Finite Group Databasebeta

← C37×#13580 #22634833

Subgroups — C37×#13580 #22634833

Order 9472.

402 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3152C211yesmaximal, characteristic
2C37×#2132C211yesmaximal, characteristic
3C37×#2126C211yesmaximal, characteristic
4C37×#1407C214yesmaximal, complemented
5C2×#137×C37—21no—
6C2×#137×C37—21no—
7C37×#532C2211yescharacteristic
8C2×C4⋊Q8×C37C411yescharacteristic, complemented
9C37×#497C412yescomplemented
10C37×#497C2212yes—
11C37×#494—21no—
12C37×#492—21no—
13C37×#413—21no—
14C37×#410—21no—
15C4×M16×C37C411yescharacteristic, complemented
16C37×#356—21no—
17C37×#355C2212yes—
18C37×#354C2212yes—
19C37×#353—21no—
20C2×#41×C37D411yescharacteristic
21C2×#41×C37D411yescharacteristic
22C22×Q8×C37—21no—
23#137×C37—42no—
24#137×C37—42no—
25#137×C37—42no—
26#137×C37—42no—
27C2×Q16×C37—22no—
28C2×Q16×C37—22no—
29C2×SD16×C37—22no—
30C2×SD16×C37—22no—
31C2×M16×C37—21no—
32C2×M16×C37—41no—
33C4⋊Q8×C37—21no—
34C4⋊Q8×C37—41no—
35C4⋊Q8×C37C2×C412yes—
36C4⋊Q8×C37D411yescharacteristic
37#127×C37D411yescharacteristic
38#124×C37C2×C411yescharacteristic
39#124×C37C2311yescharacteristic
40#121×C37—41no—
41C4×D4×C37—41no—
42#117×C37—41no—
43C2×C4⋊C4×C37—41no—
44C2×C42×C37C2×C411yescharacteristic
45#101×C37—22no—
46#100×C37—41no—
47#99×C37—22no—
48#99×C37—41no—
49#97×C37C2×C412yes—
50C4×C8×C37—21no—
51#41×C37—41no—
52#41×C37—41no—
53#41×C37—41no—
54#41×C37—41no—
55C2×Q8×C37—22no—
56C2×Q8×C37—41no—
57C2×Q8×C37—41no—
58C2×Q8×C37—41no—
59C2×Q8×C37—41no—
60C2×Q8×C37—41no—
61C2×Q8×C37C22⋊C411yescharacteristic
62C2×Q8×C37C2×D411yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37—21no—
65C2×D4×C37—41no—
66C2×D4×C37C22⋊C411yescharacteristic
67C2×D4×C37C2×D411yescharacteristic
68C22×C4×C37—21no—
69C22×C4×C37—21no—
70C22×C4×C37—21no—
71C22×C4×C37—41no—
72C22×C4×C37C22⋊C411yescharacteristic
73Q16×C37—44no—
74Q16×C37—44no—
75SD16×C37—44no—
76SD16×C37—44no—
77M16×C37—22no—
78M16×C37—22no—
79M16×C37—42no—
80M16×C37—81no—
81C2×C8×C37—22no—
82C2×C8×C37—81no—
83C4⋊C4×C37—41no—
84C4⋊C4×C37—42no—
85C4⋊C4×C37—42no—
86C4⋊C4×C37—81no—
87C22⋊C4×C37—41no—
88C22⋊C4×C37—41no—
89C22⋊C4×C37—42no—
90C42×C37—21no—
91C42×C37—81no—
92C42×C37C22⋊C411yescharacteristic
93C42×C37C22×C411yescharacteristic
94C23×C37—21no—
95C23×C37—21no—
96C23×C37#9911yescharacteristic
97Q8×C37—41no—
98Q8×C37—41no—
99Q8×C37—42no—
100Q8×C37—42no—
101Q8×C37—81no—
102Q8×C37—81no—
103D4×C37—41no—
104D4×C37—41no—
105D4×C37—82no—
106D4×C37—81no—
107D4×C37—81no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—42no—
115C2×C4×C37—41no—
116C2×C4×C37—41no—
117C2×C4×C37—41no—
118C2×C4×C37—41no—
119C2×C4×C37—42no—
120C2×C4×C37—81no—
121C2×C4×C37—81no—
122C2×C4×C37—82no—
123C2×C4×C37#9911yescharacteristic
124C2×C4×C37C2×C22⋊C411yescharacteristic
125C8×C37—24no—
126C8×C37—82no—
127#13580C3711yesmaximal, characteristic, direct product factor, Sylow
128C22×C37—21no—
129C22×C37—41no—
130C22×C37—41no—
131C22×C37—41no—
132C22×C37—81no—
133C22×C37—81no—
134C22×C37C2×#9911yescharacteristic
135C4×C37—22no—
136C4×C37—21no—
137C4×C37—41no—
138C4×C37—41no—
139C4×C37—41no—
140C4×C37—82no—
141C4×C37—162no—
142C4×C37#35311yescharacteristic
143C4×C37#35311yescharacteristic
144#3152C2×C3711yescharacteristic
145#2132C2×C3711yescharacteristic
146#2126C2×C3711yescharacteristic
147#1407C2×C3714yescomplemented
148C2×C37—21no—
149C2×C37—41no—
150C2×C37—81no—
151C2×C37—81no—
152C2×C37C2×#35311yescharacteristic
153C2×#137—21no—
154C2×#137—21no—
155#532C22×C3711yescharacteristic
156C2×C4⋊Q8C4×C3711yescharacteristic, complemented
157#497C4×C3712yescomplemented
158#497C22×C3712yes—
159#494—21no—
160#492—21no—
161#413—21no—
162#410—21no—
163C4×M16C4×C3711yescharacteristic, complemented
164#356—21no—
165#355C22×C3712yes—
166#354C22×C3712yes—
167#353—21no—
168C37#1358011yescharacteristic, direct product factor, Sylow
169C2×#41D4×C3711yescharacteristic
170C2×#41D4×C3711yescharacteristic
171C22×Q8—21no—
172#137—42no—
173#137—42no—
174#137—42no—
175#137—42no—
176C2×Q16—22no—
177C2×Q16—22no—
178C2×SD16—22no—
179C2×SD16—22no—
180C2×M16—21no—
181C2×M16—41no—
182C4⋊Q8—21no—
183C4⋊Q8—41no—
184C4⋊Q8C2×C4×C3712yes—
185C4⋊Q8D4×C3711yescharacteristic
186#127D4×C3711yescharacteristic
187#124C2×C4×C3711yescharacteristic
188#124C23×C3711yescharacteristic
189#121—41no—
190C4×D4—41no—
191#117—41no—
192C2×C4⋊C4—41no—
193C2×C42C2×C4×C3711yescharacteristic
194#101—22no—
195#100—41no—
196#99—22no—
197#99—41no—
198#97C2×C4×C3712yes—
199C4×C8—21no—
200#41—41no—
201#41—41no—
202#41—41no—
203#41—41no—
204C2×Q8—22no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8C22⋊C4×C3711yescharacteristic
211C2×Q8C2×D4×C3711yescharacteristic
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—41no—
215C2×D4C22⋊C4×C3711yescharacteristic
216C2×D4C2×D4×C3711yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4C22⋊C4×C3711yescharacteristic
222Q16—44no—
223Q16—44no—
224SD16—44no—
225SD16—44no—
226M16—22no—
227M16—22no—
228M16—42no—
229M16—81no—
230C2×C8—22no—
231C2×C8—81no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—81no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C42—21no—
240C42—81no—
241C42C22⋊C4×C3711yescharacteristic
242C42C22×C4×C3711yescharacteristic
243C23—21no—
244C23—21no—
245C23#99×C3711yescharacteristic
246Q8—41no—
247Q8—41no—
248Q8—42no—
249Q8—42no—
250Q8—81no—
251Q8—81no—
252D4—41no—
253D4—41no—
254D4—82no—
255D4—81no—
256D4—81no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—82no—
272C2×C4#99×C3711yescharacteristic
273C2×C4C2×C22⋊C4×C3711yescharacteristic
274C8—24no—
275C8—82no—
276C22—21no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22—81no—
282C22C2×#99×C3711yescharacteristic
283C4—22no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—82no—
289C4—162no—
290C4C37×#35311yescharacteristic
291C4C37×#35311yescharacteristic
292C2—21no—
293C2—41no—
294C2—81no—
295C2—81no—
296C2C2×C37×#35311yescharacteristic
subgroupG/H
center, socleC2×C37C2×#353
commutatorC42C22×C4×C37
Frattini, cosocle#124C23×C37
prime radicalC37×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C22×C4×C37 ◁ C37×#532 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1407C2semidirect
8. C2×C4⋊Q8×C37C4semidirect
9. C37×#497C4semidirect
15. C4×M16×C37C4semidirect
127. #13580C37direct (N × H)
147. #1407C2×C37semidirect
156. C2×C4⋊Q8C4×C37semidirect
157. #497C4×C37semidirect
163. C4×M16C4×C37semidirect
168. C37#13580direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31522
C37×#21322
C37×#21262
C37×#14072
#1358037