Finite Group Databasebeta

← #28374497

Subgroups — #28374497

Order 13952.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295647C211yesmaximal, characteristic, complemented
2#20295316C211yesmaximal, characteristic, complemented
3#20295313C211yesmaximal, characteristic, complemented
4#20295311C211yesmaximal, characteristic, complemented
5#20295308C211yesmaximal, characteristic, complemented
6#20295282C211yesmaximal, characteristic, complemented
7#20295277C211yesmaximal, characteristic
8#20295257C211yesmaximal, characteristic, complemented
9#20295253C211yesmaximal, characteristic, complemented
10#20295248C211yesmaximal, characteristic, complemented
11#20295245C211yesmaximal, characteristic, complemented
12#20295241C211yesmaximal, characteristic, complemented
13#20295238C211yesmaximal, characteristic, complemented
14#20295053C211yesmaximal, characteristic, complemented
15#542×C109C211yesmaximal, characteristic, complemented
16C2×#13182019C2211yescharacteristic
17C2×#13182017C2211yescharacteristic
18C2×#13182016C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20C2×#13182013C2211yescharacteristic
21C22×#11724784C2211yescharacteristic
22#16812699C2211yescharacteristic
23#16812694—21no—
24#16812687C2211yescharacteristic
25#16812685—21no—
26#16812681—21no—
27#16812678C2211yescharacteristic
28#16812677—21no—
29#16812673C2211yescharacteristic
30C4×Dic218C2211yescharacteristic
31C4×D436C2211yescharacteristic
32#16812630C2211yescharacteristic
33#16812630C2211yescharacteristic
34#16812630C2211yescharacteristic
35#16812630C2211yescharacteristic
36C4⋊#11724784C2211yescharacteristic
37C4⋊#11724784C2211yescharacteristic
38C4⋊#11724784C2211yescharacteristic
39C4⋊#11724784C2211yescharacteristic
40#16812623C2211yescharacteristic
41#16812623C2211yescharacteristic
42#16812622C2211yescharacteristic
43#16812622C2211yescharacteristic
44#16812620C2211yescharacteristic
45#16812620C2211yescharacteristic
46#16812619C2211yescharacteristic
47#16812619C2211yescharacteristic
48C4⋊Q8×C109C2211yescharacteristic
49#126×C109—21no—
50#124×C109—21no—
51#124×C109C2211yescharacteristic
52#123×C109—21no—
53C22⋊Q8×C109—21no—
54C22⋊Q8×C109C2211yescharacteristic
55#121×C109C2211yescharacteristic
56C4×Q8×C109C2211yescharacteristic
57C4×D4×C109C2211yescharacteristic
58#117×C109C2211yescharacteristic
59C2×Dic218—21no—
60C2×Dic218C2311yescharacteristic
61C2×D436C2311yescharacteristic
62C2×C22⋊D109—21no—
63C2×C4×D109—21no—
64#13182019—41no—
65#13182017—41no—
66#13182016—41no—
67#13182014—41no—
68#13182013—41no—
69C2×#11724784—41no—
70C2×#11724784C2311yescharacteristic
71C2×#11724784C2311yescharacteristic
72C2×#11724784C2311yescharacteristic
73C2×#11724784C2311yescharacteristic
74C4⋊Dic109—21no—
75C4⋊Dic109C2311yescharacteristic
76C4⋊Dic109C2311yescharacteristic
77#13182008—21no—
78#13182008—21no—
79C22⋊Dic109—21no—
80#13182006—21no—
81#13182006—21no—
82#13182006—21no—
83#13182006—21no—
84C4×Dic109—21no—
85C2×Q8×C109—21no—
86C2×Q8×C109C2311yescharacteristic
87C2×D4×C109—21no—
88C2×D4×C109C2311yescharacteristic
89C22×C4×C109—21no—
90C22×C4×C109C2311yescharacteristic
91C4⋊C4×C109—21no—
92C4⋊C4×C109—21no—
93C4⋊C4×C109—21no—
94C4⋊C4×C109D411yescharacteristic
95C4⋊C4×C109D411yescharacteristic
96C4⋊C4×C109C2311yescharacteristic
97C4⋊C4×C109C2311yescharacteristic
98C22⋊C4×C109—21no—
99C22⋊C4×C109—21no—
100C22⋊C4×C109—21no—
101C22⋊C4×C109—21no—
102C22⋊C4×C109—21no—
103C22⋊C4×C109D411yescharacteristic
104C22⋊C4×C109D411yescharacteristic
105C42×C109—21no—
106C42×C109C2311yescharacteristic
107C42×C109C2311yescharacteristic
108C23×C109—21no—
109C23×C109C2×D411yescharacteristic
110C22×D109—21no—
111Q8×C109—21no—
112Q8×C109—21no—
113Q8×C109—81no—
114D4×C109—21no—
115D4×C109—21no—
116D4×C109—81no—
117C2×C4×C109—21no—
118C2×C4×C109—21no—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—81no—
123C2×C4×C109C2×D411yescharacteristic
124C2×C4×C109C2×D411yescharacteristic
125C2×C4×C109C2×D411yescharacteristic
126C2×C4×C109C2×D411yescharacteristic
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2411yescharacteristic
129C22⋊D109—81no—
130C2×Dic109—21no—
131C2×Dic109—21no—
132C2×Dic109—21no—
133D436—21no—
134D436—21no—
135C4×D109—81no—
136Dic218—21no—
137Dic218—21no—
138Dic218—81no—
139#11724784—21no—
140#11724784—21no—
141#11724784—21no—
142#11724784—21no—
143C22×C109—21no—
144C22×C109—21no—
145C22×C109—21no—
146C22×C109—41no—
147C22×C109—41no—
148C22×C109—41no—
149C22×C109C22×D411yescharacteristic
150C2×D109—41no—
151C2×D109—41no—
152C2×D109—41no—
153C4×C109—21no—
154C4×C109—21no—
155C4×C109—21no—
156C4×C109—21no—
157C4×C109—21no—
158C4×C109—41no—
159C4×C109—41no—
160C4×C109—41no—
161C4×C109H(5,𝔽2)11yescharacteristic
162C4×C1092−1+411yescharacteristic
163Dic109—41no—
164Dic109—41no—
165Dic109—41no—
166C2×C109—41no—
167C2×C109—81no—
168C2×C109#53711yescharacteristic
169C2×C109#57711yescharacteristic
170C2×C109#57711yescharacteristic
171D109—81no—
172#3263—1091nomaximal, Sylow
173C109#326311yescharacteristic, complemented, Sylow
174#542—1091no—
175#542D10911yescharacteristic, complemented
176#476—1091no—
177#476—1091no—
178#475—1091no—
179#475—1091no—
180#470—1091no—
181#469—1091no—
182#465—1091no—
183#465—1091no—
184#464—1091no—
185#464—1091no—
186#463—1091no—
187#463—1091no—
188#424—1091no—
189C2×Q16—1091no—
190C2×SD16—1091no—
191C2×SD16—1091no—
192C2×D8—1091no—
193C2×M16—1091no—
194C22×C8—1091no—
195C4⋊Q8—1091no—
196C4⋊Q8C2×D10911yescharacteristic
197#126—21no—
198#126—2181no—
199#124—21no—
200#124—1091no—
201#124—2181no—
202#124C2×D10911yescharacteristic
203#123—21no—
204#123—2181no—
205C22⋊Q8—21no—
206C22⋊Q8—1091no—
207C22⋊Q8—2181no—
208C22⋊Q8C2×D10911yescharacteristic
209#121—1091no—
210#121C2×D10911yescharacteristic
211C4×Q8—1091no—
212C4×Q8C2×D10911yescharacteristic
213C4×D4—1091no—
214C4×D4C2×D10911yescharacteristic
215#117C2×D10911yescharacteristic
216#106—1091no—
217#106—1091no—
218#106—1091no—
219#106—1091no—
220C4⋊C8—1091no—
221C4⋊C8—1091no—
222C4⋊C8—1091no—
223C4⋊C8—1091no—
224#103—1091no—
225#103—1091no—
226#103—1091no—
227#103—1091no—
228#102—1091no—
229#102—1091no—
230#102—1091no—
231#102—1091no—
232C2×Q8—21no—
233C2×Q8—1091no—
234C2×Q8—2181no—
235C2×Q8C22×D10911yescharacteristic
236C2×D4—21no—
237C2×D4—1091no—
238C2×D4—2181no—
239C2×D4C22×D10911yescharacteristic
240C22×C4—21no—
241C22×C4—2181no—
242C22×C4C22×D10911yescharacteristic
243Q16—4361no—
244SD16—4361no—
245SD16—4361no—
246D8—4361no—
247M16—4361no—
248C2×C8—1091no—
249C2×C8—1091no—
250C2×C8—1091no—
251C2×C8—1091no—
252C2×C8—4361no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1091no—
257C4⋊C4—1091no—
258C4⋊C4—2181no—
259C4⋊C4—2181no—
260C4⋊C4—2181no—
261C4⋊C4C22⋊D10911yescharacteristic
262C4⋊C4C22⋊D10911yescharacteristic
263C4⋊C4C22×D10911yescharacteristic
264C4⋊C4C22×D10911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2181no—
271C22⋊C4—2181no—
272C22⋊C4—2181no—
273C22⋊C4—2181no—
274C22⋊C4—2181no—
275C22⋊C4C22⋊D10911yescharacteristic
276C22⋊C4C22⋊D10911yescharacteristic
277C42—21no—
278C42—2181no—
279C42C22×D10911yescharacteristic
280C42C22×D10911yescharacteristic
281C23—21no—
282C23—2181no—
283C23C2×C22⋊D10911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—8721no—
288Q8—2181no—
289Q8—2181no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—8721no—
294D4—2181no—
295D4—2181no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—8721no—
303C2×C4—2181no—
304C2×C4—2181no—
305C2×C4—2181no—
306C2×C4C2×C22⋊D10911yescharacteristic
307C2×C4C2×C22⋊D10911yescharacteristic
308C2×C4C2×C22⋊D10911yescharacteristic
309C2×C4C2×C22⋊D10911yescharacteristic
310C2×C4C2×C22⋊D10911yescharacteristic
311C2×C4C23×D10911yescharacteristic
312C8—2181no—
313C8—2181no—
314C8—2181no—
315C8—2181no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—4361no—
323C22—4361no—
324C22—4361no—
325C22C22×C22⋊D10911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—4361no—
335C4—4361no—
336C4—4361no—
337C4#1681274511yescharacteristic
338C4#1681274611yescharacteristic
339C2—41no—
340C2—81no—
341C2—8721no—
342C2#2029560411yescharacteristic
343C2#2029583411yescharacteristic
344C2#2029583711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#542×C109C2
socleC22×C109C22×D4
prime radical#20295277C2
hypercenter#542D109
hypocenterC109#3263
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20295647C2semidirect
2. #20295316C2semidirect
3. #20295313C2semidirect
4. #20295311C2semidirect
5. #20295308C2semidirect
6. #20295282C2semidirect
8. #20295257C2semidirect
9. #20295253C2semidirect
10. #20295248C2semidirect
11. #20295245C2semidirect
12. #20295241C2semidirect
13. #20295238C2semidirect
14. #20295053C2semidirect
15. #542×C109C2semidirect
173. C109#3263semidirect
175. #542D109semidirect

Maximal subgroups

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

subgroupindex
#202956472
#202953162
#202953132
#202953112
#202953082
#202952822
#202952772
#202952572
#202952532
#202952482
#202952452
#202952412
#202952382
#202950532
#542×C1092
#3263109