Finite Group Databasebeta

← C37×#24986 #22646239

Subgroups — C37×#24986 #22646239

Order 9472.

642 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3067C211yesmaximal, characteristic
2C37×#2943C211yesmaximal, characteristic, complemented
3C37×#2080C212yesmaximal, complemented
4C37×#2053C212yesmaximal, complemented
5C37×#1976C211yesmaximal, characteristic, complemented
6C37×#1946C211yesmaximal, characteristic, complemented
7C37×#1906C212yesmaximal, complemented
8C37×#1833C211yesmaximal, characteristic, complemented
9C37×#1827C212yesmaximal, complemented
10C37×#1812C211yesmaximal, characteristic, complemented
11C37×#1765C211yesmaximal, characteristic, complemented
12C37×#575C2212yes—
13C2×#135×C37C2211yescharacteristic
14C2×#131×C37C2211yescharacteristic
15C4×#41×C37C2212yes—
16C37×#473—21no—
17C37×#472—21no—
18C37×#471—22no—
19C37×#442—21no—
20C37×#441—21no—
21C37×#440—22no—
22C2×#108×C37C2211yescharacteristic
23C37×#427C2211yescharacteristic
24C37×#427C2211yescharacteristic
25C37×#424C2212yes—
26C37×#421C2212yes—
27C2×#104×C37C2211yescharacteristic
28C37×#416C2212yes—
29C37×#416C2211yescharacteristic
30C37×#413C2212yes—
31C37×#410C2212yes—
32C37×#410C2212yes—
33C37×#405C2211yescharacteristic
34C2×#97×C37C2211yescharacteristic
35C37×#344C2212yes—
36C37×#341C2211yescharacteristic
37C37×#339C2212yes—
38C37×#339C2211yescharacteristic
39C37×H(3,ℤ/4)C2212yes—
40C37×H(3,ℤ/4)C2212yes—
41C2×#41×C37C2312yes—
42C2×#41×C37C2311yescharacteristic
43#137×C37—22no—
44#137×C37—22no—
45AGL(1,ℤ/8)×C37—22no—
46AGL(1,ℤ/8)×C37—22no—
47#135×C37—21no—
48#135×C37—21no—
49#135×C37—21no—
50#135×C37—21no—
51#135×C37—42no—
52C2×Q16×C37D411yescharacteristic
53C2×SD16×C37D412yes—
54C2×D8×C37D411yescharacteristic
55#131×C37—21no—
56#131×C37—21no—
57#131×C37—21no—
58#131×C37—21no—
59C2×M16×C37—21no—
60C2×M16×C37C2311yescharacteristic
61C2×M16×C37C2312yes—
62C2×M16×C37C2311yescharacteristic
63C22×C8×C37—21no—
64C22×C8×C37C2311yescharacteristic
65C22×C8×C37C2311yescharacteristic
66C4×Q8×C37—22no—
67C4×D4×C37—22no—
68C4×D4×C37—42no—
69#117×C37—22no—
70#117×C37C2311yescharacteristic
71#117×C37C2312yes—
72#117×C37C2312yes—
73C2×C42×C37—22no—
74C2×C42×C37C2311yescharacteristic
75#108×C37—21no—
76#108×C37—21no—
77#107×C37—21no—
78#107×C37—21no—
79#106×C37—21no—
80#106×C37—21no—
81C4⋊C8×C37—42no—
82#104×C37—22no—
83#104×C37—42no—
84#103×C37—22no—
85#103×C37—21no—
86#102×C37—22no—
87#102×C37—21no—
88#101×C37—22no—
89#100×C37—22no—
90#99×C37—42no—
91#99×C37—42no—
92#97×C37—21no—
93#97×C37—21no—
94#97×C37—21no—
95C4×C8×C37—21no—
96#41×C37—21no—
97#41×C37—21no—
98#41×C37—21no—
99#41×C37—22no—
100#41×C37—22no—
101#41×C37—22no—
102#41×C37—22no—
103#41×C37—21no—
104C2×Q8×C37C2×D412yes—
105C2×Q8×C37#4111yescharacteristic
106C2×D4×C37—21no—
107C2×D4×C37—22no—
108C2×D4×C37C2×D412yes—
109C2×D4×C37#4111yescharacteristic
110C22×C4×C37—21no—
111C22×C4×C37—22no—
112C22×C4×C37—21no—
113C22×C4×C37—42no—
114C22×C4×C37C2411yescharacteristic
115Q16×C37—21no—
116Q16×C37—21no—
117Q16×C37—42no—
118SD16×C37—22no—
119SD16×C37—22no—
120SD16×C37—42no—
121SD16×C37—42no—
122D8×C37—21no—
123D8×C37—21no—
124D8×C37—42no—
125M16×C37—21no—
126M16×C37—22no—
127M16×C37—21no—
128M16×C37—21no—
129M16×C37—22no—
130M16×C37—21no—
131M16×C37—41no—
132M16×C37—41no—
133C2×C8×C37—21no—
134C2×C8×C37—21no—
135C2×C8×C37—21no—
136C2×C8×C37—21no—
137C2×C8×C37—21no—
138C2×C8×C37—22no—
139C2×C8×C37—41no—
140C2×C8×C37—41no—
141C2×C8×C37C2×D411yescharacteristic
142C2×C8×C37C2×D411yescharacteristic
143C2×C8×C37#4111yescharacteristic
144C2×C8×C37#4111yescharacteristic
145C2×C8×C37#4111yescharacteristic
146C2×C8×C37#4111yescharacteristic
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—22no—
150C4⋊C4×C37—42no—
151C22⋊C4×C37—22no—
152C22⋊C4×C37—21no—
153C22⋊C4×C37—22no—
154C22⋊C4×C37—42no—
155C42×C37—21no—
156C42×C37—21no—
157C42×C37—22no—
158C42×C37—22no—
159C42×C37—42no—
160C42×C37#4112yes—
161C23×C37—22no—
162C23×C37—21no—
163C23×C37H(5,𝔽2)11yescharacteristic
164Q8×C37—22no—
165Q8×C37—21no—
166Q8×C37—21no—
167Q8×C37—22no—
168D4×C37—22no—
169D4×C37—21no—
170D4×C37—21no—
171D4×C37—22no—
172D4×C37—41no—
173D4×C37—42no—
174D4×C37—41no—
175D4×C37—42no—
176C2×C4×C37—22no—
177C2×C4×C37—22no—
178C2×C4×C37—21no—
179C2×C4×C37—41no—
180C2×C4×C37—42no—
181C2×C4×C37—42no—
182C2×C4×C37—41no—
183C2×C4×C37—42no—
184C2×C4×C37—42no—
185C2×C4×C37—41no—
186C2×C4×C37—81no—
187C2×C4×C37—84no—
188C2×C4×C37C22×D411yescharacteristic
189C2×C4×C37C2×#4111yescharacteristic
190C2×C4×C37C2×#4111yescharacteristic
191C2×C4×C37C2×#4111yescharacteristic
192C2×C4×C37C2×#4111yescharacteristic
193C2×C4×C37H(5,𝔽2)11yescharacteristic
194C8×C37—41no—
195C8×C37—41no—
196C8×C37—42no—
197C8×C37—41no—
198C8×C37#12311yescharacteristic
199C8×C37#12311yescharacteristic
200C8×C37#12311yescharacteristic
201C8×C37#12311yescharacteristic
202#24986C3711yesmaximal, characteristic, direct product factor, Sylow
203C22×C37—41no—
204C22×C37—41no—
205C22×C37—42no—
206C22×C37—82no—
207C22×C37—81no—
208C22×C37#54011yescharacteristic
209C22×C37#54611yescharacteristic
210C22×C37#55311yescharacteristic
211C4×C37—42no—
212C4×C37—42no—
213C4×C37—41no—
214C4×C37—82no—
215C4×C37—81no—
216C4×C37—82no—
217C4×C37C2×#12311yescharacteristic
218C4×C37#52911yescharacteristic
219C4×C37#54611yescharacteristic
220C4×C37#55511yescharacteristic
221#3067C2×C3711yescharacteristic
222#2943C2×C3711yescharacteristic, complemented
223#2080C2×C3712yescomplemented
224#2053C2×C3712yescomplemented
225#1976C2×C3711yescharacteristic, complemented
226#1946C2×C3711yescharacteristic, complemented
227#1906C2×C3712yescomplemented
228#1833C2×C3711yescharacteristic, complemented
229#1827C2×C3712yescomplemented
230#1812C2×C3711yescharacteristic, complemented
231#1765C2×C3711yescharacteristic, complemented
232C2×C37—21no—
233C2×C37—21no—
234C2×C37—21no—
235C2×C37—82no—
236C2×C37—81no—
237C2×C37#242011yescharacteristic
238#575C22×C3712yes—
239C2×#135C22×C3711yescharacteristic
240C2×#131C22×C3711yescharacteristic
241C4×#41C22×C3712yes—
242#473—21no—
243#472—21no—
244#471—22no—
245#442—21no—
246#441—21no—
247#440—22no—
248C2×#108C22×C3711yescharacteristic
249#427C22×C3711yescharacteristic
250#427C22×C3711yescharacteristic
251#424C22×C3712yes—
252#421C22×C3712yes—
253C2×#104C22×C3711yescharacteristic
254#416C22×C3711yescharacteristic
255#416C22×C3712yes—
256#413C22×C3712yes—
257#410C22×C3712yes—
258#410C22×C3712yes—
259#405C22×C3711yescharacteristic
260C2×#97C22×C3711yescharacteristic
261#344C22×C3712yes—
262#341C22×C3711yescharacteristic
263#339C22×C3711yescharacteristic
264#339C22×C3712yes—
265H(3,ℤ/4)C22×C3712yes—
266H(3,ℤ/4)C22×C3712yes—
267C37#2498611yescharacteristic, direct product factor, Sylow
268C2×#41C23×C3712yes—
269C2×#41C23×C3711yescharacteristic
270#137—22no—
271#137—22no—
272AGL(1,ℤ/8)—22no—
273AGL(1,ℤ/8)—22no—
274#135—21no—
275#135—21no—
276#135—21no—
277#135—21no—
278#135—42no—
279C2×Q16D4×C3711yescharacteristic
280C2×SD16D4×C3712yes—
281C2×D8D4×C3711yescharacteristic
282#131—21no—
283#131—21no—
284#131—21no—
285#131—21no—
286C2×M16—21no—
287C2×M16C23×C3711yescharacteristic
288C2×M16C23×C3712yes—
289C2×M16C23×C3711yescharacteristic
290C22×C8—21no—
291C22×C8C23×C3711yescharacteristic
292C22×C8C23×C3711yescharacteristic
293C4×Q8—22no—
294C4×D4—22no—
295C4×D4—42no—
296#117—22no—
297#117C23×C3712yes—
298#117C23×C3711yescharacteristic
299#117C23×C3712yes—
300C2×C42—22no—
301C2×C42C23×C3711yescharacteristic
302#108—21no—
303#108—21no—
304#107—21no—
305#107—21no—
306#106—21no—
307#106—21no—
308C4⋊C8—42no—
309#104—22no—
310#104—42no—
311#103—22no—
312#103—21no—
313#102—22no—
314#102—21no—
315#101—22no—
316#100—22no—
317#99—42no—
318#99—42no—
319#97—21no—
320#97—21no—
321#97—21no—
322C4×C8—21no—
323#41—21no—
324#41—21no—
325#41—21no—
326#41—22no—
327#41—22no—
328#41—22no—
329#41—22no—
330#41—21no—
331C2×Q8C2×D4×C3712yes—
332C2×Q8#41×C3711yescharacteristic
333C2×D4—21no—
334C2×D4—22no—
335C2×D4C2×D4×C3712yes—
336C2×D4#41×C3711yescharacteristic
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4C24×C3711yescharacteristic
342Q16—21no—
343Q16—21no—
344Q16—42no—
345SD16—22no—
346SD16—22no—
347SD16—42no—
348SD16—42no—
349D8—21no—
350D8—21no—
351D8—42no—
352M16—21no—
353M16—22no—
354M16—21no—
355M16—21no—
356M16—22no—
357M16—21no—
358M16—41no—
359M16—41no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8C2×D4×C3711yescharacteristic
369C2×C8C2×D4×C3711yescharacteristic
370C2×C8#41×C3711yescharacteristic
371C2×C8#41×C3711yescharacteristic
372C2×C8#41×C3711yescharacteristic
373C2×C8#41×C3711yescharacteristic
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—42no—
378C22⋊C4—22no—
379C22⋊C4—21no—
380C22⋊C4—22no—
381C22⋊C4—42no—
382C42—21no—
383C42—21no—
384C42—22no—
385C42—22no—
386C42—42no—
387C42#41×C3712yes—
388C23—22no—
389C23—21no—
390C23H(5,𝔽2)×C3711yescharacteristic
391Q8—22no—
392Q8—21no—
393Q8—21no—
394Q8—22no—
395D4—22no—
396D4—21no—
397D4—21no—
398D4—22no—
399D4—41no—
400D4—42no—
401D4—41no—
402D4—42no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—84no—
415C2×C4C22×D4×C3711yescharacteristic
416C2×C4C2×#41×C3711yescharacteristic
417C2×C4C2×#41×C3711yescharacteristic
418C2×C4C2×#41×C3711yescharacteristic
419C2×C4C2×#41×C3711yescharacteristic
420C2×C4H(5,𝔽2)×C3711yescharacteristic
421C8—41no—
422C8—41no—
423C8—42no—
424C8—41no—
425C8#123×C3711yescharacteristic
426C8#123×C3711yescharacteristic
427C8#123×C3711yescharacteristic
428C8#123×C3711yescharacteristic
429C22—41no—
430C22—41no—
431C22—42no—
432C22—82no—
433C22—81no—
434C22C37×#54011yescharacteristic
435C22C37×#54611yescharacteristic
436C22C37×#55311yescharacteristic
437C4—42no—
438C4—42no—
439C4—41no—
440C4—82no—
441C4—82no—
442C4—81no—
443C4C2×#123×C3711yescharacteristic
444C4C37×#52911yescharacteristic
445C4C37×#54611yescharacteristic
446C4C37×#55511yescharacteristic
447C2—21no—
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2C37×#242011yescharacteristic
subgroupG/H
centerC4×C37#555
commutator, Frattini, cosocleC22×C4C24×C37
socleC2×C37#2420
prime radicalC37×#3067C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C37 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2943C2semidirect
3. C37×#2080C2semidirect
4. C37×#2053C2semidirect
5. C37×#1976C2semidirect
6. C37×#1946C2semidirect
7. C37×#1906C2semidirect
8. C37×#1833C2semidirect
9. C37×#1827C2semidirect
10. C37×#1812C2semidirect
11. C37×#1765C2semidirect
202. #24986C37direct (N × H)
222. #2943C2×C37semidirect
223. #2080C2×C37semidirect
224. #2053C2×C37semidirect
225. #1976C2×C37semidirect
226. #1946C2×C37semidirect
227. #1906C2×C37semidirect
228. #1833C2×C37semidirect
229. #1827C2×C37semidirect
230. #1812C2×C37semidirect
231. #1765C2×C37semidirect
267. C37#24986direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#30672
C37×#29432
C37×#20802
C37×#20532
C37×#19762
C37×#19462
C37×#19062
C37×#18332
C37×#18272
C37×#18122
C37×#17652
#2498637