Finite Group Databasebeta

← C37×#33619 #22654872

Subgroups — C37×#33619 #22654872

Order 9472.

636 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#510C211yesmaximal, characteristic, complemented
2C37×#3407C211yesmaximal, characteristic, complemented
3C37×#3067C211yesmaximal, characteristic
4C2×C37×#473C211yesmaximal, characteristic, complemented
5C37×#2223C214yesmaximal, complemented
6C37×#2222C214yesmaximal, complemented
7C37×#2161C211yesmaximal, characteristic, complemented
8C37×#2148C211yesmaximal, characteristic, complemented
9C2×C37×#362C211yesmaximal, characteristic, complemented
10C37×#575—21no—
11C2×#137×C37—21no—
12C2×#135×C37C2211yescharacteristic
13C22×Q16×C37C2211yescharacteristic
14C2×#131×C37C2211yescharacteristic
15C37×#510—22no—
16C37×#510—22no—
17C2×Q32×C37C2212yescomplemented
18C2×SD32×C37C2212yescomplemented
19C37×#504—22no—
20C37×#504C2214yes—
21C2×M32×C37—22no—
22C2×M32×C37C2211yescharacteristic
23C2×M32×C37C2211yescharacteristic
24C37×#473—22no—
25C37×#473C2212yes—
26C37×#473C2214yes—
27C37×#472C2212yes—
28C37×#471—22no—
29C2×#108×C37C2211yescharacteristic
30C2×#108×C37C2211yescharacteristic
31C37×#413—21no—
32C2×#101×C37—21no—
33C37×#368C2214yescomplemented
34C37×#362C2214yescomplemented
35C37×#362C2212yescomplemented
36C37×#361C2212yescomplemented
37C2×#41×C37—21no—
38C2×#41×C37D411yescharacteristic
39C22×Q8×C37—21no—
40#137×C37—24no—
41#137×C37—22no—
42#137×C37—42no—
43#137×C37—41no—
44AGL(1,ℤ/8)×C37—22no—
45AGL(1,ℤ/8)×C37—41no—
46#135×C37—21no—
47#135×C37—21no—
48#135×C37—21no—
49#135×C37—21no—
50#135×C37—42no—
51C2×Q16×C37—21no—
52C2×Q16×C37—21no—
53C2×Q16×C37—21no—
54C2×Q16×C37—21no—
55C2×Q16×C37—21no—
56C2×Q16×C37—41no—
57C2×Q16×C37C2312yes—
58C2×Q16×C37C2311yescharacteristic
59C2×SD16×C37—21no—
60C2×SD16×C37—41no—
61C2×D8×C37C2311yescharacteristic
62#131×C37—21no—
63#131×C37—21no—
64#131×C37D412yes—
65#131×C37C2312yes—
66C2×M16×C37—21no—
67C2×M16×C37—21no—
68C2×M16×C37—21no—
69C2×M16×C37D411yescharacteristic
70C22×C8×C37—21no—
71C22×C8×C37C2311yescharacteristic
72Q32×C37—24no—
73SD32×C37—24no—
74M32×C37—21no—
75M32×C37—24no—
76M32×C37D412yes—
77M32×C37D412yes—
78M32×C37C2312yes—
79C2×C16×C37—21no—
80C2×C16×C37—24no—
81C2×C16×C37C2312yes—
82#108×C37—21no—
83#108×C37—21no—
84#108×C37C2312yes—
85#108×C37C2312yes—
86#101×C37—24no—
87#101×C37—22no—
88#100×C37—22no—
89#41×C37—21no—
90#41×C37—21no—
91#41×C37—41no—
92#41×C37—41no—
93#41×C37—41no—
94#41×C37—41no—
95#41×C37D812yes—
96#41×C37C2×D412yes—
97C2×Q8×C37—21no—
98C2×Q8×C37—22no—
99C2×Q8×C37—41no—
100C2×Q8×C37—41no—
101C2×Q8×C37—41no—
102C2×Q8×C37—41no—
103C2×Q8×C37—41no—
104C2×Q8×C37D811yescharacteristic
105C2×D4×C37—21no—
106C2×D4×C37—21no—
107C2×D4×C37—41no—
108C2×D4×C37D811yescharacteristic
109C22×C4×C37—21no—
110C22×C4×C37—41no—
111C22×C4×C37—41no—
112C22×C4×C37C2×D411yescharacteristic
113Q16×C37—22no—
114Q16×C37—21no—
115Q16×C37—22no—
116Q16×C37—21no—
117Q16×C37—44no—
118Q16×C37—42no—
119Q16×C37—41no—
120Q16×C37—41no—
121SD16×C37—42no—
122SD16×C37—44no—
123SD16×C37—42no—
124SD16×C37—41no—
125SD16×C37—41no—
126D8×C37—21no—
127D8×C37—21no—
128D8×C37—42no—
129M16×C37—21no—
130M16×C37—22no—
131M16×C37—22no—
132M16×C37—22no—
133M16×C37—22no—
134M16×C37—41no—
135M16×C37—41no—
136M16×C37C2×D412yes—
137C2×C8×C37—21no—
138C2×C8×C37—22no—
139C2×C8×C37—22no—
140C2×C8×C37—41no—
141C2×C8×C37—41no—
142C2×C8×C37C2×D411yescharacteristic
143C2×C8×C37C2×D411yescharacteristic
144C2×C8×C37C2×D411yescharacteristic
145C2×C8×C37#4111yescharacteristic
146C2×C8×C37#4111yescharacteristic
147C2×C8×C37C2411yescharacteristic
148C16×C37—22no—
149C16×C37C2×D414yes—
150C23×C37—21no—
151C23×C37—41no—
152C23×C37#13511yescharacteristic
153Q8×C37—21no—
154Q8×C37—41no—
155Q8×C37—42no—
156Q8×C37—42no—
157Q8×C37—41no—
158Q8×C37—81no—
159Q8×C37—81no—
160Q8×C37C2×D812yes—
161D4×C37—22no—
162D4×C37—22no—
163D4×C37—21no—
164D4×C37—41no—
165D4×C37—41no—
166D4×C37—81no—
167D4×C37—81no—
168D4×C37C2×D812yes—
169C2×C4×C37—21no—
170C2×C4×C37—22no—
171C2×C4×C37—22no—
172C2×C4×C37—41no—
173C2×C4×C37—42no—
174C2×C4×C37—81no—
175C2×C4×C37—81no—
176C2×C4×C37—81no—
177C2×C4×C37—81no—
178C2×C4×C37#12111yescharacteristic
179C2×C4×C37#12111yescharacteristic
180C2×C4×C37C2×D811yescharacteristic
181C2×C4×C37C2×D811yescharacteristic
182C2×C4×C37#13511yescharacteristic
183C2×C4×C37C22×D411yescharacteristic
184C8×C37—22no—
185C8×C37—42no—
186C8×C37—42no—
187C8×C37#12111yescharacteristic
188C8×C37#12111yescharacteristic
189C8×C37C22×D411yescharacteristic
190C8×C37C2×#4111yescharacteristic
191#33619C3711yesmaximal, characteristic, direct product factor, Sylow
192C22×C37—22no—
193C22×C37—41no—
194C22×C37—81no—
195C22×C37—81no—
196C22×C37—161no—
197C22×C37#46611yescharacteristic
198C22×C37#46611yescharacteristic
199C22×C37C2×#13511yescharacteristic
200C4×C37—22no—
201C4×C37—81no—
202C4×C37—82no—
203C4×C37#46611yescharacteristic
204C4×C37#46611yescharacteristic
205C4×C37C2×#12111yescharacteristic
206C4×C37C22×D811yescharacteristic
207C2×#510C2×C3711yescharacteristic, complemented
208#3407C2×C3711yescharacteristic, complemented
209#3067C2×C3711yescharacteristic
210C2×#473C2×C3711yescharacteristic, complemented
211#2223C2×C3714yescomplemented
212#2222C2×C3714yescomplemented
213#2161C2×C3711yescharacteristic, complemented
214#2148C2×C3711yescharacteristic, complemented
215C2×#362C2×C3711yescharacteristic, complemented
216C2×C37—21no—
217C2×C37—21no—
218C2×C37—21no—
219C2×C37—42no—
220C2×C37—161no—
221C2×C37C2×#46611yescharacteristic
222#575—21no—
223C2×#137—21no—
224C2×#135C22×C3711yescharacteristic
225C22×Q16C22×C3711yescharacteristic
226C2×#131C22×C3711yescharacteristic
227#510—22no—
228#510—22no—
229C2×Q32C22×C3712yescomplemented
230C2×SD32C22×C3712yescomplemented
231#504—22no—
232#504C22×C3714yes—
233C2×M32—22no—
234C2×M32C22×C3711yescharacteristic
235C2×M32C22×C3711yescharacteristic
236#473—22no—
237#473C22×C3712yes—
238#473C22×C3714yes—
239#472C22×C3712yes—
240#471—22no—
241C2×#108C22×C3711yescharacteristic
242C2×#108C22×C3711yescharacteristic
243#413—21no—
244C2×#101—21no—
245#368C22×C3714yescomplemented
246#362C22×C3714yescomplemented
247#362C22×C3712yescomplemented
248#361C22×C3712yescomplemented
249C37#3361911yescharacteristic, direct product factor, Sylow
250C2×#41—21no—
251C2×#41D4×C3711yescharacteristic
252C22×Q8—21no—
253#137—24no—
254#137—22no—
255#137—42no—
256#137—41no—
257AGL(1,ℤ/8)—22no—
258AGL(1,ℤ/8)—41no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263#135—42no—
264C2×Q16—21no—
265C2×Q16—21no—
266C2×Q16—21no—
267C2×Q16—21no—
268C2×Q16—21no—
269C2×Q16—41no—
270C2×Q16C23×C3712yes—
271C2×Q16C23×C3711yescharacteristic
272C2×SD16—21no—
273C2×SD16—41no—
274C2×D8C23×C3711yescharacteristic
275#131—21no—
276#131—21no—
277#131D4×C3712yes—
278#131C23×C3712yes—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—21no—
282C2×M16D4×C3711yescharacteristic
283C22×C8—21no—
284C22×C8C23×C3711yescharacteristic
285Q32—24no—
286SD32—24no—
287M32—21no—
288M32—24no—
289M32D4×C3712yes—
290M32D4×C3712yes—
291M32C23×C3712yes—
292C2×C16—21no—
293C2×C16—24no—
294C2×C16C23×C3712yes—
295#108—21no—
296#108—21no—
297#108C23×C3712yes—
298#108C23×C3712yes—
299#101—24no—
300#101—22no—
301#100—22no—
302#41—21no—
303#41—21no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41D8×C3712yes—
309#41C2×D4×C3712yes—
310C2×Q8—21no—
311C2×Q8—22no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8D8×C3711yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4D8×C3711yescharacteristic
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4C2×D4×C3711yescharacteristic
326Q16—22no—
327Q16—21no—
328Q16—22no—
329Q16—21no—
330Q16—44no—
331Q16—42no—
332Q16—41no—
333Q16—41no—
334SD16—42no—
335SD16—44no—
336SD16—42no—
337SD16—41no—
338SD16—41no—
339D8—21no—
340D8—21no—
341D8—42no—
342M16—21no—
343M16—22no—
344M16—22no—
345M16—22no—
346M16—22no—
347M16—41no—
348M16—41no—
349M16C2×D4×C3712yes—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8C2×D4×C3711yescharacteristic
356C2×C8C2×D4×C3711yescharacteristic
357C2×C8C2×D4×C3711yescharacteristic
358C2×C8#41×C3711yescharacteristic
359C2×C8#41×C3711yescharacteristic
360C2×C8C24×C3711yescharacteristic
361C16—22no—
362C16C2×D4×C3714yes—
363C23—21no—
364C23—41no—
365C23#135×C3711yescharacteristic
366Q8—21no—
367Q8—41no—
368Q8—42no—
369Q8—42no—
370Q8—41no—
371Q8—81no—
372Q8—81no—
373Q8C2×D8×C3712yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4C2×D8×C3712yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4#121×C3711yescharacteristic
392C2×C4#121×C3711yescharacteristic
393C2×C4C2×D8×C3711yescharacteristic
394C2×C4C2×D8×C3711yescharacteristic
395C2×C4#135×C3711yescharacteristic
396C2×C4C22×D4×C3711yescharacteristic
397C8—22no—
398C8—42no—
399C8—42no—
400C8#121×C3711yescharacteristic
401C8#121×C3711yescharacteristic
402C8C22×D4×C3711yescharacteristic
403C8C2×#41×C3711yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—81no—
408C22—161no—
409C22C37×#46611yescharacteristic
410C22C37×#46611yescharacteristic
411C22C2×#135×C3711yescharacteristic
412C4—22no—
413C4—81no—
414C4—82no—
415C4C37×#46611yescharacteristic
416C4C37×#46611yescharacteristic
417C4C2×#121×C3711yescharacteristic
418C4C22×D8×C3711yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—161no—
424C2C2×C37×#46611yescharacteristic
subgroupG/H
center, socleC2×C37C2×#466
commutator, Frattini, cosocleC2×C8C24×C37
prime radicalC37×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C22×C4×C37 ◁ C2×#131×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#510C2semidirect
2. C37×#3407C2semidirect
4. C2×C37×#473C2semidirect
5. C37×#2223C2semidirect
6. C37×#2222C2semidirect
7. C37×#2161C2semidirect
8. C37×#2148C2semidirect
9. C2×C37×#362C2semidirect
17. C2×Q32×C37C22semidirect
18. C2×SD32×C37C22semidirect
33. C37×#368C22semidirect
34. C37×#362C22semidirect
35. C37×#362C22semidirect
36. C37×#361C22semidirect
191. #33619C37direct (N × H)
207. C2×#510C2×C37semidirect
208. #3407C2×C37semidirect
210. C2×#473C2×C37semidirect
211. #2223C2×C37semidirect
212. #2222C2×C37semidirect
213. #2161C2×C37semidirect
214. #2148C2×C37semidirect
215. C2×#362C2×C37semidirect
229. C2×Q32C22×C37semidirect
230. C2×SD32C22×C37semidirect
245. #368C22×C37semidirect
246. #362C22×C37semidirect
247. #362C22×C37semidirect
248. #361C22×C37semidirect
249. C37#33619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5102
C37×#34072
C37×#30672
C2×C37×#4732
C37×#22232
C37×#22222
C37×#21612
C37×#21482
C2×C37×#3622
#3361937