Finite Group Databasebeta

← #28374884

Subgroups — #28374884

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#20295722C211yesmaximal, characteristic, complemented
2#20295672C211yesmaximal, characteristic, complemented
3#20295381C211yesmaximal, characteristic, complemented
4#20295362C211yesmaximal, characteristic, complemented
5#20295351C211yesmaximal, characteristic, complemented
6#20295327C211yesmaximal, characteristic, complemented
7#20295262C211yesmaximal, characteristic, complemented
8#20295255C211yesmaximal, characteristic, complemented
9#20295242C211yesmaximal, characteristic, complemented
10#20295173C211yesmaximal, characteristic, complemented
11#20295162C211yesmaximal, characteristic, complemented
12C4×D872C211yesmaximal, characteristic, complemented
13#20295023C211yesmaximal, characteristic, complemented
14C2×#16812621C211yesmaximal, characteristic, complemented
15C8×D4×C109C211yesmaximal, characteristic, complemented
16C2×#13182029C2211yescharacteristic
17C22×D436C2211yescharacteristic
18C2×#13182018C2211yescharacteristic, complemented
19C2×D872C2211yescharacteristic
20C2×D872C2211yescharacteristic
21#16812694—21no—
22#16812691C2211yescharacteristic, complemented
23#16812687C2211yescharacteristic
24#16812684—21no—
25#16812681—21no—
26#16812678C2211yescharacteristic
27#16812673C2211yescharacteristic
28#16812673C2211yescharacteristic
29#16812673C2211yescharacteristic, complemented
30#16812672—21no—
31#16812671—21no—
32#16812667—21no—
33C4×D436C2211yescharacteristic
34C4×D436C2211yescharacteristic, complemented
35#16812659—21no—
36#16812658C2211yescharacteristic, complemented
37C2×C4⋊Dic109C2211yescharacteristic
38C22⋊C4×D109—21no—
39#16812633C2211yescharacteristic, complemented
40#16812633C2211yescharacteristic, complemented
41#16812631C2211yescharacteristic, complemented
42#16812624C2211yescharacteristic, complemented
43#16812624C2211yescharacteristic, complemented
44#16812624C2211yescharacteristic, complemented
45#16812621C2211yescharacteristic
46#16812621C2211yescharacteristic
47#16812621C2211yescharacteristic
48#16812621C2211yescharacteristic
49#16812621C2211yescharacteristic
50#16812621C2211yescharacteristic
51#16812621C2211yescharacteristic, complemented
52C22×C8×C109C2211yescharacteristic
53C22×C8×C109C2211yescharacteristic, complemented
54C4×D4×C109C2211yescharacteristic
55C4⋊C8×C109C2211yescharacteristic, complemented
56C22⋊C8×C109C2211yescharacteristic
57C22⋊C8×C109C2211yescharacteristic, complemented
58C4×C8×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60#13182029—22no—
61#13182029—41no—
62C2×Dic218C2311yescharacteristic
63C2×D436—22no—
64C2×D436—21no—
65C2×D436—41no—
66C2×D436C2311yescharacteristic
67C2×D436C2311yescharacteristic
68C2×D436C2311yescharacteristic
69C2×C22⋊D109—21no—
70C2×C22⋊D109—21no—
71C2×C22⋊D109—21no—
72C2×C22⋊D109—21no—
73C22×Dic109—21no—
74C2×C4×D109—21no—
75C2×C4×D109—21no—
76C2×C4×D109—21no—
77#13182018—41no—
78D872—22no—
79D872—41no—
80C4⋊Dic109—21no—
81C4⋊Dic109C2311yescharacteristic
82C4⋊Dic109C2311yescharacteristic
83C4⋊Dic109C2311yescharacteristic
84C4⋊Dic109C2311yescharacteristic
85#13182008—21no—
86#13182008—21no—
87#13182008—21no—
88C22⋊Dic109—21no—
89C22⋊Dic109—21no—
90#13182006—21no—
91#13182006—21no—
92#13182006—21no—
93#13182006—21no—
94#13182006—21no—
95#13182006—21no—
96#13182006—21no—
97C4×Dic109—21no—
98C2×D4×C109D411yescharacteristic
99C22×C4×C109C2311yescharacteristic
100C22×C4×C109C2311yescharacteristic
101C2×C8×C109—41no—
102C2×C8×C109—41no—
103C2×C8×C109C2311yescharacteristic
104C2×C8×C109C2311yescharacteristic
105C2×C8×C109C2311yescharacteristic
106C2×C8×C109C2311yescharacteristic
107C4⋊C4×C109D411yescharacteristic
108C22⋊C4×C109D411yescharacteristic
109C22⋊C4×C109D411yescharacteristic
110C42×C109C2311yescharacteristic
111C23×C109C2×D411yescharacteristic
112C23×C109C2×D411yescharacteristic
113C22×D109—21no—
114C22×D109—21no—
115C22×D109—21no—
116C22×D109—42no—
117C22×D109—42no—
118C22×D109—81no—
119D4×C109—22no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—21no—
124C2×C4×C109C2×D411yescharacteristic
125C2×C4×C109C2×D411yescharacteristic
126C2×C4×C109C2×D411yescharacteristic
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2411yescharacteristic
129C22⋊D109—42no—
130C22⋊D109—42no—
131C22⋊D109—81no—
132C22⋊D109—81no—
133C2×Dic109—21no—
134C2×Dic109—21no—
135C2×Dic109—21no—
136C2×Dic109—21no—
137C2×Dic109—21no—
138C2×Dic109—81no—
139D436—21no—
140D436—21no—
141D436—21no—
142D436—21no—
143D436—21no—
144D436—42no—
145D436#4112yes—
146C4×D109—42no—
147C4×D109—81no—
148C4×D109—81no—
149Dic218—21no—
150Dic218—21no—
151C8×C109—21no—
152C8×C109—21no—
153C8×C109—21no—
154C8×C109—21no—
155C22×C109—21no—
156C22×C109—21no—
157C22×C109—21no—
158C22×C109—21no—
159C22×C109—21no—
160C22×C109#13512yes—
161C22×C109C22×D411yescharacteristic
162C2×D109—22no—
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—21no—
174C4×C109—21no—
175C4×C109—21no—
176C4×C109C2×#4111yescharacteristic
177C4×C109H(5,𝔽2)11yescharacteristic
178Dic109—41no—
179Dic109—41no—
180Dic109—41no—
181Dic109—41no—
182Dic109—41no—
183C2×C109—22no—
184C2×C109—41no—
185C2×C109#54611yescharacteristic
186C2×C109C2×#13511yescharacteristic
187C2×C109#57611yescharacteristic
188D109—42no—
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×D4D10911yescharacteristic, complemented
206#416—1091no—
207C2×#102—1091no—
208C2×#41—1091no—
209C22×D4—1091no—
210C2×SD16—1091no—
211C2×D8—1091no—
212C2×D8—1091no—
213C22×C8C2×D10911yescharacteristic
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—2181no—
230C4×D4C2×D10911yescharacteristic
231#117—1091no—
232C2×C4⋊C4—1091no—
233C2×C22⋊C4—2181no—
234#107—1091no—
235#107—1091no—
236#106—1091no—
237C4⋊C8C2×D10911yescharacteristic, complemented
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#102—1091no—
247#102—1091no—
248C22⋊C8C2×D10911yescharacteristic
249C22⋊C8C2×D10911yescharacteristic, complemented
250C4×C8C2×D10911yescharacteristic, complemented
251C24—2181no—
252#41—4361no—
253#41—2182no—
254C2×Q8—1091no—
255C2×D4—1091no—
256C2×D4—1091no—
257C2×D4—1091no—
258C2×D4—4361no—
259C2×D4—2182no—
260C2×D4—2181no—
261C2×D4—2181no—
262C2×D4—2181no—
263C2×D4—2181no—
264C2×D4—2181no—
265C2×D4D43611yescharacteristic
266C22×C4—2181no—
267C22×C4—2181no—
268C22×C4—2181no—
269C22×C4—2181no—
270C22×C4C22×D10911yescharacteristic
271C22×C4C22×D10911yescharacteristic
272SD16—4361no—
273D8—4361no—
274D8—2182no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D10911yescharacteristic
278C2×C8C22×D10911yescharacteristic
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⋊C4D43611yescharacteristic
290C22⋊C4—2181no—
291C22⋊C4—2181no—
292C22⋊C4—2181no—
293C22⋊C4—2181no—
294C22⋊C4—2181no—
295C22⋊C4—2181no—
296C22⋊C4—2181no—
297C22⋊C4—2181no—
298C22⋊C4—2181no—
299C22⋊C4D43611yescharacteristic
300C22⋊C4D43611yescharacteristic
301C42—2181no—
302C42C22×D10911yescharacteristic
303C23—8721no—
304C23—4362no—
305C23—4362no—
306C23—2181no—
307C23—2181no—
308C23—2181no—
309C23C2×D43611yescharacteristic
310C23C2×D43611yescharacteristic
311Q8—2181no—
312Q8—2181no—
313D4—22no—
314D4—8721no—
315D4—8721no—
316D4—1092no—
317D4—4362no—
318D4—4362no—
319D4—4362no—
320D4—2181no—
321D4—2181no—
322D4—2181no—
323D4—2181no—
324D4—2181no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—8721no—
330C2×C4—8721no—
331C2×C4—8721no—
332C2×C4—4362no—
333C2×C4—2181no—
334C2×C4—2181no—
335C2×C4—2181no—
336C2×C4—2181no—
337C2×C4—2181no—
338C2×C4C2×D43611yescharacteristic
339C2×C4C2×D43611yescharacteristic
340C2×C4C2×D43611yescharacteristic
341C2×C4C2×D43611yescharacteristic
342C2×C4C23×D10911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—8724no—
353C22—4361no—
354C22—4361no—
355C22—4361no—
356C22—4361no—
357C22—4361no—
358C22—4361no—
359C22—4361no—
360C22—4361no—
361C22—2182no—
362C22#1681272112yes—
363C22C22×D43611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—4361no—
369C4—4361no—
370C4—4361no—
371C4—4361no—
372C4—4361no—
373C4#41×D10911yescharacteristic
374C4#1681274411yescharacteristic
375C2—22no—
376C2—41no—
377C2—8721no—
378C2—8721no—
379C2—4362no—
380C2#2029567111yescharacteristic
381C2C2×#1681272111yescharacteristic
382C2#2029583111yescharacteristic
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC8×D4×C109C2
socleC22×C109C22×D4
hypercenterC8×D4D109
hypocenterC109#3297
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20295722C2semidirect
2. #20295672C2semidirect
3. #20295381C2semidirect
4. #20295362C2semidirect
5. #20295351C2semidirect
6. #20295327C2semidirect
7. #20295262C2semidirect
8. #20295255C2semidirect
9. #20295242C2semidirect
10. #20295173C2semidirect
11. #20295162C2semidirect
12. C4×D872C2semidirect
13. #20295023C2semidirect
14. C2×#16812621C2semidirect
15. C8×D4×C109C2semidirect
18. C2×#13182018C22semidirect
22. #16812691C22semidirect
29. #16812673C22semidirect
34. C4×D436C22semidirect
36. #16812658C22semidirect
39. #16812633C22semidirect
40. #16812633C22semidirect
41. #16812631C22semidirect
42. #16812624C22semidirect
43. #16812624C22semidirect
44. #16812624C22semidirect
51. #16812621C22semidirect
53. C22×C8×C109C22semidirect
55. C4⋊C8×C109C22semidirect
57. C22⋊C8×C109C22semidirect
58. C4×C8×C109C22semidirect
192. C109#3297semidirect
205. C8×D4D109semidirect
214. C22×C8C2×D109semidirect
237. C4⋊C8C2×D109semidirect
249. C22⋊C8C2×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
#202957222
#202956722
#202953812
#202953622
#202953512
#202953272
#202952622
#202952552
#202952422
#202951732
#202951622
C4×D8722
#202950232
C2×#168126212
C8×D4×C1092
#3297109