Finite Group Databasebeta

← #28374886

Subgroups — #28374886

Order 13952.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295728C211yesmaximal, characteristic, complemented
2#20295670C211yesmaximal, characteristic, complemented
3#20295379C211yesmaximal, characteristic, complemented
4#20295362C211yesmaximal, characteristic, complemented
5#20295348C211yesmaximal, characteristic, complemented
6#20295324C211yesmaximal, characteristic, complemented
7#20295259C211yesmaximal, characteristic, complemented
8#20295253C211yesmaximal, characteristic, complemented
9#20295239C211yesmaximal, characteristic, complemented
10#20295168C211yesmaximal, characteristic, complemented
11D8×Dic109C211yesmaximal, characteristic, complemented
12#20295089C211yesmaximal, characteristic, complemented
13#20295019C211yesmaximal, characteristic, complemented
14C2×#16812620C211yesmaximal, characteristic, complemented
15#447×C109C211yesmaximal, characteristic, complemented
16C2×#13182028C2211yescharacteristic
17C2×#13182017C2211yescharacteristic, complemented
18C22×#11724784C2211yescharacteristic
19C2×C8×D109C2211yescharacteristic, complemented
20#16812692—21no—
21#16812690C2211yescharacteristic, complemented
22#16812686C2211yescharacteristic
23#16812683—21no—
24#16812680—21no—
25#16812678C2211yescharacteristic
26#16812671—21no—
27#16812671—21no—
28#16812670C2211yescharacteristic
29#16812670C2211yescharacteristic, complemented
30#16812668—21no—
31D4×Dic109—21no—
32D4×Dic109C2211yescharacteristic
33D4×Dic109C2211yescharacteristic, complemented
34C4×C22⋊D109C2211yescharacteristic
35#16812657C2211yescharacteristic, complemented
36C2×C4⋊Dic109C2211yescharacteristic
37C2×C22⋊Dic109—21no—
38#16812633C2211yescharacteristic, complemented
39#16812633C2211yescharacteristic, complemented
40#16812630C2211yescharacteristic, complemented
41#16812628C2211yescharacteristic, complemented
42#16812624C2211yescharacteristic, complemented
43#16812624C2211yescharacteristic, complemented
44#16812622C2211yescharacteristic, complemented
45#16812620C2211yescharacteristic
46#16812620C2211yescharacteristic
47#16812620C2211yescharacteristic
48#16812620C2211yescharacteristic
49#16812620C2211yescharacteristic, complemented
50#16812611C2211yescharacteristic, complemented
51C8×Dic109C2211yescharacteristic, complemented
52C22×D4×C109C2211yescharacteristic
53C2×D8×C109C2211yescharacteristic
54C2×D8×C109C2211yescharacteristic
55#121×C109C2211yescharacteristic
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic
58C22⋊C8×C109C2211yescharacteristic
59#13182028—22no—
60#13182028—41no—
61C2×Dic218C2311yescharacteristic
62C2×C22⋊D109—21no—
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C22⋊D109D411yescharacteristic
66C22×Dic109—21no—
67C22×Dic109—21no—
68C22×Dic109—21no—
69C22×Dic109—21no—
70C2×C4×D109C2311yescharacteristic
71#13182017—41no—
72C2×#11724784—41no—
73C2×#11724784C2311yescharacteristic
74C2×#11724784C2311yescharacteristic
75C8×D109—41no—
76C4⋊Dic109—21no—
77C4⋊Dic109—21no—
78C4⋊Dic109C2311yescharacteristic
79C4⋊Dic109C2311yescharacteristic
80C4⋊Dic109C2311yescharacteristic
81#13182008—21no—
82#13182008—21no—
83#13182008D411yescharacteristic
84C22⋊Dic109—21no—
85C22⋊Dic109—21no—
86C22⋊Dic109—21no—
87C22⋊Dic109—21no—
88C22⋊Dic109—21no—
89C22⋊Dic109—21no—
90C22⋊Dic109—21no—
91C22⋊Dic109D411yescharacteristic
92#13182006—21no—
93#13182006D411yescharacteristic
94C4×Dic109—21no—
95C4×Dic109C2311yescharacteristic
96C24×C109—21no—
97C2×D4×C109—22no—
98C2×D4×C109—21no—
99C2×D4×C109—21no—
100C2×D4×C109—41no—
101C2×D4×C109C2311yescharacteristic
102C2×D4×C109C2311yescharacteristic
103C2×D4×C109C2311yescharacteristic
104C22×C4×C109C2311yescharacteristic
105D8×C109—22no—
106D8×C109—41no—
107C2×C8×C109C2311yescharacteristic
108C2×C8×C109C2311yescharacteristic
109C4⋊C4×C109C2311yescharacteristic
110C22⋊C4×C109—21no—
111C23×C109—21no—
112C23×C109—21no—
113C23×C109—21no—
114C23×C109—42no—
115C23×C109—42no—
116C23×C109—81no—
117C23×C109C2×D411yescharacteristic
118C22×D109C2×D411yescharacteristic
119D4×C109—21no—
120D4×C109—21no—
121D4×C109—21no—
122D4×C109—21no—
123D4×C109—21no—
124D4×C109—42no—
125D4×C109—42no—
126D4×C109#4112yes—
127C2×C4×C109—21no—
128C2×C4×C109—21no—
129C2×C4×C109—21no—
130C2×C4×C109C2×D411yescharacteristic
131C2×C4×C109C2411yescharacteristic
132C22⋊D109—22no—
133C22⋊D109—42no—
134C22⋊D109—81no—
135C22⋊D109—81no—
136C2×Dic109—21no—
137C2×Dic109—21no—
138C2×Dic109—21no—
139C2×Dic109—21no—
140C2×Dic109—42no—
141C2×Dic109—81no—
142C2×Dic109—81no—
143C2×Dic109—81no—
144C2×Dic109C2×D411yescharacteristic
145C2×Dic109C2×D411yescharacteristic
146C2×Dic109C2×D411yescharacteristic
147C4×D109—21no—
148C4×D109—21no—
149Dic218—21no—
150Dic218—21no—
151C8×C109—21no—
152C8×C109—21no—
153#11724784—21no—
154#11724784—21no—
155C22×C109—21no—
156C22×C109—21no—
157C22×C109—22no—
158C22×C109—41no—
159C22×C109—41no—
160C22×C109—41no—
161C22×C109—41no—
162C22×C109—41no—
163C22×C109—41no—
164C22×C109—41no—
165C22×C109—41no—
166C22×C109—84no—
167C22×C109#13512yes—
168C22×C109C22×D411yescharacteristic
169C2×D109—21no—
170C2×D109—21no—
171C2×D109—21no—
172C4×C109—21no—
173C4×C109—41no—
174C4×C109C2×#4111yescharacteristic
175C4×C109H(5,𝔽2)11yescharacteristic
176Dic109—21no—
177Dic109—21no—
178Dic109—21no—
179Dic109—41no—
180Dic109—41no—
181Dic109—41no—
182Dic109—41no—
183C2×C109—22no—
184C2×C109—42no—
185C2×C109—81no—
186C2×C109—81no—
187C2×C109#54611yescharacteristic
188C2×C109C2×#13511yescharacteristic
189C2×C109#57611yescharacteristic
190D109—41no—
191#3297—1091nomaximal, Sylow
192C109#329711yescharacteristic, complemented, Sylow
193#553—1091no—
194#546—1091no—
195#488—1091no—
196#484—1091no—
197#482—1091no—
198#478—1091no—
199#466—1091no—
200#465—1091no—
201#463—1091no—
202#449—1091no—
203#447D10911yescharacteristic, complemented
204C4×D8—1091no—
205C8×D4—1091no—
206#416—1091no—
207C2×#102—1091no—
208C2×#41—1091no—
209C22×D4C2×D10911yescharacteristic
210C2×SD16—1091no—
211C2×D8C2×D10911yescharacteristic
212C2×D8C2×D10911yescharacteristic
213C22×C8—1091no—
214C22×C8—1091no—
215#126—2181no—
216#125—1091no—
217#124—1091no—
218#123—2181no—
219#123—2181no—
220C22⋊Q8—1091no—
221#121—1091no—
222#121—1091no—
223#121—2181no—
224#121—2181no—
225#121C2×D10911yescharacteristic
226#120—2181no—
227C4×D4—1091no—
228C4×D4—1091no—
229C4×D4—1091no—
230C4×D4—2181no—
231#117—1091no—
232C2×C4⋊C4—1091no—
233C2×C22⋊C4—2181no—
234#107—1091no—
235#107—1091no—
236#106—1091no—
237C4⋊C8—1091no—
238#103—1091no—
239#103—1091no—
240#103—1091no—
241#102—1091no—
242#102—1091no—
243#102—1091no—
244#102—1091no—
245#102—1091no—
246#102C2×D10911yescharacteristic
247#102C2×D10911yescharacteristic
248C22⋊C8—1091no—
249C22⋊C8C2×D10911yescharacteristic
250C4×C8—1091no—
251C24—21no—
252#41—4361no—
253#41—2182no—
254C2×Q8—1091no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—1091no—
260C2×D4—2181no—
261C2×D4—2181no—
262C2×D4—2181no—
263C2×D4C22×D10911yescharacteristic
264C2×D4C22×D10911yescharacteristic
265C2×D4C22×D10911yescharacteristic
266C22×C4—1091no—
267C22×C4—2181no—
268C22×C4—2181no—
269C22×C4—2181no—
270C22×C4—2181no—
271C22×C4C22×D10911yescharacteristic
272SD16—4361no—
273D8—22no—
274D8—41no—
275C2×C8—1091no—
276C2×C8—1091no—
277C2×C8—4361no—
278C2×C8—4361no—
279C2×C8C22×D10911yescharacteristic
280C2×C8C22×D10911yescharacteristic
281C4⋊C4—1091no—
282C4⋊C4—1091no—
283C4⋊C4—1091no—
284C4⋊C4—1091no—
285C4⋊C4—2181no—
286C4⋊C4—2181no—
287C4⋊C4—2181no—
288C4⋊C4—2181no—
289C4⋊C4C22×D10911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—1091no—
292C22⋊C4—1091no—
293C22⋊C4—2181no—
294C22⋊C4—2181no—
295C22⋊C4—2181no—
296C22⋊C4—2181no—
297C22⋊C4—2181no—
298C22⋊C4—2181no—
299C22⋊C4—2181no—
300C22⋊C4—2181no—
301C42—1091no—
302C42—2181no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—1091no—
310C23D4×D10911yescharacteristic
311Q8—2181no—
312Q8—2181no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—8721no—
321D4—8721no—
322D4—4362no—
323D4—2182no—
324D4#1318202812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—8721no—
329C2×C4—8721no—
330C2×C4—8721no—
331C2×C4—1091no—
332C2×C4—1091no—
333C2×C4—1091no—
334C2×C4—4362no—
335C2×C4—2181no—
336C2×C4—2181no—
337C2×C4—2181no—
338C2×C4—2181no—
339C2×C4—2181no—
340C2×C4—2181no—
341C2×C4D4×D10911yescharacteristic
342C2×C4C23×D10911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2181no—
346C8—2181no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—2181no—
360C22—2181no—
361C22—2181no—
362C22#1681271812yes—
363C22C2×D4×D10911yescharacteristic
364C4—21no—
365C4—41no—
366C4—4361no—
367C4—4361no—
368C4—4361no—
369C4—4361no—
370C4—2181no—
371C4—2181no—
372C4—2181no—
373C4C2×#1318202811yescharacteristic
374C4#1681274411yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—4361no—
380C2#2029566311yescharacteristic
381C2C2×#1681271811yescharacteristic
382C2#2029583011yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#447×C109C2
socleC22×C109C22×D4
hypercenter#447D109
hypocenterC109#3297
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20295728C2semidirect
2. #20295670C2semidirect
3. #20295379C2semidirect
4. #20295362C2semidirect
5. #20295348C2semidirect
6. #20295324C2semidirect
7. #20295259C2semidirect
8. #20295253C2semidirect
9. #20295239C2semidirect
10. #20295168C2semidirect
11. D8×Dic109C2semidirect
12. #20295089C2semidirect
13. #20295019C2semidirect
14. C2×#16812620C2semidirect
15. #447×C109C2semidirect
17. C2×#13182017C22semidirect
19. C2×C8×D109C22semidirect
21. #16812690C22semidirect
29. #16812670C22semidirect
33. D4×Dic109C22semidirect
35. #16812657C22semidirect
38. #16812633C22semidirect
39. #16812633C22semidirect
40. #16812630C22semidirect
41. #16812628C22semidirect
42. #16812624C22semidirect
43. #16812624C22semidirect
44. #16812622C22semidirect
49. #16812620C22semidirect
50. #16812611C22semidirect
51. C8×Dic109C22semidirect
192. C109#3297semidirect
203. #447D109semidirect

Maximal subgroups

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

subgroupindex
#202957282
#202956702
#202953792
#202953622
#202953482
#202953242
#202952592
#202952532
#202952392
#202951682
D8×Dic1092
#202950892
#202950192
C2×#168126202
#447×C1092
#3297109