Finite Group Databasebeta

← #28374852

Subgroups — #28374852

Order 13952.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295731C211yesmaximal, characteristic, complemented
2D4×C22⋊D109C211yesmaximal, characteristic
3#20295371C211yesmaximal, characteristic, complemented
4#20295344C211yesmaximal, characteristic, complemented
5#20295343C211yesmaximal, characteristic, complemented
6#20295314C211yesmaximal, characteristic, complemented
7#20295255C211yesmaximal, characteristic, complemented
8#20295254C211yesmaximal, characteristic, complemented
9#20295225C211yesmaximal, characteristic, complemented
10#20295178C211yesmaximal, characteristic, complemented
11#20295177C211yesmaximal, characteristic, complemented
12#20295117C211yesmaximal, characteristic, complemented
13C8×C22⋊D109C211yesmaximal, characteristic, complemented
14#102×D109C211yesmaximal, characteristic, complemented
15C2×#102×C109C211yesmaximal, characteristic, complemented
16C22×C22⋊D109—21no—
17C2×D4×D109C2211yescharacteristic
18C2×#13182018C2211yescharacteristic, complemented
19C2×#13182017C2211yescharacteristic
20C2×#13182017C2211yescharacteristic, complemented
21C2×C8×D109C2211yescharacteristic, complemented
22#16812698C2211yescharacteristic, complemented
23#16812695C2211yescharacteristic
24#16812689—21no—
25#16812679C2211yescharacteristic, complemented
26#16812678—21no—
27#16812678C2211yescharacteristic, complemented
28#16812677—21no—
29#16812673C2211yescharacteristic
30#16812671—21no—
31#16812670C2211yescharacteristic
32#16812668—21no—
33#16812667—21no—
34#16812664C2211yescharacteristic, complemented
35D4×Dic109C2211yescharacteristic
36C4×C22⋊D109—21no—
37C4×C22⋊D109C2211yescharacteristic
38C4⋊C4×D109C2211yescharacteristic, complemented
39#16812631C2211yescharacteristic, complemented
40#16812630C2211yescharacteristic, complemented
41#16812630C2211yescharacteristic, complemented
42#16812628C2211yescharacteristic, complemented
43#16812624C2211yescharacteristic, complemented
44#16812621C2211yescharacteristic, complemented
45#16812620C2211yescharacteristic
46#16812620C2211yescharacteristic, complemented
47#16812619C2211yescharacteristic, complemented
48#16812619C2211yescharacteristic, complemented
49C22⋊#11724784C2211yescharacteristic, complemented
50#16812611C2211yescharacteristic, complemented
51C8×Dic109C2211yescharacteristic, complemented
52C22×D4×C109C2211yescharacteristic
53C22×C8×C109C2211yescharacteristic, complemented
54C2×C4⋊C4×C109C2211yescharacteristic, complemented
55#102×C109C2211yescharacteristic
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic, complemented
58#102×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60C2×Dic218—21no—
61C2×Dic218C2311yescharacteristic
62C2×D436C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C22⋊D109—21no—
66C2×C22⋊D109—21no—
67C2×C22⋊D109—21no—
68C2×C22⋊D109—44no—
69C2×C22⋊D109D411yescharacteristic
70D4×D109—22no—
71D4×D109—41no—
72C22×Dic109—21no—
73C2×C4×D109—21no—
74C2×C4×D109C2311yescharacteristic
75#13182018—41no—
76#13182017—22no—
77#13182017—41no—
78C2×#11724784C2311yescharacteristic
79C2×#11724784C2311yescharacteristic
80C8×D109—41no—
81C4⋊Dic109—21no—
82C4⋊Dic109C2311yescharacteristic
83C4⋊Dic109C2311yescharacteristic
84#13182008—21no—
85#13182008—21no—
86#13182008—21no—
87#13182008—21no—
88#13182008D411yescharacteristic
89C22⋊Dic109—21no—
90C22⋊Dic109—21no—
91C22⋊Dic109—21no—
92C22⋊Dic109D411yescharacteristic
93#13182006—21no—
94#13182006—21no—
95#13182006D411yescharacteristic
96C4×Dic109—21no—
97C4×Dic109C2311yescharacteristic
98C24×C109—21no—
99C2×D4×C109—22no—
100C2×D4×C109—21no—
101C2×D4×C109—41no—
102C2×D4×C109C2311yescharacteristic
103C2×D4×C109C2311yescharacteristic
104C22×C4×C109—21no—
105C22×C4×C109C2311yescharacteristic
106C2×C8×C109—41no—
107C2×C8×C109C2311yescharacteristic
108C2×C8×C109C2311yescharacteristic
109C4⋊C4×C109—21no—
110C4⋊C4×C109C2311yescharacteristic
111C4⋊C4×C109C2311yescharacteristic
112C23×C109—21no—
113C23×C109—21no—
114C23×C109—42no—
115C23×C109—42no—
116C23×C109—81no—
117C23×C109C2×D411yescharacteristic
118C22×D109—21no—
119C22×D109—42no—
120C22×D109—42no—
121C22×D109—81no—
122C22×D109C2×D411yescharacteristic
123D4×C109—21no—
124D4×C109—21no—
125D4×C109—21no—
126D4×C109—42no—
127D4×C109#4112yes—
128C2×C4×C109—21no—
129C2×C4×C109—21no—
130C2×C4×C109—21no—
131C2×C4×C109—21no—
132C2×C4×C109—81no—
133C2×C4×C109C2×D411yescharacteristic
134C2×C4×C109C2411yescharacteristic
135C22⋊D109—42no—
136C22⋊D109—42no—
137C22⋊D109—42no—
138C22⋊D109—42no—
139C22⋊D109—81no—
140C22⋊D109SD1614yescomplemented
141C2×Dic109—21no—
142C2×Dic109—21no—
143C2×Dic109—21no—
144C2×Dic109—42no—
145C2×Dic109C2×D411yescharacteristic
146C2×Dic109C2×D411yescharacteristic
147C2×Dic109C2×D411yescharacteristic
148D436—21no—
149D436—21no—
150C4×D109—21no—
151C4×D109—21no—
152C4×D109—81no—
153Dic218—21no—
154Dic218—21no—
155Dic218—81no—
156C8×C109—21no—
157C8×C109—21no—
158#11724784—21no—
159#11724784—21no—
160C22×C109—21no—
161C22×C109—21no—
162C22×C109—22no—
163C22×C109—41no—
164C22×C109—41no—
165C22×C109—41no—
166C22×C109—41no—
167C22×C109—41no—
168C22×C109—84no—
169C22×C109C2×SD1612yes—
170C22×C109C22×D411yescharacteristic
171C2×D109—21no—
172C2×D109—21no—
173C2×D109—41no—
174C2×D109—41no—
175C2×D109—41no—
176C2×D109—84no—
177C2×D109C2×SD1612yes—
178C4×C109—21no—
179C4×C109—41no—
180C4×C109—41no—
181C4×C109C2×#4111yescharacteristic
182C4×C109H(5,𝔽2)11yescharacteristic
183Dic109—21no—
184Dic109—21no—
185Dic109—41no—
186Dic109—41no—
187Dic109—41no—
188Dic109C2×SD1612yes—
189C2×C109—22no—
190C2×C109—42no—
191C2×C109—81no—
192C2×C109#54611yescharacteristic
193C2×C109C22×SD1611yescharacteristic
194C2×C109#57611yescharacteristic
195D109—22no—
196D109—81no—
197#3295—1091nomaximal, Sylow
198C109#329511yescharacteristic, complemented, Sylow
199#554—1091no—
200D42—1091no—
201#486—1091no—
202#481—1091no—
203#481—1091no—
204#476—1091no—
205#465—1091no—
206#465—1091no—
207#460—1091no—
208#450—1091no—
209#450—1091no—
210C4×SD16—1091no—
211C8×D4—1091no—
212C2×#102—1091no—
213C2×#102D10911yescharacteristic, complemented
214C22×D4—1091no—
215C22×D4—2181no—
216C22×D4C2×D10911yescharacteristic
217C2×SD16—1091no—
218C2×SD16—1091no—
219C2×SD16—1091no—
220C22×C8—1091no—
221C22×C8C2×D10911yescharacteristic, complemented
222C4⋊Q8—1091no—
223#127—1091no—
224#125—2181no—
225C22⋊Q8—1091no—
226C22⋊Q8—1091no—
227C22⋊Q8—2181no—
228C22⋊Q8—2181no—
229#121—1091no—
230#121—1091no—
231#121—2181no—
232#120—2181no—
233#120—2181no—
234C4×Q8—1091no—
235C4×D4—1091no—
236C4×D4—1091no—
237C4×D4—2181no—
238C2×C4⋊C4—1091no—
239C2×C4⋊C4C2×D10911yescharacteristic, complemented
240#106—1091no—
241#106—1091no—
242#106—1091no—
243C4⋊C8—1091no—
244#103—1091no—
245#102—1091no—
246#102—1091no—
247#102—1091no—
248#102—1091no—
249#102—1091no—
250#102C2×D10911yescharacteristic
251#102C2×D10911yescharacteristic
252#102C2×D10911yescharacteristic, complemented
253#102C2×D10911yescharacteristic, complemented
254C22⋊C8—1091no—
255C22⋊C8—1091no—
256C4×C8—1091no—
257C24—21no—
258C24—2181no—
259C2×Q8—1091no—
260C2×Q8—2181no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—1091no—
265C2×D4—1091no—
266C2×D4—4364no—
267C2×D4—4361no—
268C2×D4—2181no—
269C2×D4—2181no—
270C2×D4—2181no—
271C2×D4—2181no—
272C2×D4—2181no—
273C2×D4—2182no—
274C2×D4C22×D10911yescharacteristic
275C2×D4C22×D10911yescharacteristic
276C22×C4—21no—
277C22×C4—1091no—
278C22×C4—2181no—
279C22×C4—2181no—
280C22×C4C22×D10911yescharacteristic
281SD16—4361no—
282SD16—4361no—
283SD16—2182no—
284C2×C8—41no—
285C2×C8—1091no—
286C2×C8—1091no—
287C2×C8—4361no—
288C2×C8C22×D10911yescharacteristic
289C2×C8C22×D10911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1091no—
292C4⋊C4—1091no—
293C4⋊C4—1091no—
294C4⋊C4—2181no—
295C4⋊C4—2181no—
296C4⋊C4—2181no—
297C4⋊C4—2181no—
298C4⋊C4—2181no—
299C4⋊C4C22×D10911yescharacteristic
300C4⋊C4C22×D10911yescharacteristic
301C22⋊C4—1091no—
302C22⋊C4—1091no—
303C22⋊C4—2181no—
304C22⋊C4—2181no—
305C22⋊C4—2181no—
306C22⋊C4—2181no—
307C22⋊C4—2181no—
308C42—1091no—
309C42—2181no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—8721no—
316C23—1091no—
317C23—4362no—
318C23—4362no—
319C23—2181no—
320C23D4×D10911yescharacteristic
321Q8—8721no—
322Q8—2181no—
323Q8—2181no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—8721no—
329D4—1094no—
330D4—4362no—
331D4—4362no—
332D4—4362no—
333D4—4362no—
334D4—2181no—
335D4—2181no—
336D4#1318202912yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—8721no—
343C2×C4—1091no—
344C2×C4—1091no—
345C2×C4—1091no—
346C2×C4—4362no—
347C2×C4—2181no—
348C2×C4—2181no—
349C2×C4—2181no—
350C2×C4—2181no—
351C2×C4—2181no—
352C2×C4D4×D10911yescharacteristic
353C2×C4C23×D10911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2181no—
357C8—2181no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—8724no—
368C22—1092no—
369C22—4361no—
370C22—4361no—
371C22—4361no—
372C22—2181no—
373C22—2181no—
374C22SD16×D10912yes—
375C22C2×D4×D10911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—1092no—
380C4—4361no—
381C4—4361no—
382C4—4361no—
383C4—2181no—
384C4—2181no—
385C4C2×#1318202911yescharacteristic
386C4#1681274411yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—8721no—
391C2—2182no—
392C2#2029566611yescharacteristic
393C2C2×SD16×D10911yescharacteristic
394C2#2029582711yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#102×C109C2
socleC22×C109C22×D4
prime radicalD4×C22⋊D109C2
hypercenterC2×#102D109
hypocenterC109#3295
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #20295731C2semidirect
3. #20295371C2semidirect
4. #20295344C2semidirect
5. #20295343C2semidirect
6. #20295314C2semidirect
7. #20295255C2semidirect
8. #20295254C2semidirect
9. #20295225C2semidirect
10. #20295178C2semidirect
11. #20295177C2semidirect
12. #20295117C2semidirect
13. C8×C22⋊D109C2semidirect
14. #102×D109C2semidirect
15. C2×#102×C109C2semidirect
18. C2×#13182018C22semidirect
20. C2×#13182017C22semidirect
21. C2×C8×D109C22semidirect
22. #16812698C22semidirect
25. #16812679C22semidirect
27. #16812678C22semidirect
34. #16812664C22semidirect
38. C4⋊C4×D109C22semidirect
39. #16812631C22semidirect
40. #16812630C22semidirect
41. #16812630C22semidirect
42. #16812628C22semidirect
43. #16812624C22semidirect
44. #16812621C22semidirect
46. #16812620C22semidirect
47. #16812619C22semidirect
48. #16812619C22semidirect
49. C22⋊#11724784C22semidirect
50. #16812611C22semidirect
51. C8×Dic109C22semidirect
53. C22×C8×C109C22semidirect
54. C2×C4⋊C4×C109C22semidirect
57. #102×C109C22semidirect
58. #102×C109C22semidirect
140. C22⋊D109SD16semidirect
198. C109#3295semidirect
213. C2×#102D109semidirect
221. C22×C8C2×D109semidirect
239. C2×C4⋊C4C2×D109semidirect
252. #102C2×D109semidirect
253. #102C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202957312
D4×C22⋊D1092
#202953712
#202953442
#202953432
#202953142
#202952552
#202952542
#202952252
#202951782
#202951772
#202951172
C8×C22⋊D1092
#102×D1092
C2×#102×C1092
#3295109