Finite Group Databasebeta

← C37×#9182 #22630435

Subgroups — C37×#9182 #22630435

Order 9472.

500 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3037C211yesmaximal, characteristic
2C37×#2356C211yesmaximal, characteristic, complemented
3C37×#1517C211yesmaximal, characteristic
4C37×#1502C211yesmaximal, characteristic
5C37×#1479C211yesmaximal, characteristic, complemented
6C37×#1303C211yesmaximal, characteristic, complemented
7C37×#1286C211yesmaximal, characteristic, complemented
8C2×#137×C37—21no—
9C37×#532C2211yescharacteristic
10C2×C4×Q8×C37C2211yescharacteristic
11C37×#464—22no—
12C37×#462C412yescomplemented
13C37×#460C412yescomplemented
14C37×#431C2211yescharacteristic
15C37×#431C2211yescharacteristic
16C37×#423C2211yescharacteristic
17C37×#417—21no—
18C37×#391—21no—
19C37×#387—22no—
20C37×#383—21no—
21C37×#382C2211yescharacteristic
22C4×C4⋊C4×C37—21no—
23C4×C4⋊C4×C37C2211yescharacteristic
24C37×#376—21no—
25C37×#327—21no—
26C37×#327—21no—
27C37×#327—22no—
28C37×Q8⋊C8—22no—
29C2×#41×C37—21no—
30C22×Q8×C37D411yescharacteristic
31#137×C37—42no—
32#137×C37—42no—
33C2×Q16×C37—22no—
34C2×SD16×C37—22no—
35C2×M16×C37—21no—
36C4⋊Q8×C37C2×C411yescharacteristic
37#127×C37C2×C411yescharacteristic
38#124×C37—21no—
39#121×C37—21no—
40#121×C37—21no—
41C4×Q8×C37—21no—
42C4×Q8×C37—21no—
43C4×Q8×C37C2×C412yes—
44C4×Q8×C37D412yes—
45C4×D4×C37—21no—
46C4×D4×C37—21no—
47C2×C4⋊C4×C37—21no—
48C2×C4⋊C4×C37—21no—
49C2×C4⋊C4×C37—21no—
50C2×C4⋊C4×C37D411yescharacteristic
51C2×C42×C37—21no—
52C2×C42×C37—22no—
53C2×C42×C37—21no—
54C2×C42×C37C2311yescharacteristic
55C4⋊C8×C37—21no—
56C4⋊C8×C37—21no—
57C4⋊C8×C37—21no—
58C4⋊C8×C37C2×C412yes—
59#103×C37—22no—
60#102×C37—22no—
61C22⋊C8×C37—21no—
62C22⋊C8×C37—21no—
63C4×C8×C37—21no—
64C4×C8×C37—21no—
65#95×C37—22no—
66#95×C37—22no—
67#95×C37—22no—
68#95×C37—21no—
69#95×C37D411yescharacteristic
70#95×C37D411yescharacteristic
71#95×C37D412yes—
72#41×C37—41no—
73#41×C37—41no—
74#41×C37—41no—
75#41×C37—41no—
76C2×Q8×C37—21no—
77C2×Q8×C37—21no—
78C2×Q8×C37—21no—
79C2×Q8×C37—21no—
80C2×Q8×C37—21no—
81C2×Q8×C37—21no—
82C2×Q8×C37C22⋊C412yes—
83C2×D4×C37—21no—
84C2×D4×C37—21no—
85C2×D4×C37—21no—
86C2×D4×C37—41no—
87C22×C4×C37—21no—
88C22×C4×C37—21no—
89C22×C4×C37—21no—
90C22×C4×C37—22no—
91C22×C4×C37—21no—
92C22×C4×C37—41no—
93C22×C4×C37C2×D411yescharacteristic
94C22×C4×C37C2×D411yescharacteristic
95C22×C4×C37C2×D411yescharacteristic
96Q16×C37—44no—
97SD16×C37—44no—
98M16×C37—41no—
99M16×C37—41no—
100C2×C8×C37—22no—
101C2×C8×C37—41no—
102C2×C8×C37—41no—
103C4⋊C4×C37—22no—
104C4⋊C4×C37—22no—
105C4⋊C4×C37—21no—
106C4⋊C4×C37—21no—
107C4⋊C4×C37—21no—
108C4⋊C4×C37—42no—
109C4⋊C4×C37—41no—
110C4⋊C4×C37—41no—
111C4⋊C4×C37C22⋊C412yes—
112C22⋊C4×C37—41no—
113C22⋊C4×C37—41no—
114C42×C37—22no—
115C42×C37—22no—
116C42×C37—44no—
117C42×C37—41no—
118C42×C37—41no—
119C42×C37C22×C411yescharacteristic
120C42×C37C2×D411yescharacteristic
121C42×C37#4111yescharacteristic
122C42×C37#4111yescharacteristic
123C23×C37—41no—
124C23×C37#12011yescharacteristic
125Q8×C37—22no—
126Q8×C37—22no—
127Q8×C37—41no—
128Q8×C37—41no—
129Q8×C37—41no—
130Q8×C37—41no—
131D4×C37—41no—
132D4×C37—41no—
133D4×C37—81no—
134D4×C37—81no—
135D4×C37—81no—
136D4×C37—81no—
137C2×C4×C37—22no—
138C2×C4×C37—22no—
139C2×C4×C37—22no—
140C2×C4×C37—41no—
141C2×C4×C37—41no—
142C2×C4×C37—42no—
143C2×C4×C37—41no—
144C2×C4×C37—41no—
145C2×C4×C37—41no—
146C2×C4×C37—41no—
147C2×C4×C37—42no—
148C2×C4×C37—41no—
149C2×C4×C37—41no—
150C2×C4×C37—42no—
151C2×C4×C37—41no—
152C2×C4×C37—41no—
153C2×C4×C37—42no—
154C2×C4×C37—81no—
155C2×C4×C37—81no—
156C2×C4×C37C2×C22⋊C411yescharacteristic
157C2×C4×C37C4×D411yescharacteristic
158C2×C4×C37C4×D411yescharacteristic
159C2×C4×C37#12111yescharacteristic
160C2×C4×C37#12111yescharacteristic
161C2×C4×C37#12311yescharacteristic
162C2×C4×C37#13511yescharacteristic
163C2×C4×C37#13511yescharacteristic
164C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
166C8×C37—42no—
167C8×C37—81no—
168C8×C37—81no—
169#9182C3711yesmaximal, characteristic, direct product factor, Sylow
170C22×C37—21no—
171C22×C37—21no—
172C22×C37—81no—
173C22×C37—81no—
174C22×C37—81no—
175C22×C37#38611yescharacteristic
176C22×C37#44911yescharacteristic
177C22×C37#44911yescharacteristic
178C4×C37—21no—
179C4×C37—21no—
180C4×C37—21no—
181C4×C37—21no—
182C4×C37—42no—
183C4×C37—42no—
184C4×C37—42no—
185C4×C37—81no—
186C4×C37—82no—
187C4×C37—81no—
188C4×C37#41611yescharacteristic
189C4×C37#41811yescharacteristic
190C4×C37#48211yescharacteristic
191C4×C37#48211yescharacteristic
192#3037C2×C3711yescharacteristic
193#2356C2×C3711yescharacteristic, complemented
194#1517C2×C3711yescharacteristic
195#1502C2×C3711yescharacteristic
196#1479C2×C3711yescharacteristic, complemented
197#1303C2×C3711yescharacteristic, complemented
198#1286C2×C3711yescharacteristic, complemented
199C2×C37—21no—
200C2×C37—21no—
201C2×C37—161no—
202C2×C37#187511yescharacteristic
203C2×C37#190511yescharacteristic
204C2×C37#190611yescharacteristic
205C2×#137—21no—
206#532C22×C3711yescharacteristic
207C2×C4×Q8C22×C3711yescharacteristic
208#464—22no—
209#462C4×C3712yescomplemented
210#460C4×C3712yescomplemented
211#431C22×C3711yescharacteristic
212#431C22×C3711yescharacteristic
213#423C22×C3711yescharacteristic
214#417—21no—
215#391—21no—
216#387—22no—
217#383—21no—
218#382C22×C3711yescharacteristic
219C4×C4⋊C4—21no—
220C4×C4⋊C4C22×C3711yescharacteristic
221#376—21no—
222#327—21no—
223#327—21no—
224#327—22no—
225Q8⋊C8—22no—
226C37#918211yescharacteristic, direct product factor, Sylow
227C2×#41—21no—
228C22×Q8D4×C3711yescharacteristic
229#137—42no—
230#137—42no—
231C2×Q16—22no—
232C2×SD16—22no—
233C2×M16—21no—
234C4⋊Q8C2×C4×C3711yescharacteristic
235#127C2×C4×C3711yescharacteristic
236#124—21no—
237#121—21no—
238#121—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C2×C4×C3712yes—
242C4×Q8D4×C3712yes—
243C4×D4—21no—
244C4×D4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C3711yescharacteristic
249C2×C42—21no—
250C2×C42—22no—
251C2×C42—21no—
252C2×C42C23×C3711yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8C2×C4×C3712yes—
257#103—22no—
258#102—22no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C4×C8—21no—
262C4×C8—21no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95—21no—
267#95D4×C3711yescharacteristic
268#95D4×C3711yescharacteristic
269#95D4×C3712yes—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8C22⋊C4×C3712yes—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4C2×D4×C3711yescharacteristic
292C22×C4C2×D4×C3711yescharacteristic
293C22×C4C2×D4×C3711yescharacteristic
294Q16—44no—
295SD16—44no—
296M16—41no—
297M16—41no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4C22⋊C4×C3712yes—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—22no—
313C42—22no—
314C42—44no—
315C42—41no—
316C42—41no—
317C42C22×C4×C3711yescharacteristic
318C42C2×D4×C3711yescharacteristic
319C42#41×C3711yescharacteristic
320C42#41×C3711yescharacteristic
321C23—41no—
322C23#120×C3711yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4C2×C22⋊C4×C3711yescharacteristic
355C2×C4C4×D4×C3711yescharacteristic
356C2×C4C4×D4×C3711yescharacteristic
357C2×C4#121×C3711yescharacteristic
358C2×C4#121×C3711yescharacteristic
359C2×C4#123×C3711yescharacteristic
360C2×C4#135×C3711yescharacteristic
361C2×C4#135×C3711yescharacteristic
362C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
363C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
364C8—42no—
365C8—81no—
366C8—81no—
367C22—21no—
368C22—21no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22C37×#38611yescharacteristic
373C22C37×#44911yescharacteristic
374C22C37×#44911yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—42no—
381C4—42no—
382C4—81no—
383C4—82no—
384C4—81no—
385C4C37×#41611yescharacteristic
386C4C37×#41811yescharacteristic
387C4C37×#48211yescharacteristic
388C4C37×#48211yescharacteristic
389C2—21no—
390C2—21no—
391C2—161no—
392C2C37×#187511yescharacteristic
393C2C37×#190511yescharacteristic
394C2C37×#190611yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC37×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2356C2semidirect
5. C37×#1479C2semidirect
6. C37×#1303C2semidirect
7. C37×#1286C2semidirect
12. C37×#462C4semidirect
13. C37×#460C4semidirect
169. #9182C37direct (N × H)
193. #2356C2×C37semidirect
196. #1479C2×C37semidirect
197. #1303C2×C37semidirect
198. #1286C2×C37semidirect
209. #462C4×C37semidirect
210. #460C4×C37semidirect
226. C37#9182direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#30372
C37×#23562
C37×#15172
C37×#15022
C37×#14792
C37×#13032
C37×#12862
#918237