Finite Group Databasebeta

← C37×#9156 #22630409

Subgroups — C37×#9156 #22630409

Order 9472.

692 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2854C211yesmaximal, characteristic
2C2×C37×#382C211yesmaximal, characteristic, complemented
3C37×#1817C211yesmaximal, characteristic, complemented
4C2×C37×#327C212yesmaximal
5C37×#1294C212yesmaximal, complemented
6C2×#123×C37—21no—
7C2×#121×C37C2211yescharacteristic
8C22×C4⋊C4×C37—21no—
9C22×C42×C37C2211yescharacteristic
10C2×C22⋊C8×C37C2212yes—
11C37×#390C412yescomplemented
12C37×#389C412yescomplemented
13C37×#388—22no—
14C37×#386—21no—
15C37×#382—24no—
16C37×#380C2211yescharacteristic
17C2×#95×C37—21no—
18C2×#95×C37C2212yes—
19C37×#336—22no—
20C37×#327—24no—
21C22×D4×C37—21no—
22C22×D4×C37C2×C411yescharacteristic
23C23×C4×C37—22no—
24C23×C4×C37D411yescharacteristic
25C23×C4×C37D411yescharacteristic
26C23×C4×C37C2311yescharacteristic
27C22×C8×C37—22no—
28#123×C37—42no—
29#123×C37—42no—
30#121×C37—22no—
31#121×C37—22no—
32C2×C4⋊C4×C37—24no—
33C2×C4⋊C4×C37—22no—
34C2×C4⋊C4×C37—42no—
35C2×C4⋊C4×C37—42no—
36C2×C4⋊C4×C37C2×C411yescharacteristic
37C2×C4⋊C4×C37C2×C412yes—
38C2×C22⋊C4×C37—21no—
39C2×C22⋊C4×C37—22no—
40C2×C22⋊C4×C37—22no—
41C2×C22⋊C4×C37—21no—
42C2×C42×C37—22no—
43C2×C42×C37—22no—
44C2×C42×C37C2×C412yes—
45C2×C42×C37D412yes—
46C22⋊C8×C37—22no—
47C22⋊C8×C37—22no—
48#95×C37—24no—
49#95×C37—22no—
50#95×C37—22no—
51#95×C37—21no—
52#95×C37D414yes—
53C24×C37—21no—
54C24×C37C2×D411yescharacteristic
55C2×D4×C37—22no—
56C2×D4×C37—42no—
57C2×D4×C37—41no—
58C2×D4×C37—41no—
59C2×D4×C37—41no—
60C2×D4×C37—41no—
61C2×D4×C37—41no—
62C2×D4×C37—41no—
63C22×C4×C37—21no—
64C22×C4×C37—21no—
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37—22no—
70C22×C4×C37—21no—
71C22×C4×C37—24no—
72C22×C4×C37—42no—
73C22×C4×C37—42no—
74C22×C4×C37—44no—
75C22×C4×C37—44no—
76C22×C4×C37—42no—
77C22×C4×C37—42no—
78C22×C4×C37C22⋊C412yes—
79C22×C4×C37C22⋊C412yes—
80C22×C4×C37D812yes—
81C22×C4×C37SD1612yes—
82C22×C4×C37C22×C411yescharacteristic
83C22×C4×C37C2×D411yescharacteristic
84C22×C4×C37C2×D412yes—
85C22×C4×C37#4112yes—
86C2×C8×C37—44no—
87C2×C8×C37—42no—
88C4⋊C4×C37—22no—
89C4⋊C4×C37—42no—
90C4⋊C4×C37—48no—
91C4⋊C4×C37—44no—
92C22⋊C4×C37—44no—
93C22⋊C4×C37—41no—
94C22⋊C4×C37—41no—
95C22⋊C4×C37—44no—
96C22⋊C4×C37—42no—
97C42×C37—24no—
98C42×C37—24no—
99C23×C37—22no—
100C23×C37—22no—
101C23×C37—41no—
102C23×C37—42no—
103C23×C37—41no—
104C23×C37—41no—
105C23×C37—42no—
106C23×C37C2×C22⋊C411yescharacteristic
107C23×C37#12011yescharacteristic
108C23×C37#12311yescharacteristic
109C23×C37C2×D811yescharacteristic
110C23×C37C2×SD1611yescharacteristic
111C23×C37AGL(1,ℤ/8)11yescharacteristic
112C23×C37#13711yescharacteristic
113D4×C37—82no—
114D4×C37—81no—
115D4×C37—81no—
116D4×C37—81no—
117D4×C37—81no—
118C2×C4×C37—22no—
119C2×C4×C37—22no—
120C2×C4×C37—22no—
121C2×C4×C37—22no—
122C2×C4×C37—22no—
123C2×C4×C37—22no—
124C2×C4×C37—22no—
125C2×C4×C37—22no—
126C2×C4×C37—22no—
127C2×C4×C37—22no—
128C2×C4×C37—22no—
129C2×C4×C37—42no—
130C2×C4×C37—42no—
131C2×C4×C37—42no—
132C2×C4×C37—42no—
133C2×C4×C37—44no—
134C2×C4×C37—44no—
135C2×C4×C37—41no—
136C2×C4×C37—42no—
137C2×C4×C37—42no—
138C2×C4×C37—41no—
139C2×C4×C37—41no—
140C2×C4×C37—42no—
141C2×C4×C37—44no—
142C2×C4×C37—84no—
143C2×C4×C37—84no—
144C2×C4×C37#10214yes—
145C2×C4×C37C4×D412yes—
146C2×C4×C37#12112yes—
147C8×C37—82no—
148#9156C3711yesmaximal, characteristic, direct product factor, Sylow
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—22no—
154C22×C37—22no—
155C22×C37—22no—
156C22×C37—22no—
157C22×C37—81no—
158C22×C37—81no—
159C22×C37—81no—
160C22×C37—82no—
161C22×C37—82no—
162C22×C37#38611yescharacteristic
163C22×C37#41012yes—
164C22×C37C2×#10211yescharacteristic
165C22×C37#41711yescharacteristic
166C22×C37#42112yes—
167C22×C37#44711yescharacteristic
168C22×C37#44811yescharacteristic
169C22×C37#48011yescharacteristic
170C22×C37#48111yescharacteristic
171C4×C37—24no—
172C4×C37—22no—
173C4×C37—22no—
174C4×C37—42no—
175C4×C37—84no—
176C4×C37—81no—
177C4×C37—82no—
178#2854C2×C3711yescharacteristic
179C2×#382C2×C3711yescharacteristic, complemented
180#1817C2×C3711yescharacteristic, complemented
181C2×#327C2×C3712yes—
182#1294C2×C3712yescomplemented
183C2×C37—21no—
184C2×C37—21no—
185C2×C37—21no—
186C2×C37—21no—
187C2×C37—161no—
188C2×C37#151212yes—
189C2×C37#151712yes—
190C2×C37#187411yescharacteristic
191C2×C37#189711yescharacteristic
192C2×C37#189911yescharacteristic
193C2×#123—21no—
194C2×#121C22×C3711yescharacteristic
195C22×C4⋊C4—21no—
196C22×C42C22×C3711yescharacteristic
197C2×C22⋊C8C22×C3712yes—
198#390C4×C3712yescomplemented
199#389C4×C3712yescomplemented
200#388—22no—
201#386—21no—
202#382—24no—
203#380C22×C3711yescharacteristic
204C2×#95—21no—
205C2×#95C22×C3712yes—
206#336—22no—
207#327—24no—
208C37#915611yescharacteristic, direct product factor, Sylow
209C22×D4—21no—
210C22×D4C2×C4×C3711yescharacteristic
211C23×C4—22no—
212C23×C4D4×C3711yescharacteristic
213C23×C4D4×C3711yescharacteristic
214C23×C4C23×C3711yescharacteristic
215C22×C8—22no—
216#123—42no—
217#123—42no—
218#121—22no—
219#121—22no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4C2×C4×C3711yescharacteristic
225C2×C4⋊C4C2×C4×C3712yes—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42C2×C4×C3712yes—
233C2×C42D4×C3712yes—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#95—24no—
237#95—22no—
238#95—22no—
239#95—21no—
240#95D4×C3714yes—
241C24—21no—
242C24C2×D4×C3711yescharacteristic
243C2×D4—22no—
244C2×D4—42no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C4×C3712yes—
267C22×C4C22⋊C4×C3712yes—
268C22×C4D8×C3712yes—
269C22×C4SD16×C3712yes—
270C22×C4C22×C4×C3711yescharacteristic
271C22×C4C2×D4×C3711yescharacteristic
272C22×C4C2×D4×C3712yes—
273C22×C4#41×C3712yes—
274C2×C8—44no—
275C2×C8—42no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—44no—
280C22⋊C4—44no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C42—24no—
286C42—24no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—42no—
291C23—41no—
292C23—41no—
293C23—42no—
294C23C2×C22⋊C4×C3711yescharacteristic
295C23#120×C3711yescharacteristic
296C23#123×C3711yescharacteristic
297C23C2×D8×C3711yescharacteristic
298C23C2×SD16×C3711yescharacteristic
299C23AGL(1,ℤ/8)×C3711yescharacteristic
300C23#137×C3711yescharacteristic
301D4—82no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—84no—
331C2×C4—84no—
332C2×C4#102×C3714yes—
333C2×C4C4×D4×C3712yes—
334C2×C4#121×C3712yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—82no—
348C22—82no—
349C22C37×#38611yescharacteristic
350C22C37×#41012yes—
351C22C2×#102×C3711yescharacteristic
352C22C37×#41711yescharacteristic
353C22C37×#42112yes—
354C22C37×#44711yescharacteristic
355C22C37×#44811yescharacteristic
356C22C37×#48011yescharacteristic
357C22C37×#48111yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—81no—
364C4—82no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—161no—
370C2C37×#151212yes—
371C2C37×#151712yes—
372C2C37×#187411yescharacteristic
373C2C37×#189711yescharacteristic
374C2C37×#189911yescharacteristic
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#382C2semidirect
3. C37×#1817C2semidirect
5. C37×#1294C2semidirect
11. C37×#390C4semidirect
12. C37×#389C4semidirect
148. #9156C37direct (N × H)
179. C2×#382C2×C37semidirect
180. #1817C2×C37semidirect
182. #1294C2×C37semidirect
198. #390C4×C37semidirect
199. #389C4×C37semidirect
208. C37#9156direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#28542
C2×C37×#3822
C37×#18172
C2×C37×#3272
C37×#12942
#915637