Finite Group Databasebeta

← C37×#10224 #22631477

Subgroups — C37×#10224 #22631477

Order 9472.

462 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3230C211yesmaximal, characteristic
2C37×#3209C211yesmaximal, characteristic
3C37×#3162C211yesmaximal, characteristic
4C37×#1993C211yesmaximal, characteristic
5C37×#1518C211yesmaximal, characteristic
6C37×#1518C211yesmaximal, characteristic
7C37×#1281C211yesmaximal, characteristic
8C37×#533C2211yescharacteristic
9C37×#533C2211yescharacteristic
10C2×C4⋊Q8×C37C2211yescharacteristic
11C37×#501—21no—
12C37×#501—21no—
13C37×#501—21no—
14C37×#501—21no—
15C37×#500—21no—
16C37×#494—21no—
17C37×#487—21no—
18C37×#487—21no—
19C37×#484—22no—
20C37×#477—22no—
21C37×#462—22no—
22C37×#451—22no—
23C37×#431C2211yescharacteristic
24C37×#431C2211yescharacteristic
25C37×#427—22no—
26C2×#97×C37C2211yescharacteristic
27C37×#382C2211yescharacteristic
28C37×#340—22no—
29C37×#328—22no—
30C37×#328—22no—
31C22×Q8×C37—21no—
32C2×Q16×C37—24no—
33C22×C8×C37D412yes—
34C4⋊Q8×C37—21no—
35C4⋊Q8×C37—21no—
36C4⋊Q8×C37—21no—
37C4⋊Q8×C37D412yes—
38C4⋊Q8×C37D411yescharacteristic
39C4⋊Q8×C37D411yescharacteristic
40C4⋊Q8×C37D411yescharacteristic
41C4⋊Q8×C37D411yescharacteristic
42#125×C37—21no—
43#125×C37—21no—
44C22⋊Q8×C37—21no—
45C22⋊Q8×C37—21no—
46C22⋊Q8×C37—21no—
47C22⋊Q8×C37—21no—
48C4×Q8×C37—21no—
49C4×Q8×C37—21no—
50C4×Q8×C37—21no—
51C4×Q8×C37—21no—
52#117×C37—21no—
53#117×C37—21no—
54C2×C4⋊C4×C37—21no—
55C2×C4⋊C4×C37—21no—
56C2×C4⋊C4×C37—21no—
57C2×C42×C37C2311yescharacteristic
58#107×C37—22no—
59#107×C37—22no—
60#107×C37—24no—
61#106×C37—22no—
62#106×C37—22no—
63C4⋊C8×C37—21no—
64C4⋊C8×C37—21no—
65#103×C37—24no—
66#103×C37—24no—
67C22⋊C8×C37D412yes—
68C22⋊C8×C37D412yes—
69#97×C37—21no—
70#97×C37—21no—
71C4×C8×C37—21no—
72C4×C8×C37—21no—
73#95×C37—21no—
74#95×C37—21no—
75C2×Q8×C37—21no—
76C2×Q8×C37—22no—
77C2×Q8×C37—21no—
78C2×Q8×C37—21no—
79C2×Q8×C37—21no—
80C2×Q8×C37—41no—
81C2×Q8×C37—82no—
82C22×C4×C37—41no—
83C22×C4×C37—41no—
84C22×C4×C37C2×D411yescharacteristic
85C22×C4×C37C2×D411yescharacteristic
86C22×C4×C37C2×D411yescharacteristic
87Q16×C37—84no—
88C2×C8×C37—22no—
89C2×C8×C37—22no—
90C2×C8×C37—22no—
91C2×C8×C37—22no—
92C2×C8×C37Q1614yescomplemented
93C4⋊C4×C37—21no—
94C4⋊C4×C37—22no—
95C4⋊C4×C37—21no—
96C4⋊C4×C37—21no—
97C4⋊C4×C37—21no—
98C4⋊C4×C37—21no—
99C4⋊C4×C37—21no—
100C4⋊C4×C37—22no—
101C4⋊C4×C37—21no—
102C4⋊C4×C37—21no—
103C4⋊C4×C37—41no—
104C4⋊C4×C37—41no—
105C4⋊C4×C37—41no—
106C4⋊C4×C37—41no—
107C4⋊C4×C37—41no—
108C4⋊C4×C37—41no—
109C4⋊C4×C37—42no—
110C22⋊C4×C37—41no—
111C22⋊C4×C37—41no—
112C42×C37—41no—
113C42×C37—41no—
114C42×C37C2×D411yescharacteristic
115C42×C37C2×D411yescharacteristic
116C42×C37C2×D411yescharacteristic
117C42×C37#4111yescharacteristic
118C23×C37#12711yescharacteristic
119Q8×C37—42no—
120Q8×C37—44no—
121Q8×C37—42no—
122Q8×C37—81no—
123Q8×C37—81no—
124Q8×C37—82no—
125C2×C4×C37—41no—
126C2×C4×C37—41no—
127C2×C4×C37—41no—
128C2×C4×C37—41no—
129C2×C4×C37—41no—
130C2×C4×C37—41no—
131C2×C4×C37—42no—
132C2×C4×C37—82no—
133C2×C4×C37—81no—
134C2×C4×C37—81no—
135C2×C4×C37—81no—
136C2×C4×C37#12011yescharacteristic
137C2×C4×C37#12011yescharacteristic
138C2×C4×C37#12011yescharacteristic
139C2×C4×C37#12111yescharacteristic
140C2×C4×C37#12111yescharacteristic
141C2×C4×C37#12111yescharacteristic
142C2×C4×C37C2×Q1612yes—
143C2×C4×C37#13712yes—
144C8×C37—24no—
145C8×C37—42no—
146C8×C37—42no—
147#10224C3711yesmaximal, characteristic, direct product factor, Sylow
148C22×C37—21no—
149C22×C37—21no—
150C22×C37#39211yescharacteristic
151C22×C37#49411yescharacteristic
152C22×C37#49711yescharacteristic
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—82no—
158C4×C37—81no—
159C4×C37—81no—
160C4×C37—81no—
161C4×C37—81no—
162C4×C37—161no—
163C4×C37#45112yes—
164C4×C37#46212yes—
165#3230C2×C3711yescharacteristic
166#3209C2×C3711yescharacteristic
167#3162C2×C3711yescharacteristic
168#1993C2×C3711yescharacteristic
169#1518C2×C3711yescharacteristic
170#1518C2×C3711yescharacteristic
171#1281C2×C3711yescharacteristic
172C2×C37—21no—
173C2×C37—21no—
174C2×C37#200811yescharacteristic
175C2×C37#200911yescharacteristic
176C2×C37#201611yescharacteristic
177#533C22×C3711yescharacteristic
178#533C22×C3711yescharacteristic
179C2×C4⋊Q8C22×C3711yescharacteristic
180#501—21no—
181#501—21no—
182#501—21no—
183#501—21no—
184#500—21no—
185#494—21no—
186#487—21no—
187#487—21no—
188#484—22no—
189#477—22no—
190#462—22no—
191#451—22no—
192#431C22×C3711yescharacteristic
193#431C22×C3711yescharacteristic
194#427—22no—
195C2×#97C22×C3711yescharacteristic
196#382C22×C3711yescharacteristic
197#340—22no—
198#328—22no—
199#328—22no—
200C37#1022411yescharacteristic, direct product factor, Sylow
201C22×Q8—21no—
202C2×Q16—24no—
203C22×C8D4×C3712yes—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8D4×C3712yes—
208C4⋊Q8D4×C3711yescharacteristic
209C4⋊Q8D4×C3711yescharacteristic
210C4⋊Q8D4×C3711yescharacteristic
211C4⋊Q8D4×C3711yescharacteristic
212#125—21no—
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C23×C3711yescharacteristic
228#107—22no—
229#107—22no—
230#107—24no—
231#106—22no—
232#106—22no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—24no—
236#103—24no—
237C22⋊C8D4×C3712yes—
238C22⋊C8D4×C3712yes—
239#97—21no—
240#97—21no—
241C4×C8—21no—
242C4×C8—21no—
243#95—21no—
244#95—21no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—82no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C3711yescharacteristic
255C22×C4C2×D4×C3711yescharacteristic
256C22×C4C2×D4×C3711yescharacteristic
257Q16—84no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8Q16×C3714yescomplemented
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42C2×D4×C3711yescharacteristic
285C42C2×D4×C3711yescharacteristic
286C42C2×D4×C3711yescharacteristic
287C42#41×C3711yescharacteristic
288C23#127×C3711yescharacteristic
289Q8—42no—
290Q8—44no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—82no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4#120×C3711yescharacteristic
307C2×C4#120×C3711yescharacteristic
308C2×C4#120×C3711yescharacteristic
309C2×C4#121×C3711yescharacteristic
310C2×C4#121×C3711yescharacteristic
311C2×C4#121×C3711yescharacteristic
312C2×C4C2×Q16×C3712yes—
313C2×C4#137×C3712yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22—21no—
318C22—21no—
319C22C37×#39211yescharacteristic
320C22C37×#49411yescharacteristic
321C22C37×#49711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4C37×#45112yes—
333C4C37×#46212yes—
334C2—21no—
335C2—21no—
336C2C37×#200811yescharacteristic
337C2C37×#200911yescharacteristic
338C2C37×#201611yescharacteristic
subgroupG/H
center, socleC22×C37#392
commutator, Frattini, cosocleC2×C42C23×C37
prime radicalC23×C37#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
92. C2×C8×C37Q16semidirect
147. #10224C37direct (N × H)
200. C37#10224direct (N × H)
262. C2×C8Q16×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#32302
C37×#32092
C37×#31622
C37×#19932
C37×#15182
C37×#12812
#1022437