Finite Group Databasebeta

← C37×#8902 #22630155

Subgroups — C37×#8902 #22630155

Order 9472.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2906C211yesmaximal, characteristic
2C37×#1806C211yesmaximal, characteristic
3C37×#1571C211yesmaximal, characteristic, complemented
4C37×#1567C211yesmaximal, characteristic, complemented
5C37×#1476C211yesmaximal, characteristic
6C37×#1303C211yesmaximal, characteristic, complemented
7C37×#1279C211yesmaximal, characteristic, complemented
8C2×#131×C37—21no—
9C4×#41×C37C2211yescharacteristic
10C37×#431C2211yescharacteristic
11C37×#424—21no—
12C37×#424—22no—
13C37×#423—21no—
14C37×#423C2211yescharacteristic
15C37×#423C2211yescharacteristic
16C2×C4⋊C8×C37—21no—
17C2×C4⋊C8×C37C2211yescharacteristic
18C2×#104×C37—21no—
19C2×C4×C8×C37C2211yescharacteristic
20C4×C4⋊C4×C37C2211yescharacteristic
21C37×#339—21no—
22C37×#335—22no—
23C37×#335—21no—
24C37×#335—21no—
25C37×Q8⋊C8C411yescharacteristic, complemented
26C37×Q8⋊C8C411yescharacteristic, complemented
27C37×D4⋊C8C411yescharacteristic, complemented
28C37×D4⋊C8C411yescharacteristic, complemented
29C2×#41×C37D411yescharacteristic
30#131×C37—42no—
31#131×C37—42no—
32C2×M16×C37—22no—
33C2×M16×C37—21no—
34C2×M16×C37—21no—
35C22×C8×C37—22no—
36C22×C8×C37—21no—
37C22×C8×C37—21no—
38C4×Q8×C37C2×C411yescharacteristic
39C4×Q8×C37Q811yescharacteristic
40C4×D4×C37—21no—
41C4×D4×C37—21no—
42C4×D4×C37C2×C411yescharacteristic
43C4×D4×C37Q811yescharacteristic
44#117×C37—21no—
45#117×C37D411yescharacteristic
46C2×C4⋊C4×C37—21no—
47C2×C42×C37—21no—
48C2×C42×C37—21no—
49C2×C42×C37C2311yescharacteristic
50C4⋊C8×C37—22no—
51C4⋊C8×C37—22no—
52C4⋊C8×C37—21no—
53C4⋊C8×C37—21no—
54C4⋊C8×C37—21no—
55C4⋊C8×C37—21no—
56C4⋊C8×C37C2×C411yescharacteristic
57C4⋊C8×C37C2×C411yescharacteristic
58C4⋊C8×C37D411yescharacteristic
59C4⋊C8×C37D411yescharacteristic
60C4⋊C8×C37D412yes—
61#104×C37—42no—
62C22⋊C8×C37—21no—
63C4×C8×C37—21no—
64C4×C8×C37—21no—
65C4×C8×C37C2×C411yescharacteristic
66C4×C8×C37C2×C411yescharacteristic
67#95×C37—21no—
68#41×C37—21no—
69#41×C37—21no—
70#41×C37D812yes—
71#41×C37Q1612yes—
72C2×Q8×C37C4⋊C411yescharacteristic
73C2×D4×C37—21no—
74C2×D4×C37C4⋊C411yescharacteristic
75C22×C4×C37—21no—
76C22×C4×C37—21no—
77C22×C4×C37—21no—
78C22×C4×C37—41no—
79C22×C4×C37C2×D411yescharacteristic
80C22×C4×C37#4111yescharacteristic
81C22×C4×C37#4111yescharacteristic
82M16×C37—44no—
83M16×C37—41no—
84M16×C37—41no—
85M16×C37—41no—
86M16×C37—41no—
87C2×C8×C37—21no—
88C2×C8×C37—21no—
89C2×C8×C37—21no—
90C2×C8×C37—21no—
91C2×C8×C37—21no—
92C2×C8×C37—22no—
93C2×C8×C37—21no—
94C2×C8×C37—42no—
95C2×C8×C37—44no—
96C2×C8×C37—41no—
97C2×C8×C37—41no—
98C2×C8×C37—41no—
99C4⋊C4×C37—21no—
100C4⋊C4×C37—21no—
101C4⋊C4×C37—22no—
102C4⋊C4×C37—41no—
103C4⋊C4×C37C4⋊C411yescharacteristic
104C4⋊C4×C37C4⋊C411yescharacteristic
105C22⋊C4×C37—21no—
106C22⋊C4×C37—21no—
107C22⋊C4×C37—21no—
108C42×C37—21no—
109C42×C37—21no—
110C42×C37—21no—
111C42×C37—41no—
112C42×C37—41no—
113C42×C37C22×C411yescharacteristic
114C42×C37C2×D411yescharacteristic
115C42×C37C2×D411yescharacteristic
116C42×C37C2×Q811yescharacteristic
117C23×C37—21no—
118C23×C37#12311yescharacteristic
119Q8×C37—21no—
120Q8×C37#10712yes—
121D4×C37—22no—
122D4×C37—22no—
123D4×C37—21no—
124D4×C37#10712yes—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—22no—
129C2×C4×C37—22no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—41no—
133C2×C4×C37—41no—
134C2×C4×C37—41no—
135C2×C4×C37—42no—
136C2×C4×C37—81no—
137C2×C4×C37—81no—
138C2×C4×C37—81no—
139C2×C4×C37C2×C4⋊C411yescharacteristic
140C2×C4×C37C4×D411yescharacteristic
141C2×C4×C37C4×D411yescharacteristic
142C2×C4×C37#12011yescharacteristic
143C2×C4×C37C22⋊Q811yescharacteristic
144C2×C4×C37C22⋊Q811yescharacteristic
145C2×C4×C37C2×D811yescharacteristic
146C2×C4×C37C2×Q1611yescharacteristic
147C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C37#13711yescharacteristic
149C8×C37—22no—
150C8×C37—41no—
151C8×C37—41no—
152C8×C37—41no—
153C8×C37—41no—
154C8×C37—42no—
155C8×C37—41no—
156C8×C37—81no—
157#8902C3711yesmaximal, characteristic, direct product factor, Sylow
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—22no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37#38511yescharacteristic
164C22×C37#48011yescharacteristic
165C22×C37#48411yescharacteristic
166C4×C37—22no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37—82no—
173C4×C37C2×#10711yescharacteristic
174C4×C37#42811yescharacteristic
175C4×C37#44311yescharacteristic
176C4×C37#44411yescharacteristic
177C4×C37#44711yescharacteristic
178C4×C37#45111yescharacteristic
179#2906C2×C3711yescharacteristic
180#1806C2×C3711yescharacteristic
181#1571C2×C3711yescharacteristic, complemented
182#1567C2×C3711yescharacteristic, complemented
183#1476C2×C3711yescharacteristic
184#1303C2×C3711yescharacteristic, complemented
185#1279C2×C3711yescharacteristic, complemented
186C2×C37—21no—
187C2×C37—21no—
188C2×C37—42no—
189C2×C37#185211yescharacteristic
190C2×C37#186111yescharacteristic
191C2×C37#186611yescharacteristic
192C2×#131—21no—
193C4×#41C22×C3711yescharacteristic
194#431C22×C3711yescharacteristic
195#424—21no—
196#424—22no—
197#423—21no—
198#423C22×C3711yescharacteristic
199#423C22×C3711yescharacteristic
200C2×C4⋊C8—21no—
201C2×C4⋊C8C22×C3711yescharacteristic
202C2×#104—21no—
203C2×C4×C8C22×C3711yescharacteristic
204C4×C4⋊C4C22×C3711yescharacteristic
205#339—21no—
206#335—22no—
207#335—21no—
208#335—21no—
209Q8⋊C8C4×C3711yescharacteristic, complemented
210Q8⋊C8C4×C3711yescharacteristic, complemented
211D4⋊C8C4×C3711yescharacteristic, complemented
212D4⋊C8C4×C3711yescharacteristic, complemented
213C37#890211yescharacteristic, direct product factor, Sylow
214C2×#41D4×C3711yescharacteristic
215#131—42no—
216#131—42no—
217C2×M16—22no—
218C2×M16—21no—
219C2×M16—21no—
220C22×C8—22no—
221C22×C8—21no—
222C22×C8—21no—
223C4×Q8C2×C4×C3711yescharacteristic
224C4×Q8Q8×C3711yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4C2×C4×C3711yescharacteristic
228C4×D4Q8×C3711yescharacteristic
229#117—21no—
230#117D4×C3711yescharacteristic
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C23×C3711yescharacteristic
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C3711yescharacteristic
242C4⋊C8C2×C4×C3711yescharacteristic
243C4⋊C8D4×C3711yescharacteristic
244C4⋊C8D4×C3711yescharacteristic
245C4⋊C8D4×C3712yes—
246#104—42no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×C4×C3711yescharacteristic
251C4×C8C2×C4×C3711yescharacteristic
252#95—21no—
253#41—21no—
254#41—21no—
255#41D8×C3712yes—
256#41Q16×C3712yes—
257C2×Q8C4⋊C4×C3711yescharacteristic
258C2×D4—21no—
259C2×D4C4⋊C4×C3711yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4C2×D4×C3711yescharacteristic
265C22×C4#41×C3711yescharacteristic
266C22×C4#41×C3711yescharacteristic
267M16—44no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—41no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—44no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4C4⋊C4×C3711yescharacteristic
289C4⋊C4C4⋊C4×C3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—41no—
297C42—41no—
298C42C22×C4×C3711yescharacteristic
299C42C2×D4×C3711yescharacteristic
300C42C2×D4×C3711yescharacteristic
301C42C2×Q8×C3711yescharacteristic
302C23—21no—
303C23#123×C3711yescharacteristic
304Q8—21no—
305Q8#107×C3712yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#107×C3712yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×C4⋊C4×C3711yescharacteristic
325C2×C4C4×D4×C3711yescharacteristic
326C2×C4C4×D4×C3711yescharacteristic
327C2×C4#120×C3711yescharacteristic
328C2×C4C22⋊Q8×C3711yescharacteristic
329C2×C4C22⋊Q8×C3711yescharacteristic
330C2×C4C2×D8×C3711yescharacteristic
331C2×C4C2×Q16×C3711yescharacteristic
332C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
333C2×C4#137×C3711yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—41no—
339C8—42no—
340C8—41no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22C37×#38511yescharacteristic
348C22C37×#48011yescharacteristic
349C22C37×#48411yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4C2×#107×C3711yescharacteristic
358C4C37×#42811yescharacteristic
359C4C37×#44311yescharacteristic
360C4C37×#44411yescharacteristic
361C4C37×#44711yescharacteristic
362C4C37×#45111yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2C37×#185211yescharacteristic
367C2C37×#186111yescharacteristic
368C2C37×#186611yescharacteristic
subgroupG/H
centerC2×C4×C37#120
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
socleC22×C37#385
prime radicalC2×#41×C37D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1571C2semidirect
4. C37×#1567C2semidirect
6. C37×#1303C2semidirect
7. C37×#1279C2semidirect
25. C37×Q8⋊C8C4semidirect
26. C37×Q8⋊C8C4semidirect
27. C37×D4⋊C8C4semidirect
28. C37×D4⋊C8C4semidirect
157. #8902C37direct (N × H)
181. #1571C2×C37semidirect
182. #1567C2×C37semidirect
184. #1303C2×C37semidirect
185. #1279C2×C37semidirect
209. Q8⋊C8C4×C37semidirect
210. Q8⋊C8C4×C37semidirect
211. D4⋊C8C4×C37semidirect
212. D4⋊C8C4×C37semidirect
213. C37#8902direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#29062
C37×#18062
C37×#15712
C37×#15672
C37×#14762
C37×#13032
C37×#12792
#890237