Finite Group Databasebeta

← #28374887

Subgroups — #28374887

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#20295726C211yesmaximal, characteristic, complemented
2#20295671C211yesmaximal, characteristic, complemented
3#20295381C211yesmaximal, characteristic, complemented
4#20295363C211yesmaximal, characteristic, complemented
5#20295353C211yesmaximal, characteristic, complemented
6#20295326C211yesmaximal, characteristic, complemented
7#20295261C211yesmaximal, characteristic, complemented
8#20295254C211yesmaximal, characteristic, complemented
9#20295241C211yesmaximal, characteristic, complemented
10#20295168C211yesmaximal, characteristic, complemented
11#20295158C211yesmaximal, characteristic, complemented
12C8×D436C211yesmaximal, characteristic, complemented
13#20295019C211yesmaximal, characteristic, complemented
14#102×D109C211yesmaximal, characteristic, complemented
15C4×D8×C109C211yesmaximal, characteristic, complemented
16C2×#13182028C2211yescharacteristic
17C2×D4×D109C2211yescharacteristic
18C2×#13182017C2211yescharacteristic, complemented
19C2×#13182014C2211yescharacteristic
20C2×C8×D109C2211yescharacteristic
21C2×C8×D109C2211yescharacteristic, complemented
22#16812692—21no—
23#16812691C2211yescharacteristic, complemented
24#16812687C2211yescharacteristic
25#16812683—21no—
26#16812682—21no—
27#16812679C2211yescharacteristic
28#16812674C2211yescharacteristic
29#16812673—21no—
30#16812672—21no—
31#16812670C2211yescharacteristic
32#16812670C2211yescharacteristic, complemented
33#16812669—21no—
34C4×D436C2211yescharacteristic
35C4×C22⋊D109—21no—
36#16812657C2211yescharacteristic, complemented
37C4⋊C4×D109C2211yescharacteristic
38C2×#13182006—21no—
39#16812632C2211yescharacteristic, complemented
40#16812630C2211yescharacteristic, complemented
41C4⋊#11724784C2211yescharacteristic, complemented
42#16812624C2211yescharacteristic, complemented
43#16812624C2211yescharacteristic, complemented
44#16812622C2211yescharacteristic, complemented
45#16812621C2211yescharacteristic
46#16812621C2211yescharacteristic
47#16812620C2211yescharacteristic
48#16812620C2211yescharacteristic
49#16812619C2211yescharacteristic
50#16812611C2211yescharacteristic
51#16812611C2211yescharacteristic, complemented
52C2×D8×C109C2211yescharacteristic
53C4×D4×C109C2211yescharacteristic
54C4×D4×C109C2211yescharacteristic, complemented
55#107×C109C2211yescharacteristic, complemented
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic, complemented
58C4×C8×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60#13182028—22no—
61#13182028—41no—
62C2×Dic218C2311yescharacteristic
63C2×D436—21no—
64C2×D436D411yescharacteristic
65C2×D436C2311yescharacteristic
66C2×C22⋊D109—21no—
67C2×C22⋊D109—21no—
68C2×C22⋊D109—21no—
69C2×C22⋊D109—21no—
70D4×D109—22no—
71D4×D109—41no—
72C22×Dic109—21no—
73C2×C4×D109—21no—
74C2×C4×D109C2311yescharacteristic
75C2×C4×D109C2311yescharacteristic
76#13182017—41no—
77#13182014—41no—
78C2×#11724784C2311yescharacteristic
79C2×#11724784C2311yescharacteristic
80C8×D109—41no—
81C8×D109—41no—
82C4⋊Dic109—21no—
83C4⋊Dic109D411yescharacteristic
84C4⋊Dic109C2311yescharacteristic
85C4⋊Dic109C2311yescharacteristic
86#13182008—21no—
87#13182008—21no—
88#13182008—21no—
89C22⋊Dic109—21no—
90C22⋊Dic109—21no—
91#13182006—21no—
92#13182006—21no—
93#13182006—21no—
94#13182006—21no—
95#13182006—21no—
96#13182006D411yescharacteristic
97#13182006D411yescharacteristic
98C4×Dic109—21no—
99C2×D4×C109C2311yescharacteristic
100C2×D4×C109C2311yescharacteristic
101C22×C4×C109—21no—
102C22×C4×C109—21no—
103D8×C109—22no—
104C2×C8×C109C2311yescharacteristic
105C2×C8×C109C2311yescharacteristic
106C4⋊C4×C109C2311yescharacteristic
107C4⋊C4×C109C2311yescharacteristic
108C22⋊C4×C109—21no—
109C22⋊C4×C109—21no—
110C42×C109C2311yescharacteristic
111C23×C109—21no—
112C23×C109—21no—
113C22×D109—21no—
114C22×D109—42no—
115C22×D109—42no—
116C22×D109—81no—
117C22×D109C2×D411yescharacteristic
118C22×D109C2×D411yescharacteristic
119D4×C109—21no—
120D4×C109—21no—
121D4×C109—21no—
122D4×C109#4112yes—
123C2×C4×C109—21no—
124C2×C4×C109—21no—
125C2×C4×C109—81no—
126C2×C4×C109—81no—
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2411yescharacteristic
130C22⋊D109—42no—
131C22⋊D109—42no—
132C22⋊D109—42no—
133C22⋊D109—81no—
134C2×Dic109—21no—
135C2×Dic109—21no—
136C2×Dic109—21no—
137C2×Dic109—42no—
138C2×Dic109C2×D411yescharacteristic
139C2×Dic109C2×D411yescharacteristic
140D436—22no—
141D436—21no—
142D436—21no—
143D436—81no—
144C4×D109—21no—
145C4×D109—21no—
146C4×D109—21no—
147C4×D109—21no—
148C4×D109—81no—
149Dic218—21no—
150Dic218—21no—
151C8×C109—21no—
152C8×C109—21no—
153#11724784—21no—
154#11724784—21no—
155C22×C109—22no—
156C22×C109—41no—
157C22×C109—41no—
158C22×C109—41no—
159C22×C109—41no—
160C22×C109—41no—
161C22×C109C22×D411yescharacteristic
162C2×D109—21no—
163C2×D109—21no—
164C2×D109—21no—
165C2×D109—21no—
166C2×D109—21no—
167C2×D109—41no—
168C2×D109—41no—
169C2×D109—41no—
170C2×D109—84no—
171C2×D109#13512yes—
172C4×C109—21no—
173C4×C109—21no—
174C4×C109—41no—
175C4×C109—41no—
176C4×C109C2×#4111yescharacteristic
177C4×C109H(5,𝔽2)11yescharacteristic
178Dic109—21no—
179Dic109—21no—
180Dic109—41no—
181Dic109—41no—
182Dic109—41no—
183C2×C109—42no—
184C2×C109—81no—
185C2×C109#54611yescharacteristic
186C2×C109C2×#13511yescharacteristic
187C2×C109#57611yescharacteristic
188D109—22no—
189D109—41no—
190D109—81no—
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#447—1091no—
204C4×D8D10911yescharacteristic, complemented
205C8×D4—1091no—
206#416—1091no—
207C2×#102—1091no—
208C2×#41—1091no—
209C22×D4—1091no—
210C2×SD16—1091no—
211C2×D8—1091no—
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—1091no—
224#121—2181no—
225#121—2181no—
226#120—2181no—
227C4×D4—1091no—
228C4×D4—2181no—
229C4×D4C2×D10911yescharacteristic
230C4×D4C2×D10911yescharacteristic, complemented
231#117—1091no—
232C2×C4⋊C4—1091no—
233C2×C22⋊C4—2181no—
234#107—1091no—
235#107C2×D10911yescharacteristic, complemented
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, complemented
248C22⋊C8—1091no—
249C22⋊C8—1091no—
250C4×C8C2×D10911yescharacteristic, complemented
251C24—2181no—
252#41—4361no—
253#41—2182no—
254C2×Q8—1091no—
255C2×D4—1091no—
256C2×D4—1091no—
257C2×D4—4361no—
258C2×D4—2181no—
259C2×D4—2181no—
260C2×D4—2181no—
261C2×D4—2181no—
262C2×D4—2181no—
263C2×D4—2182no—
264C2×D4C22×D10911yescharacteristic
265C2×D4C22×D10911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—1091no—
269C22×C4—1091no—
270C22×C4—2181no—
271C22×C4—2181no—
272SD16—4361no—
273D8—22no—
274D8—4361no—
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—2181no—
285C4⋊C4—2181no—
286C4⋊C4—2181no—
287C4⋊C4—2181no—
288C4⋊C4C22×D10911yescharacteristic
289C4⋊C4C22×D10911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1091no—
293C22⋊C4—1091no—
294C22⋊C4—2181no—
295C22⋊C4—2181no—
296C22⋊C4—2181no—
297C22⋊C4—2181no—
298C22⋊C4—2181no—
299C22⋊C4—2181no—
300C22⋊C4—2181no—
301C42—2181no—
302C42C22×D10911yescharacteristic
303C23—21no—
304C23—21no—
305C23—8721no—
306C23—1091no—
307C23—1091no—
308C23—4362no—
309C23—4362no—
310C23—2181no—
311Q8—2181no—
312Q8—2181no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—8721no—
317D4—8721no—
318D4—4362no—
319D4—4362no—
320D4—4362no—
321D4—2182no—
322D4—2181no—
323D4—2181no—
324D4#1318202912yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—8721no—
330C2×C4—1091no—
331C2×C4—1091no—
332C2×C4—4362no—
333C2×C4—2181no—
334C2×C4—2181no—
335C2×C4—2181no—
336C2×C4—2181no—
337C2×C4—2181no—
338C2×C4—2181no—
339C2×C4—2181no—
340C2×C4D4×D10911yescharacteristic
341C2×C4D4×D10911yescharacteristic
342C2×C4C23×D10911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2181no—
346C8—2181no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—8724no—
354C22—1092no—
355C22—4361no—
356C22—4361no—
357C22—4361no—
358C22—2181no—
359C22—2181no—
360C22—2181no—
361C22—2181no—
362C22—2181no—
363C22C2×D4×D10911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—4361no—
369C4—4361no—
370C4—4361no—
371C4—2181no—
372C4—2181no—
373C4C2×#1318202911yescharacteristic
374C4#1681274511yescharacteristic
375C2—42no—
376C2—81no—
377C2—8721no—
378C2—4361no—
379C2—2182no—
380C2#2029567211yescharacteristic
381C2#135×D10911yescharacteristic
382C2#2029582711yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC4×D8×C109C2
socleC22×C109C22×D4
hypercenterC4×D8D109
hypocenterC109#3297
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20295726C2semidirect
2. #20295671C2semidirect
3. #20295381C2semidirect
4. #20295363C2semidirect
5. #20295353C2semidirect
6. #20295326C2semidirect
7. #20295261C2semidirect
8. #20295254C2semidirect
9. #20295241C2semidirect
10. #20295168C2semidirect
11. #20295158C2semidirect
12. C8×D436C2semidirect
13. #20295019C2semidirect
14. #102×D109C2semidirect
15. C4×D8×C109C2semidirect
18. C2×#13182017C22semidirect
21. C2×C8×D109C22semidirect
23. #16812691C22semidirect
32. #16812670C22semidirect
36. #16812657C22semidirect
39. #16812632C22semidirect
40. #16812630C22semidirect
41. C4⋊#11724784C22semidirect
42. #16812624C22semidirect
43. #16812624C22semidirect
44. #16812622C22semidirect
51. #16812611C22semidirect
54. C4×D4×C109C22semidirect
55. #107×C109C22semidirect
57. #102×C109C22semidirect
58. C4×C8×C109C22semidirect
192. C109#3297semidirect
204. C4×D8D109semidirect
230. C4×D4C2×D109semidirect
235. #107C2×D109semidirect
247. #102C2×D109semidirect
250. C4×C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202957262
#202956712
#202953812
#202953632
#202953532
#202953262
#202952612
#202952542
#202952412
#202951682
#202951582
C8×D4362
#202950192
#102×D1092
C4×D8×C1092
#3297109