Finite Group Databasebeta

← C37×#28459 #22649712

Subgroups — C37×#28459 #22649712

Order 9472.

1126 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#495C212yesmaximal
2C2×C37×#494C211yesmaximal, characteristic, complemented
3C2×C37×#461C212yesmaximal, complemented
4C2×C4×D8×C37C211yesmaximal, characteristic
5C37×#2547C212yesmaximal, complemented
6C37×#2015C214yesmaximal, complemented
7C37×#1969C212yesmaximal, complemented
8C8×C4⋊C4×C37C211yesmaximal, characteristic, complemented
9C22×Q16×C37C2212yes—
10C22×Q16×C37C2212yes—
11C22×SD16×C37C2214yes—
12C22×D8×C37C2211yescharacteristic
13C2×C4⋊Q8×C37C2212yes—
14C2×#124×C37C2214yes—
15C2×C4×D4×C37C2212yes—
16C37×#495—28no—
17C37×#494—24no—
18C37×#461—28no—
19C4×D8×C37—24no—
20C2×#107×C37C2211yescharacteristic
21C2×C4⋊C8×C37C2211yescharacteristic
22C2×#103×C37C2214yes—
23C2×#102×C37C2212yes—
24C2×C4×C8×C37C2212yes—
25C2×C4×C8×C37C2211yescharacteristic
26C37×#397—24no—
27C37×#391C2214yes—
28C37×#380—24no—
29C4×C4⋊C4×C37C2211yescharacteristic
30C37×#336C2212yes—
31C22×Q8×C37C2314yes—
32C22×D4×C37C2312yes—
33C23×C4×C37—22no—
34C2×Q16×C37—24no—
35C2×Q16×C37—24no—
36C2×Q16×C37—24no—
37C2×Q16×C37—24no—
38C2×Q16×C37—42no—
39C2×Q16×C37—42no—
40C2×SD16×C37—28no—
41C2×SD16×C37—28no—
42C2×SD16×C37—44no—
43C2×D8×C37—22no—
44C2×D8×C37—22no—
45C2×D8×C37D414yes—
46C22×C8×C37C2312yes—
47C22×C8×C37C2311yescharacteristic
48C22×C8×C37C2311yescharacteristic
49C4⋊Q8×C37—24no—
50C4⋊Q8×C37—24no—
51#124×C37—28no—
52#124×C37—44no—
53C4×D4×C37—24no—
54C4×D4×C37—24no—
55C2×C4⋊C4×C37—22no—
56C2×C4⋊C4×C37—22no—
57C2×C4⋊C4×C37D412yes—
58C2×C4⋊C4×C37C2312yes—
59C2×C22⋊C4×C37—28no—
60C2×C22⋊C4×C37—22no—
61C2×C42×C37C2312yes—
62C2×C42×C37C2311yescharacteristic
63#107×C37—22no—
64C4⋊C8×C37D414yes—
65#103×C37—28no—
66#102×C37—24no—
67C4×C8×C37—24no—
68C4×C8×C37D414yes—
69#95×C37—28no—
70#95×C37D412yes—
71C24×C37—22no—
72C2×Q8×C37—24no—
73C2×Q8×C37—24no—
74C2×Q8×C37—24no—
75C2×Q8×C37—24no—
76C2×Q8×C37—24no—
77C2×Q8×C37—24no—
78C2×D4×C37—22no—
79C2×D4×C37—22no—
80C2×D4×C37—22no—
81C2×D4×C37—22no—
82C2×D4×C37—22no—
83C2×D4×C37C2×D414yes—
84C22×C4×C37—22no—
85C22×C4×C37—24no—
86C22×C4×C37—44no—
87C22×C4×C37—48no—
88C22×C4×C37C2×D414yes—
89C22×C4×C37C2×D411yescharacteristic
90C22×C4×C37C2×D411yescharacteristic
91C22×C4×C37C2411yescharacteristic
92Q16×C37—48no—
93Q16×C37—48no—
94SD16×C37—416no—
95D8×C37—28no—
96C2×C8×C37—22no—
97C2×C8×C37—22no—
98C2×C8×C37—21no—
99C2×C8×C37—21no—
100C2×C8×C37C2×D412yes—
101C2×C8×C37C2×D414yes—
102C2×C8×C37C2×D412yes—
103C2×C8×C37C2×D412yes—
104C2×C8×C37#4112yes—
105C4⋊C4×C37—24no—
106C4⋊C4×C37—22no—
107C4⋊C4×C37—22no—
108C4⋊C4×C37—44no—
109C4⋊C4×C37—44no—
110C22⋊C4×C37—416no—
111C22⋊C4×C37—44no—
112C42×C37—22no—
113C42×C37—22no—
114C42×C37C2×D412yes—
115C42×C37C2×D412yes—
116C23×C37—24no—
117C23×C37—42no—
118C23×C37—42no—
119C23×C37—44no—
120C23×C37—44no—
121C23×C37C22×D411yescharacteristic
122Q8×C37—44no—
123Q8×C37—44no—
124Q8×C37—44no—
125Q8×C37—44no—
126D4×C37—24no—
127D4×C37—24no—
128D4×C37—42no—
129D4×C37—42no—
130C2×C4×C37—22no—
131C2×C4×C37—24no—
132C2×C4×C37—24no—
133C2×C4×C37—24no—
134C2×C4×C37—42no—
135C2×C4×C37—44no—
136C2×C4×C37—44no—
137C2×C4×C37—44no—
138C2×C4×C37—44no—
139C2×C4×C37—88no—
140C2×C4×C37#12712yes—
141C2×C4×C37#12712yes—
142C2×C4×C37#13514yes—
143C2×C4×C37C22×D411yescharacteristic
144C2×C4×C37C22×D411yescharacteristic
145C2×C4×C37C22×D411yescharacteristic
146C2×C4×C37C2×#4111yescharacteristic
147C2×C4×C37H(5,𝔽2)11yescharacteristic
148C2×C4×C37H(5,𝔽2)11yescharacteristic
149C8×C37—22no—
150C8×C37—24no—
151C8×C37#12114yes—
152#28459C3711yesmaximal, characteristic, direct product factor, Sylow
153C22×C37—48no—
154C22×C37—44no—
155C22×C37—84no—
156C22×C37—82no—
157C22×C37—82no—
158C22×C37C2×#12711yescharacteristic
159C22×C37D4211yescharacteristic
160C22×C37#55011yescharacteristic
161C22×C37C2×#13512yes—
162C22×C37#57812yes—
163C4×C37—22no—
164C4×C37—44no—
165C4×C37—82no—
166C4×C37—84no—
167C4×C37#49514yescomplemented
168C4×C37C2×#12111yescharacteristic
169C4×C37#53511yescharacteristic
170C4×C37D4211yescharacteristic
171C4×C37#55011yescharacteristic
172C2×#495C2×C3712yes—
173C2×#494C2×C3711yescharacteristic, complemented
174C2×#461C2×C3712yescomplemented
175C2×C4×D8C2×C3711yescharacteristic
176#2547C2×C3712yescomplemented
177#2015C2×C3714yescomplemented
178#1969C2×C3712yescomplemented
179C8×C4⋊C4C2×C3711yescharacteristic, complemented
180C2×C37—84no—
181C2×C37#254111yescharacteristic
182C2×C37C2×#49511yescharacteristic
183C2×C37#315611yescharacteristic
184C2×C37#328312yes—
185C2×C37#339312yes—
186C22×Q16C22×C3712yes—
187C22×Q16C22×C3712yes—
188C22×SD16C22×C3714yes—
189C22×D8C22×C3711yescharacteristic
190C2×C4⋊Q8C22×C3712yes—
191C2×#124C22×C3714yes—
192C2×C4×D4C22×C3712yes—
193#495—28no—
194#494—24no—
195#461—28no—
196C4×D8—24no—
197C2×#107C22×C3711yescharacteristic
198C2×C4⋊C8C22×C3711yescharacteristic
199C2×#103C22×C3714yes—
200C2×#102C22×C3712yes—
201C2×C4×C8C22×C3712yes—
202C2×C4×C8C22×C3711yescharacteristic
203#397—24no—
204#391C22×C3714yes—
205#380—24no—
206C4×C4⋊C4C22×C3711yescharacteristic
207#336C22×C3712yes—
208C37#2845911yescharacteristic, direct product factor, Sylow
209C22×Q8C23×C3714yes—
210C22×D4C23×C3712yes—
211C23×C4—22no—
212C2×Q16—24no—
213C2×Q16—24no—
214C2×Q16—24no—
215C2×Q16—24no—
216C2×Q16—42no—
217C2×Q16—42no—
218C2×SD16—28no—
219C2×SD16—28no—
220C2×SD16—44no—
221C2×D8—22no—
222C2×D8—22no—
223C2×D8D4×C3714yes—
224C22×C8C23×C3712yes—
225C22×C8C23×C3711yescharacteristic
226C22×C8C23×C3711yescharacteristic
227C4⋊Q8—24no—
228C4⋊Q8—24no—
229#124—28no—
230#124—44no—
231C4×D4—24no—
232C4×D4—24no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4D4×C3712yes—
236C2×C4⋊C4C23×C3712yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—28no—
239C2×C42C23×C3712yes—
240C2×C42C23×C3711yescharacteristic
241#107—22no—
242C4⋊C8D4×C3714yes—
243#103—28no—
244#102—24no—
245C4×C8—24no—
246C4×C8D4×C3714yes—
247#95—28no—
248#95D4×C3712yes—
249C24—22no—
250C2×Q8—24no—
251C2×Q8—24no—
252C2×Q8—24no—
253C2×Q8—24no—
254C2×Q8—24no—
255C2×Q8—24no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4C2×D4×C3714yes—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—44no—
265C22×C4—48no—
266C22×C4C2×D4×C3714yes—
267C22×C4C2×D4×C3711yescharacteristic
268C22×C4C2×D4×C3711yescharacteristic
269C22×C4C24×C3711yescharacteristic
270Q16—48no—
271Q16—48no—
272SD16—416no—
273D8—28no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8C2×D4×C3712yes—
279C2×C8C2×D4×C3714yes—
280C2×C8C2×D4×C3712yes—
281C2×C8C2×D4×C3712yes—
282C2×C8#41×C3712yes—
283C4⋊C4—24no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—44no—
287C4⋊C4—44no—
288C22⋊C4—416no—
289C22⋊C4—44no—
290C42—22no—
291C42—22no—
292C42C2×D4×C3712yes—
293C42C2×D4×C3712yes—
294C23—24no—
295C23—42no—
296C23—42no—
297C23—44no—
298C23—44no—
299C23C22×D4×C3711yescharacteristic
300Q8—44no—
301Q8—44no—
302Q8—44no—
303Q8—44no—
304D4—24no—
305D4—24no—
306D4—42no—
307D4—42no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—88no—
318C2×C4#127×C3712yes—
319C2×C4#127×C3712yes—
320C2×C4#135×C3714yes—
321C2×C4C22×D4×C3711yescharacteristic
322C2×C4C22×D4×C3711yescharacteristic
323C2×C4C22×D4×C3711yescharacteristic
324C2×C4C2×#41×C3711yescharacteristic
325C2×C4H(5,𝔽2)×C3711yescharacteristic
326C2×C4H(5,𝔽2)×C3711yescharacteristic
327C8—22no—
328C8—24no—
329C8#121×C3714yes—
330C22—48no—
331C22—44no—
332C22—84no—
333C22—82no—
334C22—82no—
335C22C2×#127×C3711yescharacteristic
336C22D42×C3711yescharacteristic
337C22C37×#55011yescharacteristic
338C22C2×#135×C3712yes—
339C22C37×#57812yes—
340C4—22no—
341C4—44no—
342C4—82no—
343C4—84no—
344C4C37×#49514yescomplemented
345C4C2×#121×C3711yescharacteristic
346C4C37×#53511yescharacteristic
347C4D42×C3711yescharacteristic
348C4C37×#55011yescharacteristic
349C2—84no—
350C2C37×#254111yescharacteristic
351C2C2×C37×#49511yescharacteristic
352C2C37×#315611yescharacteristic
353C2C37×#328312yes—
354C2C37×#339312yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×D8×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C4⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#494C2semidirect
3. C2×C37×#461C2semidirect
5. C37×#2547C2semidirect
6. C37×#2015C2semidirect
7. C37×#1969C2semidirect
8. C8×C4⋊C4×C37C2semidirect
152. #28459C37direct (N × H)
167. C4×C37#495semidirect
173. C2×#494C2×C37semidirect
174. C2×#461C2×C37semidirect
176. #2547C2×C37semidirect
177. #2015C2×C37semidirect
178. #1969C2×C37semidirect
179. C8×C4⋊C4C2×C37semidirect
208. C37#28459direct (N × H)
344. C4C37×#495semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4952
C2×C37×#4942
C2×C37×#4612
C2×C4×D8×C372
C37×#25472
C37×#20152
C37×#19692
C8×C4⋊C4×C372
#2845937