Finite Group Databasebeta

← C37×#13677 #22634930

Subgroups — C37×#13677 #22634930

Order 9472.

420 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3288C211yesmaximal, characteristic, complemented
2C37×#2202C211yesmaximal, characteristic, complemented
3C37×#2199C211yesmaximal, characteristic, complemented
4C37×#1655C211yesmaximal, characteristic, complemented
5C37×#1406C211yesmaximal, characteristic, complemented
6C37×#1404C211yesmaximal, characteristic, complemented
7C37×#1403C211yesmaximal, characteristic, complemented
8C37×#577—21no—
9C37×#576—21no—
10C37×H(3,𝔽4)C2211yescharacteristic, complemented
11C37×#496—21no—
12C37×#496C2211yescharacteristic
13C37×#472—21no—
14C37×#471—21no—
15C37×B(4,𝔽2)—21no—
16C37×#455C2211yescharacteristic
17C37×#454—21no—
18C37×#454C2211yescharacteristic
19C37×#453—21no—
20C37×#444—21no—
21C37×#355—21no—
22C37×#355C2211yescharacteristic, complemented
23C37×#354C2211yescharacteristic, complemented
24C37×AΣL(1,𝔽16)—21no—
25C37×#329—21no—
26C37×#329C2211yescharacteristic, complemented
272−1+4×C37D411yescharacteristic, complemented
28H(5,𝔽2)×C37—21no—
29H(5,𝔽2)×C37D411yescharacteristic
30#137×C37—21no—
31#137×C37—41no—
32AGL(1,ℤ/8)×C37—21no—
33AGL(1,ℤ/8)×C37—21no—
34AGL(1,ℤ/8)×C37—21no—
35AGL(1,ℤ/8)×C37—41no—
36AGL(1,ℤ/8)×C37—41no—
37AGL(1,ℤ/8)×C37—41no—
38AGL(1,ℤ/8)×C37—41no—
39#135×C37—21no—
40#135×C37—41no—
41#135×C37—41no—
42C2×SD16×C37—21no—
43C2×SD16×C37—41no—
44C2×SD16×C37—41no—
45C2×D8×C37—21no—
46C2×D8×C37—41no—
47C2×D8×C37—41no—
48#131×C37—21no—
49#131×C37—21no—
50#127×C37D411yescharacteristic, complemented
51#124×C37—21no—
52#124×C37—21no—
53#124×C37—41no—
54#124×C37C2311yescharacteristic
55#120×C37—21no—
56#120×C37—41no—
57#120×C37—41no—
58#108×C37—21no—
59#104×C37—21no—
60#104×C37—21no—
61#104×C37—41no—
62#101×C37—21no—
63#101×C37D411yescharacteristic, complemented
64#100×C37—21no—
65#100×C37D411yescharacteristic
66#99×C37—21no—
67#99×C37—41no—
68#97×C37—21no—
69#97×C37D411yescharacteristic, complemented
70C24×C37—21no—
71#41×C37—21no—
72#41×C37—21no—
73#41×C37—41no—
74#41×C37—41no—
75#41×C37—41no—
76#41×C37—41no—
77#41×C37—41no—
78C2×Q8×C37—21no—
79C2×Q8×C37—41no—
80C2×Q8×C37C2×D411yescharacteristic
81C2×D4×C37—21no—
82C2×D4×C37—21no—
83C2×D4×C37—21no—
84C2×D4×C37—41no—
85C2×D4×C37—41no—
86C2×D4×C37—41no—
87C2×D4×C37—41no—
88C2×D4×C37—41no—
89C2×D4×C37—41no—
90C2×D4×C37—81no—
91C2×D4×C37—81no—
92C2×D4×C37C2×D411yescharacteristic
93Q16×C37—21no—
94Q16×C37—41no—
95SD16×C37—21no—
96SD16×C37—21no—
97SD16×C37—41no—
98SD16×C37—41no—
99SD16×C37—41no—
100SD16×C37—41no—
101SD16×C37—41no—
102SD16×C37—41no—
103SD16×C37—82no—
104SD16×C37—81no—
105D8×C37—21no—
106D8×C37—41no—
107D8×C37—41no—
108D8×C37—41no—
109D8×C37—41no—
110D8×C37—41no—
111D8×C37—82no—
112D8×C37—81no—
113M16×C37—21no—
114M16×C37—21no—
115M16×C37—41no—
116M16×C37—41no—
117M16×C37—41no—
118C2×C8×C37—21no—
119C2×C8×C37—41no—
120C2×C8×C37—41no—
121C2×C8×C37—41no—
122C22⋊C4×C37—21no—
123C22⋊C4×C37—41no—
124C22⋊C4×C37—41no—
125C22⋊C4×C37—41no—
126C22⋊C4×C37—41no—
127C22⋊C4×C37—41no—
128C22⋊C4×C37—81no—
129C42×C37—21no—
130C42×C37C2×D411yescharacteristic
131C23×C37—21no—
132C23×C37—41no—
133C23×C37—41no—
134C23×C37—41no—
135C23×C37—81no—
136C23×C37—81no—
137C23×C37—161no—
138Q8×C37—21no—
139Q8×C37—21no—
140Q8×C37—41no—
141Q8×C37—41no—
142Q8×C37—81no—
143D4×C37—21no—
144D4×C37—21no—
145D4×C37—41no—
146D4×C37—41no—
147D4×C37—41no—
148D4×C37—41no—
149D4×C37—41no—
150D4×C37—41no—
151D4×C37—81no—
152D4×C37—81no—
153D4×C37—81no—
154D4×C37—81no—
155D4×C37—81no—
156D4×C37—81no—
157D4×C37—81no—
158D4×C37—161no—
159D4×C37—162no—
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—41no—
163C2×C4×C37—41no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
166C2×C4×C37—81no—
167C2×C4×C37—81no—
168C2×C4×C37—81no—
169C2×C4×C37#12011yescharacteristic
170C8×C37—21no—
171C8×C37—21no—
172C8×C37—41no—
173C8×C37—41no—
174C8×C37—42no—
175C8×C37—81no—
176#13677C3711yesmaximal, characteristic, direct product factor, Sylow
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—81no—
181C22×C37—81no—
182C22×C37—81no—
183C22×C37—82no—
184C22×C37—81no—
185C22×C37—81no—
186C22×C37—161no—
187C22×C37—161no—
188C22×C37—161no—
189C22×C37—321no—
190C22×C37B(4,𝔽2)11yescharacteristic
191C4×C37—21no—
192C4×C37—41no—
193C4×C37—41no—
194C4×C37—41no—
195C4×C37—41no—
196C4×C37—81no—
197C4×C37—161no—
198#3288C2×C3711yescharacteristic, complemented
199#2202C2×C3711yescharacteristic, complemented
200#2199C2×C3711yescharacteristic, complemented
201#1655C2×C3711yescharacteristic, complemented
202#1406C2×C3711yescharacteristic, complemented
203#1404C2×C3711yescharacteristic, complemented
204#1403C2×C3711yescharacteristic, complemented
205C2×C37—21no—
206C2×C37—81no—
207C2×C37—81no—
208C2×C37—81no—
209C2×C37—161no—
210C2×C37—161no—
211C2×C37#219611yescharacteristic
212#577—21no—
213#576—21no—
214H(3,𝔽4)C22×C3711yescharacteristic, complemented
215#496—21no—
216#496C22×C3711yescharacteristic
217#472—21no—
218#471—21no—
219B(4,𝔽2)—21no—
220#455C22×C3711yescharacteristic
221#454—21no—
222#454C22×C3711yescharacteristic
223#453—21no—
224#444—21no—
225#355—21no—
226#355C22×C3711yescharacteristic, complemented
227#354C22×C3711yescharacteristic, complemented
228AΣL(1,𝔽16)—21no—
229#329—21no—
230#329C22×C3711yescharacteristic, complemented
231C37#1367711yescharacteristic, direct product factor, Sylow
2322−1+4D4×C3711yescharacteristic, complemented
233H(5,𝔽2)—21no—
234H(5,𝔽2)D4×C3711yescharacteristic
235#137—21no—
236#137—41no—
237AGL(1,ℤ/8)—21no—
238AGL(1,ℤ/8)—21no—
239AGL(1,ℤ/8)—21no—
240AGL(1,ℤ/8)—41no—
241AGL(1,ℤ/8)—41no—
242AGL(1,ℤ/8)—41no—
243AGL(1,ℤ/8)—41no—
244#135—21no—
245#135—41no—
246#135—41no—
247C2×SD16—21no—
248C2×SD16—41no—
249C2×SD16—41no—
250C2×D8—21no—
251C2×D8—41no—
252C2×D8—41no—
253#131—21no—
254#131—21no—
255#127D4×C3711yescharacteristic, complemented
256#124—21no—
257#124—21no—
258#124—41no—
259#124C23×C3711yescharacteristic
260#120—21no—
261#120—41no—
262#120—41no—
263#108—21no—
264#104—21no—
265#104—21no—
266#104—41no—
267#101—21no—
268#101D4×C3711yescharacteristic, complemented
269#100—21no—
270#100D4×C3711yescharacteristic
271#99—21no—
272#99—41no—
273#97—21no—
274#97D4×C3711yescharacteristic, complemented
275C24—21no—
276#41—21no—
277#41—21no—
278#41—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8C2×D4×C3711yescharacteristic
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4C2×D4×C3711yescharacteristic
298Q16—21no—
299Q16—41no—
300SD16—21no—
301SD16—21no—
302SD16—41no—
303SD16—41no—
304SD16—41no—
305SD16—41no—
306SD16—41no—
307SD16—41no—
308SD16—82no—
309SD16—81no—
310D8—21no—
311D8—41no—
312D8—41no—
313D8—41no—
314D8—41no—
315D8—41no—
316D8—82no—
317D8—81no—
318M16—21no—
319M16—21no—
320M16—41no—
321M16—41no—
322M16—41no—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C42—21no—
335C42C2×D4×C3711yescharacteristic
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—81no—
341C23—81no—
342C23—161no—
343Q8—21no—
344Q8—21no—
345Q8—41no—
346Q8—41no—
347Q8—81no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—161no—
364D4—162no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4#120×C3711yescharacteristic
375C8—21no—
376C8—21no—
377C8—41no—
378C8—41no—
379C8—42no—
380C8—81no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—82no—
388C22—81no—
389C22—81no—
390C22—161no—
391C22—161no—
392C22—161no—
393C22—321no—
394C22C37×B(4,𝔽2)11yescharacteristic
395C4—21no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—81no—
401C4—161no—
402C2—21no—
403C2—81no—
404C2—81no—
405C2—81no—
406C2—161no—
407C2—161no—
408C2C37×#219611yescharacteristic
subgroupG/H
center, socleC2×C37#2196
commutator, Frattini, cosocle#124C23×C37
LCSG ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C22×C37 ◁ C2×C4×C37 ◁ #124×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3288C2semidirect
2. C37×#2202C2semidirect
3. C37×#2199C2semidirect
4. C37×#1655C2semidirect
5. C37×#1406C2semidirect
6. C37×#1404C2semidirect
7. C37×#1403C2semidirect
10. C37×H(3,𝔽4)C22semidirect
22. C37×#355C22semidirect
23. C37×#354C22semidirect
26. C37×#329C22semidirect
27. 2−1+4×C37D4semidirect
50. #127×C37D4semidirect
63. #101×C37D4semidirect
69. #97×C37D4semidirect
176. #13677C37direct (N × H)
198. #3288C2×C37semidirect
199. #2202C2×C37semidirect
200. #2199C2×C37semidirect
201. #1655C2×C37semidirect
202. #1406C2×C37semidirect
203. #1404C2×C37semidirect
204. #1403C2×C37semidirect
214. H(3,𝔽4)C22×C37semidirect
226. #355C22×C37semidirect
227. #354C22×C37semidirect
230. #329C22×C37semidirect
231. C37#13677direct (N × H)
232. 2−1+4D4×C37semidirect
255. #127D4×C37semidirect
268. #101D4×C37semidirect
274. #97D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#32882
C37×#22022
C37×#21992
C37×#16552
C37×#14062
C37×#14042
C37×#14032
#1367737