Finite Group Databasebeta

← #28374883

Subgroups — #28374883

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#20295720C211yesmaximal, characteristic, complemented
2#20295664C211yesmaximal, characteristic, complemented
3#20295382C211yesmaximal, characteristic, complemented
4#20295360C211yesmaximal, characteristic, complemented
5#20295350C211yesmaximal, characteristic, complemented
6#20295324C211yesmaximal, characteristic, complemented
7#20295262C211yesmaximal, characteristic, complemented
8#20295258C211yesmaximal, characteristic, complemented
9#20295244C211yesmaximal, characteristic, complemented
10#20295171C211yesmaximal, characteristic, complemented
11#20295161C211yesmaximal, characteristic, complemented
12#20295106C211yesmaximal, characteristic, complemented
13C8×C22⋊D109C211yesmaximal, characteristic, complemented
14#102×D109C211yesmaximal, characteristic, complemented
15#416×C109C211yesmaximal, characteristic, complemented
16C2×D4×D109C2211yescharacteristic
17C2×#13182016C2211yescharacteristic, complemented
18C2×D872C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20C2×C8×D109C2211yescharacteristic
21#16812693—21no—
22#16812690C2211yescharacteristic, complemented
23#16812688C2211yescharacteristic
24#16812682—21no—
25#16812681—21no—
26#16812675C2211yescharacteristic
27#16812674C2211yescharacteristic
28#16812673C2211yescharacteristic
29#16812673C2211yescharacteristic, complemented
30#16812672—21no—
31#16812671—21no—
32#16812667—21no—
33C4×D436—21no—
34D4×Dic109C2211yescharacteristic
35#16812661C2211yescharacteristic, complemented
36C4×C22⋊D109C2211yescharacteristic
37C4⋊C4×D109C2211yescharacteristic
38C2×#13182006—21no—
39#16812633C2211yescharacteristic, complemented
40#16812632C2211yescharacteristic, complemented
41#16812630C2211yescharacteristic, complemented
42#16812628C2211yescharacteristic, complemented
43#16812623C2211yescharacteristic, complemented
44#16812621C2211yescharacteristic
45#16812621C2211yescharacteristic, complemented
46#16812620C2211yescharacteristic
47#16812619C2211yescharacteristic
48#16812619C2211yescharacteristic
49C22⋊#11724784C2211yescharacteristic, complemented
50#16812611C2211yescharacteristic
51C8×Dic109C2211yescharacteristic, complemented
52C2×#41×C109C2211yescharacteristic
53C22×C8×C109C2211yescharacteristic, complemented
54#117×C109C2211yescharacteristic, complemented
55#103×C109C2211yescharacteristic, complemented
56#103×C109C2211yescharacteristic, complemented
57#102×C109C2211yescharacteristic
58#102×C109C2211yescharacteristic
59C23×D109—21no—
60C2×D436—21no—
61C2×D436C2311yescharacteristic
62C2×D436C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C22⋊D109—21no—
66C2×C22⋊D109D411yescharacteristic
67D4×D109—22no—
68D4×D109—41no—
69C22×Dic109—21no—
70C2×C4×D109—21no—
71C2×C4×D109—21no—
72C2×C4×D109C2311yescharacteristic
73#13182016—41no—
74D872—41no—
75#13182014—22no—
76C2×#11724784C2311yescharacteristic
77C2×#11724784C2311yescharacteristic
78C8×D109—41no—
79C4⋊Dic109—21no—
80C4⋊Dic109C2311yescharacteristic
81C4⋊Dic109C2311yescharacteristic
82#13182008—21no—
83#13182008—21no—
84#13182008—21no—
85#13182008D411yescharacteristic
86C22⋊Dic109—21no—
87C22⋊Dic109D411yescharacteristic
88#13182006—21no—
89#13182006—21no—
90#13182006—21no—
91#13182006—21no—
92#13182006—21no—
93#13182006—21no—
94#13182006—21no—
95#13182006D411yescharacteristic
96C4×Dic109C2311yescharacteristic
97#41×C109—22no—
98#41×C109—41no—
99C2×Q8×C109C2311yescharacteristic
100C2×D4×C109—21no—
101C2×D4×C109C2311yescharacteristic
102C22×C4×C109—21no—
103C22×C4×C109C2311yescharacteristic
104C2×C8×C109—41no—
105C2×C8×C109C2311yescharacteristic
106C2×C8×C109C2311yescharacteristic
107C4⋊C4×C109C2311yescharacteristic
108C4⋊C4×C109C2311yescharacteristic
109C22⋊C4×C109—21no—
110C42×C109—21no—
111C23×C109—21no—
112C23×C109C2×D411yescharacteristic
113C22×D109—21no—
114C22×D109—21no—
115C22×D109—42no—
116C22×D109—42no—
117C22×D109—81no—
118C22×D109C2×D411yescharacteristic
119Q8×C109—21no—
120Q8×C109—21no—
121D4×C109—21no—
122D4×C109—42no—
123D4×C109#4112yes—
124C2×C4×C109—21no—
125C2×C4×C109—21no—
126C2×C4×C109—21no—
127C2×C4×C109—21no—
128C2×C4×C109—21no—
129C2×C4×C109—42no—
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—81no—
139C2×Dic109C2×D411yescharacteristic
140C2×Dic109C2×D411yescharacteristic
141C2×Dic109C2×D411yescharacteristic
142D436—21no—
143D436—21no—
144D436—21no—
145D436—21no—
146D436—42no—
147C4×D109—21no—
148C4×D109—21no—
149C4×D109—81no—
150C4×D109—81no—
151C8×C109—21no—
152C8×C109—21no—
153#11724784—21no—
154#11724784—21no—
155C22×C109—22no—
156C22×C109—21no—
157C22×C109—21no—
158C22×C109—21no—
159C22×C109—41no—
160C22×C109—41no—
161C22×C109C22×D411yescharacteristic
162C2×D109—21no—
163C2×D109—21no—
164C2×D109—41no—
165C2×D109—41no—
166C2×D109—41no—
167C2×D109—41no—
168C2×D109—41no—
169C2×D109—41no—
170C2×D109—84no—
171C2×D109#13512yes—
172C4×C109—21no—
173C4×C109—41no—
174C4×C109—41no—
175C4×C109—41no—
176C4×C109C2×#4111yescharacteristic
177C4×C109H(5,𝔽2)11yescharacteristic
178Dic109—21no—
179Dic109—21no—
180Dic109—21no—
181Dic109—41no—
182Dic109—41no—
183C2×C109—42no—
184C2×C109—41no—
185C2×C109#54611yescharacteristic
186C2×C109C2×#13511yescharacteristic
187C2×C109#57611yescharacteristic
188D109—22no—
189D109—81no—
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×D8—1091no—
205C8×D4—1091no—
206#416D10911yescharacteristic, complemented
207C2×#102—1091no—
208C2×#41C2×D10911yescharacteristic
209C22×D4—1091no—
210C2×SD16—1091no—
211C2×D8—1091no—
212C2×D8—1091no—
213C22×C8—1091no—
214C22×C8C2×D10911yescharacteristic, complemented
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—1091no—
229C4×D4—1091no—
230C4×D4—2181no—
231#117C2×D10911yescharacteristic, complemented
232C2×C4⋊C4—1091no—
233C2×C22⋊C4—2181no—
234#107—1091no—
235#107—1091no—
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#102C2×D10911yescharacteristic
247#102C2×D10911yescharacteristic
248C22⋊C8—1091no—
249C22⋊C8—1091no—
250C4×C8—1091no—
251C24—2181no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D10911yescharacteristic
255C2×D4—21no—
256C2×D4—1091no—
257C2×D4—1091no—
258C2×D4—1091no—
259C2×D4—4361no—
260C2×D4—2181no—
261C2×D4—2181no—
262C2×D4—2181no—
263C2×D4—2181no—
264C2×D4—2182no—
265C2×D4C22×D10911yescharacteristic
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—41no—
276C2×C8—1091no—
277C2×C8—1091no—
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—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—21no—
302C42—1091no—
303C23—21no—
304C23—8721no—
305C23—1091no—
306C23—4362no—
307C23—4362no—
308C23—2181no—
309C23—2181no—
310C23D4×D10911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—8721no—
316D4—8721no—
317D4—4362no—
318D4—4362no—
319D4—2182no—
320D4—2181no—
321D4—2181no—
322D4—2181no—
323D4—2181no—
324D4#1318202912yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—8721no—
332C2×C4—8721no—
333C2×C4—8721no—
334C2×C4—1091no—
335C2×C4—1091no—
336C2×C4—1091no—
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—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—8724no—
354C22—1092no—
355C22—4361no—
356C22—4361no—
357C22—4361no—
358C22—4361no—
359C22—4361no—
360C22—4361no—
361C22—2181no—
362C22—2181no—
363C22C2×D4×D10911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—4361no—
369C4—4361no—
370C4—2181no—
371C4—2181no—
372C4—2181no—
373C4C2×#1318202911yescharacteristic
374C4#1681274411yescharacteristic
375C2—41no—
376C2—42no—
377C2—8721no—
378C2—8721no—
379C2—2182no—
380C2#2029566611yescharacteristic
381C2#135×D10911yescharacteristic
382C2#2029582811yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#416×C109C2
socleC22×C109C22×D4
hypercenter#416D109
hypocenterC109#3297
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20295720C2semidirect
2. #20295664C2semidirect
3. #20295382C2semidirect
4. #20295360C2semidirect
5. #20295350C2semidirect
6. #20295324C2semidirect
7. #20295262C2semidirect
8. #20295258C2semidirect
9. #20295244C2semidirect
10. #20295171C2semidirect
11. #20295161C2semidirect
12. #20295106C2semidirect
13. C8×C22⋊D109C2semidirect
14. #102×D109C2semidirect
15. #416×C109C2semidirect
17. C2×#13182016C22semidirect
22. #16812690C22semidirect
29. #16812673C22semidirect
35. #16812661C22semidirect
39. #16812633C22semidirect
40. #16812632C22semidirect
41. #16812630C22semidirect
42. #16812628C22semidirect
43. #16812623C22semidirect
45. #16812621C22semidirect
49. C22⋊#11724784C22semidirect
51. C8×Dic109C22semidirect
53. C22×C8×C109C22semidirect
54. #117×C109C22semidirect
55. #103×C109C22semidirect
56. #103×C109C22semidirect
192. C109#3297semidirect
206. #416D109semidirect
214. C22×C8C2×D109semidirect
231. #117C2×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
#202957202
#202956642
#202953822
#202953602
#202953502
#202953242
#202952622
#202952582
#202952442
#202951712
#202951612
#202951062
C8×C22⋊D1092
#102×D1092
#416×C1092
#3297109