Finite Group Databasebeta

← C37×#19520 #22640773

Subgroups — C37×#19520 #22640773

Order 9472.

612 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3237C211yesmaximal, characteristic, complemented
2C37×#3208C211yesmaximal, characteristic
3C37×#3208C211yesmaximal, characteristic
4C37×#2985C211yesmaximal, characteristic, complemented
5C37×#1698C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1678C212yesmaximal, complemented
8C37×#1666C212yesmaximal, complemented
9C37×#1572C211yesmaximal, characteristic, complemented
10C37×#1555C211yesmaximal, characteristic
11C37×#1554C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C37×#533C2211yescharacteristic
14C2×#127×C37C2211yescharacteristic
15C37×#501—21no—
16C37×#492—21no—
17C37×#492C2211yescharacteristic
18C37×#492C2211yescharacteristic
19C37×#491—21no—
20C37×#486—21no—
21C37×#486C2211yescharacteristic
22C37×#486C2211yescharacteristic
23C37×#485—22no—
24C37×#477C2212yescomplemented
25C37×#475C2212yescomplemented
26C37×#460—22no—
27C37×#460C2212yes—
28C37×#460C2212yes—
29C37×#450—22no—
30C37×#450—22no—
31C37×#446—22no—
32C37×#446C2212yescomplemented
33C8×Q8×C37C2212yescomplemented
34C37×#433—22no—
35C37×#432C2211yescharacteristic
36C37×#432C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#431C2211yescharacteristic
39C37×#335C2212yescomplemented
40C37×#334C2212yescomplemented
41C37×#333C2212yescomplemented
42C37×#332C2212yescomplemented
43C37×#331C2212yes—
44C37×#331C2212yes—
45C22×D4×C37—21no—
46C22×D4×C37—21no—
47C22×D4×C37—21no—
48C2×SD16×C37—22no—
49C2×SD16×C37—22no—
50C2×SD16×C37—22no—
51C2×SD16×C37—22no—
52C4⋊Q8×C37D411yescharacteristic
53C4⋊Q8×C37D411yescharacteristic
54C4⋊Q8×C37C2311yescharacteristic
55C4⋊Q8×C37C2311yescharacteristic
56#127×C37—21no—
57#127×C37—21no—
58#127×C37—21no—
59#127×C37C2311yescharacteristic
60#127×C37C2311yescharacteristic
61#125×C37—21no—
62#125×C37—21no—
63C22⋊Q8×C37—21no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—21no—
66C22⋊Q8×C37D412yes—
67C4×Q8×C37—21no—
68C4×Q8×C37—21no—
69C4×Q8×C37—21no—
70C4×Q8×C37C2312yes—
71#117×C37—21no—
72#117×C37—21no—
73C2×C42×C37C2311yescharacteristic
74#107×C37—22no—
75#106×C37—22no—
76C4⋊C8×C37—22no—
77C4⋊C8×C37—22no—
78C4⋊C8×C37D412yes—
79C4⋊C8×C37C2312yes—
80C4⋊C8×C37C2312yes—
81C4⋊C8×C37C2312yes—
82#103×C37—22no—
83#103×C37—22no—
84#102×C37—22no—
85#102×C37—22no—
86#102×C37—22no—
87#102×C37—22no—
88C22⋊C8×C37—21no—
89C22⋊C8×C37—21no—
90C22⋊C8×C37—21no—
91C22⋊C8×C37D412yes—
92#97×C37—22no—
93#97×C37—21no—
94#97×C37—21no—
95C4×C8×C37—22no—
96C4×C8×C37—21no—
97C4×C8×C37C2311yescharacteristic
98C4×C8×C37C2311yescharacteristic
99C24×C37—41no—
100C2×Q8×C37—21no—
101C2×Q8×C37—21no—
102C2×Q8×C37—21no—
103C2×Q8×C37C2×D412yes—
104C2×D4×C37—21no—
105C2×D4×C37—21no—
106C2×D4×C37—21no—
107C2×D4×C37—21no—
108C2×D4×C37—21no—
109C2×D4×C37—21no—
110C2×D4×C37—41no—
111C2×D4×C37—41no—
112C2×D4×C37—41no—
113C2×D4×C37—82no—
114C2×D4×C37—82no—
115C2×D4×C37—82no—
116C22×C4×C37C2×D411yescharacteristic
117C22×C4×C37C2×D411yescharacteristic
118C22×C4×C37#4111yescharacteristic
119SD16×C37—82no—
120SD16×C37—82no—
121SD16×C37—82no—
122SD16×C37—82no—
123C2×C8×C37—22no—
124C2×C8×C37—22no—
125C2×C8×C37—22no—
126C2×C8×C37C2×D412yes—
127C2×C8×C37C2×D412yes—
128C4⋊C4×C37—21no—
129C4⋊C4×C37—21no—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—22no—
132C4⋊C4×C37—22no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—21no—
136C4⋊C4×C37—21no—
137C4⋊C4×C37—41no—
138C4⋊C4×C37—41no—
139C4⋊C4×C37C2×D412yes—
140C22⋊C4×C37—22no—
141C22⋊C4×C37—41no—
142C42×C37—22no—
143C42×C37—41no—
144C42×C37C2×D411yescharacteristic
145C42×C37C2×D411yescharacteristic
146C42×C37#4111yescharacteristic
147C42×C37C2411yescharacteristic
148C23×C37—41no—
149C23×C37—41no—
150C23×C37—82no—
151C23×C37—82no—
152C23×C37—82no—
153C23×C37#12111yescharacteristic
154Q8×C37—22no—
155Q8×C37—22no—
156Q8×C37—42no—
157Q8×C37—81no—
158Q8×C37—81no—
159D4×C37—42no—
160D4×C37—42no—
161D4×C37—42no—
162D4×C37—42no—
163D4×C37—81no—
164D4×C37—81no—
165D4×C37—82no—
166D4×C37—82no—
167D4×C37—82no—
168C2×C4×C37—22no—
169C2×C4×C37—22no—
170C2×C4×C37—22no—
171C2×C4×C37—22no—
172C2×C4×C37—41no—
173C2×C4×C37—41no—
174C2×C4×C37—41no—
175C2×C4×C37#12111yescharacteristic
176C2×C4×C37#12111yescharacteristic
177C2×C4×C37#12111yescharacteristic
178C2×C4×C37C22×D411yescharacteristic
179C2×C4×C37C22×D411yescharacteristic
180C2×C4×C37C2×#4111yescharacteristic
181C8×C37—22no—
182C8×C37—22no—
183C8×C37—42no—
184C8×C37—42no—
185C8×C37—42no—
186#19520C3711yesmaximal, characteristic, direct product factor, Sylow
187C22×C37—21no—
188C22×C37—21no—
189C22×C37—21no—
190C22×C37—81no—
191C22×C37—81no—
192C22×C37—81no—
193C22×C37—81no—
194C22×C37—81no—
195C22×C37—81no—
196C22×C37—164no—
197C22×C37C2×#12111yescharacteristic
198C4×C37—21no—
199C4×C37—21no—
200C4×C37—21no—
201C4×C37—21no—
202C4×C37—42no—
203C4×C37—42no—
204C4×C37—81no—
205C4×C37—81no—
206C4×C37#57712yes—
207C4×C37#57712yes—
208#3237C2×C3711yescharacteristic, complemented
209#3208C2×C3711yescharacteristic
210#3208C2×C3711yescharacteristic
211#2985C2×C3711yescharacteristic, complemented
212#1698C2×C3712yescomplemented
213#1686C2×C3712yescomplemented
214#1678C2×C3712yescomplemented
215#1666C2×C3712yescomplemented
216#1572C2×C3711yescharacteristic, complemented
217#1555C2×C3711yescharacteristic
218#1554C2×C3711yescharacteristic, complemented
219C2×C37—41no—
220C2×C37—161no—
221C2×C37—161no—
222C2×C37#304311yescharacteristic
223C2×C37#305711yescharacteristic
224C2×C37#306811yescharacteristic
225#533C22×C3711yescharacteristic
226#533C22×C3711yescharacteristic
227C2×#127C22×C3711yescharacteristic
228#501—21no—
229#492—21no—
230#492C22×C3711yescharacteristic
231#492C22×C3711yescharacteristic
232#491—21no—
233#486—21no—
234#486C22×C3711yescharacteristic
235#486C22×C3711yescharacteristic
236#485—22no—
237#477C22×C3712yescomplemented
238#475C22×C3712yescomplemented
239#460—22no—
240#460C22×C3712yes—
241#460C22×C3712yes—
242#450—22no—
243#450—22no—
244#446—22no—
245#446C22×C3712yescomplemented
246C8×Q8C22×C3712yescomplemented
247#433—22no—
248#432C22×C3711yescharacteristic
249#432C22×C3711yescharacteristic
250#431C22×C3711yescharacteristic
251#431C22×C3711yescharacteristic
252#335C22×C3712yescomplemented
253#334C22×C3712yescomplemented
254#333C22×C3712yescomplemented
255#332C22×C3712yescomplemented
256#331C22×C3712yes—
257#331C22×C3712yes—
258C37#1952011yescharacteristic, direct product factor, Sylow
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C2×SD16—22no—
263C2×SD16—22no—
264C2×SD16—22no—
265C2×SD16—22no—
266C4⋊Q8D4×C3711yescharacteristic
267C4⋊Q8D4×C3711yescharacteristic
268C4⋊Q8C23×C3711yescharacteristic
269C4⋊Q8C23×C3711yescharacteristic
270#127—21no—
271#127—21no—
272#127—21no—
273#127C23×C3711yescharacteristic
274#127C23×C3711yescharacteristic
275#125—21no—
276#125—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8D4×C3712yes—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8C23×C3712yes—
285#117—21no—
286#117—21no—
287C2×C42C23×C3711yescharacteristic
288#107—22no—
289#106—22no—
290C4⋊C8—22no—
291C4⋊C8—22no—
292C4⋊C8D4×C3712yes—
293C4⋊C8C23×C3712yes—
294C4⋊C8C23×C3712yes—
295C4⋊C8C23×C3712yes—
296#103—22no—
297#103—22no—
298#102—22no—
299#102—22no—
300#102—22no—
301#102—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8D4×C3712yes—
306#97—22no—
307#97—21no—
308#97—21no—
309C4×C8—22no—
310C4×C8—21no—
311C4×C8C23×C3711yescharacteristic
312C4×C8C23×C3711yescharacteristic
313C24—41no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8C2×D4×C3712yes—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—82no—
328C2×D4—82no—
329C2×D4—82no—
330C22×C4C2×D4×C3711yescharacteristic
331C22×C4C2×D4×C3711yescharacteristic
332C22×C4#41×C3711yescharacteristic
333SD16—82no—
334SD16—82no—
335SD16—82no—
336SD16—82no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8C2×D4×C3712yes—
341C2×C8C2×D4×C3712yes—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4C2×D4×C3712yes—
354C22⋊C4—22no—
355C22⋊C4—41no—
356C42—22no—
357C42—41no—
358C42C2×D4×C3711yescharacteristic
359C42C2×D4×C3711yescharacteristic
360C42#41×C3711yescharacteristic
361C42C24×C3711yescharacteristic
362C23—41no—
363C23—41no—
364C23—82no—
365C23—82no—
366C23—82no—
367C23#121×C3711yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—42no—
371Q8—81no—
372Q8—81no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—82no—
380D4—82no—
381D4—82no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4#121×C3711yescharacteristic
390C2×C4#121×C3711yescharacteristic
391C2×C4#121×C3711yescharacteristic
392C2×C4C22×D4×C3711yescharacteristic
393C2×C4C22×D4×C3711yescharacteristic
394C2×C4C2×#41×C3711yescharacteristic
395C8—22no—
396C8—22no—
397C8—42no—
398C8—42no—
399C8—42no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—164no—
410C22C2×#121×C3711yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4C37×#57712yes—
420C4C37×#57712yes—
421C2—41no—
422C2—161no—
423C2—161no—
424C2C37×#304311yescharacteristic
425C2C37×#305711yescharacteristic
426C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×#127×C37C22
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
1. C37×#3237C2semidirect
4. C37×#2985C2semidirect
5. C37×#1698C2semidirect
6. C37×#1686C2semidirect
7. C37×#1678C2semidirect
8. C37×#1666C2semidirect
9. C37×#1572C2semidirect
11. C37×#1554C2semidirect
24. C37×#477C22semidirect
25. C37×#475C22semidirect
32. C37×#446C22semidirect
33. C8×Q8×C37C22semidirect
39. C37×#335C22semidirect
40. C37×#334C22semidirect
41. C37×#333C22semidirect
42. C37×#332C22semidirect
186. #19520C37direct (N × H)
208. #3237C2×C37semidirect
211. #2985C2×C37semidirect
212. #1698C2×C37semidirect
213. #1686C2×C37semidirect
214. #1678C2×C37semidirect
215. #1666C2×C37semidirect
216. #1572C2×C37semidirect
218. #1554C2×C37semidirect
237. #477C22×C37semidirect
238. #475C22×C37semidirect
245. #446C22×C37semidirect
246. C8×Q8C22×C37semidirect
252. #335C22×C37semidirect
253. #334C22×C37semidirect
254. #333C22×C37semidirect
255. #332C22×C37semidirect
258. C37#19520direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32372
C37×#32082
C37×#29852
C37×#16982
C37×#16862
C37×#16782
C37×#16662
C37×#15722
C37×#15552
C37×#15542
#1952037