Finite Group Databasebeta

← C37×#3349 #17992167

Subgroups — C37×#3349 #17992167

Order 4736.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#556C211yesmaximal, characteristic
2C37×#552C211yesmaximal, characteristic
3C37×#501C211yesmaximal, characteristic, complemented
4C37×#485C211yesmaximal, characteristic, complemented
5C37×#485C211yesmaximal, characteristic, complemented
6C37×#485C211yesmaximal, characteristic, complemented
7C37×#484C211yesmaximal, characteristic, complemented
8C37×#479C211yesmaximal, characteristic, complemented
9C37×#477C211yesmaximal, characteristic, complemented
10C37×#470C211yesmaximal, characteristic, complemented
11C37×#467C211yesmaximal, characteristic, complemented
12C37×#441C211yesmaximal, characteristic, complemented
13C37×#435C211yesmaximal, characteristic
14C37×#428C211yesmaximal, characteristic, complemented
15C37×#427C211yesmaximal, characteristic, complemented
16C2×Q16×C37C2211yescharacteristic
17C2×M16×C37C2211yescharacteristic
18C22×C8×C37C2211yescharacteristic
19C4⋊Q8×C37C2211yescharacteristic
20#126×C37—21no—
21#126×C37—21no—
22#126×C37—21no—
23#125×C37—21no—
24#125×C37C2211yescharacteristic
25#124×C37—21no—
26#123×C37—21no—
27C22⋊Q8×C37C2211yescharacteristic
28C22⋊Q8×C37C2211yescharacteristic
29C22⋊Q8×C37C2211yescharacteristic
30C22⋊Q8×C37C2211yescharacteristic
31C4×Q8×C37—21no—
32C4×Q8×C37C2211yescharacteristic
33C4×Q8×C37C2211yescharacteristic
34C4×D4×C37C2211yescharacteristic
35#117×C37—21no—
36#117×C37C2211yescharacteristic
37#117×C37C2211yescharacteristic
38#117×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic
40#107×C37C2211yescharacteristic
41#107×C37C2211yescharacteristic
42#107×C37C2211yescharacteristic
43#107×C37C2211yescharacteristic
44#107×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×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66Q16×C37—22no—
67M16×C37—22no—
68C2×C8×C37—22no—
69C2×C8×C37C2311yescharacteristic
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
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×C37D411yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C4⋊C4×C37C2311yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C22⋊C4×C37—21no—
91C22⋊C4×C37—21no—
92C22⋊C4×C37—21no—
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37D411yescharacteristic
98C22⋊C4×C37D411yescharacteristic
99C42×C37—21no—
100C42×C37—21no—
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—42no—
112D4×C37—41no—
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×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2411yescharacteristic
131C8×C37—21no—
132C8×C37—21no—
133C8×C37—21no—
134C8×C37#4112yes—
135C22×C37—21no—
136C22×C37—21no—
137C22×C37—21no—
138C22×C37—21no—
139C22×C37—21no—
140C22×C37—21no—
141C22×C37C22×D411yescharacteristic
142C4×C37—21no—
143C4×C37—21no—
144C4×C37—21no—
145C4×C37—21no—
146C4×C37—41no—
147C4×C37—41no—
148C4×C37—41no—
149C4×C37—41no—
150C4×C37—41no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37C2×#4111yescharacteristic
155C4×C372−1+411yescharacteristic
156#3349C3711yesmaximal, characteristic, direct product factor, Sylow
157C2×C37—41no—
158C2×C37—41no—
159C2×C37#54711yescharacteristic
160C2×C37#57511yescharacteristic
161C2×C37#57811yescharacteristic
162#556C2×C3711yescharacteristic
163#552C2×C3711yescharacteristic
164#501C2×C3711yescharacteristic, complemented
165#485C2×C3711yescharacteristic, complemented
166#485C2×C3711yescharacteristic, complemented
167#485C2×C3711yescharacteristic, complemented
168#484C2×C3711yescharacteristic, complemented
169#479C2×C3711yescharacteristic, complemented
170#477C2×C3711yescharacteristic, complemented
171#470C2×C3711yescharacteristic, complemented
172#467C2×C3711yescharacteristic, complemented
173#441C2×C3711yescharacteristic, complemented
174#435C2×C3711yescharacteristic
175#428C2×C3711yescharacteristic, complemented
176#427C2×C3711yescharacteristic, complemented
177C37#334911yescharacteristic, direct product factor, Sylow
178C2×Q16C22×C3711yescharacteristic
179C2×M16C22×C3711yescharacteristic
180C22×C8C22×C3711yescharacteristic
181C4⋊Q8C22×C3711yescharacteristic
182#126—21no—
183#126—21no—
184#126—21no—
185#125—21no—
186#125C22×C3711yescharacteristic
187#124—21no—
188#123—21no—
189C22⋊Q8C22×C3711yescharacteristic
190C22⋊Q8C22×C3711yescharacteristic
191C22⋊Q8C22×C3711yescharacteristic
192C22⋊Q8C22×C3711yescharacteristic
193C4×Q8—21no—
194C4×Q8C22×C3711yescharacteristic
195C4×Q8C22×C3711yescharacteristic
196C4×D4C22×C3711yescharacteristic
197#117—21no—
198#117C22×C3711yescharacteristic
199#117C22×C3711yescharacteristic
200#117C22×C3711yescharacteristic
201C2×C4⋊C4C22×C3711yescharacteristic
202#107C22×C3711yescharacteristic
203#107C22×C3711yescharacteristic
204#107C22×C3711yescharacteristic
205#107C22×C3711yescharacteristic
206#107C22×C3711yescharacteristic
207#106C22×C3711yescharacteristic
208#106C22×C3711yescharacteristic
209#106C22×C3711yescharacteristic
210#106C22×C3711yescharacteristic
211C4⋊C8C22×C3711yescharacteristic
212#103C22×C3711yescharacteristic
213#103C22×C3711yescharacteristic
214#103C22×C3711yescharacteristic
215#103C22×C3711yescharacteristic
216#103C22×C3711yescharacteristic
217#103C22×C3711yescharacteristic
218C22⋊C8C22×C3711yescharacteristic
219C22⋊C8C22×C3711yescharacteristic
220#97C22×C3711yescharacteristic
221C2×Q8—21no—
222C2×Q8C23×C3711yescharacteristic
223C2×Q8C23×C3711yescharacteristic
224C2×D4D4×C3711yescharacteristic
225C22×C4—21no—
226C22×C4C23×C3711yescharacteristic
227C22×C4C23×C3711yescharacteristic
228Q16—22no—
229M16—22no—
230C2×C8—22no—
231C2×C8C23×C3711yescharacteristic
232C2×C8C23×C3711yescharacteristic
233C2×C8C23×C3711yescharacteristic
234C2×C8C23×C3711yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4D4×C3711yescharacteristic
246C4⋊C4C23×C3711yescharacteristic
247C4⋊C4C23×C3711yescharacteristic
248C4⋊C4C23×C3711yescharacteristic
249C4⋊C4C23×C3711yescharacteristic
250C4⋊C4C23×C3711yescharacteristic
251C4⋊C4C23×C3711yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4D4×C3711yescharacteristic
260C22⋊C4D4×C3711yescharacteristic
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42C23×C3711yescharacteristic
267C23C2×D4×C3711yescharacteristic
268C23C2×D4×C3711yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—42no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
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—42no—
288C2×C4C2×D4×C3711yescharacteristic
289C2×C4C2×D4×C3711yescharacteristic
290C2×C4C2×D4×C3711yescharacteristic
291C2×C4C2×D4×C3711yescharacteristic
292C2×C4C24×C3711yescharacteristic
293C8—21no—
294C8—21no—
295C8—21no—
296C8#41×C3712yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×D4×C3711yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4C2×#41×C3711yescharacteristic
317C42−1+4×C3711yescharacteristic
318C2—41no—
319C2—41no—
320C2C37×#54711yescharacteristic
321C2C37×#57511yescharacteristic
322C2C37×#57811yescharacteristic
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×#485C2semidirect
6. C37×#485C2semidirect
7. C37×#484C2semidirect
8. C37×#479C2semidirect
9. C37×#477C2semidirect
10. C37×#470C2semidirect
11. C37×#467C2semidirect
12. C37×#441C2semidirect
14. C37×#428C2semidirect
15. C37×#427C2semidirect
156. #3349C37direct (N × H)
164. #501C2×C37semidirect
165. #485C2×C37semidirect
166. #485C2×C37semidirect
167. #485C2×C37semidirect
168. #484C2×C37semidirect
169. #479C2×C37semidirect
170. #477C2×C37semidirect
171. #470C2×C37semidirect
172. #467C2×C37semidirect
173. #441C2×C37semidirect
175. #428C2×C37semidirect
176. #427C2×C37semidirect
177. C37#3349direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#5562
C37×#5522
C37×#5012
C37×#4852
C37×#4842
C37×#4792
C37×#4772
C37×#4702
C37×#4672
C37×#4412
C37×#4352
C37×#4282
C37×#4272
#334937