Finite Group Databasebeta

← C37×#3327 #17992145

Subgroups — C37×#3327 #17992145

Order 4736.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#552C211yesmaximal, characteristic, complemented
2C37×#548C211yesmaximal, characteristic
3C37×#488C211yesmaximal, characteristic, complemented
4C37×#484C211yesmaximal, characteristic, complemented
5C37×#482C211yesmaximal, characteristic, complemented
6C37×#479C211yesmaximal, characteristic, complemented
7C37×#470C211yesmaximal, characteristic, complemented
8C37×#468C211yesmaximal, characteristic, complemented
9C37×#464C211yesmaximal, characteristic, complemented
10C37×#452C211yesmaximal, characteristic, complemented
11C37×#451C211yesmaximal, characteristic, complemented
12C4×Q16×C37C211yesmaximal, characteristic, complemented
13C37×#436C211yesmaximal, characteristic, complemented
14C37×#419C211yesmaximal, characteristic, complemented
15C37×#417C211yesmaximal, characteristic, complemented
16C2×#41×C37C2211yescharacteristic
17C22×Q8×C37C2211yescharacteristic
18C2×Q16×C37C2211yescharacteristic
19C2×Q16×C37C2211yescharacteristic
20C2×SD16×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic
22C2×M16×C37C2211yescharacteristic
23#126×C37—21no—
24#125×C37—21no—
25#125×C37C2211yescharacteristic
26#124×C37—21no—
27#124×C37C2211yescharacteristic
28#123×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×C37C2211yescharacteristic
39#117×C37—21no—
40#117×C37C2211yescharacteristic
41C2×C4⋊C4×C37C2211yescharacteristic
42#107×C37C2211yescharacteristic
43#107×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
58C4×C8×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—41no—
61C2×Q8×C37—21no—
62C2×Q8×C37—22no—
63C2×Q8×C37—41no—
64C2×Q8×C37C2311yescharacteristic
65C2×Q8×C37C2311yescharacteristic
66C2×Q8×C37C2311yescharacteristic
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37D411yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37C2311yescharacteristic
75C22×C4×C37C2311yescharacteristic
76Q16×C37—22no—
77Q16×C37—41no—
78SD16×C37—41no—
79M16×C37—41no—
80M16×C37—41no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C4⋊C4×C37—21no—
86C4⋊C4×C37—21no—
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×C37D411yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C4⋊C4×C37C2311yescharacteristic
96C4⋊C4×C37C2311yescharacteristic
97C4⋊C4×C37C2311yescharacteristic
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C22⋊C4×C37—21no—
101C22⋊C4×C37—21no—
102C22⋊C4×C37—21no—
103C22⋊C4×C37—21no—
104C22⋊C4×C37—21no—
105C22⋊C4×C37D411yescharacteristic
106C22⋊C4×C37D411yescharacteristic
107C42×C37—21no—
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#4112yes—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—41no—
124D4×C37—42no—
125D4×C37—42no—
126C2×C4×C37—21no—
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—42no—
138C2×C4×C37—42no—
139C2×C4×C37—42no—
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2×D411yescharacteristic
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2411yescharacteristic
145C8×C37—21no—
146C8×C37—21no—
147C8×C37—21no—
148C8×C37—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37C22×D411yescharacteristic
159C4×C37—21no—
160C4×C37—21no—
161C4×C37—22no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37H(5,𝔽2)11yescharacteristic
172#3327C3711yesmaximal, characteristic, direct product factor, Sylow
173C2×C37—41no—
174C2×C37—41no—
175C2×C37—81no—
176C2×C37#54611yescharacteristic
177C2×C37#57511yescharacteristic
178C2×C37#57811yescharacteristic
179#552C2×C3711yescharacteristic, complemented
180#548C2×C3711yescharacteristic
181#488C2×C3711yescharacteristic, complemented
182#484C2×C3711yescharacteristic, complemented
183#482C2×C3711yescharacteristic, complemented
184#479C2×C3711yescharacteristic, complemented
185#470C2×C3711yescharacteristic, complemented
186#468C2×C3711yescharacteristic, complemented
187#464C2×C3711yescharacteristic, complemented
188#452C2×C3711yescharacteristic, complemented
189#451C2×C3711yescharacteristic, complemented
190C4×Q16C2×C3711yescharacteristic, complemented
191#436C2×C3711yescharacteristic, complemented
192#419C2×C3711yescharacteristic, complemented
193#417C2×C3711yescharacteristic, complemented
194C37#332711yescharacteristic, direct product factor, Sylow
195C2×#41C22×C3711yescharacteristic
196C22×Q8C22×C3711yescharacteristic
197C2×Q16C22×C3711yescharacteristic
198C2×Q16C22×C3711yescharacteristic
199C2×SD16C22×C3711yescharacteristic
200C2×M16C22×C3711yescharacteristic
201C2×M16C22×C3711yescharacteristic
202#126—21no—
203#125—21no—
204#125C22×C3711yescharacteristic
205#124—21no—
206#124C22×C3711yescharacteristic
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C22×C3711yescharacteristic
210C22⋊Q8C22×C3711yescharacteristic
211C22⋊Q8C22×C3711yescharacteristic
212#121—21no—
213#121C22×C3711yescharacteristic
214C4×Q8C22×C3711yescharacteristic
215C4×Q8C22×C3711yescharacteristic
216C4×D4—21no—
217C4×D4C22×C3711yescharacteristic
218#117—21no—
219#117C22×C3711yescharacteristic
220C2×C4⋊C4C22×C3711yescharacteristic
221#107C22×C3711yescharacteristic
222#107C22×C3711yescharacteristic
223#106C22×C3711yescharacteristic
224C4⋊C8C22×C3711yescharacteristic
225#103C22×C3711yescharacteristic
226#103C22×C3711yescharacteristic
227#103C22×C3711yescharacteristic
228#103C22×C3711yescharacteristic
229#103C22×C3711yescharacteristic
230#103C22×C3711yescharacteristic
231#103C22×C3711yescharacteristic
232#102C22×C3711yescharacteristic
233#102C22×C3711yescharacteristic
234#102C22×C3711yescharacteristic
235C22⋊C8C22×C3711yescharacteristic
236C22⋊C8C22×C3711yescharacteristic
237C4×C8C22×C3711yescharacteristic
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8C23×C3711yescharacteristic
244C2×Q8C23×C3711yescharacteristic
245C2×Q8C23×C3711yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4D4×C3711yescharacteristic
249C2×D4C23×C3711yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C23×C3711yescharacteristic
254C22×C4C23×C3711yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—41no—
258M16—41no—
259M16—41no—
260C2×C8C23×C3711yescharacteristic
261C2×C8C23×C3711yescharacteristic
262C2×C8C23×C3711yescharacteristic
263C2×C8C23×C3711yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4D4×C3711yescharacteristic
273C4⋊C4C23×C3711yescharacteristic
274C4⋊C4C23×C3711yescharacteristic
275C4⋊C4C23×C3711yescharacteristic
276C4⋊C4C23×C3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4D4×C3711yescharacteristic
285C22⋊C4D4×C3711yescharacteristic
286C42—21no—
287C42—21no—
288C42—21no—
289C42C23×C3711yescharacteristic
290C23—21no—
291C23C2×D4×C3711yescharacteristic
292C23C2×D4×C3711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#41×C3712yes—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
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—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4C2×D4×C3711yescharacteristic
320C2×C4C2×D4×C3711yescharacteristic
321C2×C4C2×D4×C3711yescharacteristic
322C2×C4C2×D4×C3711yescharacteristic
323C2×C4C24×C3711yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×D4×C3711yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4C2×#41×C3711yescharacteristic
350C4H(5,𝔽2)×C3711yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2C37×#54611yescharacteristic
355C2C37×#57511yescharacteristic
356C2C37×#57811yescharacteristic
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×#552C2semidirect
3. C37×#488C2semidirect
4. C37×#484C2semidirect
5. C37×#482C2semidirect
6. C37×#479C2semidirect
7. C37×#470C2semidirect
8. C37×#468C2semidirect
9. C37×#464C2semidirect
10. C37×#452C2semidirect
11. C37×#451C2semidirect
12. C4×Q16×C37C2semidirect
13. C37×#436C2semidirect
14. C37×#419C2semidirect
15. C37×#417C2semidirect
172. #3327C37direct (N × H)
179. #552C2×C37semidirect
181. #488C2×C37semidirect
182. #484C2×C37semidirect
183. #482C2×C37semidirect
184. #479C2×C37semidirect
185. #470C2×C37semidirect
186. #468C2×C37semidirect
187. #464C2×C37semidirect
188. #452C2×C37semidirect
189. #451C2×C37semidirect
190. C4×Q16C2×C37semidirect
191. #436C2×C37semidirect
192. #419C2×C37semidirect
193. #417C2×C37semidirect
194. C37#3327direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#5522
C37×#5482
C37×#4882
C37×#4842
C37×#4822
C37×#4792
C37×#4702
C37×#4682
C37×#4642
C37×#4522
C37×#4512
C4×Q16×C372
C37×#4362
C37×#4192
C37×#4172
#332737