Finite Group Databasebeta

← #28375734

Subgroups — #28375734

Order 13952.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295735C211yesmaximal, characteristic, complemented
2#20295696C211yesmaximal, characteristic, complemented
3#20295390C211yesmaximal, characteristic, complemented
4#20295389C211yesmaximal, characteristic, complemented
5#20295371C211yesmaximal, characteristic, complemented
6#20295327C211yesmaximal, characteristic, complemented
7#20295324C211yesmaximal, characteristic, complemented
8#20295314C211yesmaximal, characteristic, complemented
9#20295219C211yesmaximal, characteristic, complemented
10#20295219C211yesmaximal, characteristic, complemented
11#20295155C211yesmaximal, characteristic, complemented
12#20295138C211yesmaximal, characteristic, complemented
13#20295136C211yesmaximal, characteristic, complemented
14D8×Dic109C211yesmaximal, characteristic, complemented
15#459×C109C211yesmaximal, characteristic, complemented
16C2×#13182028—21no—
17C2×#13182014C2211yescharacteristic
18#16812698C2211yescharacteristic
19#16812695C2211yescharacteristic
20#16812695C2211yescharacteristic
21#16812691C2211yescharacteristic
22#16812690C2211yescharacteristic
23#16812678—21no—
24#16812676—21no—
25#16812676—21no—
26#16812671—21no—
27#16812671—21no—
28#16812670—21no—
29C4×Dic218C2211yescharacteristic
30C4×D436C2211yescharacteristic
31D4×Dic109C2211yescharacteristic
32D4×Dic109C2211yescharacteristic
33D4×Dic109C2211yescharacteristic
34D4×Dic109C2211yescharacteristic
35C2×#13182008—21no—
36#16812633C2211yescharacteristic
37#16812631C2211yescharacteristic
38#16812630C2211yescharacteristic
39#16812628C2211yescharacteristic
40#16812628C2211yescharacteristic
41#16812621C2211yescharacteristic
42#16812621C2211yescharacteristic
43#16812620C2211yescharacteristic
44#16812620C2211yescharacteristic
45#16812620C2211yescharacteristic
46#16812620C2211yescharacteristic
47#16812620C2211yescharacteristic
48#16812619C2211yescharacteristic
49#16812610C2211yescharacteristic
50#16812609C2211yescharacteristic
51C8×Dic109C2211yescharacteristic
52C2×D8×C109C2211yescharacteristic
53C2×D8×C109C2211yescharacteristic
54#127×C109C2211yescharacteristic
55C4×D4×C109C2211yescharacteristic
56C4⋊C8×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic
58#102×C109C2211yescharacteristic
59#13182028—44no—
60C2×Dic218—21no—
61C2×Dic218D411yescharacteristic
62C2×D436C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C22⋊D109—21no—
66C2×C22⋊D109—21no—
67C22×Dic109—21no—
68C22×Dic109—21no—
69C22×Dic109—21no—
70C22×Dic109—21no—
71C2×C4×D109—21no—
72#13182014—22no—
73C2×#11724784C2311yescharacteristic
74C2×#11724784C2311yescharacteristic
75C4⋊Dic109—21no—
76C4⋊Dic109D411yescharacteristic
77C4⋊Dic109C2311yescharacteristic
78C4⋊Dic109C2311yescharacteristic
79C4⋊Dic109C2311yescharacteristic
80#13182008—21no—
81#13182008—21no—
82#13182008—21no—
83#13182008—21no—
84#13182008D411yescharacteristic
85#13182008D411yescharacteristic
86C22⋊Dic109—21no—
87C22⋊Dic109—21no—
88C22⋊Dic109—21no—
89C22⋊Dic109—21no—
90#13182006—21no—
91C4×Dic109C2311yescharacteristic
92C4×Dic109C2311yescharacteristic
93C2×D4×C109—21no—
94C2×D4×C109—21no—
95C2×D4×C109C2311yescharacteristic
96C2×D4×C109C2311yescharacteristic
97C2×D4×C109C2311yescharacteristic
98C22×C4×C109—21no—
99D8×C109—22no—
100D8×C109—22no—
101C2×C8×C109C2311yescharacteristic
102C2×C8×C109C2311yescharacteristic
103C4⋊C4×C109C2311yescharacteristic
104C22⋊C4×C109—21no—
105C42×C109C2311yescharacteristic
106C23×C109—21no—
107C23×C109—21no—
108C23×C109—21no—
109C22×D109—21no—
110D4×C109—21no—
111D4×C109—21no—
112D4×C109—21no—
113D4×C109—21no—
114D4×C109—21no—
115D4×C109—42no—
116D4×C109—81no—
117D4×C109#4112yescomplemented
118C2×C4×C109—21no—
119C2×C4×C109—81no—
120C2×C4×C109C2×D411yescharacteristic
121C2×C4×C109C2×D411yescharacteristic
122C2×C4×C109C2411yescharacteristic
123C22⋊D109—42no—
124C22⋊D109—42no—
125C22⋊D109—81no—
126C22⋊D109—81no—
127C2×Dic109—21no—
128C2×Dic109—21no—
129C2×Dic109—21no—
130C2×Dic109—42no—
131C2×Dic109—42no—
132C2×Dic109—42no—
133C2×Dic109—81no—
134C2×Dic109C2×D411yescharacteristic
135C2×Dic109C2×D411yescharacteristic
136C2×Dic109C2×D411yescharacteristic
137C2×Dic109C2×D411yescharacteristic
138D436—21no—
139D436—21no—
140C4×D109—42no—
141Dic218—22no—
142Dic218—81no—
143C8×C109—21no—
144C8×C109—21no—
145#11724784—21no—
146#11724784—21no—
147C22×C109—22no—
148C22×C109—41no—
149C22×C109—41no—
150C22×C109—41no—
151C22×C109—41no—
152C22×C109—41no—
153C22×C109—41no—
154C22×C109—41no—
155C22×C109—41no—
156C22×C109C22×D411yescharacteristic
157C2×D109—41no—
158C2×D109—41no—
159C2×D109—41no—
160C4×C109—21no—
161C4×C109—21no—
162C4×C109—41no—
163C4×C109C2×#4111yescharacteristic
164C4×C1092−1+411yescharacteristic
165Dic109—21no—
166Dic109—21no—
167Dic109—21no—
168Dic109—41no—
169Dic109—41no—
170Dic109—41no—
171Dic109AGL(1,ℤ/8)12yes—
172C2×C109—42no—
173C2×C109—81no—
174C2×C109—81no—
175C2×C109#54811yescharacteristic
176C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C109#57611yescharacteristic
178D109—81no—
179#3366—1091nomaximal, Sylow
180C109#336611yescharacteristic, complemented, Sylow
181#554—1091no—
182#550—1091no—
183#490—1091no—
184#490—1091no—
185#486—1091no—
186#478—1091no—
187#478—1091no—
188#476—1091no—
189#459—1091no—
190#459—1091no—
191#459D10911yescharacteristic, complemented
192#446—1091no—
193#442—1091no—
194#442—1091no—
195C4×D8—1091no—
196C2×#41—2181no—
197C2×D8—1091no—
198C2×D8C2×D10911yescharacteristic
199C2×D8C2×D10911yescharacteristic
200C4⋊Q8—1091no—
201#127—1091no—
202#127—1091no—
203#127C2×D10911yescharacteristic
204#125—1091no—
205#125—1091no—
206C22⋊Q8—2181no—
207C22⋊Q8—2181no—
208C22⋊Q8—2181no—
209#121—2181no—
210#121—2181no—
211#121—2181no—
212C4×Q8—1091no—
213C4×D4—1091no—
214C4×D4—1091no—
215C4×D4—1091no—
216C4×D4—1091no—
217C4×D4—1091no—
218C4×D4C2×D10911yescharacteristic
219C2×C4⋊C4—2181no—
220#107—1091no—
221#106—1091no—
222#106—1091no—
223C4⋊C8—1091no—
224C4⋊C8—1091no—
225C4⋊C8C2×D10911yescharacteristic
226#102—1091no—
227#102—1091no—
228#102—1091no—
229#102—1091no—
230#102—1091no—
231#102—1091no—
232#102—1091no—
233#102—1091no—
234#102C2×D10911yescharacteristic
235#102C2×D10911yescharacteristic
236#97—1091no—
237#97—1091no—
238C4×C8—1091no—
239#41—4364no—
240C2×Q8—1091no—
241C2×Q8—2181no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—1091no—
245C2×D4—2181no—
246C2×D4—2181no—
247C2×D4—2181no—
248C2×D4—2181no—
249C2×D4C22×D10911yescharacteristic
250C2×D4C22×D10911yescharacteristic
251C2×D4C22×D10911yescharacteristic
252C22×C4—21no—
253C22×C4—2181no—
254C22×C4—2181no—
255C22×C4—2181no—
256C22×C4—2181no—
257C22×C4—2181no—
258D8—22no—
259D8—22no—
260D8—2182no—
261C2×C8—1091no—
262C2×C8—1091no—
263C2×C8C22×D10911yescharacteristic
264C2×C8C22×D10911yescharacteristic
265C4⋊C4—1091no—
266C4⋊C4—1091no—
267C4⋊C4—1091no—
268C4⋊C4—1091no—
269C4⋊C4—1091no—
270C4⋊C4—1091no—
271C4⋊C4—2181no—
272C4⋊C4—2181no—
273C4⋊C4—2181no—
274C4⋊C4—2181no—
275C4⋊C4—2181no—
276C4⋊C4C22×D10911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2181no—
279C22⋊C4—2181no—
280C22⋊C4—2181no—
281C22⋊C4—2181no—
282C22⋊C4—2181no—
283C42—1091no—
284C42—1091no—
285C42C22×D10911yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—2181no—
290Q8—8721no—
291Q8—2182no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—8721no—
300D4—8721no—
301D4—4362no—
302D4—4362no—
303D4—2181no—
304D4—2181no—
305D4#1318202812yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—8721no—
309C2×C4—1091no—
310C2×C4—1091no—
311C2×C4—1091no—
312C2×C4—1091no—
313C2×C4—4362no—
314C2×C4—4362no—
315C2×C4—4362no—
316C2×C4—4362no—
317C2×C4—2181no—
318C2×C4—2181no—
319C2×C4—2181no—
320C2×C4D4×D10911yescharacteristic
321C2×C4D4×D10911yescharacteristic
322C2×C4C23×D10911yescharacteristic
323C8—21no—
324C8—21no—
325C8—2181no—
326C8—2181no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—4361no—
337C22—4361no—
338C22—4361no—
339C22C2×D4×D10911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—1092no—
344C4—4361no—
345C4—4361no—
346C4—4361no—
347C4—2181no—
348C4—2181no—
349C4—2181no—
350C4C2×#1318202811yescharacteristic
351C4#1681274611yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—8721no—
356C2#2029568211yescharacteristic
357C2AGL(1,ℤ/8)×D10911yescharacteristic
358C2#2029582711yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#459×C109C2
socleC22×C109C22×D4
hypercenter#459D109
hypocenterC109#3366
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20295735C2semidirect
2. #20295696C2semidirect
3. #20295390C2semidirect
4. #20295389C2semidirect
5. #20295371C2semidirect
6. #20295327C2semidirect
7. #20295324C2semidirect
8. #20295314C2semidirect
9. #20295219C2semidirect
10. #20295219C2semidirect
11. #20295155C2semidirect
12. #20295138C2semidirect
13. #20295136C2semidirect
14. D8×Dic109C2semidirect
15. #459×C109C2semidirect
117. D4×C109#41semidirect
180. C109#3366semidirect
191. #459D109semidirect
305. D4#13182028semidirect

Maximal subgroups

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

subgroupindex
#202957352
#202956962
#202953902
#202953892
#202953712
#202953272
#202953242
#202953142
#202952192
#202951552
#202951382
#202951362
D8×Dic1092
#459×C1092
#3366109