Finite Group Databasebeta

← C37×#29770 #22651023

Subgroups — C37×#29770 #22651023

Order 9472.

958 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#466C211yesmaximal, characteristic
2C22×C4⋊C8×C37C211yesmaximal, characteristic, complemented
3C37×#2854C212yesmaximal, complemented
4C37×#2086C212yesmaximal, complemented
5C37×#2067C214yesmaximal, complemented
6C37×#2054C212yesmaximal, complemented
7C37×#1893C212yesmaximal, complemented
8C37×#1808C211yesmaximal, characteristic, complemented
9C22×D8×C37C2211yescharacteristic
10C23×C8×C37C2211yescharacteristic
11C23×C8×C37C2211yescharacteristic
12C2×#123×C37—22no—
13C2×#121×C37C2212yes—
14C22×C42×C37C2211yescharacteristic
15C37×#466—24no—
16C2×#107×C37C2211yescharacteristic
17C2×#107×C37C2212yes—
18C2×C4⋊C8×C37—24no—
19C2×C4⋊C8×C37C2212yes—
20C2×C4⋊C8×C37C2212yes—
21C2×#102×C37C2212yes—
22C2×#102×C37C2214yes—
23C37×#390C2214yes—
24C37×#389C2214yes—
25C37×#388—24no—
26C37×#386—22no—
27C37×#380C2212yes—
28C37×#340C2214yes—
29C37×#340C2212yes—
30C22×D4×C37—22no—
31C22×D4×C37C2312yes—
32C23×C4×C37D411yescharacteristic
33C23×C4×C37D411yescharacteristic
34C23×C4×C37C2311yescharacteristic
35C2×D8×C37—22no—
36C2×D8×C37—42no—
37C22×C8×C37—22no—
38C22×C8×C37—42no—
39C22×C8×C37—42no—
40C22×C8×C37D414yes—
41C22×C8×C37C2312yes—
42C22×C8×C37C2311yescharacteristic
43C22×C8×C37C2311yescharacteristic
44#123×C37—48no—
45#121×C37—24no—
46#121×C37—24no—
47C2×C4⋊C4×C37—24no—
48C2×C4⋊C4×C37C2312yes—
49C2×C4⋊C4×C37C2314yes—
50C2×C22⋊C4×C37—22no—
51C2×C22⋊C4×C37—22no—
52C2×C22⋊C4×C37—24no—
53C2×C22⋊C4×C37—24no—
54C2×C42×C37—22no—
55C2×C42×C37—22no—
56C2×C42×C37D412yes—
57C2×C42×C37C2312yes—
58#107×C37—22no—
59#107×C37—42no—
60C4⋊C8×C37—24no—
61C4⋊C8×C37—24no—
62#102×C37—24no—
63#102×C37—44no—
64#95×C37—22no—
65#95×C37—24no—
66C24×C37—22no—
67C24×C37C2×D411yescharacteristic
68C2×D4×C37—22no—
69C2×D4×C37—22no—
70C2×D4×C37—24no—
71C2×D4×C37—24no—
72C2×D4×C37—44no—
73C2×D4×C37—44no—
74C2×D4×C37—44no—
75C22×C4×C37—22no—
76C22×C4×C37—22no—
77C22×C4×C37—22no—
78C22×C4×C37—22no—
79C22×C4×C37—22no—
80C22×C4×C37—24no—
81C22×C4×C37—22no—
82C22×C4×C37—42no—
83C22×C4×C37D814yescomplemented
84C22×C4×C37C2×D412yes—
85C22×C4×C37C2×D411yescharacteristic
86C22×C4×C37C2×D412yes—
87C22×C4×C37C2×D412yes—
88C22×C4×C37#4112yes—
89C22×C4×C37C2411yescharacteristic
90D8×C37—44no—
91C2×C8×C37—22no—
92C2×C8×C37—22no—
93C2×C8×C37—22no—
94C2×C8×C37—24no—
95C2×C8×C37—44no—
96C2×C8×C37—44no—
97C2×C8×C37C2×D412yes—
98C2×C8×C37C2×D412yes—
99C4⋊C4×C37—22no—
100C4⋊C4×C37—22no—
101C4⋊C4×C37—24no—
102C4⋊C4×C37—24no—
103C4⋊C4×C37—48no—
104C22⋊C4×C37—48no—
105C22⋊C4×C37—44no—
106C22⋊C4×C37—44no—
107C22⋊C4×C37—48no—
108C42×C37—24no—
109C42×C37—22no—
110C42×C37—22no—
111C23×C37—22no—
112C23×C37—22no—
113C23×C37—42no—
114C23×C37—44no—
115C23×C37—42no—
116C23×C37—42no—
117C23×C37—44no—
118C23×C37#12112yes—
119C23×C37C2×D812yes—
120C23×C37#13512yes—
121C23×C37C22×D411yescharacteristic
122D4×C37—42no—
123D4×C37—42no—
124D4×C37—44no—
125D4×C37—88no—
126C2×C4×C37—22no—
127C2×C4×C37—22no—
128C2×C4×C37—22no—
129C2×C4×C37—28no—
130C2×C4×C37—22no—
131C2×C4×C37—22no—
132C2×C4×C37—24no—
133C2×C4×C37—22no—
134C2×C4×C37—24no—
135C2×C4×C37—44no—
136C2×C4×C37—42no—
137C2×C4×C37—44no—
138C2×C4×C37—44no—
139C2×C4×C37—42no—
140C2×C4×C37—42no—
141C2×C4×C37—44no—
142C2×C4×C37#12112yes—
143C2×C4×C37C2×D814yes—
144C2×C4×C37C22×D411yescharacteristic
145C2×C4×C37C2×#4111yescharacteristic
146C2×C4×C37H(5,𝔽2)12yes—
147C2×C4×C372−1+412yes—
148C8×C37—22no—
149C8×C37—22no—
150C8×C37—42no—
151#29770C3711yesmaximal, characteristic, direct product factor, Sylow
152C22×C37—22no—
153C22×C37—24no—
154C22×C37—24no—
155C22×C37—22no—
156C22×C37—82no—
157C22×C37—84no—
158C22×C37—84no—
159C22×C37—82no—
160C22×C37—82no—
161C22×C37#46614yes—
162C22×C37C2×#12111yescharacteristic
163C22×C37#53712yes—
164C22×C37C22×D811yescharacteristic
165C22×C37C2×#13511yescharacteristic
166C22×C37#57512yes—
167C4×C37—22no—
168C4×C37—24no—
169C4×C37—42no—
170C4×C37—84no—
171C4×C37—82no—
172C4×C37#53411yescharacteristic
173C4×C37#53611yescharacteristic
174C4×C37#53912yes—
175C2×#466C2×C3711yescharacteristic
176C22×C4⋊C8C2×C3711yescharacteristic, complemented
177#2854C2×C3712yescomplemented
178#2086C2×C3712yescomplemented
179#2067C2×C3714yescomplemented
180#2054C2×C3712yescomplemented
181#1893C2×C3712yescomplemented
182#1808C2×C3711yescharacteristic, complemented
183C2×C37—24no—
184C2×C37—162no—
185C2×C37#261811yescharacteristic
186C2×C37C2×#46611yescharacteristic
187C2×C37#305411yescharacteristic
188C2×C37#324512yes—
189C2×C37#325012yes—
190C22×D8C22×C3711yescharacteristic
191C23×C8C22×C3711yescharacteristic
192C23×C8C22×C3711yescharacteristic
193C2×#123—22no—
194C2×#121C22×C3712yes—
195C22×C42C22×C3711yescharacteristic
196#466—24no—
197C2×#107C22×C3711yescharacteristic
198C2×#107C22×C3712yes—
199C2×C4⋊C8—24no—
200C2×C4⋊C8C22×C3712yes—
201C2×C4⋊C8C22×C3712yes—
202C2×#102C22×C3712yes—
203C2×#102C22×C3714yes—
204#390C22×C3714yes—
205#389C22×C3714yes—
206#388—24no—
207#386—22no—
208#380C22×C3712yes—
209#340C22×C3712yes—
210#340C22×C3714yes—
211C37#2977011yescharacteristic, direct product factor, Sylow
212C22×D4—22no—
213C22×D4C23×C3712yes—
214C23×C4D4×C3711yescharacteristic
215C23×C4D4×C3711yescharacteristic
216C23×C4C23×C3711yescharacteristic
217C2×D8—22no—
218C2×D8—42no—
219C22×C8—22no—
220C22×C8—42no—
221C22×C8—42no—
222C22×C8D4×C3714yes—
223C22×C8C23×C3712yes—
224C22×C8C23×C3711yescharacteristic
225C22×C8C23×C3711yescharacteristic
226#123—48no—
227#121—24no—
228#121—24no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4C23×C3712yes—
231C2×C4⋊C4C23×C3714yes—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—24no—
235C2×C22⋊C4—24no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42D4×C3712yes—
239C2×C42C23×C3712yes—
240#107—22no—
241#107—42no—
242C4⋊C8—24no—
243C4⋊C8—24no—
244#102—24no—
245#102—44no—
246#95—22no—
247#95—24no—
248C24—22no—
249C24C2×D4×C3711yescharacteristic
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—24no—
253C2×D4—24no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4D8×C3714yescomplemented
266C22×C4C2×D4×C3712yes—
267C22×C4C2×D4×C3711yescharacteristic
268C22×C4C2×D4×C3712yes—
269C22×C4C2×D4×C3712yes—
270C22×C4#41×C3712yes—
271C22×C4C24×C3711yescharacteristic
272D8—44no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—24no—
277C2×C8—44no—
278C2×C8—44no—
279C2×C8C2×D4×C3712yes—
280C2×C8C2×D4×C3712yes—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—48no—
286C22⋊C4—48no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—48no—
290C42—24no—
291C42—22no—
292C42—22no—
293C23—22no—
294C23—22no—
295C23—42no—
296C23—44no—
297C23—42no—
298C23—42no—
299C23—44no—
300C23#121×C3712yes—
301C23C2×D8×C3712yes—
302C23#135×C3712yes—
303C23C22×D4×C3711yescharacteristic
304D4—42no—
305D4—42no—
306D4—44no—
307D4—88no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—28no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4#121×C3712yes—
325C2×C4C2×D8×C3714yes—
326C2×C4C22×D4×C3711yescharacteristic
327C2×C4C2×#41×C3711yescharacteristic
328C2×C4H(5,𝔽2)×C3712yes—
329C2×C42−1+4×C3712yes—
330C8—22no—
331C8—22no—
332C8—42no—
333C22—22no—
334C22—24no—
335C22—24no—
336C22—22no—
337C22—82no—
338C22—84no—
339C22—84no—
340C22—82no—
341C22—82no—
342C22C37×#46614yes—
343C22C2×#121×C3711yescharacteristic
344C22C37×#53712yes—
345C22C22×D8×C3711yescharacteristic
346C22C2×#135×C3711yescharacteristic
347C22C37×#57512yes—
348C4—22no—
349C4—24no—
350C4—42no—
351C4—84no—
352C4—82no—
353C4C37×#53411yescharacteristic
354C4C37×#53611yescharacteristic
355C4C37×#53912yes—
356C2—24no—
357C2—162no—
358C2C37×#261811yescharacteristic
359C2C2×C37×#46611yescharacteristic
360C2C37×#305411yescharacteristic
361C2C37×#324512yes—
362C2C37×#325012yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C8×C37C2semidirect
3. C37×#2854C2semidirect
4. C37×#2086C2semidirect
5. C37×#2067C2semidirect
6. C37×#2054C2semidirect
7. C37×#1893C2semidirect
8. C37×#1808C2semidirect
83. C22×C4×C37D8semidirect
151. #29770C37direct (N × H)
176. C22×C4⋊C8C2×C37semidirect
177. #2854C2×C37semidirect
178. #2086C2×C37semidirect
179. #2067C2×C37semidirect
180. #2054C2×C37semidirect
181. #1893C2×C37semidirect
182. #1808C2×C37semidirect
211. C37#29770direct (N × H)
265. C22×C4D8×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4662
C22×C4⋊C8×C372
C37×#28542
C37×#20862
C37×#20672
C37×#20542
C37×#18932
C37×#18082
#2977037