Finite Group Databasebeta

← #28374880

Subgroups — #28374880

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#20295724C211yesmaximal, characteristic, complemented
2#20295667C211yesmaximal, characteristic, complemented
3#20295382C211yesmaximal, characteristic, complemented
4#20295353C211yesmaximal, characteristic, complemented
5#20295329C211yesmaximal, characteristic, complemented
6#20295263C211yesmaximal, characteristic, complemented
7#20295257C211yesmaximal, characteristic, complemented
8#20295244C211yesmaximal, characteristic, complemented
9#20295174C211yesmaximal, characteristic, complemented
10#20295162C211yesmaximal, characteristic, complemented
11#20295108C211yesmaximal, characteristic, complemented
12#20295089C211yesmaximal, characteristic, complemented
13#20295021C211yesmaximal, characteristic, complemented
14C2×#16812619C211yesmaximal, characteristic, complemented
15#484×C109C211yesmaximal, characteristic, complemented
16C2×#13182030C2211yescharacteristic
17C22×D436C2211yescharacteristic
18C2×#13182016C2211yescharacteristic, complemented
19C2×D872C2211yescharacteristic
20C2×D872C2211yescharacteristic
21C22×#11724784C2211yescharacteristic
22C2×C8×D109C2211yescharacteristic, complemented
23#16812694—21no—
24#16812690C2211yescharacteristic, complemented
25#16812688C2211yescharacteristic
26#16812684—21no—
27#16812684—21no—
28#16812674—21no—
29#16812674C2211yescharacteristic
30#16812674C2211yescharacteristic, complemented
31#16812673—21no—
32#16812673C2211yescharacteristic
33#16812669—21no—
34#16812661C2211yescharacteristic
35#16812661C2211yescharacteristic, complemented
36C4×C22⋊D109—21no—
37C4×C22⋊D109C2211yescharacteristic
38#16812657C2211yescharacteristic, complemented
39C22⋊C4×D109—21no—
40#16812630C2211yescharacteristic, complemented
41#16812628C2211yescharacteristic, complemented
42#16812623C2211yescharacteristic, complemented
43#16812621C2211yescharacteristic
44#16812621C2211yescharacteristic
45#16812619C2211yescharacteristic
46#16812619C2211yescharacteristic
47#16812619C2211yescharacteristic
48#16812619C2211yescharacteristic
49#16812619C2211yescharacteristic, complemented
50#16812611C2211yescharacteristic, complemented
51C8×Dic109C2211yescharacteristic, complemented
52C22⋊Q8×C109C2211yescharacteristic
53C2×C4⋊C4×C109C2211yescharacteristic
54#107×C109C2211yescharacteristic, complemented
55#107×C109C2211yescharacteristic, complemented
56#103×C109C2211yescharacteristic, complemented
57#103×C109C2211yescharacteristic, complemented
58C22⋊C8×C109C2211yescharacteristic
59C23×D109—21no—
60#13182030—22no—
61#13182030—41no—
62C2×D436—22no—
63C2×D436—21no—
64C2×D436—21no—
65C2×D436—21no—
66C2×D436—21no—
67C2×D436—41no—
68C2×D436C2311yescharacteristic
69C2×D436C2311yescharacteristic
70C2×D436C2311yescharacteristic
71C2×C22⋊D109—21no—
72C2×C22⋊D109D411yescharacteristic
73C2×C4×D109—21no—
74C2×C4×D109—21no—
75C2×C4×D109—21no—
76C2×C4×D109C2311yescharacteristic
77#13182016—41no—
78D872—22no—
79D872—41no—
80C2×#11724784—41no—
81C2×#11724784C2311yescharacteristic
82C2×#11724784C2311yescharacteristic
83C8×D109—41no—
84C4⋊Dic109—21no—
85C4⋊Dic109C2311yescharacteristic
86#13182008—21no—
87#13182008D411yescharacteristic
88C22⋊Dic109D411yescharacteristic
89#13182006—21no—
90#13182006—21no—
91#13182006—21no—
92#13182006—21no—
93#13182006—21no—
94#13182006—21no—
95#13182006—21no—
96#13182006—21no—
97#13182006D411yescharacteristic
98C4×Dic109—21no—
99C4×Dic109C2311yescharacteristic
100C2×Q8×C109C2311yescharacteristic
101C22×C4×C109—21no—
102C22×C4×C109C2311yescharacteristic
103C2×C8×C109C2311yescharacteristic
104C2×C8×C109C2311yescharacteristic
105C4⋊C4×C109—21no—
106C4⋊C4×C109—21no—
107C4⋊C4×C109C2311yescharacteristic
108C4⋊C4×C109C2311yescharacteristic
109C4⋊C4×C109C2311yescharacteristic
110C22⋊C4×C109—21no—
111C23×C109C2×D411yescharacteristic
112C22×D109—21no—
113C22×D109—21no—
114C22×D109—21no—
115C22×D109—42no—
116C22×D109—42no—
117C22×D109—81no—
118C22×D109C2×D411yescharacteristic
119Q8×C109—21no—
120Q8×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—21no—
124C2×C4×C109—21no—
125C2×C4×C109—21no—
126C2×C4×C109—21no—
127C2×C4×C109—81no—
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2411yescharacteristic
130C22⋊D109—22no—
131C22⋊D109—42no—
132C2×Dic109—21no—
133C2×Dic109C2×D411yescharacteristic
134C2×Dic109C2×D411yescharacteristic
135C2×Dic109C2×D411yescharacteristic
136D436—21no—
137D436—21no—
138D436—21no—
139D436—21no—
140D436—21no—
141D436—42no—
142D436—42no—
143D436—81no—
144D436—81no—
145D436#4112yes—
146C4×D109—21no—
147C4×D109—21no—
148C4×D109—42no—
149C4×D109—81no—
150C4×D109—81no—
151C8×C109—21no—
152C8×C109—21no—
153#11724784—21no—
154#11724784—21no—
155C22×C109—21no—
156C22×C109—21no—
157C22×C109#13512yes—
158C22×C109C22×D411yescharacteristic
159C2×D109—21no—
160C2×D109—22no—
161C2×D109—21no—
162C2×D109—21no—
163C2×D109—41no—
164C2×D109—41no—
165C2×D109—41no—
166C2×D109—41no—
167C2×D109—41no—
168C2×D109—41no—
169C2×D109—41no—
170C2×D109—41no—
171C2×D109—84no—
172C4×C109—21no—
173C4×C109—41no—
174C4×C109—41no—
175C4×C109—41no—
176C4×C109—41no—
177C4×C109C2×#4111yescharacteristic
178C4×C109H(5,𝔽2)11yescharacteristic
179Dic109—21no—
180Dic109—21no—
181Dic109—21no—
182Dic109—41no—
183C2×C109—22no—
184C2×C109#54611yescharacteristic
185C2×C109C2×#13511yescharacteristic
186C2×C109#57611yescharacteristic
187D109—41no—
188D109—42no—
189D109—81no—
190D109—81no—
191#3297—1091nomaximal, Sylow
192C109#329711yescharacteristic, complemented, Sylow
193#553—1091no—
194#546—1091no—
195#488—1091no—
196#484D10911yescharacteristic, complemented
197#482—1091no—
198#478—1091no—
199#466—1091no—
200#465—1091no—
201#463—1091no—
202#449—1091no—
203#447—1091no—
204C4×D8—1091no—
205C8×D4—1091no—
206#416—1091no—
207C2×#102—1091no—
208C2×#41—1091no—
209C22×D4—1091no—
210C2×SD16—1091no—
211C2×D8—1091no—
212C2×D8—1091no—
213C22×C8—1091no—
214C22×C8—1091no—
215#126—2181no—
216#125—1091no—
217#124—1091no—
218#123—2181no—
219#123—2181no—
220C22⋊Q8C2×D10911yescharacteristic
221#121—1091no—
222#121—1091no—
223#121—1091no—
224#121—2181no—
225#121—2181no—
226#120—2181no—
227C4×D4—1091no—
228C4×D4—1091no—
229C4×D4—1091no—
230C4×D4—2181no—
231#117—1091no—
232C2×C4⋊C4C2×D10911yescharacteristic
233C2×C22⋊C4—2181no—
234#107C2×D10911yescharacteristic, complemented
235#107C2×D10911yescharacteristic, complemented
236#106—1091no—
237C4⋊C8—1091no—
238#103—1091no—
239#103C2×D10911yescharacteristic, complemented
240#103C2×D10911yescharacteristic, complemented
241#102—1091no—
242#102—1091no—
243#102—1091no—
244#102—1091no—
245#102—1091no—
246#102—1091no—
247#102—1091no—
248C22⋊C8—1091no—
249C22⋊C8C2×D10911yescharacteristic
250C4×C8—1091no—
251C24—2181no—
252#41—4361no—
253#41—2182no—
254C2×Q8C22×D10911yescharacteristic
255C2×D4—1091no—
256C2×D4—1091no—
257C2×D4—1091no—
258C2×D4—1091no—
259C2×D4—4361no—
260C2×D4—2181no—
261C2×D4—2181no—
262C2×D4—2182no—
263C2×D4—2181no—
264C2×D4—2181no—
265C2×D4—2181no—
266C22×C4—21no—
267C22×C4—1091no—
268C22×C4—2181no—
269C22×C4—2181no—
270C22×C4—2181no—
271C22×C4C22×D10911yescharacteristic
272SD16—4361no—
273D8—4361no—
274D8—2182no—
275C2×C8—1091no—
276C2×C8—1091no—
277C2×C8—4361no—
278C2×C8—4361no—
279C2×C8C22×D10911yescharacteristic
280C2×C8C22×D10911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1091no—
284C4⋊C4—1091no—
285C4⋊C4—2181no—
286C4⋊C4—2181no—
287C4⋊C4C22×D10911yescharacteristic
288C4⋊C4C22×D10911yescharacteristic
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—8721no—
304C23—1091no—
305C23—4362no—
306C23—4362no—
307C23—2181no—
308C23—2181no—
309C23—2181no—
310C23D4×D10911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—8721no—
314D4—8721no—
315D4—1092no—
316D4—4362no—
317D4—4362no—
318D4—4362no—
319D4—2182no—
320D4—2181no—
321D4—2181no—
322D4—2181no—
323D4—2181no—
324D4—2181no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—8721no—
333C2×C4—8721no—
334C2×C4—1091no—
335C2×C4—1091no—
336C2×C4—1091no—
337C2×C4—4362no—
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—8724no—
350C22—4361no—
351C22—4361no—
352C22—4361no—
353C22—4361no—
354C22—4361no—
355C22—4361no—
356C22—4361no—
357C22—4361no—
358C22—2181no—
359C22—2181no—
360C22—2182no—
361C22—2181no—
362C22#1681272212yes—
363C22C2×D4×D10911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4361no—
370C4—2181no—
371C4—2181no—
372C4—2181no—
373C4#41×D10911yescharacteristic
374C4#1681274511yescharacteristic
375C2—22no—
376C2—8721no—
377C2—8721no—
378C2—4362no—
379C2—4361no—
380C2#2029566811yescharacteristic
381C2C2×#1681272211yescharacteristic
382C2#2029583011yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#484×C109C2
socleC22×C109C22×D4
hypercenter#484D109
hypocenterC109#3297
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #20295724C2semidirect
2. #20295667C2semidirect
3. #20295382C2semidirect
4. #20295353C2semidirect
5. #20295329C2semidirect
6. #20295263C2semidirect
7. #20295257C2semidirect
8. #20295244C2semidirect
9. #20295174C2semidirect
10. #20295162C2semidirect
11. #20295108C2semidirect
12. #20295089C2semidirect
13. #20295021C2semidirect
14. C2×#16812619C2semidirect
15. #484×C109C2semidirect
18. C2×#13182016C22semidirect
22. C2×C8×D109C22semidirect
24. #16812690C22semidirect
30. #16812674C22semidirect
35. #16812661C22semidirect
38. #16812657C22semidirect
40. #16812630C22semidirect
41. #16812628C22semidirect
42. #16812623C22semidirect
49. #16812619C22semidirect
50. #16812611C22semidirect
51. C8×Dic109C22semidirect
54. #107×C109C22semidirect
55. #107×C109C22semidirect
56. #103×C109C22semidirect
57. #103×C109C22semidirect
192. C109#3297semidirect
196. #484D109semidirect
234. #107C2×D109semidirect
235. #107C2×D109semidirect
239. #103C2×D109semidirect
240. #103C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202957242
#202956672
#202953822
#202953532
#202953292
#202952632
#202952572
#202952442
#202951742
#202951622
#202951082
#202950892
#202950212
C2×#168126192
#484×C1092
#3297109