Finite Group Databasebeta

← C37×#19964 #22641217

Subgroups — C37×#19964 #22641217

Order 9472.

568 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3398C212yesmaximal
2C37×#3383C211yesmaximal, characteristic, complemented
3C37×#3342C211yesmaximal, characteristic
4C37×#1713C211yesmaximal, characteristic, complemented
5C37×#1690C212yesmaximal, complemented
6C37×#1674C211yesmaximal, characteristic, complemented
7C37×#1673C211yesmaximal, characteristic
8C37×#1650C212yesmaximal
9C37×#1648C212yesmaximal, complemented
10C37×#1591C211yesmaximal, characteristic, complemented
11C8×SD16×C37C211yesmaximal, characteristic
12C37×#557C2212yes—
13C37×#556C2212yes—
14C37×#500C2211yescharacteristic
15C37×#500C2211yescharacteristic
16C37×#500C2212yes—
17C37×#499—21no—
18C37×#497—22no—
19C37×#494C2212yes—
20C37×#485—22no—
21C37×#479—22no—
22C37×#475C2212yes—
23C37×#475C2212yes—
24C37×#467—21no—
25C37×#464—22no—
26C37×#462—22no—
27C37×#462C2212yes—
28C37×#461C2212yes—
29C37×#446C2212yes—
30C8×Q8×C37C2211yescharacteristic
31C37×#441—22no—
32C4×Q16×C37—21no—
33C4×Q16×C37C2211yescharacteristic
34C4×SD16×C37C2211yescharacteristic
35C8×D4×C37C2211yescharacteristic
36C37×#427—21no—
37C37×#335C2211yescharacteristic
38C37×#334C2211yescharacteristic
39C37×#332C2212yes—
40C37×#332C2212yes—
41C37×Q8⋊C8C2212yes—
42C37×Q8⋊C8C2211yescharacteristic
43C37×D4⋊C8C2211yescharacteristic
44C82×C37C2211yescharacteristic
45C2×Q16×C37—22no—
46C2×Q16×C37—22no—
47C2×Q16×C37—22no—
48C2×Q16×C37D411yescharacteristic
49C2×SD16×C37—22no—
50C2×SD16×C37D411yescharacteristic
51C22×C8×C37—21no—
52C4⋊Q8×C37—22no—
53C4⋊Q8×C37C2312yes—
54C4⋊Q8×C37C2312yes—
55#126×C37—42no—
56#125×C37—22no—
57#125×C37—42no—
58#124×C37—22no—
59C22⋊Q8×C37—22no—
60C4×Q8×C37—22no—
61C4×Q8×C37—22no—
62C4×Q8×C37—22no—
63C4×Q8×C37C2312yes—
64C4×Q8×C37C2311yescharacteristic
65C4×D4×C37C2311yescharacteristic
66#117×C37—22no—
67#107×C37—21no—
68#107×C37—21no—
69#107×C37—21no—
70#107×C37—21no—
71#107×C37—42no—
72#107×C37D411yescharacteristic
73#106×C37—22no—
74#106×C37—22no—
75#106×C37D411yescharacteristic
76C4⋊C8×C37—21no—
77C4⋊C8×C37—22no—
78C4⋊C8×C37C2311yescharacteristic
79C4⋊C8×C37C2311yescharacteristic
80C4⋊C8×C37C2312yes—
81#103×C37—22no—
82#103×C37—22no—
83#103×C37—22no—
84#103×C37—22no—
85#103×C37D411yescharacteristic
86#103×C37D412yes—
87#102×C37D411yescharacteristic
88C22⋊C8×C37—21no—
89#97×C37—22no—
90C4×C8×C37—21no—
91C4×C8×C37C2311yescharacteristic
92C4×C8×C37C2311yescharacteristic
93C4×C8×C37C2311yescharacteristic
94C2×Q8×C37—22no—
95C2×Q8×C37—22no—
96C2×Q8×C37C2×D412yes—
97C2×Q8×C37C2×D411yescharacteristic
98C2×D4×C37C2×D411yescharacteristic
99C22×C4×C37—21no—
100Q16×C37—22no—
101Q16×C37—44no—
102Q16×C37—82no—
103Q16×C37—82no—
104SD16×C37—22no—
105SD16×C37—82no—
106C2×C8×C37—21no—
107C2×C8×C37—21no—
108C2×C8×C37—22no—
109C2×C8×C37—21no—
110C2×C8×C37—42no—
111C2×C8×C37C2×D411yescharacteristic
112C2×C8×C37C2×D411yescharacteristic
113C2×C8×C37C2×D411yescharacteristic
114C2×C8×C37C2×D411yescharacteristic
115C4⋊C4×C37—21no—
116C4⋊C4×C37—22no—
117C4⋊C4×C37—22no—
118C4⋊C4×C37—22no—
119C4⋊C4×C37—22no—
120C4⋊C4×C37—22no—
121C4⋊C4×C37—42no—
122C4⋊C4×C37—42no—
123C4⋊C4×C37—42no—
124C4⋊C4×C37—42no—
125C4⋊C4×C37C2×D411yescharacteristic
126C4⋊C4×C37C2×D411yescharacteristic
127C4⋊C4×C37C2×D412yes—
128C22⋊C4×C37—21no—
129C22⋊C4×C37—42no—
130C22⋊C4×C37—42no—
131C42×C37—21no—
132C42×C37—22no—
133C42×C37—42no—
134C42×C37—42no—
135C42×C37C2411yescharacteristic
136C23×C37—21no—
137Q8×C37—21no—
138Q8×C37—22no—
139Q8×C37—21no—
140Q8×C37—22no—
141Q8×C37—42no—
142Q8×C37—42no—
143Q8×C37—42no—
144Q8×C37—42no—
145D4×C37—21no—
146D4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—22no—
149C2×C4×C37—22no—
150C2×C4×C37—21no—
151C2×C4×C37—21no—
152C2×C4×C37—41no—
153C2×C4×C37—41no—
154C2×C4×C37—42no—
155C2×C4×C37—42no—
156C2×C4×C37C22×D411yescharacteristic
157C2×C4×C37C22×D411yescharacteristic
158C2×C4×C37H(5,𝔽2)11yescharacteristic
159C8×C37—22no—
160C8×C37—21no—
161C8×C37—21no—
162C8×C37—41no—
163C8×C37—42no—
164C8×C37—41no—
165C8×C37#13512yes—
166C8×C37#13712yes—
167#19964C3711yesmaximal, characteristic, direct product factor, Sylow
168C22×C37—41no—
169C22×C37—41no—
170C22×C37—41no—
171C22×C37D4211yescharacteristic
172C4×C37—21no—
173C4×C37—41no—
174C4×C37—42no—
175C4×C37—41no—
176C4×C37—41no—
177C4×C37—42no—
178C4×C37—82no—
179C4×C37—82no—
180C4×C37C2×#13511yescharacteristic
181C4×C37C2×#13711yescharacteristic
182C4×C37#57611yescharacteristic
183C4×C37#57811yescharacteristic
184#3398C2×C3712yes—
185#3383C2×C3711yescharacteristic, complemented
186#3342C2×C3711yescharacteristic
187#1713C2×C3711yescharacteristic, complemented
188#1690C2×C3712yescomplemented
189#1674C2×C3711yescharacteristic, complemented
190#1673C2×C3711yescharacteristic
191#1650C2×C3712yes—
192#1648C2×C3712yescomplemented
193#1591C2×C3711yescharacteristic, complemented
194C8×SD16C2×C3711yescharacteristic
195C2×C37—81no—
196C2×C37#327611yescharacteristic
197C2×C37#328711yescharacteristic
198C2×C37#329311yescharacteristic
199#557C22×C3712yes—
200#556C22×C3712yes—
201#500C22×C3711yescharacteristic
202#500C22×C3711yescharacteristic
203#500C22×C3712yes—
204#499—21no—
205#497—22no—
206#494C22×C3712yes—
207#485—22no—
208#479—22no—
209#475C22×C3712yes—
210#475C22×C3712yes—
211#467—21no—
212#464—22no—
213#462—22no—
214#462C22×C3712yes—
215#461C22×C3712yes—
216#446C22×C3712yes—
217C8×Q8C22×C3711yescharacteristic
218#441—22no—
219C4×Q16—21no—
220C4×Q16C22×C3711yescharacteristic
221C4×SD16C22×C3711yescharacteristic
222C8×D4C22×C3711yescharacteristic
223#427—21no—
224#335C22×C3711yescharacteristic
225#334C22×C3711yescharacteristic
226#332C22×C3712yes—
227#332C22×C3712yes—
228Q8⋊C8C22×C3711yescharacteristic
229Q8⋊C8C22×C3712yes—
230D4⋊C8C22×C3711yescharacteristic
231C82C22×C3711yescharacteristic
232C37#1996411yescharacteristic, direct product factor, Sylow
233C2×Q16—22no—
234C2×Q16—22no—
235C2×Q16—22no—
236C2×Q16D4×C3711yescharacteristic
237C2×SD16—22no—
238C2×SD16D4×C3711yescharacteristic
239C22×C8—21no—
240C4⋊Q8—22no—
241C4⋊Q8C23×C3712yes—
242C4⋊Q8C23×C3712yes—
243#126—42no—
244#125—22no—
245#125—42no—
246#124—22no—
247C22⋊Q8—22no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—22no—
251C4×Q8C23×C3712yes—
252C4×Q8C23×C3711yescharacteristic
253C4×D4C23×C3711yescharacteristic
254#117—22no—
255#107—21no—
256#107—21no—
257#107—21no—
258#107—21no—
259#107—42no—
260#107D4×C3711yescharacteristic
261#106—22no—
262#106—22no—
263#106D4×C3711yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—22no—
266C4⋊C8C23×C3711yescharacteristic
267C4⋊C8C23×C3711yescharacteristic
268C4⋊C8C23×C3712yes—
269#103—22no—
270#103—22no—
271#103—22no—
272#103—22no—
273#103D4×C3711yescharacteristic
274#103D4×C3712yes—
275#102D4×C3711yescharacteristic
276C22⋊C8—21no—
277#97—22no—
278C4×C8—21no—
279C4×C8C23×C3711yescharacteristic
280C4×C8C23×C3711yescharacteristic
281C4×C8C23×C3711yescharacteristic
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8C2×D4×C3712yes—
285C2×Q8C2×D4×C3711yescharacteristic
286C2×D4C2×D4×C3711yescharacteristic
287C22×C4—21no—
288Q16—22no—
289Q16—44no—
290Q16—82no—
291Q16—82no—
292SD16—22no—
293SD16—82no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—42no—
299C2×C8C2×D4×C3711yescharacteristic
300C2×C8C2×D4×C3711yescharacteristic
301C2×C8C2×D4×C3711yescharacteristic
302C2×C8C2×D4×C3711yescharacteristic
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4C2×D4×C3711yescharacteristic
314C4⋊C4C2×D4×C3711yescharacteristic
315C4⋊C4C2×D4×C3712yes—
316C22⋊C4—21no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C42—21no—
320C42—22no—
321C42—42no—
322C42—42no—
323C42C24×C3711yescharacteristic
324C23—21no—
325Q8—21no—
326Q8—22no—
327Q8—21no—
328Q8—22no—
329Q8—42no—
330Q8—42no—
331Q8—42no—
332Q8—42no—
333D4—21no—
334D4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4C22×D4×C3711yescharacteristic
345C2×C4C22×D4×C3711yescharacteristic
346C2×C4H(5,𝔽2)×C3711yescharacteristic
347C8—22no—
348C8—21no—
349C8—21no—
350C8—41no—
351C8—42no—
352C8—41no—
353C8#135×C3712yes—
354C8#137×C3712yes—
355C22—41no—
356C22—41no—
357C22—41no—
358C22D42×C3711yescharacteristic
359C4—21no—
360C4—41no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—42no—
365C4—82no—
366C4—82no—
367C4C2×#135×C3711yescharacteristic
368C4C2×#137×C3711yescharacteristic
369C4C37×#57611yescharacteristic
370C4C37×#57811yescharacteristic
371C2—81no—
372C2C37×#327611yescharacteristic
373C2C37×#328711yescharacteristic
374C2C37×#329311yescharacteristic
subgroupG/H
center, socleC22×C37D42
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×D4×C37C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3383C2semidirect
4. C37×#1713C2semidirect
5. C37×#1690C2semidirect
6. C37×#1674C2semidirect
9. C37×#1648C2semidirect
10. C37×#1591C2semidirect
167. #19964C37direct (N × H)
185. #3383C2×C37semidirect
187. #1713C2×C37semidirect
188. #1690C2×C37semidirect
189. #1674C2×C37semidirect
192. #1648C2×C37semidirect
193. #1591C2×C37semidirect
232. C37#19964direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#33982
C37×#33832
C37×#33422
C37×#17132
C37×#16902
C37×#16742
C37×#16732
C37×#16502
C37×#16482
C37×#15912
C8×SD16×C372
#1996437