Finite Group Databasebeta

← C37×#61900 #22683153

Subgroups — C37×#61900 #22683153

Order 9472.

1692 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3523C211yesmaximal, characteristic
2C2×C37×#557C211yesmaximal, characteristic, complemented
3C37×#3398C216yesmaximal, complemented
4C37×#3395C212yesmaximal, complemented
5C37×#3374C216yesmaximal, complemented
6C37×#3359C212yesmaximal, complemented
7C37×#3218C213yesmaximal
8C37×#3209C213yesmaximal, complemented
9C37×#3113C213yesmaximal, complemented
10C37×#3108C213yesmaximal
11C37×#2984C211yesmaximal, characteristic, complemented
12C37×#557—21no—
13C37×#557—23no—
14C37×#557C2216yes—
15C37×#557C2211yescharacteristic
16C37×#557C2212yes—
17C37×#557C2213yes—
18C37×#556C2213yes—
19C37×#552—23no—
20D4×Q8×C37—21no—
21D4×Q8×C37C2211yescharacteristic
22C37×#541—23no—
23C37×#533C2213yes—
24C2×C4⋊Q8×C37C2213yes—
25C37×#529C2213yes—
26C2×#125×C37—23no—
27C37×#519—21no—
28C2×C4×Q8×C37—21no—
29C2×C4×Q8×C37C2213yes—
30C2×C4×Q8×C37C2211yescharacteristic
31C37×#497C2216yes—
32C37×#494C2216yes—
33C37×#491C2216yes—
34C37×#487C2216yes—
35C37×#483C2213yes—
36C37×#480C2211yescharacteristic
37C37×#479C2216yes—
38C37×#475C2216yes—
39C37×#464C2216yes—
40C37×#462C2216yes—
41C37×#462C22112yes—
42C37×#462C2216yes—
43C37×#461C2216yes—
44C37×#451C2213yes—
45C37×#451C2216yes—
46C37×#448C2213yes—
47C37×#446C2216yes—
48C8×Q8×C37C2212yes—
49C37×#441C22112yes—
50C4×Q16×C37C2216yes—
51C4×SD16×C37C2216yes—
52C37×#432C2213yes—
53C37×#431C2213yes—
54C22×Q8×C37—21no—
55C22×Q8×C37D411yescharacteristic
56C22×Q8×C37C2313yes—
57C2×Q16×C37C2316yes—
58C2×Q16×C37C23112yes—
59C2×SD16×C37C2316yes—
60C4⋊Q8×C37—23no—
61C4⋊Q8×C37—23no—
62C4⋊Q8×C37—23no—
63C4⋊Q8×C37C2316yes—
64C4⋊Q8×C37C2316yes—
65C4⋊Q8×C37C2313yes—
66C4⋊Q8×C37C2313yes—
67#126×C37—26no—
68#126×C37—23no—
69#125×C37—26no—
70#125×C37—26no—
71#125×C37—212no—
72#125×C37—26no—
73#125×C37—23no—
74#125×C37—23no—
75#125×C37C2313yes—
76#124×C37C2313yes—
77#123×C37—23no—
78C22⋊Q8×C37—23no—
79C22⋊Q8×C37—23no—
80C22⋊Q8×C37—23no—
81C22⋊Q8×C37C2313yes—
82#121×C37C2311yescharacteristic
83C4×Q8×C37—21no—
84C4×Q8×C37—26no—
85C4×Q8×C37—22no—
86C4×Q8×C37—23no—
87C4×Q8×C37—23no—
88C4×Q8×C37—23no—
89C4×Q8×C37—23no—
90C4×Q8×C37D411yescharacteristic
91C4×Q8×C37D413yes—
92C4×Q8×C37C2313yes—
93C4×Q8×C37C2316yes—
94C4×Q8×C37C2316yes—
95C4×Q8×C37C2316yes—
96C4×Q8×C37C2311yescharacteristic
97C4×Q8×C37C2313yes—
98C4×D4×C37—23no—
99C4×D4×C37C2313yes—
100#117×C37—23no—
101#117×C37—23no—
102#117×C37—23no—
103C2×C4⋊C4×C37—23no—
104C2×C4⋊C4×C37—23no—
105C2×C4⋊C4×C37—23no—
106C2×C4⋊C4×C37D413yes—
107C2×C4⋊C4×C37C2311yescharacteristic
108C2×C42×C37—23no—
109C2×C42×C37C2313yes—
110#107×C37C2312yes—
111#106×C37C2316yes—
112C4⋊C8×C37C2316yes—
113C4⋊C8×C37C2316yes—
114#103×C37C2316yes—
115#103×C37C2316yes—
116#103×C37C2316yes—
117#103×C37C23112yes—
118#102×C37C2312yes—
119C22⋊C8×C37C2311yescharacteristic
120C22⋊C8×C37C2313yes—
121#97×C37C2316yes—
122C4×C8×C37C2316yes—
123C2×Q8×C37—24no—
124C2×Q8×C37—23no—
125C2×Q8×C37—23no—
126C2×Q8×C37—46no—
127C2×Q8×C37—44no—
128C2×Q8×C37C2×D413yes—
129C2×Q8×C37C2×D411yescharacteristic
130C2×Q8×C37C2416yes—
131C2×Q8×C37C2413yes—
132C2×D4×C37—21no—
133C2×D4×C37C2411yescharacteristic
134C22×C4×C37—21no—
135C22×C4×C37—23no—
136C22×C4×C37—23no—
137C22×C4×C37C2×D413yes—
138C22×C4×C37C2×D413yes—
139C22×C4×C37C2411yescharacteristic
140Q16×C37—412no—
141Q16×C37—46no—
142SD16×C37—46no—
143C2×C8×C37C2412yes—
144C2×C8×C37C2416yes—
145C4⋊C4×C37—26no—
146C4⋊C4×C37—26no—
147C4⋊C4×C37—26no—
148C4⋊C4×C37—26no—
149C4⋊C4×C37—26no—
150C4⋊C4×C37—26no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—23no—
153C4⋊C4×C37—23no—
154C4⋊C4×C37—23no—
155C4⋊C4×C37—23no—
156C4⋊C4×C37—23no—
157C4⋊C4×C37—23no—
158C4⋊C4×C37—26no—
159C4⋊C4×C37—23no—
160C4⋊C4×C37C2×D413yes—
161C4⋊C4×C37C2×D413yes—
162C4⋊C4×C37C2×D416yes—
163C4⋊C4×C37C2412yes—
164C4⋊C4×C37C2413yes—
165C4⋊C4×C37C2411yescharacteristic
166C22⋊C4×C37—23no—
167C22⋊C4×C37—21no—
168C22⋊C4×C37—23no—
169C22⋊C4×C37—23no—
170C22⋊C4×C37—23no—
171C42×C37—26no—
172C42×C37—26no—
173C42×C37—26no—
174C42×C37—23no—
175C42×C37C2×D413yes—
176C42×C37C2×D413yes—
177C42×C37C2413yes—
178C42×C37C2413yes—
179C23×C37—21no—
180C23×C37C22×D411yescharacteristic
181Q8×C37—26no—
182Q8×C37—26no—
183Q8×C37—26no—
184Q8×C37—26no—
185Q8×C37—46no—
186Q8×C37—46no—
187Q8×C37#13714yes—
188D4×C37—22no—
189D4×C37—42no—
190C2×C4×C37—26no—
191C2×C4×C37—26no—
192C2×C4×C37—22no—
193C2×C4×C37—22no—
194C2×C4×C37—23no—
195C2×C4×C37—21no—
196C2×C4×C37—23no—
197C2×C4×C37—26no—
198C2×C4×C37—46no—
199C2×C4×C37—42no—
200C2×C4×C37—46no—
201C2×C4×C37C22×D413yes—
202C2×C4×C37C22×D413yes—
203C2×C4×C37C22×D411yescharacteristic
204C2×C4×C37C22×D413yes—
205C2×C4×C37C22×D413yes—
206C2×C4×C37C2511yescharacteristic
207C8×C37—26no—
208C8×C37—22no—
209#61900C3711yesmaximal, characteristic, direct product factor, Sylow
210C22×C37—21no—
211C22×C37—21no—
212C22×C37—41no—
213C22×C37—41no—
214C22×C37—41no—
215C22×C37#57812yes—
216C22×C37C23×D411yescharacteristic
217C4×C37—21no—
218C4×C37—23no—
219C4×C37—23no—
220C4×C37—23no—
221C4×C37—46no—
222C4×C37—43no—
223C4×C37—43no—
224C4×C37—42no—
225C4×C37—41no—
226C4×C37C2×#13716yes—
227C4×C37#58512yes—
228#3523C2×C3711yescharacteristic
229C2×#557C2×C3711yescharacteristic, complemented
230#3398C2×C3716yescomplemented
231#3395C2×C3712yescomplemented
232#3374C2×C3716yescomplemented
233#3359C2×C3712yescomplemented
234#3218C2×C3713yes—
235#3209C2×C3713yescomplemented
236#3113C2×C3713yescomplemented
237#3108C2×C3713yes—
238#2984C2×C3711yescharacteristic, complemented
239C2×C37—22no—
240C2×C37—81no—
241C2×C37#348711yescharacteristic
242C2×C37C22×#13711yescharacteristic
243C2×C37C2×#57811yescharacteristic
244#557—21no—
245#557—23no—
246#557C22×C3712yes—
247#557C22×C3716yes—
248#557C22×C3711yescharacteristic
249#557C22×C3713yes—
250#556C22×C3713yes—
251#552—23no—
252D4×Q8—21no—
253D4×Q8C22×C3711yescharacteristic
254#541—23no—
255#533C22×C3713yes—
256C2×C4⋊Q8C22×C3713yes—
257#529C22×C3713yes—
258C2×#125—23no—
259#519—21no—
260C2×C4×Q8—21no—
261C2×C4×Q8C22×C3713yes—
262C2×C4×Q8C22×C3711yescharacteristic
263#497C22×C3716yes—
264#494C22×C3716yes—
265#491C22×C3716yes—
266#487C22×C3716yes—
267#483C22×C3713yes—
268#480C22×C3711yescharacteristic
269#479C22×C3716yes—
270#475C22×C3716yes—
271#464C22×C3716yes—
272#462C22×C3716yes—
273#462C22×C3716yes—
274#462C22×C37112yes—
275#461C22×C3716yes—
276#451C22×C3713yes—
277#451C22×C3716yes—
278#448C22×C3713yes—
279#446C22×C3716yes—
280C8×Q8C22×C3712yes—
281#441C22×C37112yes—
282C4×Q16C22×C3716yes—
283C4×SD16C22×C3716yes—
284#432C22×C3713yes—
285#431C22×C3713yes—
286C37#6190011yescharacteristic, direct product factor, Sylow
287C22×Q8—21no—
288C22×Q8D4×C3711yescharacteristic
289C22×Q8C23×C3713yes—
290C2×Q16C23×C3716yes—
291C2×Q16C23×C37112yes—
292C2×SD16C23×C3716yes—
293C4⋊Q8—23no—
294C4⋊Q8—23no—
295C4⋊Q8—23no—
296C4⋊Q8C23×C3716yes—
297C4⋊Q8C23×C3716yes—
298C4⋊Q8C23×C3713yes—
299C4⋊Q8C23×C3713yes—
300#126—26no—
301#126—23no—
302#125—26no—
303#125—26no—
304#125—212no—
305#125—26no—
306#125—23no—
307#125—23no—
308#125C23×C3713yes—
309#124C23×C3713yes—
310#123—23no—
311C22⋊Q8—23no—
312C22⋊Q8—23no—
313C22⋊Q8—23no—
314C22⋊Q8C23×C3713yes—
315#121C23×C3711yescharacteristic
316C4×Q8—26no—
317C4×Q8—22no—
318C4×Q8—21no—
319C4×Q8—23no—
320C4×Q8—23no—
321C4×Q8—23no—
322C4×Q8—23no—
323C4×Q8D4×C3711yescharacteristic
324C4×Q8D4×C3713yes—
325C4×Q8C23×C3716yes—
326C4×Q8C23×C3716yes—
327C4×Q8C23×C3713yes—
328C4×Q8C23×C3716yes—
329C4×Q8C23×C3711yescharacteristic
330C4×Q8C23×C3713yes—
331C4×D4—23no—
332C4×D4C23×C3713yes—
333#117—23no—
334#117—23no—
335#117—23no—
336C2×C4⋊C4—23no—
337C2×C4⋊C4—23no—
338C2×C4⋊C4—23no—
339C2×C4⋊C4D4×C3713yes—
340C2×C4⋊C4C23×C3711yescharacteristic
341C2×C42—23no—
342C2×C42C23×C3713yes—
343#107C23×C3712yes—
344#106C23×C3716yes—
345C4⋊C8C23×C3716yes—
346C4⋊C8C23×C3716yes—
347#103C23×C3716yes—
348#103C23×C3716yes—
349#103C23×C3716yes—
350#103C23×C37112yes—
351#102C23×C3712yes—
352C22⋊C8C23×C3711yescharacteristic
353C22⋊C8C23×C3713yes—
354#97C23×C3716yes—
355C4×C8C23×C3716yes—
356C2×Q8—24no—
357C2×Q8—23no—
358C2×Q8—23no—
359C2×Q8—46no—
360C2×Q8—44no—
361C2×Q8C2×D4×C3713yes—
362C2×Q8C2×D4×C3711yescharacteristic
363C2×Q8C24×C3716yes—
364C2×Q8C24×C3713yes—
365C2×D4—21no—
366C2×D4C24×C3711yescharacteristic
367C22×C4—21no—
368C22×C4—23no—
369C22×C4—23no—
370C22×C4C2×D4×C3713yes—
371C22×C4C2×D4×C3713yes—
372C22×C4C24×C3711yescharacteristic
373Q16—412no—
374Q16—46no—
375SD16—46no—
376C2×C8C24×C3712yes—
377C2×C8C24×C3716yes—
378C4⋊C4—26no—
379C4⋊C4—26no—
380C4⋊C4—26no—
381C4⋊C4—26no—
382C4⋊C4—26no—
383C4⋊C4—26no—
384C4⋊C4—21no—
385C4⋊C4—23no—
386C4⋊C4—23no—
387C4⋊C4—23no—
388C4⋊C4—23no—
389C4⋊C4—23no—
390C4⋊C4—23no—
391C4⋊C4—26no—
392C4⋊C4—23no—
393C4⋊C4C2×D4×C3713yes—
394C4⋊C4C2×D4×C3713yes—
395C4⋊C4C2×D4×C3716yes—
396C4⋊C4C24×C3712yes—
397C4⋊C4C24×C3713yes—
398C4⋊C4C24×C3711yescharacteristic
399C22⋊C4—23no—
400C22⋊C4—21no—
401C22⋊C4—23no—
402C22⋊C4—23no—
403C22⋊C4—23no—
404C42—26no—
405C42—26no—
406C42—26no—
407C42—23no—
408C42C2×D4×C3713yes—
409C42C2×D4×C3713yes—
410C42C24×C3713yes—
411C42C24×C3713yes—
412C23—21no—
413C23C22×D4×C3711yescharacteristic
414Q8—26no—
415Q8—26no—
416Q8—26no—
417Q8—26no—
418Q8—46no—
419Q8—46no—
420Q8#137×C3714yes—
421D4—22no—
422D4—42no—
423C2×C4—26no—
424C2×C4—26no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—23no—
428C2×C4—21no—
429C2×C4—23no—
430C2×C4—26no—
431C2×C4—46no—
432C2×C4—42no—
433C2×C4—46no—
434C2×C4C22×D4×C3713yes—
435C2×C4C22×D4×C3713yes—
436C2×C4C22×D4×C3711yescharacteristic
437C2×C4C22×D4×C3713yes—
438C2×C4C22×D4×C3713yes—
439C2×C4C25×C3711yescharacteristic
440C8—26no—
441C8—22no—
442C22—21no—
443C22—21no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22C37×#57812yes—
448C22C23×D4×C3711yescharacteristic
449C4—21no—
450C4—23no—
451C4—23no—
452C4—23no—
453C4—46no—
454C4—43no—
455C4—43no—
456C4—42no—
457C4—41no—
458C4C2×#137×C3716yes—
459C4C37×#58512yes—
460C2—22no—
461C2—81no—
462C2C37×#348711yescharacteristic
463C2C22×#137×C3711yescharacteristic
464C2C2×C37×#57811yescharacteristic
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
prime radical#121×C37C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C4×Q8×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#557C2semidirect
3. C37×#3398C2semidirect
4. C37×#3395C2semidirect
5. C37×#3374C2semidirect
6. C37×#3359C2semidirect
8. C37×#3209C2semidirect
9. C37×#3113C2semidirect
11. C37×#2984C2semidirect
209. #61900C37direct (N × H)
229. C2×#557C2×C37semidirect
230. #3398C2×C37semidirect
231. #3395C2×C37semidirect
232. #3374C2×C37semidirect
233. #3359C2×C37semidirect
235. #3209C2×C37semidirect
236. #3113C2×C37semidirect
238. #2984C2×C37semidirect
286. C37#61900direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35232
C2×C37×#5572
C37×#33982
C37×#33952
C37×#33742
C37×#33592
C37×#32182
C37×#32092
C37×#31132
C37×#31082
C37×#29842
#6190037