Finite Group Databasebeta

← C37×#12254 #22633507

Subgroups — C37×#12254 #22633507

Order 9472.

388 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2742C211yesmaximal, characteristic
2C37×#2062C211yesmaximal, characteristic
3C37×#1614C211yesmaximal, characteristic
4C37×#1602C211yesmaximal, characteristic
5C37×#1352C211yesmaximal, characteristic
6C37×#1351C211yesmaximal, characteristic
7C37×#1326C211yesmaximal, characteristic
8C37×#543C2211yescharacteristic
9C37×#484—21no—
10C37×#451—21no—
11C37×#400—21no—
12C37×#399C2211yescharacteristic
13C37×#395—21no—
14C37×#393C2211yescharacteristic
15C37×#389—21no—
16C37×#388—21no—
17C37×#387—21no—
18C37×#385—21no—
19C37×#385C2211yescharacteristic
20C37×#380—21no—
21C37×#342—21no—
22C37×#342C2211yescharacteristic
23C37×#328—21no—
24C37×#328—21no—
25C37×#323C2211yescharacteristic
26C37×#323C2211yescharacteristic
27C22×Q8×C37D411yescharacteristic
28C23×C4×C37D411yescharacteristic
29C2×Q16×C37—41no—
30C22⋊Q8×C37—21no—
31C22⋊Q8×C37—21no—
32C22⋊Q8×C37—41no—
33C22⋊Q8×C37—41no—
34C2×C4⋊C4×C37—21no—
35C2×C4⋊C4×C37—21no—
36C2×C4⋊C4×C37—21no—
37C2×C4⋊C4×C37—21no—
38C2×C4⋊C4×C37—21no—
39C2×C4⋊C4×C37—41no—
40C2×C4⋊C4×C37D411yescharacteristic
41C2×C22⋊C4×C37—21no—
42C2×C22⋊C4×C37—21no—
43C2×C22⋊C4×C37—21no—
44C2×C22⋊C4×C37—21no—
45C2×C22⋊C4×C37D411yescharacteristic
46C2×C22⋊C4×C37C2311yescharacteristic
47C2×C42×C37—21no—
48#107×C37—41no—
49#103×C37—41no—
50#103×C37—41no—
51C22⋊C8×C37—21no—
52C22⋊C8×C37—21no—
53#95×C37—21no—
54#95×C37—21no—
55#95×C37—21no—
56#95×C37—21no—
57#95×C37—21no—
58#95×C37—21no—
59#95×C37—41no—
60#95×C37D411yescharacteristic
61#95×C37D411yescharacteristic
62C24×C37C2×D411yescharacteristic
63C2×Q8×C37—21no—
64C2×Q8×C37—21no—
65C2×Q8×C37—41no—
66C2×Q8×C37—81no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37—21no—
70C22×C4×C37—21no—
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37—21no—
75C22×C4×C37—42no—
76C22×C4×C37—41no—
77C22×C4×C37—41no—
78C22×C4×C37C2×D411yescharacteristic
79C22×C4×C37C2×D411yescharacteristic
80Q16×C37—82no—
81C2×C8×C37—41no—
82C2×C8×C37—41no—
83C4⋊C4×C37—21no—
84C4⋊C4×C37—21no—
85C4⋊C4×C37—41no—
86C4⋊C4×C37—42no—
87C4⋊C4×C37—42no—
88C4⋊C4×C37—41no—
89C4⋊C4×C37—41no—
90C4⋊C4×C37—81no—
91C4⋊C4×C37—81no—
92C4⋊C4×C37—81no—
93C4⋊C4×C37—82no—
94C22⋊C4×C37—21no—
95C22⋊C4×C37—22no—
96C22⋊C4×C37—41no—
97C22⋊C4×C37—41no—
98C22⋊C4×C37—41no—
99C22⋊C4×C37—41no—
100C22⋊C4×C37—81no—
101C22⋊C4×C37—81no—
102C22⋊C4×C37Q1612yescomplemented
103C42×C37—81no—
104C23×C37—21no—
105C23×C37—21no—
106C23×C37—41no—
107C23×C37—41no—
108C23×C37#12011yescharacteristic
109C23×C37C2×Q1611yescharacteristic
110C23×C37#13711yescharacteristic
111Q8×C37—42no—
112Q8×C37—81no—
113Q8×C37—81no—
114Q8×C37—81no—
115C2×C4×C37—22no—
116C2×C4×C37—22no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—41no—
120C2×C4×C37—41no—
121C2×C4×C37—41no—
122C2×C4×C37—41no—
123C2×C4×C37—41no—
124C2×C4×C37—41no—
125C2×C4×C37—42no—
126C2×C4×C37—41no—
127C2×C4×C37—41no—
128C2×C4×C37—42no—
129C2×C4×C37—41no—
130C2×C4×C37—41no—
131C2×C4×C37—41no—
132C2×C4×C37—41no—
133C2×C4×C37—41no—
134C2×C4×C37—41no—
135C2×C4×C37—41no—
136C2×C4×C37—41no—
137C2×C4×C37—41no—
138C2×C4×C37—41no—
139C2×C4×C37—41no—
140C2×C4×C37—41no—
141C2×C4×C37—81no—
142C2×C4×C37—81no—
143C2×C4×C37—81no—
144C2×C4×C37—81no—
145C2×C4×C37—81no—
146C8×C37—81no—
147C8×C37—81no—
148#12254C3711yesmaximal, characteristic, direct product factor, Sylow
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—81no—
158C22×C37#45111yescharacteristic
159C22×C37#45611yescharacteristic
160C22×C37B(4,𝔽2)11yescharacteristic
161C4×C37—42no—
162C4×C37—41no—
163C4×C37—42no—
164C4×C37—41no—
165C4×C37—81no—
166C4×C37—81no—
167C4×C37—82no—
168C4×C37—81no—
169C4×C37—81no—
170C4×C37—81no—
171C4×C37—81no—
172#2742C2×C3711yescharacteristic
173#2062C2×C3711yescharacteristic
174#1614C2×C3711yescharacteristic
175#1602C2×C3711yescharacteristic
176#1352C2×C3711yescharacteristic
177#1351C2×C3711yescharacteristic
178#1326C2×C3711yescharacteristic
179C2×C37—21no—
180C2×C37—21no—
181C2×C37—41no—
182C2×C37—41no—
183C2×C37#160511yescharacteristic
184C2×C37#219711yescharacteristic
185C2×C37#220011yescharacteristic
186#543C22×C3711yescharacteristic
187#484—21no—
188#451—21no—
189#400—21no—
190#399C22×C3711yescharacteristic
191#395—21no—
192#393C22×C3711yescharacteristic
193#389—21no—
194#388—21no—
195#387—21no—
196#385—21no—
197#385C22×C3711yescharacteristic
198#380—21no—
199#342—21no—
200#342C22×C3711yescharacteristic
201#328—21no—
202#328—21no—
203#323C22×C3711yescharacteristic
204#323C22×C3711yescharacteristic
205C37#1225411yescharacteristic, direct product factor, Sylow
206C22×Q8D4×C3711yescharacteristic
207C23×C4D4×C3711yescharacteristic
208C2×Q16—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8—41no—
212C22⋊Q8—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4D4×C3711yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4D4×C3711yescharacteristic
225C2×C22⋊C4C23×C3711yescharacteristic
226C2×C42—21no—
227#107—41no—
228#103—41no—
229#103—41no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—41no—
239#95D4×C3711yescharacteristic
240#95D4×C3711yescharacteristic
241C24C2×D4×C3711yescharacteristic
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—41no—
245C2×Q8—81no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C3711yescharacteristic
258C22×C4C2×D4×C3711yescharacteristic
259Q16—82no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—82no—
273C22⋊C4—21no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C22⋊C4Q16×C3712yescomplemented
282C42—81no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#120×C3711yescharacteristic
288C23C2×Q16×C3711yescharacteristic
289C23#137×C3711yescharacteristic
290Q8—42no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C8—81no—
326C8—81no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22C37×#45111yescharacteristic
337C22C37×#45611yescharacteristic
338C22C37×B(4,𝔽2)11yescharacteristic
339C4—42no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2C37×#160511yescharacteristic
355C2C37×#219711yescharacteristic
356C2C37×#220011yescharacteristic
subgroupG/H
center, socleC22×C37B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C37
prime radicalC24×C37C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C37 ◁ C2×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
102. C22⋊C4×C37Q16semidirect
148. #12254C37direct (N × H)
205. C37#12254direct (N × H)
281. C22⋊C4Q16×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#27422
C37×#20622
C37×#16142
C37×#16022
C37×#13522
C37×#13512
C37×#13262
#1225437