Finite Group Databasebeta

← C37×#9281 #22630534

Subgroups — C37×#9281 #22630534

Order 9472.

456 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×#3207C211yesmaximal, characteristic
2C37×#2981C211yesmaximal, characteristic, complemented
3C37×#1505C211yesmaximal, characteristic, complemented
4C37×#1505C211yesmaximal, characteristic, complemented
5C37×#1496C211yesmaximal, characteristic, complemented
6C37×#1287C211yesmaximal, characteristic, complemented
7C37×#1274C211yesmaximal, characteristic, complemented
8C37×#532C2211yescharacteristic
9C37×#532C2211yescharacteristic
10C37×#493C411yescharacteristic, complemented
11C37×#492C411yescharacteristic, complemented
12C37×#487C411yescharacteristic, complemented
13C37×#486C411yescharacteristic, complemented
14C37×#463—22no—
15C37×#449—22no—
16C37×#436—21no—
17C37×#435—22no—
18C8×D4×C37—21no—
19C37×#432C2211yescharacteristic
20C37×#432C2211yescharacteristic
21C37×#431C2211yescharacteristic
22C37×#431C2211yescharacteristic
23C37×#408—22no—
24C37×#376C2211yescharacteristic
25C37×#327—22no—
26C37×#327—22no—
27C37×D4⋊C8—21no—
28C37×D4⋊C8—21no—
29C2×#41×C37—21no—
30C2×#41×C37—21no—
31C2×SD16×C37—22no—
32C2×D8×C37—22no—
33C2×M16×C37—22no—
34C22×C8×C37—22no—
35C4⋊Q8×C37C2×C411yescharacteristic
36C4⋊Q8×C37C2×C411yescharacteristic
37#127×C37C2×C411yescharacteristic
38#127×C37C2×C411yescharacteristic
39#124×C37—21no—
40#124×C37—21no—
41#121×C37—21no—
42#121×C37—21no—
43#121×C37—21no—
44#121×C37D412yes—
45C4×D4×C37—21no—
46C4×D4×C37—21no—
47C4×D4×C37—21no—
48C4×D4×C37D412yes—
49C2×C42×C37—21no—
50C2×C42×C37C2311yescharacteristic
51C4⋊C8×C37—21no—
52C4⋊C8×C37—21no—
53C4⋊C8×C37—21no—
54C4⋊C8×C37—21no—
55#103×C37—22no—
56#102×C37—22no—
57C22⋊C8×C37—22no—
58C22⋊C8×C37—22no—
59C22⋊C8×C37—21no—
60C22⋊C8×C37—21no—
61C22⋊C8×C37—21no—
62C22⋊C8×C37D412yes—
63#97×C37—21no—
64#97×C37—21no—
65C4×C8×C37C2×C411yescharacteristic
66C4×C8×C37C2×C411yescharacteristic
67C4×C8×C37D411yescharacteristic
68C4×C8×C37D411yescharacteristic
69#95×C37—21no—
70#95×C37—21no—
71#41×C37—82no—
72#41×C37—82no—
73C2×Q8×C37—21no—
74C2×Q8×C37—21no—
75C2×D4×C37—22no—
76C2×D4×C37—21no—
77C2×D4×C37—21no—
78C2×D4×C37—21no—
79C2×D4×C37—21no—
80C2×D4×C37—21no—
81C2×D4×C37—41no—
82C2×D4×C37C22⋊C412yes—
83C22×C4×C37—22no—
84C22×C4×C37—41no—
85C22×C4×C37—41no—
86C22×C4×C37C2×D411yescharacteristic
87C22×C4×C37C2×D411yescharacteristic
88C22×C4×C37#4111yescharacteristic
89SD16×C37—82no—
90D8×C37—82no—
91M16×C37—82no—
92C2×C8×C37—21no—
93C2×C8×C37—21no—
94C2×C8×C37—21no—
95C2×C8×C37—21no—
96C2×C8×C37—22no—
97C2×C8×C37—41no—
98C2×C8×C37—82no—
99C4⋊C4×C37—21no—
100C4⋊C4×C37—21no—
101C4⋊C4×C37—21no—
102C4⋊C4×C37C22⋊C412yes—
103C22⋊C4×C37—22no—
104C22⋊C4×C37—22no—
105C22⋊C4×C37—41no—
106C22⋊C4×C37—41no—
107C42×C37—22no—
108C42×C37—41no—
109C42×C37C22×C411yescharacteristic
110C42×C37C2×D411yescharacteristic
111C42×C37C2×D411yescharacteristic
112C42×C37#4111yescharacteristic
113C23×C37—22no—
114C23×C37—41no—
115C23×C37#12111yescharacteristic
116Q8×C37—42no—
117Q8×C37—81no—
118D4×C37—42no—
119D4×C37—42no—
120D4×C37—41no—
121D4×C37—41no—
122D4×C37—41no—
123D4×C37—41no—
124D4×C37—81no—
125D4×C37—81no—
126D4×C37—82no—
127D4×C37—82no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—22no—
131C2×C4×C37—41no—
132C2×C4×C37—41no—
133C2×C4×C37—42no—
134C2×C4×C37—42no—
135C2×C4×C37—42no—
136C2×C4×C37—41no—
137C2×C4×C37—82no—
138C2×C4×C37—81no—
139C2×C4×C37—81no—
140C2×C4×C37C2×C22⋊C411yescharacteristic
141C2×C4×C37C4×D411yescharacteristic
142C2×C4×C37C4×D411yescharacteristic
143C2×C4×C37#12011yescharacteristic
144C2×C4×C37#12111yescharacteristic
145C2×C4×C37#12311yescharacteristic
146C8×C37—41no—
147C8×C37—42no—
148C8×C37—41no—
149C8×C37—41no—
150C8×C37—41no—
151C8×C37—81no—
152#9281C3711yesmaximal, characteristic, direct product factor, Sylow
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—42no—
157C22×C37—42no—
158C22×C37—42no—
159C22×C37—81no—
160C22×C37—81no—
161C22×C37—81no—
162C22×C37#38611yescharacteristic
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—42no—
169C4×C37—82no—
170C4×C37—81no—
171C4×C37#44311yescharacteristic
172C4×C37#44411yescharacteristic
173#3207C2×C3711yescharacteristic
174#2981C2×C3711yescharacteristic, complemented
175#1505C2×C3711yescharacteristic, complemented
176#1505C2×C3711yescharacteristic, complemented
177#1496C2×C3711yescharacteristic, complemented
178#1287C2×C3711yescharacteristic, complemented
179#1274C2×C3711yescharacteristic, complemented
180C2×C37—41no—
181C2×C37—82no—
182C2×C37—161no—
183C2×C37#187611yescharacteristic
184C2×C37#190411yescharacteristic
185C2×C37#191011yescharacteristic
186#532C22×C3711yescharacteristic
187#532C22×C3711yescharacteristic
188#493C4×C3711yescharacteristic, complemented
189#492C4×C3711yescharacteristic, complemented
190#487C4×C3711yescharacteristic, complemented
191#486C4×C3711yescharacteristic, complemented
192#463—22no—
193#449—22no—
194#436—21no—
195#435—22no—
196C8×D4—21no—
197#432C22×C3711yescharacteristic
198#432C22×C3711yescharacteristic
199#431C22×C3711yescharacteristic
200#431C22×C3711yescharacteristic
201#408—22no—
202#376C22×C3711yescharacteristic
203#327—22no—
204#327—22no—
205D4⋊C8—21no—
206D4⋊C8—21no—
207C37#928111yescharacteristic, direct product factor, Sylow
208C2×#41—21no—
209C2×#41—21no—
210C2×SD16—22no—
211C2×D8—22no—
212C2×M16—22no—
213C22×C8—22no—
214C4⋊Q8C2×C4×C3711yescharacteristic
215C4⋊Q8C2×C4×C3711yescharacteristic
216#127C2×C4×C3711yescharacteristic
217#127C2×C4×C3711yescharacteristic
218#124—21no—
219#124—21no—
220#121—21no—
221#121—21no—
222#121—21no—
223#121D4×C3712yes—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4D4×C3712yes—
228C2×C42—21no—
229C2×C42C23×C3711yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234#103—22no—
235#102—22no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8D4×C3712yes—
242#97—21no—
243#97—21no—
244C4×C8C2×C4×C3711yescharacteristic
245C4×C8C2×C4×C3711yescharacteristic
246C4×C8D4×C3711yescharacteristic
247C4×C8D4×C3711yescharacteristic
248#95—21no—
249#95—21no—
250#41—82no—
251#41—82no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4C22⋊C4×C3712yes—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C3711yescharacteristic
266C22×C4C2×D4×C3711yescharacteristic
267C22×C4#41×C3711yescharacteristic
268SD16—82no—
269D8—82no—
270M16—82no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—82no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4C22⋊C4×C3712yes—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42—22no—
287C42—41no—
288C42C22×C4×C3711yescharacteristic
289C42C2×D4×C3711yescharacteristic
290C42C2×D4×C3711yescharacteristic
291C42#41×C3711yescharacteristic
292C23—22no—
293C23—41no—
294C23#121×C3711yescharacteristic
295Q8—42no—
296Q8—81no—
297D4—42no—
298D4—42no—
299D4—41no—
300D4—41no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—82no—
306D4—82no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4C2×C22⋊C4×C3711yescharacteristic
320C2×C4C4×D4×C3711yescharacteristic
321C2×C4C4×D4×C3711yescharacteristic
322C2×C4#120×C3711yescharacteristic
323C2×C4#121×C3711yescharacteristic
324C2×C4#123×C3711yescharacteristic
325C8—41no—
326C8—42no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—81no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C37×#38611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—82no—
348C4—81no—
349C4C37×#44311yescharacteristic
350C4C37×#44411yescharacteristic
351C2—41no—
352C2—82no—
353C2—161no—
354C2C37×#187611yescharacteristic
355C2C37×#190411yescharacteristic
356C2C37×#191011yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC37×#3207C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2981C2semidirect
3. C37×#1505C2semidirect
4. C37×#1505C2semidirect
5. C37×#1496C2semidirect
6. C37×#1287C2semidirect
7. C37×#1274C2semidirect
10. C37×#493C4semidirect
11. C37×#492C4semidirect
12. C37×#487C4semidirect
13. C37×#486C4semidirect
152. #9281C37direct (N × H)
174. #2981C2×C37semidirect
175. #1505C2×C37semidirect
176. #1505C2×C37semidirect
177. #1496C2×C37semidirect
178. #1287C2×C37semidirect
179. #1274C2×C37semidirect
188. #493C4×C37semidirect
189. #492C4×C37semidirect
190. #487C4×C37semidirect
191. #486C4×C37semidirect
207. C37#9281direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32072
C37×#29812
C37×#15052
C37×#14962
C37×#12872
C37×#12742
#928137