Finite Group Databasebeta

← C37×#29341 #22650594

Subgroups — C37×#29341 #22650594

Order 9472.

730 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2621C211yesmaximal, characteristic
2C37×#2316C211yesmaximal, characteristic
3C37×#2101C212yesmaximal, complemented
4C37×#2043C212yesmaximal, complemented
5C37×#1935C212yesmaximal, complemented
6C37×#1933C212yesmaximal, complemented
7C37×#1873C212yesmaximal
8C37×#1872C212yesmaximal
9C37×#1750C211yesmaximal, characteristic
10C2×C4⋊Q8×C37C2211yescharacteristic
11C2×C22⋊Q8×C37C2212yes—
12C2×#117×C37C2211yescharacteristic
13C2×#117×C37C2211yescharacteristic
14C22×C4⋊C4×C37C2211yescharacteristic
15C2×#103×C37C2212yes—
16C2×#103×C37C2212yes—
17C2×#103×C37C2212yes—
18C2×#103×C37C2212yes—
19C2×C22⋊C8×C37C2212yes—
20C2×#97×C37C2211yescharacteristic
21C2×C4×C8×C37C2211yescharacteristic
22C37×#398—22no—
23C37×#397—22no—
24C37×#391C2212yes—
25C37×#389—22no—
26C37×#389C2212yes—
27C37×#389C2212yes—
28C37×#382C2211yescharacteristic
29C37×#380—22no—
30C37×#340C2212yes—
31C37×#340C2212yes—
32C37×#340C2212yes—
33C37×#340C2212yes—
34C37×#336C2212yes—
35C22×Q8×C37C2312yes—
36C23×C4×C37—21no—
37C23×C4×C37C2311yescharacteristic
38C22×C8×C37C2312yes—
39C22×C8×C37C2312yes—
40C4⋊Q8×C37—41no—
41C4⋊Q8×C37—41no—
42C22⋊Q8×C37—24no—
43C22⋊Q8×C37—24no—
44#117×C37—41no—
45#117×C37—41no—
46#117×C37—41no—
47#117×C37—41no—
48C2×C4⋊C4×C37—21no—
49C2×C4⋊C4×C37—24no—
50C2×C4⋊C4×C37—22no—
51C2×C4⋊C4×C37—22no—
52C2×C4⋊C4×C37—22no—
53C2×C4⋊C4×C37—22no—
54C2×C4⋊C4×C37D412yes—
55C2×C4⋊C4×C37C2312yes—
56C2×C4⋊C4×C37C2312yes—
57C2×C4⋊C4×C37C2312yes—
58C2×C22⋊C4×C37—22no—
59C2×C22⋊C4×C37—21no—
60C2×C22⋊C4×C37D412yes—
61C2×C42×C37—21no—
62C2×C42×C37C2311yescharacteristic
63C2×C42×C37C2311yescharacteristic
64#103×C37—24no—
65#103×C37—24no—
66#103×C37—42no—
67#103×C37—42no—
68C22⋊C8×C37—24no—
69#97×C37—41no—
70C4×C8×C37—41no—
71#95×C37—22no—
72#95×C37—22no—
73#95×C37—22no—
74#95×C37—24no—
75C24×C37C2×D411yescharacteristic
76C2×Q8×C37—22no—
77C2×Q8×C37—22no—
78C2×Q8×C37—22no—
79C2×Q8×C37—22no—
80C2×Q8×C37—22no—
81C2×Q8×C37—22no—
82C22×C4×C37—22no—
83C22×C4×C37—21no—
84C22×C4×C37—21no—
85C22×C4×C37—22no—
86C22×C4×C37—24no—
87C22×C4×C37—22no—
88C22×C4×C37—22no—
89C22×C4×C37—22no—
90C22×C4×C37—82no—
91C22×C4×C37C2×D412yes—
92C22×C4×C37C2×D412yes—
93C22×C4×C37C2×D411yescharacteristic
94C22×C4×C37#4114yes—
95C22×C4×C37C2411yescharacteristic
96C2×C8×C37—22no—
97C2×C8×C37—22no—
98C2×C8×C37—22no—
99C2×C8×C37—22no—
100C2×C8×C37—22no—
101C2×C8×C37—22no—
102C4⋊C4×C37—24no—
103C4⋊C4×C37—22no—
104C4⋊C4×C37—22no—
105C4⋊C4×C37—22no—
106C4⋊C4×C37—22no—
107C4⋊C4×C37—22no—
108C4⋊C4×C37—42no—
109C4⋊C4×C37—44no—
110C4⋊C4×C37—44no—
111C4⋊C4×C37—82no—
112C4⋊C4×C37—82no—
113C4⋊C4×C37#4114yes—
114C22⋊C4×C37—42no—
115C22⋊C4×C37—42no—
116C22⋊C4×C37—44no—
117C42×C37—21no—
118C42×C37—21no—
119C42×C37—21no—
120C42×C37—21no—
121C42×C37—42no—
122C23×C37—21no—
123C23×C37—21no—
124C23×C37—22no—
125C23×C37—22no—
126C23×C37#12412yes—
127C23×C37C22×D411yescharacteristic
128Q8×C37—42no—
129Q8×C37—42no—
130Q8×C37—42no—
131Q8×C37—42no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—24no—
135C2×C4×C37—24no—
136C2×C4×C37—24no—
137C2×C4×C37—22no—
138C2×C4×C37—22no—
139C2×C4×C37—22no—
140C2×C4×C37—22no—
141C2×C4×C37—22no—
142C2×C4×C37—22no—
143C2×C4×C37—42no—
144C2×C4×C37—42no—
145C2×C4×C37—42no—
146C2×C4×C37—42no—
147C2×C4×C37—42no—
148C2×C4×C37—42no—
149C2×C4×C37—42no—
150C2×C4×C37—42no—
151C2×C4×C37—42no—
152C2×C4×C37—42no—
153C2×C4×C37—42no—
154C2×C4×C37—84no—
155C2×C4×C37#12412yes—
156C2×C4×C37C2×#4112yes—
157C2×C4×C37C2×#4112yes—
158C2×C4×C37H(5,𝔽2)11yescharacteristic
159C2×C4×C37H(5,𝔽2)11yescharacteristic
160C8×C37—42no—
161C8×C37—42no—
162#29341C3711yesmaximal, characteristic, direct product factor, Sylow
163C22×C37—22no—
164C22×C37—24no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—42no—
168C22×C37#52511yescharacteristic
169C22×C37C2×#12411yescharacteristic
170C22×C37#53411yescharacteristic
171C22×C37#57712yes—
172C22×C37#57812yes—
173C4×C37—22no—
174C4×C37—44no—
175C4×C37—42no—
176C4×C37—42no—
177C4×C37—82no—
178C4×C37—82no—
179C4×C37—82no—
180C4×C37#55312yes—
181C4×C37#55312yes—
182#2621C2×C3711yescharacteristic
183#2316C2×C3711yescharacteristic
184#2101C2×C3712yescomplemented
185#2043C2×C3712yescomplemented
186#1935C2×C3712yescomplemented
187#1933C2×C3712yescomplemented
188#1873C2×C3712yes—
189#1872C2×C3712yes—
190#1750C2×C3711yescharacteristic
191C2×C37—42no—
192C2×C37#259111yescharacteristic
193C2×C37#312311yescharacteristic
194C2×C37#312711yescharacteristic
195C2×C37#313712yes—
196C2×C37#320112yes—
197C2×C4⋊Q8C22×C3711yescharacteristic
198C2×C22⋊Q8C22×C3712yes—
199C2×#117C22×C3711yescharacteristic
200C2×#117C22×C3711yescharacteristic
201C22×C4⋊C4C22×C3711yescharacteristic
202C2×#103C22×C3712yes—
203C2×#103C22×C3712yes—
204C2×#103C22×C3712yes—
205C2×#103C22×C3712yes—
206C2×C22⋊C8C22×C3712yes—
207C2×#97C22×C3711yescharacteristic
208C2×C4×C8C22×C3711yescharacteristic
209#398—22no—
210#397—22no—
211#391C22×C3712yes—
212#389—22no—
213#389C22×C3712yes—
214#389C22×C3712yes—
215#382C22×C3711yescharacteristic
216#380—22no—
217#340C22×C3712yes—
218#340C22×C3712yes—
219#340C22×C3712yes—
220#340C22×C3712yes—
221#336C22×C3712yes—
222C37#2934111yescharacteristic, direct product factor, Sylow
223C22×Q8C23×C3712yes—
224C23×C4—21no—
225C23×C4C23×C3711yescharacteristic
226C22×C8C23×C3712yes—
227C22×C8C23×C3712yes—
228C4⋊Q8—41no—
229C4⋊Q8—41no—
230C22⋊Q8—24no—
231C22⋊Q8—24no—
232#117—41no—
233#117—41no—
234#117—41no—
235#117—41no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4D4×C3712yes—
243C2×C4⋊C4C23×C3712yes—
244C2×C4⋊C4C23×C3712yes—
245C2×C4⋊C4C23×C3712yes—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4D4×C3712yes—
249C2×C42—21no—
250C2×C42C23×C3711yescharacteristic
251C2×C42C23×C3711yescharacteristic
252#103—24no—
253#103—24no—
254#103—42no—
255#103—42no—
256C22⋊C8—24no—
257#97—41no—
258C4×C8—41no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95—24no—
263C24C2×D4×C3711yescharacteristic
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—82no—
279C22×C4C2×D4×C3712yes—
280C22×C4C2×D4×C3712yes—
281C22×C4C2×D4×C3711yescharacteristic
282C22×C4#41×C3714yes—
283C22×C4C24×C3711yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C4⋊C4—24no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—82no—
300C4⋊C4—82no—
301C4⋊C4#41×C3714yes—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—44no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42—42no—
310C23—21no—
311C23—21no—
312C23—22no—
313C23—22no—
314C23#124×C3712yes—
315C23C22×D4×C3711yescharacteristic
316Q8—42no—
317Q8—42no—
318Q8—42no—
319Q8—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—84no—
343C2×C4#124×C3712yes—
344C2×C4C2×#41×C3712yes—
345C2×C4C2×#41×C3712yes—
346C2×C4H(5,𝔽2)×C3711yescharacteristic
347C2×C4H(5,𝔽2)×C3711yescharacteristic
348C8—42no—
349C8—42no—
350C22—24no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—42no—
355C22C37×#52511yescharacteristic
356C22C2×#124×C3711yescharacteristic
357C22C37×#53411yescharacteristic
358C22C37×#57712yes—
359C22C37×#57812yes—
360C4—22no—
361C4—44no—
362C4—42no—
363C4—42no—
364C4—82no—
365C4—82no—
366C4—82no—
367C4C37×#55312yes—
368C4C37×#55312yes—
369C2—42no—
370C2C37×#259111yescharacteristic
371C2C37×#312311yescharacteristic
372C2C37×#312711yescharacteristic
373C2C37×#313712yes—
374C2C37×#320112yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#2101C2semidirect
4. C37×#2043C2semidirect
5. C37×#1935C2semidirect
6. C37×#1933C2semidirect
162. #29341C37direct (N × H)
184. #2101C2×C37semidirect
185. #2043C2×C37semidirect
186. #1935C2×C37semidirect
187. #1933C2×C37semidirect
222. C37#29341direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#26212
C37×#23162
C37×#21012
C37×#20432
C37×#19352
C37×#19332
C37×#18732
C37×#18722
C37×#17502
#2934137