Finite Group Databasebeta

← C37×#3343 #17992161

Subgroups — C37×#3343 #17992161

Order 4736.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#552C211yesmaximal, characteristic, complemented
2C37×#547C211yesmaximal, characteristic
3C37×#501C211yesmaximal, characteristic, complemented
4C37×#484C211yesmaximal, characteristic, complemented
5C37×#483C211yesmaximal, characteristic, complemented
6C37×#482C211yesmaximal, characteristic, complemented
7C37×#480C211yesmaximal, characteristic, complemented
8C37×#478C211yesmaximal, characteristic, complemented
9C37×#477C211yesmaximal, characteristic, complemented
10C37×#468C211yesmaximal, characteristic, complemented
11C37×#465C211yesmaximal, characteristic, complemented
12C37×#440C211yesmaximal, characteristic, complemented
13C37×#435C211yesmaximal, characteristic, complemented
14C37×#428C211yesmaximal, characteristic, complemented
15C2×#107×C37C211yesmaximal, characteristic, complemented
16C2×#41×C37—21no—
17C2×SD16×C37C2211yescharacteristic
18C2×M16×C37C2211yescharacteristic
19C22×C8×C37C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21#126×C37—21no—
22#125×C37—21no—
23#125×C37C2211yescharacteristic
24#123×C37—21no—
25#123×C37—21no—
26#123×C37—21no—
27C22⋊Q8×C37—21no—
28C22⋊Q8×C37C2211yescharacteristic
29C22⋊Q8×C37C2211yescharacteristic
30#121×C37C2211yescharacteristic
31#121×C37C2211yescharacteristic
32C4×Q8×C37C2211yescharacteristic
33C4×D4×C37C2211yescharacteristic
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#107×C37C2211yescharacteristic
44#107×C37C2211yescharacteristic
45#107×C37C2211yescharacteristic
46#106×C37C2211yescharacteristic
47#106×C37C2211yescharacteristic
48#106×C37C2211yescharacteristic
49C4⋊C8×C37C2211yescharacteristic
50#103×C37C2211yescharacteristic
51#103×C37C2211yescharacteristic
52#103×C37C2211yescharacteristic
53#102×C37C2211yescharacteristic
54#102×C37C2211yescharacteristic
55#102×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59#41×C37—44no—
60C2×Q8×C37—21no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37D411yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37—21no—
70C22×C4×C37C2311yescharacteristic
71C22×C4×C37C2311yescharacteristic
72SD16×C37—22no—
73M16×C37—22no—
74C2×C8×C37—22no—
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
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×C37—21no—
88C4⋊C4×C37D411yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C4⋊C4×C37C2311yescharacteristic
91C4⋊C4×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C22⋊C4×C37—21no—
101C22⋊C4×C37D411yescharacteristic
102C22⋊C4×C37D411yescharacteristic
103C42×C37—21no—
104C42×C37—21no—
105C42×C37C2311yescharacteristic
106C23×C37—21no—
107C23×C37C2×D411yescharacteristic
108C23×C37C2×D411yescharacteristic
109Q8×C37—21no—
110Q8×C37—21no—
111Q8×C37—42no—
112D4×C37—22no—
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—42no—
116D4×C37—42no—
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—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—42no—
129C2×C4×C37—42no—
130C2×C4×C37—42no—
131C2×C4×C37—42no—
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2411yescharacteristic
137C8×C37—21no—
138C8×C37—21no—
139C8×C37—21no—
140C8×C37#4112yescomplemented
141C22×C37—21no—
142C22×C37—21no—
143C22×C37—21no—
144C22×C37—21no—
145C22×C37—21no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37AGL(1,ℤ/8)12yes—
150C22×C37C22×D411yescharacteristic
151C4×C37—21no—
152C4×C37—21no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—41no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37C2×#4111yescharacteristic
163C4×C372−1+411yescharacteristic
164#3343C3711yesmaximal, characteristic, direct product factor, Sylow
165C2×C37—22no—
166C2×C37—41no—
167C2×C37—81no—
168C2×C37#54711yescharacteristic
169C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C37#57811yescharacteristic
171#552C2×C3711yescharacteristic, complemented
172#547C2×C3711yescharacteristic
173#501C2×C3711yescharacteristic, complemented
174#484C2×C3711yescharacteristic, complemented
175#483C2×C3711yescharacteristic, complemented
176#482C2×C3711yescharacteristic, complemented
177#480C2×C3711yescharacteristic, complemented
178#478C2×C3711yescharacteristic, complemented
179#477C2×C3711yescharacteristic, complemented
180#468C2×C3711yescharacteristic, complemented
181#465C2×C3711yescharacteristic, complemented
182#440C2×C3711yescharacteristic, complemented
183#435C2×C3711yescharacteristic, complemented
184#428C2×C3711yescharacteristic, complemented
185C2×#107C2×C3711yescharacteristic, complemented
186C37#334311yescharacteristic, direct product factor, Sylow
187C2×#41—21no—
188C2×SD16C22×C3711yescharacteristic
189C2×M16C22×C3711yescharacteristic
190C22×C8C22×C3711yescharacteristic
191C4⋊Q8C22×C3711yescharacteristic
192#126—21no—
193#125—21no—
194#125C22×C3711yescharacteristic
195#123—21no—
196#123—21no—
197#123—21no—
198C22⋊Q8—21no—
199C22⋊Q8C22×C3711yescharacteristic
200C22⋊Q8C22×C3711yescharacteristic
201#121C22×C3711yescharacteristic
202#121C22×C3711yescharacteristic
203C4×Q8C22×C3711yescharacteristic
204C4×D4C22×C3711yescharacteristic
205C4×D4C22×C3711yescharacteristic
206#117—21no—
207#117C22×C3711yescharacteristic
208C2×C4⋊C4C22×C3711yescharacteristic
209C2×C4⋊C4C22×C3711yescharacteristic
210C2×C4⋊C4C22×C3711yescharacteristic
211#107C22×C3711yescharacteristic
212#107C22×C3711yescharacteristic
213#107C22×C3711yescharacteristic
214#107C22×C3711yescharacteristic
215#107C22×C3711yescharacteristic
216#107C22×C3711yescharacteristic
217#106C22×C3711yescharacteristic
218#106C22×C3711yescharacteristic
219#106C22×C3711yescharacteristic
220C4⋊C8C22×C3711yescharacteristic
221#103C22×C3711yescharacteristic
222#103C22×C3711yescharacteristic
223#103C22×C3711yescharacteristic
224#102C22×C3711yescharacteristic
225#102C22×C3711yescharacteristic
226#102C22×C3711yescharacteristic
227C22⋊C8C22×C3711yescharacteristic
228C22⋊C8C22×C3711yescharacteristic
229#97C22×C3711yescharacteristic
230#41—44no—
231C2×Q8—21no—
232C2×Q8C23×C3711yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4D4×C3711yescharacteristic
236C2×D4C23×C3711yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C23×C3711yescharacteristic
242C22×C4C23×C3711yescharacteristic
243SD16—22no—
244M16—22no—
245C2×C8—22no—
246C2×C8C23×C3711yescharacteristic
247C2×C8C23×C3711yescharacteristic
248C2×C8C23×C3711yescharacteristic
249C2×C8C23×C3711yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4D4×C3711yescharacteristic
260C4⋊C4C23×C3711yescharacteristic
261C4⋊C4C23×C3711yescharacteristic
262C4⋊C4C23×C3711yescharacteristic
263C4⋊C4C23×C3711yescharacteristic
264C4⋊C4C23×C3711yescharacteristic
265C4⋊C4C23×C3711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4D4×C3711yescharacteristic
273C22⋊C4D4×C3711yescharacteristic
274C42—21no—
275C42—21no—
276C42C23×C3711yescharacteristic
277C23—21no—
278C23C2×D4×C3711yescharacteristic
279C23C2×D4×C3711yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—42no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×D4×C3711yescharacteristic
304C2×C4C2×D4×C3711yescharacteristic
305C2×C4C2×D4×C3711yescharacteristic
306C2×C4C2×D4×C3711yescharacteristic
307C2×C4C24×C3711yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8#41×C3712yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22AGL(1,ℤ/8)×C3712yes—
321C22C22×D4×C3711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4C2×#41×C3711yescharacteristic
334C42−1+4×C3711yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2C37×#54711yescharacteristic
339C2C2×AGL(1,ℤ/8)×C3711yescharacteristic
340C2C37×#57811yescharacteristic
subgroupG/H
center, socleC22×C37C22×D4
commutator, Frattini, cosocleC2×C4C24×C37
prime radicalC37×#547C2
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
1. C37×#552C2semidirect
3. C37×#501C2semidirect
4. C37×#484C2semidirect
5. C37×#483C2semidirect
6. C37×#482C2semidirect
7. C37×#480C2semidirect
8. C37×#478C2semidirect
9. C37×#477C2semidirect
10. C37×#468C2semidirect
11. C37×#465C2semidirect
12. C37×#440C2semidirect
13. C37×#435C2semidirect
14. C37×#428C2semidirect
15. C2×#107×C37C2semidirect
140. C8×C37#41semidirect
164. #3343C37direct (N × H)
171. #552C2×C37semidirect
173. #501C2×C37semidirect
174. #484C2×C37semidirect
175. #483C2×C37semidirect
176. #482C2×C37semidirect
177. #480C2×C37semidirect
178. #478C2×C37semidirect
179. #477C2×C37semidirect
180. #468C2×C37semidirect
181. #465C2×C37semidirect
182. #440C2×C37semidirect
183. #435C2×C37semidirect
184. #428C2×C37semidirect
185. C2×#107C2×C37semidirect
186. C37#3343direct (N × H)
311. C8#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#5522
C37×#5472
C37×#5012
C37×#4842
C37×#4832
C37×#4822
C37×#4802
C37×#4782
C37×#4772
C37×#4682
C37×#4652
C37×#4402
C37×#4352
C37×#4282
C2×#107×C372
#334337