8—2181no—
338C8—2181no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—8724no—
346C22—4361no—
347C22—4361no—
348C22—4361no—
349C22—4361no—
350C22—4361no—
351C22—2181no—
352C22—2182no—
353C22—2181no—
354C22—2181no—
355C22C2×D4×D10911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—4361no—
361C4—4361no—
362C4—2181no—
363C4—2181no—
364C4—2181no—
365C4#41×D10911yescharacteristic
366C4C2×#1318202911yescharacteristic
367C2—42no—
368C2—81no—
369C2—8721no—
370C2—4361no—
371C2—4362no—
372C2#2029553511yescharacteristic
373C2#2029583011yescharacteristic
374C2#2029583011yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#442×C109C2
socleC22×C109C22×D4
hypercenter#442D109
hypocenterC109#3122
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. #20295627C2semidirect
2. #20295498C2semidirect
3. #20295352C2semidirect
4. #20295349C2semidirect
5. #20295328C2semidirect
6. #20295325C2semidirect
7. #20295220C2semidirect
8. #20295219C2semidirect
9. #20295161C2semidirect
10. #20295158C2semidirect
11. #20295139C2semidirect
12. C4×#13182014C2semidirect
13. C4×#13182014C2semidirect
14. #20295088C2semidirect
15. #442×C109C2semidirect
20. #16812695C22semidirect
21. #16812690C22semidirect
29. C4×D436C22semidirect
38. #16812632C22semidirect
39. #16812632C22semidirect
40. #16812631C22semidirect
41. #16812628C22semidirect
42. #16812628C22semidirect
44. #16812621C22semidirect
46. #16812620C22semidirect
48. #16812619C22semidirect
51. C4×#11724784C22semidirect
54. C4×D4×C109C22semidirect
55. #106×C109C22semidirect
57. #102×C109C22semidirect
58. #97×C109C22semidirect
188. C109#3122semidirect
200. #442D109semidirect
224. C4×D4C2×D109semidirect
232. #106C2×D109semidirect
242. #102C2×D109semidirect
245. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956272
#202954982
#202953522
#202953492
#202953282
#202953252
#202952202
#202952192
#202951612
#202951582
#202951392
C4×#131820142
#202950882
#442×C1092
#3122109