Finite Group Databasebeta

← C37×#9382 #22630635

Subgroups — C37×#9382 #22630635

Order 9472.

462 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×#3234C211yesmaximal, characteristic
2C37×#2336C211yesmaximal, characteristic, complemented
3C37×#1980C211yesmaximal, characteristic
4C37×#1528C211yesmaximal, characteristic, complemented
5C37×#1514C211yesmaximal, characteristic
6C37×#1288C211yesmaximal, characteristic, complemented
7C37×#1285C211yesmaximal, characteristic, complemented
8C37×#532C2211yescharacteristic
9C2×#125×C37C2211yescharacteristic
10C37×#501C412yescomplemented
11C37×#490C412yescomplemented
12C37×#481—21no—
13C37×#480—21no—
14C37×#478—22no—
15C37×#432C2211yescharacteristic
16C37×#432C2211yescharacteristic
17C2×#104×C37—21no—
18C2×#104×C37—21no—
19C4×M16×C37C2211yescharacteristic
20C37×#389—21no—
21C37×#387—21no—
22C37×#387—21no—
23C37×#387—21no—
24C37×#387—21no—
25C37×#383C2211yescharacteristic
26C4×C4⋊C4×C37—21no—
27C4×C4⋊C4×C37C2211yescharacteristic
28C37×#330—22no—
29C37×#327—21no—
30C37×#327—21no—
31C2×#41×C37—21no—
32C2×M16×C37—21no—
33C4⋊Q8×C37C2×C411yescharacteristic
34#127×C37C2×C411yescharacteristic
35#125×C37—21no—
36#125×C37—21no—
37#125×C37C2×C412yes—
38#125×C37D412yes—
39#124×C37—21no—
40#121×C37—21no—
41#121×C37—21no—
42C4×D4×C37—21no—
43C4×D4×C37—21no—
44C2×C4⋊C4×C37—21no—
45C2×C4⋊C4×C37—21no—
46C2×C4⋊C4×C37—21no—
47C2×C4⋊C4×C37—21no—
48C2×C4⋊C4×C37—21no—
49C2×C4⋊C4×C37D411yescharacteristic
50C2×C4⋊C4×C37D411yescharacteristic
51C2×C42×C37—21no—
52C2×C42×C37—21no—
53C2×C42×C37D411yescharacteristic
54C2×C42×C37D411yescharacteristic
55C2×C42×C37C2311yescharacteristic
56#107×C37—22no—
57#106×C37—22no—
58C4⋊C8×C37—21no—
59C4⋊C8×C37—21no—
60#104×C37—42no—
61#104×C37—42no—
62#102×C37—22no—
63#102×C37—22no—
64C22⋊C8×C37—21no—
65C22⋊C8×C37—21no—
66#97×C37—21no—
67#97×C37—21no—
68#97×C37C2×C412yes—
69C4×C8×C37—21no—
70#95×C37—21no—
71#95×C37—21no—
72#95×C37—21no—
73#95×C37—21no—
74#95×C37—21no—
75#95×C37—21no—
76#95×C37—21no—
77#95×C37D411yescharacteristic
78#95×C37D411yescharacteristic
79#41×C37—41no—
80#41×C37—41no—
81#41×C37—41no—
82#41×C37—41no—
83C2×Q8×C37—21no—
84C2×D4×C37—21no—
85C2×D4×C37—21no—
86C2×D4×C37—21no—
87C2×D4×C37—41no—
88C22×C4×C37—21no—
89C22×C4×C37—21no—
90C22×C4×C37—21no—
91C22×C4×C37—21no—
92C22×C4×C37—21no—
93C22×C4×C37—21no—
94C22×C4×C37—41no—
95C22×C4×C37C2×D411yescharacteristic
96C22×C4×C37C2×D411yescharacteristic
97C22×C4×C37C2×D411yescharacteristic
98M16×C37—22no—
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—22no—
106C4⋊C4×C37—22no—
107C4⋊C4×C37—21no—
108C4⋊C4×C37—21no—
109C4⋊C4×C37—21no—
110C4⋊C4×C37—21no—
111C4⋊C4×C37—42no—
112C4⋊C4×C37—42no—
113C4⋊C4×C37—81no—
114C4⋊C4×C37C22⋊C412yes—
115C4⋊C4×C37C22⋊C412yes—
116C22⋊C4×C37—41no—
117C22⋊C4×C37—41no—
118C42×C37—41no—
119C42×C37—41no—
120C42×C37—42no—
121C42×C37—81no—
122C42×C37C22×C411yescharacteristic
123C42×C37C2×D411yescharacteristic
124C42×C37#4111yescharacteristic
125C42×C37#4111yescharacteristic
126C23×C37—41no—
127C23×C37#12011yescharacteristic
128Q8×C37—41no—
129Q8×C37—41no—
130D4×C37—42no—
131D4×C37—41no—
132D4×C37—41no—
133D4×C37—81no—
134D4×C37—81no—
135D4×C37—81no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—22no—
139C2×C4×C37—22no—
140C2×C4×C37—22no—
141C2×C4×C37—41no—
142C2×C4×C37—41no—
143C2×C4×C37—41no—
144C2×C4×C37—41no—
145C2×C4×C37—41no—
146C2×C4×C37—41no—
147C2×C4×C37—41no—
148C2×C4×C37—41no—
149C2×C4×C37—41no—
150C2×C4×C37—41no—
151C2×C4×C37—41no—
152C2×C4×C37—41no—
153C2×C4×C37—41no—
154C2×C4×C37—41no—
155C2×C4×C37—41no—
156C2×C4×C37—41no—
157C2×C4×C37—41no—
158C2×C4×C37—41no—
159C2×C4×C37—81no—
160C2×C4×C37—81no—
161C2×C4×C37C2×C22⋊C411yescharacteristic
162C2×C4×C37C4×D411yescharacteristic
163C2×C4×C37C4×D411yescharacteristic
164C2×C4×C37#12111yescharacteristic
165C2×C4×C37#12111yescharacteristic
166C2×C4×C37#12311yescharacteristic
167C8×C37—42no—
168C8×C37—42no—
169C8×C37—81no—
170#9382C3711yesmaximal, characteristic, direct product factor, Sylow
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—81no—
174C22×C37—81no—
175C22×C37—81no—
176C22×C37#38611yescharacteristic
177C22×C37#45311yescharacteristic
178C22×C37#45411yescharacteristic
179C4×C37—21no—
180C4×C37—21no—
181C4×C37—21no—
182C4×C37—21no—
183C4×C37—21no—
184C4×C37—21no—
185C4×C37—42no—
186C4×C37—42no—
187C4×C37—42no—
188C4×C37—81no—
189C4×C37—81no—
190C4×C37—81no—
191C4×C37—81no—
192#3234C2×C3711yescharacteristic
193#2336C2×C3711yescharacteristic, complemented
194#1980C2×C3711yescharacteristic
195#1528C2×C3711yescharacteristic, complemented
196#1514C2×C3711yescharacteristic
197#1288C2×C3711yescharacteristic, complemented
198#1285C2×C3711yescharacteristic, complemented
199C2×C37—21no—
200C2×C37—21no—
201C2×C37—161no—
202C2×C37#188311yescharacteristic
203C2×C37#190611yescharacteristic
204C2×C37#191211yescharacteristic
205#532C22×C3711yescharacteristic
206C2×#125C22×C3711yescharacteristic
207#501C4×C3712yescomplemented
208#490C4×C3712yescomplemented
209#481—21no—
210#480—21no—
211#478—22no—
212#432C22×C3711yescharacteristic
213#432C22×C3711yescharacteristic
214C2×#104—21no—
215C2×#104—21no—
216C4×M16C22×C3711yescharacteristic
217#389—21no—
218#387—21no—
219#387—21no—
220#387—21no—
221#387—21no—
222#383C22×C3711yescharacteristic
223C4×C4⋊C4—21no—
224C4×C4⋊C4C22×C3711yescharacteristic
225#330—22no—
226#327—21no—
227#327—21no—
228C37#938211yescharacteristic, direct product factor, Sylow
229C2×#41—21no—
230C2×M16—21no—
231C4⋊Q8C2×C4×C3711yescharacteristic
232#127C2×C4×C3711yescharacteristic
233#125—21no—
234#125—21no—
235#125C2×C4×C3712yes—
236#125D4×C3712yes—
237#124—21no—
238#121—21no—
239#121—21no—
240C4×D4—21no—
241C4×D4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C3711yescharacteristic
248C2×C4⋊C4D4×C3711yescharacteristic
249C2×C42—21no—
250C2×C42—21no—
251C2×C42D4×C3711yescharacteristic
252C2×C42D4×C3711yescharacteristic
253C2×C42C23×C3711yescharacteristic
254#107—22no—
255#106—22no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258#104—42no—
259#104—42no—
260#102—22no—
261#102—22no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#97—21no—
265#97—21no—
266#97C2×C4×C3712yes—
267C4×C8—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95D4×C3711yescharacteristic
276#95D4×C3711yescharacteristic
277#41—41no—
278#41—41no—
279#41—41no—
280#41—41no—
281C2×Q8—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4C2×D4×C3711yescharacteristic
294C22×C4C2×D4×C3711yescharacteristic
295C22×C4C2×D4×C3711yescharacteristic
296M16—22no—
297M16—41no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—81no—
312C4⋊C4C22⋊C4×C3712yes—
313C4⋊C4C22⋊C4×C3712yes—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C42—41no—
318C42—42no—
319C42—81no—
320C42C22×C4×C3711yescharacteristic
321C42C2×D4×C3711yescharacteristic
322C42#41×C3711yescharacteristic
323C42#41×C3711yescharacteristic
324C23—41no—
325C23#120×C3711yescharacteristic
326Q8—41no—
327Q8—41no—
328D4—41no—
329D4—41no—
330D4—42no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C22⋊C4×C3711yescharacteristic
360C2×C4C4×D4×C3711yescharacteristic
361C2×C4C4×D4×C3711yescharacteristic
362C2×C4#121×C3711yescharacteristic
363C2×C4#121×C3711yescharacteristic
364C2×C4#123×C3711yescharacteristic
365C8—42no—
366C8—42no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22C37×#38611yescharacteristic
374C22C37×#45311yescharacteristic
375C22C37×#45411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—42no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C2—21no—
390C2—21no—
391C2—161no—
392C2C37×#188311yescharacteristic
393C2C37×#190611yescharacteristic
394C2C37×#191211yescharacteristic
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×#2336C2semidirect
4. C37×#1528C2semidirect
6. C37×#1288C2semidirect
7. C37×#1285C2semidirect
10. C37×#501C4semidirect
11. C37×#490C4semidirect
170. #9382C37direct (N × H)
193. #2336C2×C37semidirect
195. #1528C2×C37semidirect
197. #1288C2×C37semidirect
198. #1285C2×C37semidirect
207. #501C4×C37semidirect
208. #490C4×C37semidirect
228. C37#9382direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32342
C37×#23362
C37×#19802
C37×#15282
C37×#15142
C37×#12882
C37×#12852
#938237