Finite Group Databasebeta

← C37×#18433 #22639686

Subgroups — C37×#18433 #22639686

Order 9472.

872 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3563C211yesmaximal, characteristic
2C37×#3218C211yesmaximal, characteristic
3C37×#3209C211yesmaximal, characteristic, complemented
4C37×#2660C211yesmaximal, characteristic, complemented
5C37×#1605C214yesmaximal, complemented
6C37×#1603C214yesmaximal
7C37×#1506C211yesmaximal, characteristic, complemented
8C37×#1500C211yesmaximal, characteristic
9C37×#1470C211yesmaximal, characteristic, complemented
10C37×#564—21no—
11C37×#563—21no—
12C37×#557—21no—
13C37×#554—21no—
14C37×#552—21no—
15C37×#552—21no—
16C37×#552—22no—
17C37×#544—21no—
18C37×#544C2212yes—
19C37×#541—21no—
20C37×#541—22no—
21C37×#539C2212yes—
22C37×#533C2211yescharacteristic
23C2×C4⋊Q8×C37C2211yescharacteristic
24C37×#529C2211yescharacteristic
25C2×#125×C37C2211yescharacteristic
26C37×#497—21no—
27C37×#494—21no—
28C37×#491—21no—
29C37×#487—21no—
30C37×#462—22no—
31C37×#462—21no—
32C37×#461—21no—
33C37×#451C2214yes—
34C37×#451C2212yes—
35C37×#448C2212yes—
36C37×#432C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#398—22no—
39C37×#395C2214yes—
40C37×#384—21no—
41C37×#382—21no—
42C37×#376C2211yescharacteristic
43C37×#328C2214yes—
44C37×#328C2212yes—
45C37×#327C2212yes—
46C37×#324C2214yes—
47C22×Q8×C37C2312yes—
48C2×Q16×C37—24no—
49C2×Q16×C37—22no—
50C2×SD16×C37—22no—
51C4⋊Q8×C37—21no—
52C4⋊Q8×C37—22no—
53C4⋊Q8×C37—22no—
54C4⋊Q8×C37—21no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37D411yescharacteristic
59C4⋊Q8×C37D411yescharacteristic
60#126×C37—22no—
61#126×C37—22no—
62#126×C37—22no—
63#126×C37—22no—
64#126×C37—21no—
65#125×C37—22no—
66#125×C37—22no—
67#125×C37—22no—
68#125×C37—22no—
69#125×C37—21no—
70#125×C37—22no—
71#125×C37—22no—
72#125×C37—22no—
73#125×C37—22no—
74#125×C37—21no—
75#125×C37—21no—
76#125×C37—21no—
77#125×C37—21no—
78#125×C37—21no—
79#125×C37D411yescharacteristic
80#124×C37D411yescharacteristic
81#123×C37—22no—
82#123×C37—21no—
83#123×C37—22no—
84C22⋊Q8×C37—21no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37—22no—
87C22⋊Q8×C37—22no—
88C22⋊Q8×C37—22no—
89C22⋊Q8×C37—21no—
90C22⋊Q8×C37—22no—
91C22⋊Q8×C37C2311yescharacteristic
92C22⋊Q8×C37C2312yes—
93#121×C37C2311yescharacteristic
94C4×Q8×C37—21no—
95C4×Q8×C37—22no—
96C4×Q8×C37—21no—
97C4×Q8×C37—21no—
98C4×Q8×C37D411yescharacteristic
99C4×Q8×C37D412yes—
100C4×D4×C37—21no—
101C4×D4×C37—22no—
102C4×D4×C37D411yescharacteristic
103#117×C37—22no—
104#117×C37—21no—
105#117×C37—21no—
106#117×C37—22no—
107#117×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—24no—
112C2×C4⋊C4×C37D411yescharacteristic
113C2×C4⋊C4×C37D412yes—
114C2×C4⋊C4×C37D411yescharacteristic
115C2×C4⋊C4×C37C2312yes—
116C2×C42×C37—21no—
117C2×C42×C37C2311yescharacteristic
118C4⋊C8×C37—21no—
119C4⋊C8×C37—21no—
120#103×C37—22no—
121#103×C37—22no—
122#103×C37—24no—
123C22⋊C8×C37C2312yes—
124C22⋊C8×C37C2312yes—
125#97×C37—21no—
126C4×C8×C37—21no—
127#95×C37—21no—
128#95×C37—24no—
129#95×C37C2312yes—
130C2×Q8×C37—22no—
131C2×Q8×C37—21no—
132C2×Q8×C37—22no—
133C2×Q8×C37—22no—
134C2×Q8×C37—82no—
135C2×Q8×C37C2×D412yes—
136C2×Q8×C37C2×D411yescharacteristic
137C2×D4×C37—21no—
138C2×D4×C37C2×D411yescharacteristic
139C22×C4×C37—22no—
140C22×C4×C37—22no—
141C22×C4×C37—21no—
142C22×C4×C37—22no—
143C22×C4×C37C2×D412yes—
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146C22×C4×C37C2×D412yes—
147C22×C4×C37C2411yescharacteristic
148Q16×C37—82no—
149Q16×C37—84no—
150SD16×C37—82no—
151C2×C8×C37—22no—
152C2×C8×C37—22no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—22no—
156C4⋊C4×C37—22no—
157C4⋊C4×C37—22no—
158C4⋊C4×C37—22no—
159C4⋊C4×C37—22no—
160C4⋊C4×C37—22no—
161C4⋊C4×C37—21no—
162C4⋊C4×C37—21no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—21no—
166C4⋊C4×C37—22no—
167C4⋊C4×C37—21no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—21no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—21no—
173C4⋊C4×C37—22no—
174C4⋊C4×C37—22no—
175C4⋊C4×C37—22no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—41no—
179C4⋊C4×C37—41no—
180C4⋊C4×C37—41no—
181C4⋊C4×C37—41no—
182C4⋊C4×C37—84no—
183C4⋊C4×C37C2×D411yescharacteristic
184C4⋊C4×C37C2×D411yescharacteristic
185C4⋊C4×C37C2×D412yes—
186C22⋊C4×C37—22no—
187C22⋊C4×C37—22no—
188C22⋊C4×C37—22no—
189C22⋊C4×C37—22no—
190C22⋊C4×C37—21no—
191C22⋊C4×C37—21no—
192C22⋊C4×C37—21no—
193C22⋊C4×C37—21no—
194C22⋊C4×C37—21no—
195C42×C37—24no—
196C42×C37—22no—
197C42×C37—22no—
198C42×C37—22no—
199C42×C37—22no—
200C42×C37—21no—
201C42×C37C2×D411yescharacteristic
202C42×C37C2×D411yescharacteristic
203C42×C37C2×D411yescharacteristic
204C42×C37C2×D411yescharacteristic
205C23×C37—21no—
206C23×C37C22×D411yescharacteristic
207Q8×C37—41no—
208Q8×C37—42no—
209Q8×C37—42no—
210Q8×C37—42no—
211Q8×C37—44no—
212Q8×C37—42no—
213Q8×C37—82no—
214D4×C37—41no—
215D4×C37—42no—
216C2×C4×C37—22no—
217C2×C4×C37—22no—
218C2×C4×C37—24no—
219C2×C4×C37—22no—
220C2×C4×C37—21no—
221C2×C4×C37—21no—
222C2×C4×C37—22no—
223C2×C4×C37—21no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
226C2×C4×C37—24no—
227C2×C4×C37—41no—
228C2×C4×C37—42no—
229C2×C4×C37—42no—
230C2×C4×C37—42no—
231C2×C4×C37—42no—
232C2×C4×C37—44no—
233C2×C4×C37—42no—
234C2×C4×C37—82no—
235C2×C4×C37#12011yescharacteristic
236C2×C4×C37#12011yescharacteristic
237C2×C4×C37#12011yescharacteristic
238C2×C4×C37#12011yescharacteristic
239C2×C4×C37C22×D411yescharacteristic
240C2×C4×C37C22×D411yescharacteristic
241C8×C37—42no—
242C8×C37—42no—
243#18433C3711yesmaximal, characteristic, direct product factor, Sylow
244C22×C37—21no—
245C22×C37—21no—
246C22×C37—41no—
247C22×C37—41no—
248C22×C37—41no—
249C22×C37C2×#12011yescharacteristic
250C22×C37#57812yes—
251C4×C37—21no—
252C4×C37—21no—
253C4×C37—21no—
254C4×C37—21no—
255C4×C37—21no—
256C4×C37—44no—
257C4×C37—42no—
258C4×C37—41no—
259C4×C37—41no—
260C4×C37—42no—
261C4×C37—42no—
262C4×C37—42no—
263C4×C37—41no—
264C4×C37—82no—
265C4×C37#45612yes—
266#3563C2×C3711yescharacteristic
267#3218C2×C3711yescharacteristic
268#3209C2×C3711yescharacteristic, complemented
269#2660C2×C3711yescharacteristic, complemented
270#1605C2×C3714yescomplemented
271#1603C2×C3714yes—
272#1506C2×C3711yescharacteristic, complemented
273#1500C2×C3711yescharacteristic
274#1470C2×C3711yescharacteristic, complemented
275C2×C37—22no—
276C2×C37—81no—
277C2×C37#301111yescharacteristic
278C2×C37C2×#45611yescharacteristic
279C2×C37#302711yescharacteristic
280#564—21no—
281#563—21no—
282#557—21no—
283#554—21no—
284#552—21no—
285#552—21no—
286#552—22no—
287#544—21no—
288#544C22×C3712yes—
289#541—21no—
290#541—22no—
291#539C22×C3712yes—
292#533C22×C3711yescharacteristic
293C2×C4⋊Q8C22×C3711yescharacteristic
294#529C22×C3711yescharacteristic
295C2×#125C22×C3711yescharacteristic
296#497—21no—
297#494—21no—
298#491—21no—
299#487—21no—
300#462—22no—
301#462—21no—
302#461—21no—
303#451C22×C3714yes—
304#451C22×C3712yes—
305#448C22×C3712yes—
306#432C22×C3711yescharacteristic
307#431C22×C3711yescharacteristic
308#398—22no—
309#395C22×C3714yes—
310#384—21no—
311#382—21no—
312#376C22×C3711yescharacteristic
313#328C22×C3714yes—
314#328C22×C3712yes—
315#327C22×C3712yes—
316#324C22×C3714yes—
317C37#1843311yescharacteristic, direct product factor, Sylow
318C22×Q8C23×C3712yes—
319C2×Q16—24no—
320C2×Q16—22no—
321C2×SD16—22no—
322C4⋊Q8—21no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8D4×C3711yescharacteristic
330C4⋊Q8D4×C3711yescharacteristic
331#126—22no—
332#126—22no—
333#126—22no—
334#126—22no—
335#126—21no—
336#125—22no—
337#125—22no—
338#125—22no—
339#125—22no—
340#125—21no—
341#125—22no—
342#125—22no—
343#125—22no—
344#125—22no—
345#125—21no—
346#125—21no—
347#125—21no—
348#125—21no—
349#125—21no—
350#125D4×C3711yescharacteristic
351#124D4×C3711yescharacteristic
352#123—22no—
353#123—21no—
354#123—22no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—21no—
361C22⋊Q8—22no—
362C22⋊Q8C23×C3711yescharacteristic
363C22⋊Q8C23×C3712yes—
364#121C23×C3711yescharacteristic
365C4×Q8—21no—
366C4×Q8—22no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8D4×C3711yescharacteristic
370C4×Q8D4×C3712yes—
371C4×D4—21no—
372C4×D4—22no—
373C4×D4D4×C3711yescharacteristic
374#117—22no—
375#117—21no—
376#117—21no—
377#117—22no—
378#117—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4D4×C3711yescharacteristic
384C2×C4⋊C4D4×C3712yes—
385C2×C4⋊C4D4×C3711yescharacteristic
386C2×C4⋊C4C23×C3712yes—
387C2×C42—21no—
388C2×C42C23×C3711yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391#103—22no—
392#103—22no—
393#103—24no—
394C22⋊C8C23×C3712yes—
395C22⋊C8C23×C3712yes—
396#97—21no—
397C4×C8—21no—
398#95—21no—
399#95—24no—
400#95C23×C3712yes—
401C2×Q8—22no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—82no—
406C2×Q8C2×D4×C3712yes—
407C2×Q8C2×D4×C3711yescharacteristic
408C2×D4—21no—
409C2×D4C2×D4×C3711yescharacteristic
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4C2×D4×C3712yes—
415C22×C4C2×D4×C3711yescharacteristic
416C22×C4C2×D4×C3711yescharacteristic
417C22×C4C2×D4×C3712yes—
418C22×C4C24×C3711yescharacteristic
419Q16—82no—
420Q16—84no—
421SD16—82no—
422C2×C8—22no—
423C2×C8—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—84no—
454C4⋊C4C2×D4×C3711yescharacteristic
455C4⋊C4C2×D4×C3711yescharacteristic
456C4⋊C4C2×D4×C3712yes—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C42—24no—
467C42—22no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42—21no—
472C42C2×D4×C3711yescharacteristic
473C42C2×D4×C3711yescharacteristic
474C42C2×D4×C3711yescharacteristic
475C42C2×D4×C3711yescharacteristic
476C23—21no—
477C23C22×D4×C3711yescharacteristic
478Q8—41no—
479Q8—42no—
480Q8—42no—
481Q8—42no—
482Q8—44no—
483Q8—42no—
484Q8—82no—
485D4—41no—
486D4—42no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—82no—
506C2×C4#120×C3711yescharacteristic
507C2×C4#120×C3711yescharacteristic
508C2×C4#120×C3711yescharacteristic
509C2×C4#120×C3711yescharacteristic
510C2×C4C22×D4×C3711yescharacteristic
511C2×C4C22×D4×C3711yescharacteristic
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22C2×#120×C3711yescharacteristic
520C22C37×#57812yes—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—44no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—41no—
534C4—82no—
535C4C37×#45612yes—
536C2—22no—
537C2—81no—
538C2C37×#301111yescharacteristic
539C2C2×C37×#45611yescharacteristic
540C2C37×#302711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radical#121×C37C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#3209C2semidirect
4. C37×#2660C2semidirect
5. C37×#1605C2semidirect
7. C37×#1506C2semidirect
9. C37×#1470C2semidirect
243. #18433C37direct (N × H)
268. #3209C2×C37semidirect
269. #2660C2×C37semidirect
270. #1605C2×C37semidirect
272. #1506C2×C37semidirect
274. #1470C2×C37semidirect
317. C37#18433direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35632
C37×#32182
C37×#32092
C37×#26602
C37×#16052
C37×#16032
C37×#15062
C37×#15002
C37×#14702
#1843337