Finite Group Databasebeta

← C37×#33810 #22655063

Subgroups — C37×#33810 #22655063

Order 9472.

454 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3175C211yesmaximal, characteristic
2C37×#3164C211yesmaximal, characteristic, complemented
3C37×#2255C211yesmaximal, characteristic, complemented
4C37×#2254C211yesmaximal, characteristic, complemented
5C37×#2243C211yesmaximal, characteristic, complemented
6C37×#2242C211yesmaximal, characteristic, complemented
7C37×#2237C211yesmaximal, characteristic, complemented
8C37×#2235C211yesmaximal, characteristic, complemented
9C37×#2234C211yesmaximal, characteristic
10C37×#2233C211yesmaximal, characteristic
11C37×#2229C211yesmaximal, characteristic, complemented
12C37×#2228C211yesmaximal, characteristic, complemented
13C37×#2226C211yesmaximal, characteristic, complemented
14C37×#2225C211yesmaximal, characteristic, complemented
15C37×#2164C211yesmaximal, characteristic, complemented
16C37×#544—21no—
17C37×#542—21no—
18C37×#501—21no—
19C37×#501—21no—
20C37×#500C2211yescharacteristic
21C37×#500C2211yescharacteristic
22C37×#500C2211yescharacteristic
23C37×#499C2211yescharacteristic
24C37×#499C2211yescharacteristic
25C37×#495C2211yescharacteristic
26C37×#489—21no—
27C37×#468—21no—
28C37×#467C2211yescharacteristic
29C37×#466C2211yescharacteristic
30C37×#440—21no—
31C4×Q16×C37C2211yescharacteristic
32C4×D8×C37C2211yescharacteristic
33C37×#428—21no—
34C37×#427C2211yescharacteristic
35C2×#107×C37C2211yescharacteristic
36C37×#405C2211yescharacteristic
37C37×#367C2211yescharacteristic
38C37×#367C2211yescharacteristic
39C37×#367C2211yescharacteristic
40C37×#367C2211yescharacteristic
41C37×#367C2211yescharacteristic
42C37×#367C2211yescharacteristic
43C37×#366C2211yescharacteristic
44C37×#366C2211yescharacteristic
45C37×C4⋊C16C2211yescharacteristic
46C37×C4⋊C16C2211yescharacteristic
47C37×#358C2211yescharacteristic
48C37×#358C2211yescharacteristic
49C37×#358C2211yescharacteristic
50C37×#358C2211yescharacteristic
51C37×#357C2211yescharacteristic
52C37×#357C2211yescharacteristic
53C37×#357C2211yescharacteristic
54C37×#357C2211yescharacteristic
55C37×C22⋊C16C2211yescharacteristic
56C37×C22⋊C16C2211yescharacteristic
57C37×#346C2211yescharacteristic
58C4×C16×C37C2211yescharacteristic
59C2×Q16×C37C2311yescharacteristic
60C2×SD16×C37—21no—
61C2×D8×C37C2311yescharacteristic
62C2×M16×C37D411yescharacteristic
63C22×C8×C37C2311yescharacteristic
64C4⋊Q8×C37—21no—
65C4⋊Q8×C37—21no—
66C4⋊Q8×C37—21no—
67C4⋊Q8×C37—41no—
68#126×C37—41no—
69#125×C37—21no—
70#125×C37—21no—
71#125×C37—41no—
72#124×C37—21no—
73#124×C37—41no—
74#123×C37—41no—
75C22⋊Q8×C37—21no—
76C22⋊Q8×C37—41no—
77C22⋊Q8×C37—41no—
78C22⋊Q8×C37—41no—
79#121×C37—21no—
80C4×Q8×C37—21no—
81C4×D4×C37—21no—
82#117×C37—21no—
83#117×C37D411yescharacteristic
84C2×C4⋊C4×C37—21no—
85C2×C16×C37C2311yescharacteristic
86C2×C16×C37C2311yescharacteristic
87C2×C16×C37C2311yescharacteristic
88C2×C16×C37C2311yescharacteristic
89#107×C37—21no—
90#107×C37—21no—
91#107×C37—21no—
92#107×C37—21no—
93#107×C37C2311yescharacteristic
94#107×C37C2311yescharacteristic
95#107×C37C2311yescharacteristic
96#107×C37C2311yescharacteristic
97#107×C37C2311yescharacteristic
98#107×C37C2311yescharacteristic
99#106×C37—21no—
100#106×C37—21no—
101#106×C37—21no—
102#103×C37—21no—
103#103×C37—21no—
104#102×C37—21no—
105#102×C37—21no—
106#97×C37D411yescharacteristic
107#97×C37D411yescharacteristic
108C4×C8×C37C2311yescharacteristic
109C4×C8×C37C2311yescharacteristic
110C2×Q8×C37—21no—
111C2×Q8×C37—41no—
112C2×Q8×C37—41no—
113C2×Q8×C37—41no—
114C2×D4×C37—21no—
115C2×D4×C37—41no—
116C22×C4×C37—41no—
117C22×C4×C37—41no—
118C22×C4×C37C2×D411yescharacteristic
119Q16×C37—21no—
120Q16×C37—21no—
121SD16×C37—42no—
122D8×C37—21no—
123D8×C37—21no—
124M16×C37—22no—
125C2×C8×C37—21no—
126C2×C8×C37—21no—
127C2×C8×C37C2×D411yescharacteristic
128C2×C8×C37C2×D411yescharacteristic
129C2×C8×C37C2×D411yescharacteristic
130C2×C8×C37C2411yescharacteristic
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
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×C37—41no—
140C4⋊C4×C37—41no—
141C4⋊C4×C37—41no—
142C4⋊C4×C37—41no—
143C4⋊C4×C37—41no—
144C4⋊C4×C37—41no—
145C4⋊C4×C37—41no—
146C4⋊C4×C37—41no—
147C4⋊C4×C37D811yescharacteristic
148C4⋊C4×C37D811yescharacteristic
149C22⋊C4×C37—41no—
150C22⋊C4×C37—41no—
151C22⋊C4×C37—41no—
152C22⋊C4×C37—41no—
153C22⋊C4×C37—41no—
154C22⋊C4×C37—41no—
155C22⋊C4×C37D811yescharacteristic
156C22⋊C4×C37D811yescharacteristic
157C42×C37—41no—
158C42×C37—41no—
159C42×C37C2×D411yescharacteristic
160C42×C37C2×D411yescharacteristic
161C16×C37—21no—
162C16×C37—21no—
163C16×C37—21no—
164C16×C37—21no—
165C23×C37—41no—
166C23×C37C2×D811yescharacteristic
167Q8×C37—41no—
168Q8×C37—41no—
169Q8×C37—161no—
170Q8×C37—161no—
171Q8×C37—161no—
172D4×C37—41no—
173D4×C37—41no—
174D4×C37—161no—
175C2×C4×C37—21no—
176C2×C4×C37—21no—
177C2×C4×C37—41no—
178C2×C4×C37—41no—
179C2×C4×C37—41no—
180C2×C4×C37—41no—
181C2×C4×C37—41no—
182C2×C4×C37—41no—
183C2×C4×C37—41no—
184C2×C4×C37—161no—
185C2×C4×C37—161no—
186C2×C4×C37C2×D811yescharacteristic
187C2×C4×C37C2×D811yescharacteristic
188C2×C4×C37C2×D811yescharacteristic
189C2×C4×C37C2×D811yescharacteristic
190C2×C4×C37C2×D811yescharacteristic
191C2×C4×C37C22×D411yescharacteristic
192C8×C37—21no—
193C8×C37—21no—
194C8×C37#13712yes—
195C8×C372−1+411yescharacteristic
196C8×C372−1+411yescharacteristic
197#33810C3711yesmaximal, characteristic, direct product factor, Sylow
198C22×C37—21no—
199C22×C37—21no—
200C22×C37—21no—
201C22×C37—81no—
202C22×C37—81no—
203C22×C37—81no—
204C22×C37C22×D811yescharacteristic
205C4×C37—21no—
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—21no—
209C4×C37—21no—
210C4×C37—81no—
211C4×C37—81no—
212C4×C37—81no—
213C4×C37—81no—
214C4×C37—81no—
215C4×C37—81no—
216C4×C37—81no—
217C4×C37#53611yescharacteristic
218C4×C37C2×#13711yescharacteristic
219#3175C2×C3711yescharacteristic
220#3164C2×C3711yescharacteristic, complemented
221#2255C2×C3711yescharacteristic, complemented
222#2254C2×C3711yescharacteristic, complemented
223#2243C2×C3711yescharacteristic, complemented
224#2242C2×C3711yescharacteristic, complemented
225#2237C2×C3711yescharacteristic, complemented
226#2235C2×C3711yescharacteristic, complemented
227#2234C2×C3711yescharacteristic
228#2233C2×C3711yescharacteristic
229#2229C2×C3711yescharacteristic, complemented
230#2228C2×C3711yescharacteristic, complemented
231#2226C2×C3711yescharacteristic, complemented
232#2225C2×C3711yescharacteristic, complemented
233#2164C2×C3711yescharacteristic, complemented
234C2×C37—41no—
235C2×C37—161no—
236C2×C37#322611yescharacteristic
237C2×C37#341611yescharacteristic
238C2×C37#341611yescharacteristic
239#544—21no—
240#542—21no—
241#501—21no—
242#501—21no—
243#500C22×C3711yescharacteristic
244#500C22×C3711yescharacteristic
245#500C22×C3711yescharacteristic
246#499C22×C3711yescharacteristic
247#499C22×C3711yescharacteristic
248#495C22×C3711yescharacteristic
249#489—21no—
250#468—21no—
251#467C22×C3711yescharacteristic
252#466C22×C3711yescharacteristic
253#440—21no—
254C4×Q16C22×C3711yescharacteristic
255C4×D8C22×C3711yescharacteristic
256#428—21no—
257#427C22×C3711yescharacteristic
258C2×#107C22×C3711yescharacteristic
259#405C22×C3711yescharacteristic
260#367C22×C3711yescharacteristic
261#367C22×C3711yescharacteristic
262#367C22×C3711yescharacteristic
263#367C22×C3711yescharacteristic
264#367C22×C3711yescharacteristic
265#367C22×C3711yescharacteristic
266#366C22×C3711yescharacteristic
267#366C22×C3711yescharacteristic
268C4⋊C16C22×C3711yescharacteristic
269C4⋊C16C22×C3711yescharacteristic
270#358C22×C3711yescharacteristic
271#358C22×C3711yescharacteristic
272#358C22×C3711yescharacteristic
273#358C22×C3711yescharacteristic
274#357C22×C3711yescharacteristic
275#357C22×C3711yescharacteristic
276#357C22×C3711yescharacteristic
277#357C22×C3711yescharacteristic
278C22⋊C16C22×C3711yescharacteristic
279C22⋊C16C22×C3711yescharacteristic
280#346C22×C3711yescharacteristic
281C4×C16C22×C3711yescharacteristic
282C37#3381011yescharacteristic, direct product factor, Sylow
283C2×Q16C23×C3711yescharacteristic
284C2×SD16—21no—
285C2×D8C23×C3711yescharacteristic
286C2×M16D4×C3711yescharacteristic
287C22×C8C23×C3711yescharacteristic
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—41no—
292#126—41no—
293#125—21no—
294#125—21no—
295#125—41no—
296#124—21no—
297#124—41no—
298#123—41no—
299C22⋊Q8—21no—
300C22⋊Q8—41no—
301C22⋊Q8—41no—
302C22⋊Q8—41no—
303#121—21no—
304C4×Q8—21no—
305C4×D4—21no—
306#117—21no—
307#117D4×C3711yescharacteristic
308C2×C4⋊C4—21no—
309C2×C16C23×C3711yescharacteristic
310C2×C16C23×C3711yescharacteristic
311C2×C16C23×C3711yescharacteristic
312C2×C16C23×C3711yescharacteristic
313#107—21no—
314#107—21no—
315#107—21no—
316#107—21no—
317#107C23×C3711yescharacteristic
318#107C23×C3711yescharacteristic
319#107C23×C3711yescharacteristic
320#107C23×C3711yescharacteristic
321#107C23×C3711yescharacteristic
322#107C23×C3711yescharacteristic
323#106—21no—
324#106—21no—
325#106—21no—
326#103—21no—
327#103—21no—
328#102—21no—
329#102—21no—
330#97D4×C3711yescharacteristic
331#97D4×C3711yescharacteristic
332C4×C8C23×C3711yescharacteristic
333C4×C8C23×C3711yescharacteristic
334C2×Q8—21no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×D4—21no—
339C2×D4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C2×D4×C3711yescharacteristic
343Q16—21no—
344Q16—21no—
345SD16—42no—
346D8—21no—
347D8—21no—
348M16—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8C2×D4×C3711yescharacteristic
352C2×C8C2×D4×C3711yescharacteristic
353C2×C8C2×D4×C3711yescharacteristic
354C2×C8C24×C3711yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4D8×C3711yescharacteristic
372C4⋊C4D8×C3711yescharacteristic
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4D8×C3711yescharacteristic
380C22⋊C4D8×C3711yescharacteristic
381C42—41no—
382C42—41no—
383C42C2×D4×C3711yescharacteristic
384C42C2×D4×C3711yescharacteristic
385C16—21no—
386C16—21no—
387C16—21no—
388C16—21no—
389C23—41no—
390C23C2×D8×C3711yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—161no—
394Q8—161no—
395Q8—161no—
396D4—41no—
397D4—41no—
398D4—161no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—161no—
409C2×C4—161no—
410C2×C4C2×D8×C3711yescharacteristic
411C2×C4C2×D8×C3711yescharacteristic
412C2×C4C2×D8×C3711yescharacteristic
413C2×C4C2×D8×C3711yescharacteristic
414C2×C4C2×D8×C3711yescharacteristic
415C2×C4C22×D4×C3711yescharacteristic
416C8—21no—
417C8—21no—
418C8#137×C3712yes—
419C82−1+4×C3711yescharacteristic
420C82−1+4×C3711yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C22×D8×C3711yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4C37×#53611yescharacteristic
441C4C2×#137×C3711yescharacteristic
442C2—41no—
443C2—161no—
444C2C37×#322611yescharacteristic
445C2C37×#341611yescharacteristic
446C2C37×#341611yescharacteristic
subgroupG/H
center, socleC22×C37C22×D8
commutator, Frattini, cosocleC2×C8C24×C37
prime radicalC37×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ #117×C37 ◁ C37×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3164C2semidirect
3. C37×#2255C2semidirect
4. C37×#2254C2semidirect
5. C37×#2243C2semidirect
6. C37×#2242C2semidirect
7. C37×#2237C2semidirect
8. C37×#2235C2semidirect
11. C37×#2229C2semidirect
12. C37×#2228C2semidirect
13. C37×#2226C2semidirect
14. C37×#2225C2semidirect
15. C37×#2164C2semidirect
197. #33810C37direct (N × H)
220. #3164C2×C37semidirect
221. #2255C2×C37semidirect
222. #2254C2×C37semidirect
223. #2243C2×C37semidirect
224. #2242C2×C37semidirect
225. #2237C2×C37semidirect
226. #2235C2×C37semidirect
229. #2229C2×C37semidirect
230. #2228C2×C37semidirect
231. #2226C2×C37semidirect
232. #2225C2×C37semidirect
233. #2164C2×C37semidirect
282. C37#33810direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31752
C37×#31642
C37×#22552
C37×#22542
C37×#22432
C37×#22422
C37×#22372
C37×#22352
C37×#22342
C37×#22332
C37×#22292
C37×#22282
C37×#22262
C37×#22252
C37×#21642
#3381037