Finite Group Databasebeta

← C37×#3316 #17992134

Subgroups — C37×#3316 #17992134

Order 4736.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#554C211yesmaximal, characteristic, complemented
2C37×#548C211yesmaximal, characteristic
3C37×#489C211yesmaximal, characteristic, complemented
4C37×#483C211yesmaximal, characteristic, complemented
5C37×#481C211yesmaximal, characteristic, complemented
6C37×#475C211yesmaximal, characteristic, complemented
7C37×#470C211yesmaximal, characteristic, complemented
8C37×#465C211yesmaximal, characteristic, complemented
9C37×#464C211yesmaximal, characteristic, complemented
10C37×#452C211yesmaximal, characteristic, complemented
11C37×#451C211yesmaximal, characteristic, complemented
12C37×#441C211yesmaximal, characteristic, complemented
13C37×#435C211yesmaximal, characteristic, complemented
14C37×#417C211yesmaximal, characteristic, complemented
15C2×#103×C37C211yesmaximal, characteristic, complemented
16C2×#41×C37C2211yescharacteristic
17C22×Q8×C37C2211yescharacteristic
18C2×Q16×C37C2211yescharacteristic
19C2×Q16×C37C2211yescharacteristic
20C2×SD16×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic
22C22×C8×C37C2211yescharacteristic
23C4⋊Q8×C37C2211yescharacteristic
24#125×C37—21no—
25#124×C37—21no—
26#124×C37C2211yescharacteristic
27C22⋊Q8×C37—21no—
28C22⋊Q8×C37—21no—
29C22⋊Q8×C37—21no—
30C22⋊Q8×C37C2211yescharacteristic
31C22⋊Q8×C37C2211yescharacteristic
32C22⋊Q8×C37C2211yescharacteristic
33#121×C37—21no—
34#121×C37C2211yescharacteristic
35C4×Q8×C37C2211yescharacteristic
36C4×Q8×C37C2211yescharacteristic
37C4×D4×C37—21no—
38C4×D4×C37—21no—
39C4×D4×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41C2×C4⋊C4×C37C2211yescharacteristic
42#106×C37C2211yescharacteristic
43#106×C37C2211yescharacteristic
44#106×C37C2211yescharacteristic
45C4⋊C8×C37C2211yescharacteristic
46#103×C37C2211yescharacteristic
47#103×C37C2211yescharacteristic
48#103×C37C2211yescharacteristic
49#103×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—22no—
60#41×C37—41no—
61C2×Q8×C37—21no—
62C2×Q8×C37—21no—
63C2×Q8×C37—22no—
64C2×Q8×C37—41no—
65C2×Q8×C37C2311yescharacteristic
66C2×Q8×C37C2311yescharacteristic
67C2×Q8×C37C2311yescharacteristic
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37D411yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37—21no—
75C22×C4×C37—21no—
76C22×C4×C37C2311yescharacteristic
77C22×C4×C37C2311yescharacteristic
78Q16×C37—22no—
79Q16×C37—41no—
80SD16×C37—41no—
81M16×C37—41no—
82C2×C8×C37—41no—
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37—21no—
88C4⋊C4×C37—21no—
89C4⋊C4×C37—21no—
90C4⋊C4×C37—21no—
91C4⋊C4×C37—21no—
92C4⋊C4×C37—21no—
93C4⋊C4×C37—21no—
94C4⋊C4×C37—21no—
95C4⋊C4×C37D411yescharacteristic
96C4⋊C4×C37C2311yescharacteristic
97C4⋊C4×C37C2311yescharacteristic
98C4⋊C4×C37C2311yescharacteristic
99C4⋊C4×C37C2311yescharacteristic
100C22⋊C4×C37—21no—
101C22⋊C4×C37—21no—
102C22⋊C4×C37—21no—
103C22⋊C4×C37—21no—
104C22⋊C4×C37—21no—
105C22⋊C4×C37—21no—
106C22⋊C4×C37D411yescharacteristic
107C22⋊C4×C37D411yescharacteristic
108C42×C37—21no—
109C42×C37—21no—
110C42×C37C2311yescharacteristic
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C23×C37C2×D411yescharacteristic
114Q8×C37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118Q8×C37—21no—
119Q8×C37—42no—
120Q8×C37—81no—
121Q8×C37#4112yes—
122D4×C37—22no—
123D4×C37—21no—
124D4×C37—21no—
125D4×C37—42no—
126D4×C37—42no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—42no—
139C2×C4×C37—42no—
140C2×C4×C37—81no—
141C2×C4×C37—81no—
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2411yescharacteristic
147C8×C37—21no—
148C8×C37—21no—
149C8×C37—21no—
150C8×C37—21no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37#13712yes—
160C22×C37C22×D411yescharacteristic
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—22no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37C2×#4111yescharacteristic
173C4×C37H(5,𝔽2)11yescharacteristic
174#3316C3711yesmaximal, characteristic, direct product factor, Sylow
175C2×C37—22no—
176C2×C37—41no—
177C2×C37—81no—
178C2×C37#54611yescharacteristic
179C2×C37C2×#13711yescharacteristic
180C2×C37#57711yescharacteristic
181#554C2×C3711yescharacteristic, complemented
182#548C2×C3711yescharacteristic
183#489C2×C3711yescharacteristic, complemented
184#483C2×C3711yescharacteristic, complemented
185#481C2×C3711yescharacteristic, complemented
186#475C2×C3711yescharacteristic, complemented
187#470C2×C3711yescharacteristic, complemented
188#465C2×C3711yescharacteristic, complemented
189#464C2×C3711yescharacteristic, complemented
190#452C2×C3711yescharacteristic, complemented
191#451C2×C3711yescharacteristic, complemented
192#441C2×C3711yescharacteristic, complemented
193#435C2×C3711yescharacteristic, complemented
194#417C2×C3711yescharacteristic, complemented
195C2×#103C2×C3711yescharacteristic, complemented
196C37#331611yescharacteristic, direct product factor, Sylow
197C2×#41C22×C3711yescharacteristic
198C22×Q8C22×C3711yescharacteristic
199C2×Q16C22×C3711yescharacteristic
200C2×Q16C22×C3711yescharacteristic
201C2×SD16C22×C3711yescharacteristic
202C2×M16C22×C3711yescharacteristic
203C22×C8C22×C3711yescharacteristic
204C4⋊Q8C22×C3711yescharacteristic
205#125—21no—
206#124—21no—
207#124C22×C3711yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C22×C3711yescharacteristic
212C22⋊Q8C22×C3711yescharacteristic
213C22⋊Q8C22×C3711yescharacteristic
214#121—21no—
215#121C22×C3711yescharacteristic
216C4×Q8C22×C3711yescharacteristic
217C4×Q8C22×C3711yescharacteristic
218C4×D4—21no—
219C4×D4—21no—
220C4×D4C22×C3711yescharacteristic
221C2×C4⋊C4C22×C3711yescharacteristic
222C2×C4⋊C4C22×C3711yescharacteristic
223#106C22×C3711yescharacteristic
224#106C22×C3711yescharacteristic
225#106C22×C3711yescharacteristic
226C4⋊C8C22×C3711yescharacteristic
227#103C22×C3711yescharacteristic
228#103C22×C3711yescharacteristic
229#103C22×C3711yescharacteristic
230#103C22×C3711yescharacteristic
231#103C22×C3711yescharacteristic
232#103C22×C3711yescharacteristic
233#103C22×C3711yescharacteristic
234#102C22×C3711yescharacteristic
235#102C22×C3711yescharacteristic
236#102C22×C3711yescharacteristic
237C22⋊C8C22×C3711yescharacteristic
238C22⋊C8C22×C3711yescharacteristic
239#97C22×C3711yescharacteristic
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8C23×C3711yescharacteristic
247C2×Q8C23×C3711yescharacteristic
248C2×Q8C23×C3711yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4D4×C3711yescharacteristic
252C2×D4C23×C3711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4C23×C3711yescharacteristic
258C22×C4C23×C3711yescharacteristic
259Q16—22no—
260Q16—41no—
261SD16—41no—
262M16—41no—
263C2×C8—41no—
264C2×C8C23×C3711yescharacteristic
265C2×C8C23×C3711yescharacteristic
266C2×C8C23×C3711yescharacteristic
267C2×C8C23×C3711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4D4×C3711yescharacteristic
277C4⋊C4C23×C3711yescharacteristic
278C4⋊C4C23×C3711yescharacteristic
279C4⋊C4C23×C3711yescharacteristic
280C4⋊C4C23×C3711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4D4×C3711yescharacteristic
288C22⋊C4D4×C3711yescharacteristic
289C42—21no—
290C42—21no—
291C42C23×C3711yescharacteristic
292C23—21no—
293C23C2×D4×C3711yescharacteristic
294C23C2×D4×C3711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—81no—
302Q8#41×C3712yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×D4×C3711yescharacteristic
324C2×C4C2×D4×C3711yescharacteristic
325C2×C4C2×D4×C3711yescharacteristic
326C2×C4C2×D4×C3711yescharacteristic
327C2×C4C24×C3711yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#137×C3712yes—
341C22C22×D4×C3711yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4C2×#41×C3711yescharacteristic
354C4H(5,𝔽2)×C3711yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2C37×#54611yescharacteristic
359C2C2×#137×C3711yescharacteristic
360C2C37×#57711yescharacteristic
subgroupG/H
center, socleC22×C37C22×D4
commutator, Frattini, cosocleC2×C4C24×C37
prime radicalC37×#548C2
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×#554C2semidirect
3. C37×#489C2semidirect
4. C37×#483C2semidirect
5. C37×#481C2semidirect
6. C37×#475C2semidirect
7. C37×#470C2semidirect
8. C37×#465C2semidirect
9. C37×#464C2semidirect
10. C37×#452C2semidirect
11. C37×#451C2semidirect
12. C37×#441C2semidirect
13. C37×#435C2semidirect
14. C37×#417C2semidirect
15. C2×#103×C37C2semidirect
174. #3316C37direct (N × H)
181. #554C2×C37semidirect
183. #489C2×C37semidirect
184. #483C2×C37semidirect
185. #481C2×C37semidirect
186. #475C2×C37semidirect
187. #470C2×C37semidirect
188. #465C2×C37semidirect
189. #464C2×C37semidirect
190. #452C2×C37semidirect
191. #451C2×C37semidirect
192. #441C2×C37semidirect
193. #435C2×C37semidirect
194. #417C2×C37semidirect
195. C2×#103C2×C37semidirect
196. C37#3316direct (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×#5482
C37×#4892
C37×#4832
C37×#4812
C37×#4752
C37×#4702
C37×#4652
C37×#4642
C37×#4522
C37×#4512
C37×#4412
C37×#4352
C37×#4172
C2×#103×C372
#331637