Finite Group Databasebeta

← C37×#9283 #22630536

Subgroups — C37×#9283 #22630536

Order 9472.

448 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3207C211yesmaximal, characteristic
2C37×#2981C211yesmaximal, characteristic, complemented
3C37×#1530C211yesmaximal, characteristic, complemented
4C37×#1530C211yesmaximal, characteristic, complemented
5C37×#1496C211yesmaximal, characteristic, complemented
6C37×#1287C211yesmaximal, characteristic, complemented
7C37×#1275C211yesmaximal, characteristic, complemented
8C37×#532C2211yescharacteristic
9C37×#532C2211yescharacteristic
10C37×#493C411yescharacteristic
11C37×#492C411yescharacteristic
12C37×#487C411yescharacteristic
13C37×#486C411yescharacteristic
14C37×#463—22no—
15C37×#449—22no—
16C37×#436—21no—
17C37×#435—22no—
18C8×D4×C37—21no—
19C37×#432C2211yescharacteristic
20C37×#432C2211yescharacteristic
21C37×#431C2211yescharacteristic
22C37×#431C2211yescharacteristic
23C37×#408—22no—
24C2×#97×C37C2211yescharacteristic
25C37×#329—22no—
26C37×#329—22no—
27C37×D4⋊C8—21no—
28C37×D4⋊C8—21no—
29C2×#41×C37—21no—
30C2×#41×C37D412yes—
31C2×SD16×C37—22no—
32C2×D8×C37—22no—
33C2×M16×C37—22no—
34C22×C8×C37—21no—
35C22×C8×C37—22no—
36C4⋊Q8×C37C2×C411yescharacteristic
37C4⋊Q8×C37C2×C411yescharacteristic
38#127×C37C2×C411yescharacteristic
39#127×C37C2×C411yescharacteristic
40#124×C37—21no—
41#124×C37D412yes—
42#121×C37—21no—
43#121×C37—21no—
44#121×C37—21no—
45#121×C37—21no—
46C4×D4×C37—21no—
47C4×D4×C37—21no—
48C4×D4×C37—21no—
49C4×D4×C37—21no—
50C2×C42×C37C2311yescharacteristic
51C4⋊C8×C37—21no—
52C4⋊C8×C37—21no—
53C4⋊C8×C37—21no—
54C4⋊C8×C37—21no—
55#103×C37—22no—
56#102×C37—22no—
57C22⋊C8×C37—22no—
58C22⋊C8×C37—22no—
59C22⋊C8×C37—21no—
60C22⋊C8×C37—21no—
61C22⋊C8×C37—21no—
62C22⋊C8×C37—21no—
63#97×C37—21no—
64#97×C37—21no—
65#97×C37—21no—
66#97×C37D412yes—
67C4×C8×C37C2×C411yescharacteristic
68C4×C8×C37C2×C411yescharacteristic
69C4×C8×C37D411yescharacteristic
70C4×C8×C37D411yescharacteristic
71#41×C37—82no—
72#41×C37—82no—
73C2×Q8×C37—21no—
74C2×Q8×C37C22⋊C412yes—
75C2×D4×C37—22no—
76C2×D4×C37—21no—
77C2×D4×C37—21no—
78C2×D4×C37—21no—
79C2×D4×C37—21no—
80C2×D4×C37—21no—
81C2×D4×C37—41no—
82C2×D4×C37C22⋊C412yes—
83C22×C4×C37—22no—
84C22×C4×C37—41no—
85C22×C4×C37C2×D411yescharacteristic
86C22×C4×C37#4111yescharacteristic
87C22×C4×C37#4111yescharacteristic
88SD16×C37—82no—
89D8×C37—82no—
90M16×C37—82no—
91C2×C8×C37—22no—
92C2×C8×C37—21no—
93C2×C8×C37—21no—
94C2×C8×C37—21no—
95C2×C8×C37—21no—
96C2×C8×C37—22no—
97C2×C8×C37—41no—
98C2×C8×C37—41no—
99C2×C8×C37—41no—
100C2×C8×C37—82no—
101C4⋊C4×C37—21no—
102C4⋊C4×C37—21no—
103C4⋊C4×C37—21no—
104C4⋊C4×C37—21no—
105C22⋊C4×C37—22no—
106C22⋊C4×C37—22no—
107C22⋊C4×C37—41no—
108C22⋊C4×C37—41no—
109C42×C37C22×C411yescharacteristic
110C42×C37C2×D411yescharacteristic
111C42×C37C2×D411yescharacteristic
112C42×C37C2×D411yescharacteristic
113C23×C37—22no—
114C23×C37—41no—
115C23×C37#12311yescharacteristic
116Q8×C37—42no—
117Q8×C37—81no—
118D4×C37—42no—
119D4×C37—42no—
120D4×C37—41no—
121D4×C37—41no—
122D4×C37—41no—
123D4×C37—41no—
124D4×C37—81no—
125D4×C37—81no—
126D4×C37—82no—
127D4×C37—82no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—22no—
131C2×C4×C37—41no—
132C2×C4×C37—41no—
133C2×C4×C37—42no—
134C2×C4×C37—42no—
135C2×C4×C37—41no—
136C2×C4×C37—82no—
137C2×C4×C37C2×C22⋊C411yescharacteristic
138C2×C4×C37C4×D411yescharacteristic
139C2×C4×C37C4×D411yescharacteristic
140C2×C4×C37#12011yescharacteristic
141C2×C4×C37#12111yescharacteristic
142C2×C4×C37#12111yescharacteristic
143C8×C37—42no—
144C8×C37—41no—
145C8×C37—42no—
146C8×C37—41no—
147C8×C37—41no—
148C8×C37—41no—
149C8×C37—81no—
150#9283C3711yesmaximal, characteristic, direct product factor, Sylow
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—42no—
155C22×C37—42no—
156C22×C37—42no—
157C22×C37—81no—
158C22×C37—81no—
159C22×C37—81no—
160C22×C37#38611yescharacteristic
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—42no—
167C4×C37—81no—
168C4×C37#44311yescharacteristic
169C4×C37#44411yescharacteristic
170#3207C2×C3711yescharacteristic
171#2981C2×C3711yescharacteristic, complemented
172#1530C2×C3711yescharacteristic, complemented
173#1530C2×C3711yescharacteristic, complemented
174#1496C2×C3711yescharacteristic, complemented
175#1287C2×C3711yescharacteristic, complemented
176#1275C2×C3711yescharacteristic, complemented
177C2×C37—41no—
178C2×C37—82no—
179C2×C37—161no—
180C2×C37#187611yescharacteristic
181C2×C37#190311yescharacteristic
182C2×C37#191111yescharacteristic
183#532C22×C3711yescharacteristic
184#532C22×C3711yescharacteristic
185#493C4×C3711yescharacteristic
186#492C4×C3711yescharacteristic
187#487C4×C3711yescharacteristic
188#486C4×C3711yescharacteristic
189#463—22no—
190#449—22no—
191#436—21no—
192#435—22no—
193C8×D4—21no—
194#432C22×C3711yescharacteristic
195#432C22×C3711yescharacteristic
196#431C22×C3711yescharacteristic
197#431C22×C3711yescharacteristic
198#408—22no—
199C2×#97C22×C3711yescharacteristic
200#329—22no—
201#329—22no—
202D4⋊C8—21no—
203D4⋊C8—21no—
204C37#928311yescharacteristic, direct product factor, Sylow
205C2×#41—21no—
206C2×#41D4×C3712yes—
207C2×SD16—22no—
208C2×D8—22no—
209C2×M16—22no—
210C22×C8—21no—
211C22×C8—22no—
212C4⋊Q8C2×C4×C3711yescharacteristic
213C4⋊Q8C2×C4×C3711yescharacteristic
214#127C2×C4×C3711yescharacteristic
215#127C2×C4×C3711yescharacteristic
216#124—21no—
217#124D4×C3712yes—
218#121—21no—
219#121—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C2×C42C23×C3711yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231#103—22no—
232#102—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239#97—21no—
240#97—21no—
241#97—21no—
242#97D4×C3712yes—
243C4×C8C2×C4×C3711yescharacteristic
244C4×C8C2×C4×C3711yescharacteristic
245C4×C8D4×C3711yescharacteristic
246C4×C8D4×C3711yescharacteristic
247#41—82no—
248#41—82no—
249C2×Q8—21no—
250C2×Q8C22⋊C4×C3712yes—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊C4×C3712yes—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4C2×D4×C3711yescharacteristic
262C22×C4#41×C3711yescharacteristic
263C22×C4#41×C3711yescharacteristic
264SD16—82no—
265D8—82no—
266M16—82no—
267C2×C8—22no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—82no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42C22×C4×C3711yescharacteristic
286C42C2×D4×C3711yescharacteristic
287C42C2×D4×C3711yescharacteristic
288C42C2×D4×C3711yescharacteristic
289C23—22no—
290C23—41no—
291C23#123×C3711yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—41no—
299D4—41no—
300D4—81no—
301D4—81no—
302D4—82no—
303D4—82no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4C2×C22⋊C4×C3711yescharacteristic
314C2×C4C4×D4×C3711yescharacteristic
315C2×C4C4×D4×C3711yescharacteristic
316C2×C4#120×C3711yescharacteristic
317C2×C4#121×C3711yescharacteristic
318C2×C4#121×C3711yescharacteristic
319C8—42no—
320C8—41no—
321C8—42no—
322C8—41no—
323C8—41no—
324C8—41no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C37×#38611yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4C37×#44311yescharacteristic
344C4C37×#44411yescharacteristic
345C2—41no—
346C2—82no—
347C2—161no—
348C2C37×#187611yescharacteristic
349C2C37×#190311yescharacteristic
350C2C37×#191111yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC37×#3207C2
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×#2981C2semidirect
3. C37×#1530C2semidirect
4. C37×#1530C2semidirect
5. C37×#1496C2semidirect
6. C37×#1287C2semidirect
7. C37×#1275C2semidirect
150. #9283C37direct (N × H)
171. #2981C2×C37semidirect
172. #1530C2×C37semidirect
173. #1530C2×C37semidirect
174. #1496C2×C37semidirect
175. #1287C2×C37semidirect
176. #1275C2×C37semidirect
204. C37#9283direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32072
C37×#29812
C37×#15302
C37×#14962
C37×#12872
C37×#12752
#928337