Finite Group Databasebeta

← C37×#3344 #17992162

Subgroups — C37×#3344 #17992162

Order 4736.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#554C211yesmaximal, characteristic
2C37×#552C211yesmaximal, characteristic
3C37×#501C211yesmaximal, characteristic, complemented
4C37×#485C211yesmaximal, characteristic, complemented
5C37×#484C211yesmaximal, characteristic, complemented
6C37×#483C211yesmaximal, characteristic, complemented
7C37×#483C211yesmaximal, characteristic, complemented
8C37×#479C211yesmaximal, characteristic, complemented
9C37×#475C211yesmaximal, characteristic, complemented
10C37×#470C211yesmaximal, characteristic, complemented
11C37×#467C211yesmaximal, characteristic, complemented
12C37×#441C211yesmaximal, characteristic, complemented
13C37×#435C211yesmaximal, characteristic
14C37×#428C211yesmaximal, characteristic, complemented
15C2×#106×C37C211yesmaximal, characteristic, complemented
16C2×Q16×C37C2211yescharacteristic
17C2×M16×C37C2211yescharacteristic
18C22×C8×C37C2211yescharacteristic
19C4⋊Q8×C37C2211yescharacteristic
20#126×C37—21no—
21#125×C37—21no—
22#125×C37—21no—
23#125×C37C2211yescharacteristic
24#123×C37—21no—
25C22⋊Q8×C37—21no—
26C22⋊Q8×C37—21no—
27C22⋊Q8×C37C2211yescharacteristic
28C22⋊Q8×C37C2211yescharacteristic
29C22⋊Q8×C37C2211yescharacteristic
30C22⋊Q8×C37C2211yescharacteristic
31C4×Q8×C37C2211yescharacteristic
32C4×Q8×C37C2211yescharacteristic
33C4×D4×C37—21no—
34C4×D4×C37C2211yescharacteristic
35#117×C37—21no—
36#117×C37C2211yescharacteristic
37C2×C4⋊C4×C37C2211yescharacteristic
38C2×C4⋊C4×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic
40#107×C37C2211yescharacteristic
41#107×C37C2211yescharacteristic
42#107×C37C2211yescharacteristic
43#106×C37C2211yescharacteristic
44#106×C37C2211yescharacteristic
45#106×C37C2211yescharacteristic
46#106×C37C2211yescharacteristic
47#106×C37C2211yescharacteristic
48#106×C37C2211yescharacteristic
49C4⋊C8×C37C2211yescharacteristic
50#103×C37C2211yescharacteristic
51#103×C37C2211yescharacteristic
52#103×C37C2211yescharacteristic
53#103×C37C2211yescharacteristic
54#103×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37D411yescharacteristic
63C22×C4×C37—21no—
64C22×C4×C37—21no—
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68Q16×C37—22no—
69M16×C37—22no—
70C2×C8×C37—22no—
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C2×C8×C37C2311yescharacteristic
74C2×C8×C37C2311yescharacteristic
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37—21no—
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37—21no—
84C4⋊C4×C37—21no—
85C4⋊C4×C37—21no—
86C4⋊C4×C37—21no—
87C4⋊C4×C37D411yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C4⋊C4×C37C2311yescharacteristic
91C4⋊C4×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37—21no—
99C22⋊C4×C37D411yescharacteristic
100C22⋊C4×C37D411yescharacteristic
101C42×C37—21no—
102C42×C37—21no—
103C42×C37—21no—
104C42×C37C2311yescharacteristic
105C23×C37C2×D411yescharacteristic
106C23×C37C2×D411yescharacteristic
107Q8×C37—21no—
108Q8×C37—21no—
109Q8×C37—21no—
110Q8×C37—21no—
111Q8×C37—81no—
112D4×C37—22no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—42no—
126C2×C4×C37—81no—
127C2×C4×C37—81no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2411yescharacteristic
133C8×C37—21no—
134C8×C37—21no—
135C8×C37—21no—
136C8×C37#4112yes—
137C22×C37—21no—
138C22×C37—21no—
139C22×C37—21no—
140C22×C37—21no—
141C22×C37—21no—
142C22×C37#13712yes—
143C22×C37C22×D411yescharacteristic
144C4×C37—21no—
145C4×C37—21no—
146C4×C37—21no—
147C4×C37—21no—
148C4×C37—41no—
149C4×C37—41no—
150C4×C37—41no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37—41no—
155C4×C37—41no—
156C4×C37C2×#4111yescharacteristic
157C4×C372−1+411yescharacteristic
158#3344C3711yesmaximal, characteristic, direct product factor, Sylow
159C2×C37—22no—
160C2×C37—41no—
161C2×C37#54711yescharacteristic
162C2×C37C2×#13711yescharacteristic
163C2×C37#57711yescharacteristic
164#554C2×C3711yescharacteristic
165#552C2×C3711yescharacteristic
166#501C2×C3711yescharacteristic, complemented
167#485C2×C3711yescharacteristic, complemented
168#484C2×C3711yescharacteristic, complemented
169#483C2×C3711yescharacteristic, complemented
170#483C2×C3711yescharacteristic, complemented
171#479C2×C3711yescharacteristic, complemented
172#475C2×C3711yescharacteristic, complemented
173#470C2×C3711yescharacteristic, complemented
174#467C2×C3711yescharacteristic, complemented
175#441C2×C3711yescharacteristic, complemented
176#435C2×C3711yescharacteristic
177#428C2×C3711yescharacteristic, complemented
178C2×#106C2×C3711yescharacteristic, complemented
179C37#334411yescharacteristic, direct product factor, Sylow
180C2×Q16C22×C3711yescharacteristic
181C2×M16C22×C3711yescharacteristic
182C22×C8C22×C3711yescharacteristic
183C4⋊Q8C22×C3711yescharacteristic
184#126—21no—
185#125—21no—
186#125—21no—
187#125C22×C3711yescharacteristic
188#123—21no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191C22⋊Q8C22×C3711yescharacteristic
192C22⋊Q8C22×C3711yescharacteristic
193C22⋊Q8C22×C3711yescharacteristic
194C22⋊Q8C22×C3711yescharacteristic
195C4×Q8C22×C3711yescharacteristic
196C4×Q8C22×C3711yescharacteristic
197C4×D4—21no—
198C4×D4C22×C3711yescharacteristic
199#117—21no—
200#117C22×C3711yescharacteristic
201C2×C4⋊C4C22×C3711yescharacteristic
202C2×C4⋊C4C22×C3711yescharacteristic
203C2×C4⋊C4C22×C3711yescharacteristic
204#107C22×C3711yescharacteristic
205#107C22×C3711yescharacteristic
206#107C22×C3711yescharacteristic
207#106C22×C3711yescharacteristic
208#106C22×C3711yescharacteristic
209#106C22×C3711yescharacteristic
210#106C22×C3711yescharacteristic
211#106C22×C3711yescharacteristic
212#106C22×C3711yescharacteristic
213C4⋊C8C22×C3711yescharacteristic
214#103C22×C3711yescharacteristic
215#103C22×C3711yescharacteristic
216#103C22×C3711yescharacteristic
217#103C22×C3711yescharacteristic
218#103C22×C3711yescharacteristic
219#103C22×C3711yescharacteristic
220C22⋊C8C22×C3711yescharacteristic
221C22⋊C8C22×C3711yescharacteristic
222#97C22×C3711yescharacteristic
223C2×Q8—21no—
224C2×Q8C23×C3711yescharacteristic
225C2×Q8C23×C3711yescharacteristic
226C2×D4D4×C3711yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C23×C3711yescharacteristic
231C22×C4C23×C3711yescharacteristic
232Q16—22no—
233M16—22no—
234C2×C8—22no—
235C2×C8C23×C3711yescharacteristic
236C2×C8C23×C3711yescharacteristic
237C2×C8C23×C3711yescharacteristic
238C2×C8C23×C3711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4D4×C3711yescharacteristic
252C4⋊C4C23×C3711yescharacteristic
253C4⋊C4C23×C3711yescharacteristic
254C4⋊C4C23×C3711yescharacteristic
255C4⋊C4C23×C3711yescharacteristic
256C4⋊C4C23×C3711yescharacteristic
257C4⋊C4C23×C3711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C3711yescharacteristic
264C22⋊C4D4×C3711yescharacteristic
265C42—21no—
266C42—21no—
267C42—21no—
268C42C23×C3711yescharacteristic
269C23C2×D4×C3711yescharacteristic
270C23C2×D4×C3711yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—81no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C3711yescharacteristic
293C2×C4C2×D4×C3711yescharacteristic
294C2×C4C2×D4×C3711yescharacteristic
295C2×C4C2×D4×C3711yescharacteristic
296C2×C4C24×C3711yescharacteristic
297C8—21no—
298C8—21no—
299C8—21no—
300C8#41×C3712yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#137×C3712yes—
307C22C22×D4×C3711yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4C2×#41×C3711yescharacteristic
321C42−1+4×C3711yescharacteristic
322C2—22no—
323C2—41no—
324C2C37×#54711yescharacteristic
325C2C2×#137×C3711yescharacteristic
326C2C37×#57711yescharacteristic
subgroupG/H
center, socleC22×C37C22×D4
commutator, Frattini, cosocleC2×C4C24×C37
prime radicalC2×D4×C37D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#501C2semidirect
4. C37×#485C2semidirect
5. C37×#484C2semidirect
6. C37×#483C2semidirect
7. C37×#483C2semidirect
8. C37×#479C2semidirect
9. C37×#475C2semidirect
10. C37×#470C2semidirect
11. C37×#467C2semidirect
12. C37×#441C2semidirect
14. C37×#428C2semidirect
15. C2×#106×C37C2semidirect
158. #3344C37direct (N × H)
166. #501C2×C37semidirect
167. #485C2×C37semidirect
168. #484C2×C37semidirect
169. #483C2×C37semidirect
170. #483C2×C37semidirect
171. #479C2×C37semidirect
172. #475C2×C37semidirect
173. #470C2×C37semidirect
174. #467C2×C37semidirect
175. #441C2×C37semidirect
177. #428C2×C37semidirect
178. C2×#106C2×C37semidirect
179. C37#3344direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#5542
C37×#5522
C37×#5012
C37×#4852
C37×#4842
C37×#4832
C37×#4792
C37×#4752
C37×#4702
C37×#4672
C37×#4412
C37×#4352
C37×#4282
C2×#106×C372
#334437