Finite Group Databasebeta

← #28345283

Subgroups — #28345283

Order 13696.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812138C211yesmaximal, characteristic
2C4×#13133817C211yesmaximal, characteristic
3C4×Q8×D107C211yesmaximal, characteristic, complemented
4#20292735C211yesmaximal, characteristic, complemented
5#20292732C211yesmaximal, characteristic, complemented
6#20292727C211yesmaximal, characteristic, complemented
7#20292721C211yesmaximal, characteristic, complemented
8#20292719C211yesmaximal, characteristic, complemented
9#20292718C211yesmaximal, characteristic, complemented
10SD16×Dic107C211yesmaximal, characteristic, complemented
11#20292668C211yesmaximal, characteristic, complemented
12#20292634C211yesmaximal, characteristic, complemented
13#20292625C211yesmaximal, characteristic
14#20292579C211yesmaximal, characteristic, complemented
15#440×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C2211yescharacteristic
17C2×Q8×D107C2211yescharacteristic
18#16812138C418yescomplemented
19C2×Dic428C2211yescharacteristic
20C2×#13133808C2211yescharacteristic
21C2×#13133806C2211yescharacteristic
22C2×#13133801C2211yescharacteristic
23C2×#13133801C2211yescharacteristic
24Q8×Dic107C2211yescharacteristic
25C4×Dic214—21no—
26C4×Dic214C2211yescharacteristic
27C4×Dic214C2211yescharacteristic
28#16812074—21no—
29#16812074C2211yescharacteristic
30#16812074C2211yescharacteristic
31D4×Dic107C2211yescharacteristic
32C4×C22⋊D107—21no—
33(C22⋊D107)⋊C4—21no—
34#16812067C2211yescharacteristic
35#16812065—21no—
36C4⋊C4×D107—21no—
37C4⋊C4×D107C2211yescharacteristic
38C2×C4×Dic107—21no—
39C42×D107—21no—
40C42×D107C2211yescharacteristic
41#16812042C2211yescharacteristic
42#16812041C2211yescharacteristic
43#16812040C2211yescharacteristic
44#16812034C2211yescharacteristic
45#16812034C2211yescharacteristic
46#16812033C2211yescharacteristic
47#16812032C2211yescharacteristic
48#16812032C2211yescharacteristic
49#16812030C2211yescharacteristic
50#16812020C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C8×Dic107C2211yescharacteristic
53C2×SD16×C107C2211yescharacteristic
54C4×Q8×C107C2211yescharacteristic
55C4×D4×C107C2211yescharacteristic
56#107×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic
59#97×C107C2211yescharacteristic
60#13133817—22no—
61#13133817C2×C414yes—
62C2×Dic214—21no—
63C2×Dic214C2311yescharacteristic
64C2×Dic214C2311yescharacteristic
65Q8×D107—22no—
66Q8×D107C2×C414yescomplemented
67C2×C22⋊D107—21no—
68C22×Dic107—21no—
69C22×Dic107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107D411yescharacteristic
73C2×C4×D107D411yescharacteristic
74C2×C4×D107C2311yescharacteristic
75Dic428C2×C414yescomplemented
76#13133808C2×C414yescomplemented
77#13133806C2×C414yescomplemented
78#13133801—22no—
79#13133801C2×C414yescomplemented
80C2×C107⋊C8C2311yescharacteristic
81C2×C107⋊C8C2311yescharacteristic
82C4⋊Dic107—21no—
83C4⋊Dic107C2311yescharacteristic
84C4⋊Dic107C2311yescharacteristic
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89Dic107⋊C4—21no—
90C22⋊Dic107—21no—
91(C2×D107)⋊C4—21no—
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C4×Dic107—21no—
98C4×Dic107D411yescharacteristic
99C4×Dic107D411yescharacteristic
100C4×Dic107C2311yescharacteristic
101C2×Q8×C107C2311yescharacteristic
102C2×D4×C107C2311yescharacteristic
103C22×C4×C107—21no—
104SD16×C107C2×C414yescomplemented
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C4⋊C4×C107—21no—
108C4⋊C4×C107C2311yescharacteristic
109C4⋊C4×C107C2311yescharacteristic
110C22⋊C4×C107—21no—
111C42×C107—21no—
112C42×C107C2311yescharacteristic
113C23×C107—21no—
114C22×D107C2×D411yescharacteristic
115Q8×C107—21no—
116Q8×C107C22×C412yes—
117D4×C107—21no—
118D4×C107C22×C412yes—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—42no—
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2411yescharacteristic
126C22⋊D107—24no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107—24no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—42no—
133C2×Dic107C2×D411yescharacteristic
134C2×Dic107C2×D411yescharacteristic
135C2×Dic107C2×D411yescharacteristic
136C4×D107—24no—
137C4×D107—22no—
138C4×D107—41no—
139C4×D107—42no—
140C4×D107C22×C412yes—
141C4×D107#4112yes—
142Dic214—21no—
143Dic214—21no—
144Dic214—24no—
145Dic214C22×C412yes—
146Dic214C22×C412yes—
147C8×C107—21no—
148C8×C107C22×C412yes—
149C107⋊C8—21no—
150C107⋊C8C22×C412yes—
151C22×C107—22no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107C22×D411yescharacteristic
155C2×D107—21no—
156C2×D107—21no—
157C2×D107C4×D412yes—
158C4×C107—22no—
159C4×C107—21no—
160C4×C107—21no—
161C4×C107—41no—
162C4×C107—41no—
163C4×C107C23×C411yescharacteristic
164C4×C107C2×#4111yescharacteristic
165Dic107—22no—
166Dic107—22no—
167Dic107—21no—
168Dic107—41no—
169Dic107—41no—
170Dic107C4×D412yes—
171Dic107#13712yescomplemented
172C2×C107—42no—
173C2×C107C2×C4×D411yescharacteristic
174C2×C107C2×#13711yescharacteristic
175C2×C107#57511yescharacteristic
176D107—22no—
177C4×#137—1071nomaximal, Sylow
178C107C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—1071no—
180C4×#41—1071no—
181C2×C4×Q8—1071no—
182#441—1071no—
183#441—1071no—
184#440—1071no—
185#440D10711yescharacteristic, complemented
186C4×Q16—1071no—
187C4×Q16—1071no—
188C4×SD16—1071no—
189C4×SD16—1071no—
190#428—1071no—
191#419—1071no—
192#417—1071no—
193C4×M16—1071no—
194C2×#41—1071no—
195C22×Q8—1071no—
196#137—1078no—
197C2×Q16—1071no—
198C2×Q16—1071no—
199C2×SD16—1071no—
200C2×SD16C2×D10711yescharacteristic
201C2×M16—1071no—
202C2×M16—1071no—
203C4×Q8—1071no—
204C4×Q8—1071no—
205C4×Q8—1071no—
206C4×Q8—1071no—
207C4×Q8—1071no—
208C4×Q8—2141no—
209C4×Q8—2141no—
210C4×Q8C2×D10711yescharacteristic
211C4×D4—1071no—
212C4×D4—2141no—
213C4×D4—2141no—
214C4×D4C2×D10711yescharacteristic
215#117—1071no—
216#117—2141no—
217C2×C4⋊C4—1071no—
218C2×C4⋊C4—2141no—
219C2×C42—1071no—
220C2×C42—2141no—
221C2×C42—2141no—
222#107—1071no—
223#107C2×D10711yescharacteristic
224#106—1071no—
225#106—1071no—
226#103—1071no—
227#103—1071no—
228#103—1071no—
229#103—1071no—
230#103—1071no—
231#103C2×D10711yescharacteristic
232#102—1071no—
233#102C2×D10711yescharacteristic
234#97—1071no—
235#97C2×D10711yescharacteristic
236C4×C8—1071no—
237C4×C8—1071no—
238#41—1074no—
239#41—2142no—
240C2×Q8—1074no—
241C2×Q8—1071no—
242C2×Q8—1071no—
243C2×Q8—2141no—
244C2×Q8—2142no—
245C2×Q8C22×D10711yescharacteristic
246C2×D4—2141no—
247C2×D4C22×D10711yescharacteristic
248C22×C4—21no—
249C22×C4—1071no—
250C22×C4—1071no—
251C22×C4—1071no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4—2141no—
255C22×C4—2141no—
256Q16—1074no—
257Q16—1074no—
258SD16—1074no—
259SD16C4×D10714yescomplemented
260M16—1074no—
261M16—2142no—
262C2×C8—1071no—
263C2×C8—1071no—
264C2×C8C22×D10711yescharacteristic
265C2×C8C22×D10711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—2141no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4—2141no—
275C4⋊C4C22×D10711yescharacteristic
276C4⋊C4C22×D10711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C42—21no—
281C42—1071no—
282C42—1071no—
283C42—1071no—
284C42—2141no—
285C42—2141no—
286C42—2141no—
287C42—2141no—
288C42—2141no—
289C42—2141no—
290C42C22×D10711yescharacteristic
291C23—21no—
292C23—1071no—
293Q8—21no—
294Q8—1072no—
295Q8—1072no—
296Q8—2144no—
297Q8—2141no—
298Q8—2141no—
299Q8C2×C4×D10712yes—
300D4—21no—
301D4—2144no—
302D4C2×C4×D10712yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—1071no—
308C2×C4—1071no—
309C2×C4—1072no—
310C2×C4—1072no—
311C2×C4—1071no—
312C2×C4—4281no—
313C2×C4—4282no—
314C2×C4—4282no—
315C2×C4—2142no—
316C2×C4—2144no—
317C2×C4—2144no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4D4×D10711yescharacteristic
323C2×C4D4×D10711yescharacteristic
324C2×C4C23×D10711yescharacteristic
325C8—21no—
326C8—1072no—
327C8—2141no—
328C8C2×C4×D10712yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—1072no—
333C22—2141no—
334C22—2141no—
335C22C2×D4×D10711yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—1072no—
342C4—1072no—
343C4—4281no—
344C4—4281no—
345C4—2141no—
346C4—2142no—
347C4—2142no—
348C4C22×C4×D10711yescharacteristic
349C4#41×D10711yescharacteristic
350C2—42no—
351C2—2142no—
352C2C4×D4×D10711yescharacteristic
353C2#137×D10711yescharacteristic
354C2#2029342311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
Fitting#440×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133817C22
cosocleC2×C4×C107C24
hypercenter#440D107
hypocenterC107C4×#137
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D107C2semidirect
4. #20292735C2semidirect
5. #20292732C2semidirect
6. #20292727C2semidirect
7. #20292721C2semidirect
8. #20292719C2semidirect
9. #20292718C2semidirect
10. SD16×Dic107C2semidirect
11. #20292668C2semidirect
12. #20292634C2semidirect
14. #20292579C2semidirect
15. #440×C107C2semidirect
18. #16812138C4semidirect
66. Q8×D107C2×C4semidirect
75. Dic428C2×C4semidirect
76. #13133808C2×C4semidirect
77. #13133806C2×C4semidirect
79. #13133801C2×C4semidirect
104. SD16×C107C2×C4semidirect
171. Dic107#137semidirect
178. C107C4×#137semidirect
185. #440D107semidirect
259. SD16C4×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121382
C4×#131338172
C4×Q8×D1072
#202927352
#202927322
#202927272
#202927212
#202927192
#202927182
SD16×Dic1072
#202926682
#202926342
#202926252
#202925792
#440×C1072
C4×#137107