Finite Group Databasebeta

← C37×#2695 #17991513

Subgroups — C37×#2695 #17991513

Order 4736.

504 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×C37C211yesmaximal, characteristic, complemented
2C2×#123×C37C211yesmaximal, characteristic
3C37×#400C211yesmaximal, characteristic, complemented
4C37×#398C211yesmaximal, characteristic, complemented
5C37×#398C211yesmaximal, characteristic, complemented
6C37×#397C211yesmaximal, characteristic, complemented
7C37×#396C211yesmaximal, characteristic, complemented
8C37×#394C211yesmaximal, characteristic
9C37×#389C211yesmaximal, characteristic, complemented
10C37×#388C211yesmaximal, characteristic, complemented
11C37×#386C211yesmaximal, characteristic
12C37×#385C211yesmaximal, characteristic, complemented
13C37×#385C211yesmaximal, characteristic, complemented
14C37×#380C211yesmaximal, characteristic, complemented
15C37×#380C211yesmaximal, characteristic, complemented
16C22×D4×C37C2211yescharacteristic
17C23×C4×C37C2211yescharacteristic
18C23×C4×C37C2211yescharacteristic
19#126×C37—24no—
20#123×C37—24no—
21C2×C4⋊C4×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26C2×C4⋊C4×C37C2211yescharacteristic
27C2×C4⋊C4×C37C2211yescharacteristic
28C2×C4⋊C4×C37C2211yescharacteristic
29C2×C4⋊C4×C37C2211yescharacteristic
30C2×C4⋊C4×C37C2211yescharacteristic
31C2×C4⋊C4×C37C2211yescharacteristic
32C2×C22⋊C4×C37C2211yescharacteristic
33C2×C22⋊C4×C37C2211yescharacteristic
34C2×C22⋊C4×C37C2211yescharacteristic
35C2×C22⋊C4×C37C2211yescharacteristic
36C2×C22⋊C4×C37C2211yescharacteristic
37C2×C22⋊C4×C37C2211yescharacteristic
38C2×C22⋊C4×C37C2211yescharacteristic
39C2×C22⋊C4×C37C2211yescharacteristic
40C2×C22⋊C4×C37C2211yescharacteristic
41C2×C22⋊C4×C37C2211yescharacteristic
42C2×C42×C37C2211yescharacteristic
43#95×C37C2211yescharacteristic
44#95×C37C2211yescharacteristic
45#95×C37C2211yescharacteristic
46#95×C37C2211yescharacteristic
47#95×C37C2211yescharacteristic
48#95×C37C2211yescharacteristic
49#95×C37C2211yescharacteristic
50#95×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53C24×C37C2311yescharacteristic
54C24×C37C2311yescharacteristic
55C2×D4×C37—22no—
56C2×D4×C37—22no—
57C2×D4×C37—41no—
58C22×C4×C37—22no—
59C22×C4×C37—22no—
60C22×C4×C37—22no—
61C22×C4×C37—41no—
62C22×C4×C37—41no—
63C22×C4×C37—41no—
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C22×C4×C37C2311yescharacteristic
72C22×C4×C37C2311yescharacteristic
73C22×C4×C37C2311yescharacteristic
74C22×C4×C37C2311yescharacteristic
75C22×C4×C37C2311yescharacteristic
76C22×C4×C37C2311yescharacteristic
77C4⋊C4×C37—22no—
78C4⋊C4×C37—22no—
79C4⋊C4×C37—22no—
80C4⋊C4×C37—22no—
81C4⋊C4×C37—22no—
82C4⋊C4×C37—22no—
83C4⋊C4×C37—41no—
84C4⋊C4×C37—41no—
85C4⋊C4×C37—41no—
86C4⋊C4×C37—41no—
87C4⋊C4×C37—41no—
88C22⋊C4×C37—22no—
89C22⋊C4×C37—22no—
90C22⋊C4×C37—22no—
91C22⋊C4×C37—22no—
92C22⋊C4×C37—22no—
93C22⋊C4×C37—22no—
94C22⋊C4×C37—41no—
95C22⋊C4×C37—41no—
96C22⋊C4×C37—41no—
97C22⋊C4×C37D414yes—
98C42×C37—22no—
99C23×C37—21no—
100C23×C37—21no—
101C23×C37—21no—
102C23×C37—21no—
103C23×C37—21no—
104C23×C37—21no—
105C23×C37—21no—
106C23×C37—21no—
107C23×C37—21no—
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37C2×D412yes—
112C23×C37#4112yes—
113C23×C37C2411yescharacteristic
114D4×C37—44no—
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—21no—
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—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—44no—
152C2×C4×C37—44no—
153C2×C4×C37C2×D412yes—
154C2×C4×C37C2×D412yes—
155C2×C4×C37#4112yes—
156C22×C37—22no—
157C22×C37—22no—
158C22×C37—22no—
159C22×C37—22no—
160C22×C37—22no—
161C22×C37—22no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—41no—
170C22×C37C22×D411yescharacteristic
171C22×C37C2×#4111yescharacteristic
172C22×C37C2×#4111yescharacteristic
173C22×C37H(5,𝔽2)11yescharacteristic
174C22×C37H(5,𝔽2)11yescharacteristic
175C22×C372−1+411yescharacteristic
176C22×C372−1+411yescharacteristic
177C4×C37—22no—
178C4×C37—22no—
179C4×C37—22no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37—41no—
183C4×C37—41no—
184C4×C37—41no—
185C4×C37—41no—
186C4×C37—41no—
187C4×C37—41no—
188C4×C37—41no—
189C4×C37—41no—
190#2695C3711yesmaximal, characteristic, direct product factor, Sylow
191C2×C37—42no—
192C2×C37—42no—
193C2×C37#53711yescharacteristic
194C2×C37#53811yescharacteristic
195C2×C37#53911yescharacteristic
196C2×C37#54611yescharacteristic
197C2×C37#54711yescharacteristic
198C2×C37#55211yescharacteristic
199C2×C37#56311yescharacteristic
200C2×#126C2×C3711yescharacteristic, complemented
201C2×#123C2×C3711yescharacteristic
202#400C2×C3711yescharacteristic, complemented
203#398C2×C3711yescharacteristic, complemented
204#398C2×C3711yescharacteristic, complemented
205#397C2×C3711yescharacteristic, complemented
206#396C2×C3711yescharacteristic, complemented
207#394C2×C3711yescharacteristic
208#389C2×C3711yescharacteristic, complemented
209#388C2×C3711yescharacteristic, complemented
210#386C2×C3711yescharacteristic
211#385C2×C3711yescharacteristic, complemented
212#385C2×C3711yescharacteristic, complemented
213#380C2×C3711yescharacteristic, complemented
214#380C2×C3711yescharacteristic, complemented
215C37#269511yescharacteristic, direct product factor, Sylow
216C22×D4C22×C3711yescharacteristic
217C23×C4C22×C3711yescharacteristic
218C23×C4C22×C3711yescharacteristic
219#126—24no—
220#123—24no—
221C2×C4⋊C4C22×C3711yescharacteristic
222C2×C4⋊C4C22×C3711yescharacteristic
223C2×C4⋊C4C22×C3711yescharacteristic
224C2×C4⋊C4C22×C3711yescharacteristic
225C2×C4⋊C4C22×C3711yescharacteristic
226C2×C4⋊C4C22×C3711yescharacteristic
227C2×C4⋊C4C22×C3711yescharacteristic
228C2×C4⋊C4C22×C3711yescharacteristic
229C2×C4⋊C4C22×C3711yescharacteristic
230C2×C4⋊C4C22×C3711yescharacteristic
231C2×C4⋊C4C22×C3711yescharacteristic
232C2×C22⋊C4C22×C3711yescharacteristic
233C2×C22⋊C4C22×C3711yescharacteristic
234C2×C22⋊C4C22×C3711yescharacteristic
235C2×C22⋊C4C22×C3711yescharacteristic
236C2×C22⋊C4C22×C3711yescharacteristic
237C2×C22⋊C4C22×C3711yescharacteristic
238C2×C22⋊C4C22×C3711yescharacteristic
239C2×C22⋊C4C22×C3711yescharacteristic
240C2×C22⋊C4C22×C3711yescharacteristic
241C2×C22⋊C4C22×C3711yescharacteristic
242C2×C42C22×C3711yescharacteristic
243#95C22×C3711yescharacteristic
244#95C22×C3711yescharacteristic
245#95C22×C3711yescharacteristic
246#95C22×C3711yescharacteristic
247#95C22×C3711yescharacteristic
248#95C22×C3711yescharacteristic
249#95C22×C3711yescharacteristic
250#95C22×C3711yescharacteristic
251#95C22×C3711yescharacteristic
252#95C22×C3711yescharacteristic
253C24C23×C3711yescharacteristic
254C24C23×C3711yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C23×C3711yescharacteristic
265C22×C4C23×C3711yescharacteristic
266C22×C4C23×C3711yescharacteristic
267C22×C4C23×C3711yescharacteristic
268C22×C4C23×C3711yescharacteristic
269C22×C4C23×C3711yescharacteristic
270C22×C4C23×C3711yescharacteristic
271C22×C4C23×C3711yescharacteristic
272C22×C4C23×C3711yescharacteristic
273C22×C4C23×C3711yescharacteristic
274C22×C4C23×C3711yescharacteristic
275C22×C4C23×C3711yescharacteristic
276C22×C4C23×C3711yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4D4×C3714yes—
298C42—22no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23C2×D4×C3712yes—
312C23#41×C3712yes—
313C23C24×C3711yescharacteristic
314D4—44no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4C2×D4×C3712yes—
354C2×C4C2×D4×C3712yes—
355C2×C4#41×C3712yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C22×D4×C3711yescharacteristic
371C22C2×#41×C3711yescharacteristic
372C22C2×#41×C3711yescharacteristic
373C22H(5,𝔽2)×C3711yescharacteristic
374C22H(5,𝔽2)×C3711yescharacteristic
375C222−1+4×C3711yescharacteristic
376C222−1+4×C3711yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C2—42no—
391C2—42no—
392C2C37×#53711yescharacteristic
393C2C37×#53811yescharacteristic
394C2C37×#53911yescharacteristic
395C2C37×#54611yescharacteristic
396C2C37×#54711yescharacteristic
397C2C37×#55211yescharacteristic
398C2C37×#56311yescharacteristic
subgroupG/H
center, socleC23×C37C24
commutator, Frattini, cosocleC23C24×C37
prime radicalC22×D4×C37C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#126×C37C2semidirect
3. C37×#400C2semidirect
4. C37×#398C2semidirect
5. C37×#398C2semidirect
6. C37×#397C2semidirect
7. C37×#396C2semidirect
9. C37×#389C2semidirect
10. C37×#388C2semidirect
12. C37×#385C2semidirect
13. C37×#385C2semidirect
14. C37×#380C2semidirect
15. C37×#380C2semidirect
190. #2695C37direct (N × H)
200. C2×#126C2×C37semidirect
202. #400C2×C37semidirect
203. #398C2×C37semidirect
204. #398C2×C37semidirect
205. #397C2×C37semidirect
206. #396C2×C37semidirect
208. #389C2×C37semidirect
209. #388C2×C37semidirect
211. #385C2×C37semidirect
212. #385C2×C37semidirect
213. #380C2×C37semidirect
214. #380C2×C37semidirect
215. C37#2695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#126×C372
C2×#123×C372
C37×#4002
C37×#3982
C37×#3972
C37×#3962
C37×#3942
C37×#3892
C37×#3882
C37×#3862
C37×#3852
C37×#3802
#269537