Finite Group Databasebeta

← C37×#9164 #22630417

Subgroups — C37×#9164 #22630417

Order 9472.

458 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3112C211yesmaximal, characteristic
2C37×#2984C211yesmaximal, characteristic, complemented
3C37×#1763C211yesmaximal, characteristic, complemented
4C37×#1530C211yesmaximal, characteristic
5C37×#1502C211yesmaximal, characteristic
6C37×#1302C211yesmaximal, characteristic, complemented
7C37×#1285C211yesmaximal, characteristic, complemented
8C37×#532C2211yescharacteristic
9C2×C4×Q8×C37C2211yescharacteristic
10C37×#480—21no—
11C37×#477C411yescharacteristic, complemented
12C37×#477C411yescharacteristic, complemented
13C37×#460C411yescharacteristic, complemented
14C37×#460C411yescharacteristic, complemented
15C37×#448—21no—
16C37×#446—21no—
17C37×#446—22no—
18C8×Q8×C37—21no—
19C37×#440—21no—
20C37×#440—21no—
21C37×#432—21no—
22C37×#432C2211yescharacteristic
23C37×#432C2211yescharacteristic
24C37×#431—21no—
25C37×#431C2211yescharacteristic
26C2×#103×C37—21no—
27C2×#97×C37C2211yescharacteristic
28C4×C4⋊C4×C37C2211yescharacteristic
29C37×#340—21no—
30C37×#329—22no—
31C37×#327—21no—
32C37×#327—21no—
33C2×#41×C37—21no—
34C22×Q8×C37D411yescharacteristic
35C2×SD16×C37—21no—
36C2×SD16×C37—21no—
37C22×C8×C37—21no—
38C4⋊Q8×C37C2×C411yescharacteristic
39#127×C37C2×C411yescharacteristic
40#124×C37—21no—
41#121×C37—21no—
42#121×C37—21no—
43C4×Q8×C37—21no—
44C4×Q8×C37—21no—
45C4×Q8×C37C2×C411yescharacteristic
46C4×Q8×C37C2×C411yescharacteristic
47C4×Q8×C37D411yescharacteristic
48C4×Q8×C37D411yescharacteristic
49C4×D4×C37—21no—
50C4×D4×C37—21no—
51C2×C4⋊C4×C37—21no—
52C2×C4⋊C4×C37—21no—
53C2×C4⋊C4×C37D411yescharacteristic
54C2×C42×C37—21no—
55C2×C42×C37—21no—
56C2×C42×C37C2311yescharacteristic
57#107×C37—21no—
58#107×C37—21no—
59C4⋊C8×C37—22no—
60C4⋊C8×C37—22no—
61C4⋊C8×C37—21no—
62C4⋊C8×C37—21no—
63C4⋊C8×C37C2×C411yescharacteristic
64C4⋊C8×C37C2×C411yescharacteristic
65#103×C37—24no—
66#103×C37—21no—
67#103×C37—21no—
68#102×C37—21no—
69#102×C37—21no—
70C22⋊C8×C37—21no—
71C22⋊C8×C37—21no—
72C22⋊C8×C37D411yescharacteristic
73C22⋊C8×C37D411yescharacteristic
74#97×C37—22no—
75#97×C37—21no—
76#97×C37—21no—
77#97×C37—21no—
78#97×C37D412yes—
79C4×C8×C37—22no—
80C4×C8×C37—21no—
81#95×C37—21no—
82#41×C37—81no—
83#41×C37—81no—
84C2×Q8×C37—21no—
85C2×Q8×C37—22no—
86C2×Q8×C37—21no—
87C2×Q8×C37—41no—
88C2×Q8×C37C22⋊C411yescharacteristic
89C2×Q8×C37C22⋊C411yescharacteristic
90C2×D4×C37—21no—
91C2×D4×C37—21no—
92C2×D4×C37—21no—
93C2×D4×C37—41no—
94C22×C4×C37—21no—
95C22×C4×C37—21no—
96C22×C4×C37—41no—
97C22×C4×C37—41no—
98C22×C4×C37C2×D411yescharacteristic
99C22×C4×C37C2×D411yescharacteristic
100C22×C4×C37#4111yescharacteristic
101SD16×C37—42no—
102SD16×C37—42no—
103C2×C8×C37—22no—
104C2×C8×C37—21no—
105C2×C8×C37—21no—
106C2×C8×C37—21no—
107C2×C8×C37—21no—
108C2×C8×C37—22no—
109C2×C8×C37—41no—
110C2×C8×C37—41no—
111C4⋊C4×C37—21no—
112C4⋊C4×C37—21no—
113C4⋊C4×C37—21no—
114C4⋊C4×C37—21no—
115C4⋊C4×C37—21no—
116C4⋊C4×C37—22no—
117C4⋊C4×C37—21no—
118C4⋊C4×C37—21no—
119C4⋊C4×C37—41no—
120C4⋊C4×C37C22⋊C411yescharacteristic
121C4⋊C4×C37C22⋊C411yescharacteristic
122C22⋊C4×C37—41no—
123C22⋊C4×C37—41no—
124C42×C37—21no—
125C42×C37—21no—
126C42×C37—21no—
127C42×C37—21no—
128C42×C37—81no—
129C42×C37C22×C411yescharacteristic
130C42×C37C2×D411yescharacteristic
131C42×C37C2×D411yescharacteristic
132C42×C37#4111yescharacteristic
133C23×C37—41no—
134C23×C37#12111yescharacteristic
135Q8×C37—21no—
136Q8×C37—21no—
137Q8×C37—21no—
138Q8×C37—42no—
139Q8×C37—81no—
140Q8×C37#10412yes—
141D4×C37—41no—
142D4×C37—41no—
143D4×C37—81no—
144D4×C37—81no—
145D4×C37—81no—
146D4×C37—81no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—21no—
152C2×C4×C37—21no—
153C2×C4×C37—21no—
154C2×C4×C37—21no—
155C2×C4×C37—41no—
156C2×C4×C37—42no—
157C2×C4×C37—41no—
158C2×C4×C37—41no—
159C2×C4×C37—42no—
160C2×C4×C37—41no—
161C2×C4×C37—82no—
162C2×C4×C37—81no—
163C2×C4×C37—81no—
164C2×C4×C37C2×C22⋊C411yescharacteristic
165C2×C4×C37C4×D411yescharacteristic
166C2×C4×C37C4×D411yescharacteristic
167C2×C4×C37#12011yescharacteristic
168C2×C4×C37#12111yescharacteristic
169C2×C4×C37#12311yescharacteristic
170C8×C37—41no—
171C8×C37—41no—
172C8×C37—42no—
173C8×C37—42no—
174C8×C37—41no—
175C8×C37—41no—
176#9164C3711yesmaximal, characteristic, direct product factor, Sylow
177C22×C37—21no—
178C22×C37—21no—
179C22×C37—81no—
180C22×C37—81no—
181C22×C37—81no—
182C22×C37#38611yescharacteristic
183C22×C37#47111yescharacteristic
184C22×C37#47211yescharacteristic
185C4×C37—21no—
186C4×C37—22no—
187C4×C37—21no—
188C4×C37—21no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—41no—
192C4×C37—41no—
193C4×C37—41no—
194C4×C37—82no—
195C4×C37—81no—
196C4×C37C2×#10411yescharacteristic
197C4×C37#42111yescharacteristic
198#3112C2×C3711yescharacteristic
199#2984C2×C3711yescharacteristic, complemented
200#1763C2×C3711yescharacteristic, complemented
201#1530C2×C3711yescharacteristic
202#1502C2×C3711yescharacteristic
203#1302C2×C3711yescharacteristic, complemented
204#1285C2×C3711yescharacteristic, complemented
205C2×C37—21no—
206C2×C37—21no—
207C2×C37—161no—
208C2×C37#187111yescharacteristic
209C2×C37#190511yescharacteristic
210C2×C37#190711yescharacteristic
211#532C22×C3711yescharacteristic
212C2×C4×Q8C22×C3711yescharacteristic
213#480—21no—
214#477C4×C3711yescharacteristic, complemented
215#477C4×C3711yescharacteristic, complemented
216#460C4×C3711yescharacteristic, complemented
217#460C4×C3711yescharacteristic, complemented
218#448—21no—
219#446—21no—
220#446—22no—
221C8×Q8—21no—
222#440—21no—
223#440—21no—
224#432—21no—
225#432C22×C3711yescharacteristic
226#432C22×C3711yescharacteristic
227#431—21no—
228#431C22×C3711yescharacteristic
229C2×#103—21no—
230C2×#97C22×C3711yescharacteristic
231C4×C4⋊C4C22×C3711yescharacteristic
232#340—21no—
233#329—22no—
234#327—21no—
235#327—21no—
236C37#916411yescharacteristic, direct product factor, Sylow
237C2×#41—21no—
238C22×Q8D4×C3711yescharacteristic
239C2×SD16—21no—
240C2×SD16—21no—
241C22×C8—21no—
242C4⋊Q8C2×C4×C3711yescharacteristic
243#127C2×C4×C3711yescharacteristic
244#124—21no—
245#121—21no—
246#121—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8C2×C4×C3711yescharacteristic
250C4×Q8C2×C4×C3711yescharacteristic
251C4×Q8D4×C3711yescharacteristic
252C4×Q8D4×C3711yescharacteristic
253C4×D4—21no—
254C4×D4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C3711yescharacteristic
258C2×C42—21no—
259C2×C42—21no—
260C2×C42C23×C3711yescharacteristic
261#107—21no—
262#107—21no—
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C2×C4×C3711yescharacteristic
268C4⋊C8C2×C4×C3711yescharacteristic
269#103—24no—
270#103—21no—
271#103—21no—
272#102—21no—
273#102—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8D4×C3711yescharacteristic
277C22⋊C8D4×C3711yescharacteristic
278#97—22no—
279#97—21no—
280#97—21no—
281#97—21no—
282#97D4×C3712yes—
283C4×C8—22no—
284C4×C8—21no—
285#95—21no—
286#41—81no—
287#41—81no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8C22⋊C4×C3711yescharacteristic
293C2×Q8C22⋊C4×C3711yescharacteristic
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×D4×C3711yescharacteristic
303C22×C4C2×D4×C3711yescharacteristic
304C22×C4#41×C3711yescharacteristic
305SD16—42no—
306SD16—42no—
307C2×C8—22no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4C22⋊C4×C3711yescharacteristic
325C4⋊C4C22⋊C4×C3711yescharacteristic
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—81no—
333C42C22×C4×C3711yescharacteristic
334C42C2×D4×C3711yescharacteristic
335C42C2×D4×C3711yescharacteristic
336C42#41×C3711yescharacteristic
337C23—41no—
338C23#121×C3711yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—21no—
342Q8—42no—
343Q8—81no—
344Q8#104×C3712yes—
345D4—41no—
346D4—41no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4C2×C22⋊C4×C3711yescharacteristic
369C2×C4C4×D4×C3711yescharacteristic
370C2×C4C4×D4×C3711yescharacteristic
371C2×C4#120×C3711yescharacteristic
372C2×C4#121×C3711yescharacteristic
373C2×C4#123×C3711yescharacteristic
374C8—42no—
375C8—41no—
376C8—41no—
377C8—42no—
378C8—41no—
379C8—41no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C37×#38611yescharacteristic
386C22C37×#47111yescharacteristic
387C22C37×#47211yescharacteristic
388C4—21no—
389C4—22no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—81no—
399C4C2×#104×C3711yescharacteristic
400C4C37×#42111yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2C37×#187111yescharacteristic
405C2C37×#190511yescharacteristic
406C2C37×#190711yescharacteristic
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×#2984C2semidirect
3. C37×#1763C2semidirect
6. C37×#1302C2semidirect
7. C37×#1285C2semidirect
11. C37×#477C4semidirect
12. C37×#477C4semidirect
13. C37×#460C4semidirect
14. C37×#460C4semidirect
176. #9164C37direct (N × H)
199. #2984C2×C37semidirect
200. #1763C2×C37semidirect
203. #1302C2×C37semidirect
204. #1285C2×C37semidirect
214. #477C4×C37semidirect
215. #477C4×C37semidirect
216. #460C4×C37semidirect
217. #460C4×C37semidirect
236. C37#9164direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31122
C37×#29842
C37×#17632
C37×#15302
C37×#15022
C37×#13022
C37×#12852
#916437