Finite Group Databasebeta

← C37×#19393 #22640646

Subgroups — C37×#19393 #22640646

Order 9472.

642 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3230C211yesmaximal, characteristic, complemented
2C37×#3077C211yesmaximal, characteristic
3C2×C37×#476C211yesmaximal, characteristic
4C37×#2972C211yesmaximal, characteristic
5C37×#1683C214yesmaximal, complemented
6C37×#1675C214yesmaximal, complemented
7C37×#1571C211yesmaximal, characteristic, complemented
8C37×#1548C211yesmaximal, characteristic, complemented
9C37×#1542C211yesmaximal, characteristic, complemented
10C37×#533C2211yescharacteristic
11C2×C4⋊Q8×C37C2211yescharacteristic
12C2×C4×D4×C37C2211yescharacteristic
13C37×#500C2212yescomplemented
14C37×#487C2212yescomplemented
15C37×#484—22no—
16C37×#478—22no—
17C37×#477—22no—
18C37×#476—22no—
19C37×#476C2212yes—
20C37×#476C2214yes—
21C37×#474C2212yes—
22C8×D4×C37—22no—
23C8×D4×C37C2214yes—
24C37×#431C2211yescharacteristic
25C37×#431C2211yescharacteristic
26C37×#428—21no—
27C2×#106×C37—21no—
28C37×#423C2211yescharacteristic
29C2×C4⋊C8×C37C2211yescharacteristic
30C37×#418—21no—
31C2×#102×C37—21no—
32C2×C22⋊C8×C37—22no—
33C37×#335C2214yescomplemented
34C37×#333C2212yescomplemented
35C37×#333C2214yescomplemented
36C37×#332C2212yescomplemented
37C22×Q8×C37—21no—
38C22×D4×C37D411yescharacteristic
39C23×C4×C37—21no—
40C2×M16×C37—21no—
41C22×C8×C37—21no—
42C22×C8×C37—24no—
43C4⋊Q8×C37—21no—
44C4⋊Q8×C37—21no—
45C4⋊Q8×C37—21no—
46C4⋊Q8×C37C2312yes—
47C4⋊Q8×C37C2311yescharacteristic
48C4⋊Q8×C37C2311yescharacteristic
49#125×C37—21no—
50C22⋊Q8×C37—21no—
51C22⋊Q8×C37—21no—
52C4×Q8×C37—21no—
53C4×Q8×C37—21no—
54C4×D4×C37—21no—
55C4×D4×C37—21no—
56C4×D4×C37D412yes—
57C4×D4×C37C2312yes—
58#117×C37—21no—
59C2×C4⋊C4×C37—21no—
60C2×C4⋊C4×C37—21no—
61C2×C4⋊C4×C37D411yescharacteristic
62C2×C22⋊C4×C37—21no—
63C2×C42×C37C2311yescharacteristic
64#107×C37—24no—
65#107×C37—22no—
66#106×C37—24no—
67#106×C37—22no—
68C4⋊C8×C37—21no—
69C4⋊C8×C37—21no—
70C4⋊C8×C37D412yes—
71C4⋊C8×C37C2312yes—
72C4⋊C8×C37C2312yes—
73C4⋊C8×C37C2312yes—
74#103×C37—24no—
75#102×C37—24no—
76#102×C37—22no—
77#102×C37—22no—
78C22⋊C8×C37—21no—
79C22⋊C8×C37—24no—
80C22⋊C8×C37D412yes—
81C4×C8×C37—21no—
82C4×C8×C37C2312yes—
83C24×C37—21no—
84C2×Q8×C37—21no—
85C2×Q8×C37—21no—
86C2×Q8×C37—22no—
87C2×Q8×C37—41no—
88C2×Q8×C37—82no—
89C2×D4×C37—21no—
90C2×D4×C37—22no—
91C2×D4×C37Q1614yes—
92C2×D4×C37C2×D412yes—
93C22×C4×C37—21no—
94C22×C4×C37—22no—
95C22×C4×C37—22no—
96C22×C4×C37—41no—
97C22×C4×C37—82no—
98C22×C4×C37C2×D411yescharacteristic
99C22×C4×C37C2×D411yescharacteristic
100C22×C4×C37#4111yescharacteristic
101M16×C37—42no—
102C2×C8×C37—22no—
103C2×C8×C37—22no—
104C2×C8×C37—22no—
105C2×C8×C37—42no—
106C2×C8×C37—84no—
107C2×C8×C37C2×D414yes—
108C4⋊C4×C37—21no—
109C4⋊C4×C37—22no—
110C4⋊C4×C37—21no—
111C4⋊C4×C37—21no—
112C4⋊C4×C37—22no—
113C4⋊C4×C37—21no—
114C4⋊C4×C37—21no—
115C4⋊C4×C37—41no—
116C4⋊C4×C37—41no—
117C4⋊C4×C37—41no—
118C4⋊C4×C37—41no—
119C4⋊C4×C37C2×D412yes—
120C22⋊C4×C37—22no—
121C22⋊C4×C37—22no—
122C22⋊C4×C37—41no—
123C42×C37—41no—
124C42×C37C2×D411yescharacteristic
125C42×C37C2×D411yescharacteristic
126C42×C37#4111yescharacteristic
127C42×C37C2411yescharacteristic
128C23×C37—22no—
129C23×C37—24no—
130C23×C37—81no—
131C23×C37—81no—
132C23×C37#12111yescharacteristic
133Q8×C37—42no—
134Q8×C37—81no—
135Q8×C37—82no—
136Q8×C37—82no—
137D4×C37—22no—
138D4×C37—24no—
139D4×C37C2×Q1614yes—
140C2×C4×C37—22no—
141C2×C4×C37—22no—
142C2×C4×C37—41no—
143C2×C4×C37—44no—
144C2×C4×C37—41no—
145C2×C4×C37—41no—
146C2×C4×C37—42no—
147C2×C4×C37—82no—
148C2×C4×C37—81no—
149C2×C4×C37—82no—
150C2×C4×C37#12111yescharacteristic
151C2×C4×C37#12111yescharacteristic
152C2×C4×C37#12111yescharacteristic
153C2×C4×C37C2×Q1612yes—
154C2×C4×C37#13512yes—
155C2×C4×C37C22×D411yescharacteristic
156C2×C4×C37C22×D411yescharacteristic
157C2×C4×C37C2×#4111yescharacteristic
158C8×C37—24no—
159C8×C37—42no—
160C8×C37—42no—
161C8×C37—42no—
162#19393C3711yesmaximal, characteristic, direct product factor, Sylow
163C22×C37—21no—
164C22×C37—21no—
165C22×C37—24no—
166C22×C37—42no—
167C22×C37—42no—
168C22×C37—84no—
169C22×C37#46712yes—
170C22×C37C2×#12111yescharacteristic
171C4×C37—21no—
172C4×C37—21no—
173C4×C37—21no—
174C4×C37—42no—
175C4×C37—81no—
176C4×C37—82no—
177C4×C37—81no—
178C4×C37#46712yes—
179C4×C37C22×Q1611yescharacteristic
180C4×C37C2×#13511yescharacteristic
181C4×C37#57712yes—
182#3230C2×C3711yescharacteristic, complemented
183#3077C2×C3711yescharacteristic
184C2×#476C2×C3711yescharacteristic
185#2972C2×C3711yescharacteristic
186#1683C2×C3714yescomplemented
187#1675C2×C3714yescomplemented
188#1571C2×C3711yescharacteristic, complemented
189#1548C2×C3711yescharacteristic, complemented
190#1542C2×C3711yescharacteristic, complemented
191C2×C37—22no—
192C2×C37—44no—
193C2×C37#304211yescharacteristic
194C2×C37C2×#46711yescharacteristic
195C2×C37#306811yescharacteristic
196#533C22×C3711yescharacteristic
197C2×C4⋊Q8C22×C3711yescharacteristic
198C2×C4×D4C22×C3711yescharacteristic
199#500C22×C3712yescomplemented
200#487C22×C3712yescomplemented
201#484—22no—
202#478—22no—
203#477—22no—
204#476—22no—
205#476C22×C3712yes—
206#476C22×C3714yes—
207#474C22×C3712yes—
208C8×D4—22no—
209C8×D4C22×C3714yes—
210#431C22×C3711yescharacteristic
211#431C22×C3711yescharacteristic
212#428—21no—
213C2×#106—21no—
214#423C22×C3711yescharacteristic
215C2×C4⋊C8C22×C3711yescharacteristic
216#418—21no—
217C2×#102—21no—
218C2×C22⋊C8—22no—
219#335C22×C3714yescomplemented
220#333C22×C3712yescomplemented
221#333C22×C3714yescomplemented
222#332C22×C3712yescomplemented
223C37#1939311yescharacteristic, direct product factor, Sylow
224C22×Q8—21no—
225C22×D4D4×C3711yescharacteristic
226C23×C4—21no—
227C2×M16—21no—
228C22×C8—21no—
229C22×C8—24no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C23×C3712yes—
234C4⋊Q8C23×C3711yescharacteristic
235C4⋊Q8C23×C3711yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4D4×C3712yes—
244C4×D4C23×C3712yes—
245#117—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C3711yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42C23×C3711yescharacteristic
251#107—24no—
252#107—22no—
253#106—24no—
254#106—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C3712yes—
258C4⋊C8C23×C3712yes—
259C4⋊C8C23×C3712yes—
260C4⋊C8C23×C3712yes—
261#103—24no—
262#102—24no—
263#102—22no—
264#102—22no—
265C22⋊C8—21no—
266C22⋊C8—24no—
267C22⋊C8D4×C3712yes—
268C4×C8—21no—
269C4×C8C23×C3712yes—
270C24—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×D4—21no—
277C2×D4—22no—
278C2×D4Q16×C3714yes—
279C2×D4C2×D4×C3712yes—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—82no—
285C22×C4C2×D4×C3711yescharacteristic
286C22×C4C2×D4×C3711yescharacteristic
287C22×C4#41×C3711yescharacteristic
288M16—42no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—84no—
294C2×C8C2×D4×C3714yes—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C2×D4×C3712yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—41no—
310C42—41no—
311C42C2×D4×C3711yescharacteristic
312C42C2×D4×C3711yescharacteristic
313C42#41×C3711yescharacteristic
314C42C24×C3711yescharacteristic
315C23—22no—
316C23—24no—
317C23—81no—
318C23—81no—
319C23#121×C3711yescharacteristic
320Q8—42no—
321Q8—82no—
322Q8—81no—
323Q8—82no—
324D4—22no—
325D4—24no—
326D4C2×Q16×C3714yes—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4#121×C3711yescharacteristic
338C2×C4#121×C3711yescharacteristic
339C2×C4#121×C3711yescharacteristic
340C2×C4C2×Q16×C3712yes—
341C2×C4#135×C3712yes—
342C2×C4C22×D4×C3711yescharacteristic
343C2×C4C22×D4×C3711yescharacteristic
344C2×C4C2×#41×C3711yescharacteristic
345C8—24no—
346C8—42no—
347C8—42no—
348C8—42no—
349C22—21no—
350C22—21no—
351C22—24no—
352C22—42no—
353C22—42no—
354C22—84no—
355C22C37×#46712yes—
356C22C2×#121×C3711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4C37×#46712yes—
365C4C22×Q16×C3711yescharacteristic
366C4C2×#135×C3711yescharacteristic
367C4C37×#57712yes—
368C2—22no—
369C2—44no—
370C2C37×#304211yescharacteristic
371C2C2×C37×#46711yescharacteristic
372C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC22×D4×C37D4
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
1. C37×#3230C2semidirect
5. C37×#1683C2semidirect
6. C37×#1675C2semidirect
7. C37×#1571C2semidirect
8. C37×#1548C2semidirect
9. C37×#1542C2semidirect
13. C37×#500C22semidirect
14. C37×#487C22semidirect
33. C37×#335C22semidirect
34. C37×#333C22semidirect
35. C37×#333C22semidirect
36. C37×#332C22semidirect
162. #19393C37direct (N × H)
182. #3230C2×C37semidirect
186. #1683C2×C37semidirect
187. #1675C2×C37semidirect
188. #1571C2×C37semidirect
189. #1548C2×C37semidirect
190. #1542C2×C37semidirect
199. #500C22×C37semidirect
200. #487C22×C37semidirect
219. #335C22×C37semidirect
220. #333C22×C37semidirect
221. #333C22×C37semidirect
222. #332C22×C37semidirect
223. C37#19393direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32302
C37×#30772
C2×C37×#4762
C37×#29722
C37×#16832
C37×#16752
C37×#15712
C37×#15482
C37×#15422
#1939337