Finite Group Databasebeta

← C37×#22831 #22644084

Subgroups — C37×#22831 #22644084

Order 9472.

616 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2295C211yesmaximal, characteristic
2C37×#1985C212yesmaximal
3C37×#1917C212yesmaximal
4C37×#1916C212yesmaximal
5C37×#1840C212yesmaximal
6C37×#1831C211yesmaximal, characteristic
7C37×#1771C212yesmaximal
8C37×#1767C211yesmaximal, characteristic
9C37×#1746C212yesmaximal
10C2×C4×Q8×C37C2211yescharacteristic
11C2×C4⋊C8×C37C2212yes—
12C2×C4⋊C8×C37C2212yes—
13C2×#97×C37C2212yes—
14C2×#97×C37C2212yes—
15C2×C4×C8×C37C2212yes—
16C37×#391C411yescharacteristic
17C37×#391C411yescharacteristic
18C37×#389C411yescharacteristic
19C37×#389C411yescharacteristic
20C37×#387C412yes—
21C37×#387C412yes—
22C4×C4⋊C4×C37C2212yes—
23C4×C4⋊C4×C37C2211yescharacteristic
24C37×#376C2212yes—
25C43×C37C2211yescharacteristic
26C37×#336C2211yescharacteristic
27C37×#336C2212yes—
28C37×#336C2212yes—
29C37×#336C2212yes—
30C37×#336C2212yes—
31C37×#336C2212yes—
32C37×#336C2211yescharacteristic
33C37×#336C2212yes—
34C37×#336C2211yescharacteristic
35C37×#336C2212yes—
36C37×#336C2211yescharacteristic
37C22×Q8×C37C2×C411yescharacteristic
38C22×C8×C37C2312yes—
39C22×C8×C37C2312yes—
40C22×C8×C37C2312yes—
41C22×C8×C37C2312yes—
42C4×Q8×C37—22no—
43C4×Q8×C37—22no—
44C2×C4⋊C4×C37C2×C412yes—
45C2×C4⋊C4×C37C2×C412yes—
46C2×C4⋊C4×C37C2×C411yescharacteristic
47C2×C4⋊C4×C37C2×C412yes—
48C2×C4⋊C4×C37C2×C411yescharacteristic
49C2×C4⋊C4×C37C2×C411yescharacteristic
50C2×C42×C37C2×C411yescharacteristic
51C2×C42×C37C2×C411yescharacteristic
52C2×C42×C37C2×C411yescharacteristic
53C2×C42×C37C2×C411yescharacteristic
54C2×C42×C37C2311yescharacteristic
55C2×C42×C37C2312yes—
56C2×C42×C37C2311yescharacteristic
57C2×C42×C37C2312yes—
58C2×C42×C37C2311yescharacteristic
59C4⋊C8×C37—24no—
60C4⋊C8×C37—24no—
61#97×C37—24no—
62#97×C37—24no—
63C4×C8×C37—24no—
64#95×C37C2×C412yes—
65#95×C37C2×C412yes—
66#95×C37C2×C412yes—
67#95×C37C2×C412yes—
68#95×C37C2×C412yes—
69#95×C37C2×C412yes—
70#95×C37C2×C412yes—
71C2×Q8×C37—22no—
72C2×Q8×C37—41no—
73C2×Q8×C37—41no—
74C22×C4×C37C22×C411yescharacteristic
75C22×C4×C37C22×C411yescharacteristic
76C22×C4×C37C22×C412yes—
77C22×C4×C37C22×C412yes—
78C22×C4×C37C22×C412yes—
79C22×C4×C37C22×C411yescharacteristic
80C22×C4×C37C22×C412yes—
81C22×C4×C37C22×C411yescharacteristic
82C22×C4×C37C22×C411yescharacteristic
83C22×C4×C37C22×C411yescharacteristic
84C22×C4×C37C2411yescharacteristic
85C2×C8×C37—22no—
86C2×C8×C37—22no—
87C2×C8×C37—22no—
88C2×C8×C37—22no—
89C2×C8×C37—22no—
90C2×C8×C37—22no—
91C2×C8×C37—22no—
92C2×C8×C37—22no—
93C2×C8×C37—22no—
94C2×C8×C37—22no—
95C2×C8×C37—22no—
96C2×C8×C37#4114yes—
97C4⋊C4×C37—22no—
98C4⋊C4×C37—24no—
99C4⋊C4×C37—24no—
100C4⋊C4×C37—41no—
101C4⋊C4×C37—41no—
102C4⋊C4×C37—42no—
103C42×C37—22no—
104C42×C37—22no—
105C42×C37—22no—
106C42×C37—22no—
107C42×C37—22no—
108C42×C37—22no—
109C42×C37—22no—
110C42×C37—41no—
111C42×C37—41no—
112C42×C37—41no—
113C42×C37#4112yes—
114C42×C37#4112yes—
115C23×C37C23×C411yescharacteristic
116Q8×C37—44no—
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—22no—
124C2×C4×C37—22no—
125C2×C4×C37—22no—
126C2×C4×C37—21no—
127C2×C4×C37—22no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—22no—
132C2×C4×C37—22no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—22no—
139C2×C4×C37—22no—
140C2×C4×C37—22no—
141C2×C4×C37—22no—
142C2×C4×C37—22no—
143C2×C4×C37—22no—
144C2×C4×C37#11712yes—
145C2×C4×C37#11712yes—
146C2×C4×C37#13112yes—
147C2×C4×C37C2×#4111yescharacteristic
148C2×C4×C37C2×#4112yes—
149C2×C4×C37C2×#4111yescharacteristic
150C2×C4×C372−1+412yes—
151C8×C37—24no—
152C8×C37—42no—
153C8×C37—42no—
154C8×C37—42no—
155#22831C3711yesmaximal, characteristic, direct product factor, Sylow
156C22×C37C2×#11711yescharacteristic
157C22×C37C4×#4111yescharacteristic
158C22×C37#51911yescharacteristic
159C22×C37C2×#13111yescharacteristic
160C22×C37#56811yescharacteristic
161C22×C37#56811yescharacteristic
162C22×C37#56811yescharacteristic
163C4×C37—22no—
164C4×C37—22no—
165C4×C37—22no—
166C4×C37—42no—
167C4×C37—42no—
168C4×C37—41no—
169C4×C37—42no—
170C4×C37—42no—
171C4×C37—41no—
172C4×C37—41no—
173C4×C37#55212yes—
174C4×C37#55612yes—
175#2295C2×C3711yescharacteristic
176#1985C2×C3712yes—
177#1917C2×C3712yes—
178#1916C2×C3712yes—
179#1840C2×C3712yes—
180#1831C2×C3711yescharacteristic
181#1771C2×C3712yes—
182#1767C2×C3711yescharacteristic
183#1746C2×C3712yes—
184C2×C37#235611yescharacteristic
185C2×C37#292111yescharacteristic
186C2×C37#292511yescharacteristic
187C2×C37#296711yescharacteristic
188C2×C37#296811yescharacteristic
189C2×C37#298511yescharacteristic
190C2×C37#298711yescharacteristic
191C2×C4×Q8C22×C3711yescharacteristic
192C2×C4⋊C8C22×C3712yes—
193C2×C4⋊C8C22×C3712yes—
194C2×#97C22×C3712yes—
195C2×#97C22×C3712yes—
196C2×C4×C8C22×C3712yes—
197#391C4×C3711yescharacteristic
198#391C4×C3711yescharacteristic
199#389C4×C3711yescharacteristic
200#389C4×C3711yescharacteristic
201#387C4×C3712yes—
202#387C4×C3712yes—
203C4×C4⋊C4C22×C3712yes—
204C4×C4⋊C4C22×C3711yescharacteristic
205#376C22×C3712yes—
206C43C22×C3711yescharacteristic
207#336C22×C3712yes—
208#336C22×C3711yescharacteristic
209#336C22×C3711yescharacteristic
210#336C22×C3711yescharacteristic
211#336C22×C3712yes—
212#336C22×C3712yes—
213#336C22×C3712yes—
214#336C22×C3712yes—
215#336C22×C3712yes—
216#336C22×C3712yes—
217#336C22×C3711yescharacteristic
218C37#2283111yescharacteristic, direct product factor, Sylow
219C22×Q8C2×C4×C3711yescharacteristic
220C22×C8C23×C3712yes—
221C22×C8C23×C3712yes—
222C22×C8C23×C3712yes—
223C22×C8C23×C3712yes—
224C4×Q8—22no—
225C4×Q8—22no—
226C2×C4⋊C4C2×C4×C3712yes—
227C2×C4⋊C4C2×C4×C3711yescharacteristic
228C2×C4⋊C4C2×C4×C3712yes—
229C2×C4⋊C4C2×C4×C3712yes—
230C2×C4⋊C4C2×C4×C3711yescharacteristic
231C2×C4⋊C4C2×C4×C3711yescharacteristic
232C2×C42C2×C4×C3711yescharacteristic
233C2×C42C2×C4×C3711yescharacteristic
234C2×C42C2×C4×C3711yescharacteristic
235C2×C42C2×C4×C3711yescharacteristic
236C2×C42C23×C3712yes—
237C2×C42C23×C3711yescharacteristic
238C2×C42C23×C3711yescharacteristic
239C2×C42C23×C3712yes—
240C2×C42C23×C3711yescharacteristic
241C4⋊C8—24no—
242C4⋊C8—24no—
243#97—24no—
244#97—24no—
245C4×C8—24no—
246#95C2×C4×C3712yes—
247#95C2×C4×C3712yes—
248#95C2×C4×C3712yes—
249#95C2×C4×C3712yes—
250#95C2×C4×C3712yes—
251#95C2×C4×C3712yes—
252#95C2×C4×C3712yes—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C22×C4C22×C4×C3711yescharacteristic
257C22×C4C22×C4×C3711yescharacteristic
258C22×C4C22×C4×C3712yes—
259C22×C4C22×C4×C3712yes—
260C22×C4C22×C4×C3712yes—
261C22×C4C22×C4×C3711yescharacteristic
262C22×C4C22×C4×C3712yes—
263C22×C4C22×C4×C3711yescharacteristic
264C22×C4C22×C4×C3711yescharacteristic
265C22×C4C22×C4×C3711yescharacteristic
266C22×C4C24×C3711yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8#41×C3714yes—
279C4⋊C4—22no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—22no—
292C42—41no—
293C42—41no—
294C42—41no—
295C42#41×C3712yes—
296C42#41×C3712yes—
297C23C23×C4×C3711yescharacteristic
298Q8—44no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4#117×C3712yes—
327C2×C4#117×C3712yes—
328C2×C4#131×C3712yes—
329C2×C4C2×#41×C3711yescharacteristic
330C2×C4C2×#41×C3712yes—
331C2×C4C2×#41×C3711yescharacteristic
332C2×C42−1+4×C3712yes—
333C8—24no—
334C8—42no—
335C8—42no—
336C8—42no—
337C22C2×#117×C3711yescharacteristic
338C22C4×#41×C3711yescharacteristic
339C22C37×#51911yescharacteristic
340C22C2×#131×C3711yescharacteristic
341C22C37×#56811yescharacteristic
342C22C37×#56811yescharacteristic
343C22C37×#56811yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—42no—
348C4—42no—
349C4—41no—
350C4—42no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4C37×#55212yes—
355C4C37×#55612yes—
356C2C37×#235611yescharacteristic
357C2C37×#292111yescharacteristic
358C2C37×#292511yescharacteristic
359C2C37×#296711yescharacteristic
360C2C37×#296811yescharacteristic
361C2C37×#298511yescharacteristic
362C2C37×#298711yescharacteristic
subgroupG/H
centerC22×C4×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC22×C4C24×C37
socle, prime radicalC23×C37C23×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
155. #22831C37direct (N × H)
218. C37#22831direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#22952
C37×#19852
C37×#19172
C37×#19162
C37×#18402
C37×#18312
C37×#17712
C37×#17672
C37×#17462
#2283137