Finite Group Databasebeta

← C37×#18431 #22639684

Subgroups — C37×#18431 #22639684

Order 9472.

928 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3559C211yesmaximal, characteristic
2C37×#3218C211yesmaximal, characteristic, complemented
3C37×#3206C211yesmaximal, characteristic, complemented
4C37×#2660C211yesmaximal, characteristic, complemented
5C37×#1604C214yesmaximal, complemented
6C37×#1603C214yesmaximal, complemented
7C37×#1505C211yesmaximal, characteristic, complemented
8C37×#1500C211yesmaximal, characteristic, complemented
9C37×#1470C211yesmaximal, characteristic, complemented
10C37×#563—21no—
11C37×#562—21no—
12C37×#554—21no—
13C37×#553—21no—
14C37×#553—21no—
15C37×#547—22no—
16C37×#547—21no—
17C37×#544—21no—
18C37×#540—21no—
19C37×#539—22no—
20C37×#539C2212yes—
21C37×#537C2212yes—
22C37×#532C2211yescharacteristic
23C2×C4⋊Q8×C37C2211yescharacteristic
24C37×#529C2211yescharacteristic
25C2×#125×C37C2211yescharacteristic
26C37×#497—21no—
27C37×#492—21no—
28C37×#491—21no—
29C37×#487—21no—
30C37×#462—21no—
31C37×#461—22no—
32C37×#461—21no—
33C37×#451C2212yes—
34C37×#448C2214yes—
35C37×#448C2212yes—
36C37×#432C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#398—22no—
39C37×#395C2214yes—
40C37×#384—21no—
41C37×#382—21no—
42C37×#376C2211yescharacteristic
43C37×#328C2212yes—
44C37×#327C2214yes—
45C37×#327C2212yes—
46C37×#324C2214yes—
47C2×#41×C37—21no—
48C2×#41×C37—22no—
49C22×Q8×C37C2312yes—
50C2×Q16×C37—22no—
51C2×SD16×C37—24no—
52C2×SD16×C37—22no—
53C4⋊Q8×C37—21no—
54C4⋊Q8×C37—22no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37D411yescharacteristic
60#127×C37D411yescharacteristic
61#126×C37—22no—
62#126×C37—22no—
63#126×C37—21no—
64#125×C37—21no—
65#125×C37—22no—
66#125×C37—21no—
67#125×C37—21no—
68#125×C37—21no—
69#125×C37—21no—
70#125×C37D411yescharacteristic
71#124×C37—21no—
72#124×C37D411yescharacteristic
73#123×C37—22no—
74#123×C37—22no—
75#123×C37—22no—
76#123×C37—22no—
77#123×C37—22no—
78#123×C37—21no—
79#123×C37—22no—
80C22⋊Q8×C37—22no—
81C22⋊Q8×C37—22no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—22no—
85C22⋊Q8×C37—22no—
86C22⋊Q8×C37C2311yescharacteristic
87#121×C37—21no—
88#121×C37—22no—
89#121×C37—21no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—21no—
93#121×C37—22no—
94#121×C37C2311yescharacteristic
95#121×C37C2312yes—
96C4×Q8×C37D411yescharacteristic
97C4×D4×C37—22no—
98C4×D4×C37—21no—
99C4×D4×C37—21no—
100C4×D4×C37—21no—
101C4×D4×C37—22no—
102C4×D4×C37—21no—
103C4×D4×C37D411yescharacteristic
104C4×D4×C37D412yes—
105#117×C37—21no—
106#117×C37—21no—
107C2×C4⋊C4×C37—22no—
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—24no—
121#103×C37—22no—
122#103×C37—22no—
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—
130#41×C37—82no—
131#41×C37—84no—
132C2×Q8×C37—22no—
133C2×Q8×C37—21no—
134C2×Q8×C37—22no—
135C2×Q8×C37—22no—
136C2×Q8×C37—82no—
137C2×Q8×C37C2×D411yescharacteristic
138C2×D4×C37—21no—
139C2×D4×C37—22no—
140C2×D4×C37—22no—
141C2×D4×C37—22no—
142C2×D4×C37—21no—
143C2×D4×C37—21no—
144C2×D4×C37C2×D411yescharacteristic
145C2×D4×C37C2×D412yes—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—21no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37C2×D412yes—
154C22×C4×C37C2×D411yescharacteristic
155C22×C4×C37C2×D411yescharacteristic
156C22×C4×C37C2×D412yes—
157C22×C4×C37C2411yescharacteristic
158Q16×C37—82no—
159SD16×C37—84no—
160SD16×C37—82no—
161C2×C8×C37—22no—
162C2×C8×C37—22no—
163C4⋊C4×C37—22no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—22no—
166C4⋊C4×C37—22no—
167C4⋊C4×C37—21no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—22no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—22no—
173C4⋊C4×C37—21no—
174C4⋊C4×C37—21no—
175C4⋊C4×C37—21no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—22no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—41no—
181C4⋊C4×C37—41no—
182C4⋊C4×C37—41no—
183C4⋊C4×C37—41no—
184C4⋊C4×C37—84no—
185C4⋊C4×C37C2×D412yes—
186C4⋊C4×C37C2×D411yescharacteristic
187C4⋊C4×C37C2×D411yescharacteristic
188C22⋊C4×C37—22no—
189C22⋊C4×C37—22no—
190C22⋊C4×C37—22no—
191C22⋊C4×C37—22no—
192C22⋊C4×C37—22no—
193C22⋊C4×C37—21no—
194C22⋊C4×C37—21no—
195C22⋊C4×C37—21no—
196C22⋊C4×C37—21no—
197C22⋊C4×C37—22no—
198C22⋊C4×C37—21no—
199C22⋊C4×C37—22no—
200C42×C37—24no—
201C42×C37—22no—
202C42×C37—21no—
203C42×C37C2×D411yescharacteristic
204C42×C37C2×D411yescharacteristic
205C42×C37C2×D411yescharacteristic
206C42×C37C2×D411yescharacteristic
207C23×C37—21no—
208C23×C37—22no—
209C23×C37C22×D411yescharacteristic
210Q8×C37—41no—
211Q8×C37—44no—
212Q8×C37—42no—
213Q8×C37—42no—
214Q8×C37—81no—
215Q8×C37—82no—
216D4×C37—42no—
217D4×C37—41no—
218D4×C37—44no—
219D4×C37—42no—
220D4×C37—42no—
221D4×C37—81no—
222D4×C37—82no—
223D4×C37—82no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
226C2×C4×C37—24no—
227C2×C4×C37—21no—
228C2×C4×C37—21no—
229C2×C4×C37—22no—
230C2×C4×C37—22no—
231C2×C4×C37—21no—
232C2×C4×C37—22no—
233C2×C4×C37—24no—
234C2×C4×C37—41no—
235C2×C4×C37—42no—
236C2×C4×C37—42no—
237C2×C4×C37—42no—
238C2×C4×C37—42no—
239C2×C4×C37—44no—
240C2×C4×C37—42no—
241C2×C4×C37—82no—
242C2×C4×C37—82no—
243C2×C4×C37—82no—
244C2×C4×C37—82no—
245C2×C4×C37#12011yescharacteristic
246C2×C4×C37#12011yescharacteristic
247C2×C4×C37#12011yescharacteristic
248C2×C4×C37#12011yescharacteristic
249C2×C4×C37C22×D411yescharacteristic
250C2×C4×C37C22×D411yescharacteristic
251C8×C37—42no—
252C8×C37—42no—
253#18431C3711yesmaximal, characteristic, direct product factor, Sylow
254C22×C37—21no—
255C22×C37—21no—
256C22×C37—42no—
257C22×C37—41no—
258C22×C37—41no—
259C22×C37—42no—
260C22×C37—42no—
261C22×C37—41no—
262C22×C37C2×#12011yescharacteristic
263C22×C37#57712yes—
264C4×C37—21no—
265C4×C37—21no—
266C4×C37—21no—
267C4×C37—21no—
268C4×C37—21no—
269C4×C37—44no—
270C4×C37—42no—
271C4×C37—42no—
272C4×C37—41no—
273C4×C37—41no—
274C4×C37—42no—
275C4×C37—41no—
276C4×C37—82no—
277C4×C37#45612yes—
278#3559C2×C3711yescharacteristic
279#3218C2×C3711yescharacteristic, complemented
280#3206C2×C3711yescharacteristic, complemented
281#2660C2×C3711yescharacteristic, complemented
282#1604C2×C3714yescomplemented
283#1603C2×C3714yescomplemented
284#1505C2×C3711yescharacteristic, complemented
285#1500C2×C3711yescharacteristic, complemented
286#1470C2×C3711yescharacteristic, complemented
287C2×C37—22no—
288C2×C37—81no—
289C2×C37—82no—
290C2×C37#300911yescharacteristic
291C2×C37C2×#45611yescharacteristic
292C2×C37#302711yescharacteristic
293#563—21no—
294#562—21no—
295#554—21no—
296#553—21no—
297#553—21no—
298#547—22no—
299#547—21no—
300#544—21no—
301#540—21no—
302#539—22no—
303#539C22×C3712yes—
304#537C22×C3712yes—
305#532C22×C3711yescharacteristic
306C2×C4⋊Q8C22×C3711yescharacteristic
307#529C22×C3711yescharacteristic
308C2×#125C22×C3711yescharacteristic
309#497—21no—
310#492—21no—
311#491—21no—
312#487—21no—
313#462—21no—
314#461—22no—
315#461—21no—
316#451C22×C3712yes—
317#448C22×C3714yes—
318#448C22×C3712yes—
319#432C22×C3711yescharacteristic
320#431C22×C3711yescharacteristic
321#398—22no—
322#395C22×C3714yes—
323#384—21no—
324#382—21no—
325#376C22×C3711yescharacteristic
326#328C22×C3712yes—
327#327C22×C3714yes—
328#327C22×C3712yes—
329#324C22×C3714yes—
330C37#1843111yescharacteristic, direct product factor, Sylow
331C2×#41—21no—
332C2×#41—22no—
333C22×Q8C23×C3712yes—
334C2×Q16—22no—
335C2×SD16—24no—
336C2×SD16—22no—
337C4⋊Q8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8D4×C3711yescharacteristic
344#127D4×C3711yescharacteristic
345#126—22no—
346#126—22no—
347#126—21no—
348#125—21no—
349#125—22no—
350#125—21no—
351#125—21no—
352#125—21no—
353#125—21no—
354#125D4×C3711yescharacteristic
355#124—21no—
356#124D4×C3711yescharacteristic
357#123—22no—
358#123—22no—
359#123—22no—
360#123—22no—
361#123—22no—
362#123—21no—
363#123—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8C23×C3711yescharacteristic
371#121—21no—
372#121—22no—
373#121—21no—
374#121—22no—
375#121—22no—
376#121—21no—
377#121—22no—
378#121C23×C3711yescharacteristic
379#121C23×C3712yes—
380C4×Q8D4×C3711yescharacteristic
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4D4×C3711yescharacteristic
388C4×D4D4×C3712yes—
389#117—21no—
390#117—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4D4×C3711yescharacteristic
397C2×C4⋊C4D4×C3712yes—
398C2×C4⋊C4D4×C3711yescharacteristic
399C2×C4⋊C4C23×C3712yes—
400C2×C42—21no—
401C2×C42C23×C3711yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—21no—
404#103—24no—
405#103—22no—
406#103—22no—
407C22⋊C8C23×C3712yes—
408C22⋊C8C23×C3712yes—
409#97—21no—
410C4×C8—21no—
411#95—21no—
412#95—24no—
413#95C23×C3712yes—
414#41—82no—
415#41—84no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—82no—
421C2×Q8C2×D4×C3711yescharacteristic
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4C2×D4×C3711yescharacteristic
429C2×D4C2×D4×C3712yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4C2×D4×C3712yes—
438C22×C4C2×D4×C3711yescharacteristic
439C22×C4C2×D4×C3711yescharacteristic
440C22×C4C2×D4×C3712yes—
441C22×C4C24×C3711yescharacteristic
442Q16—82no—
443SD16—84no—
444SD16—82no—
445C2×C8—22no—
446C2×C8—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—84no—
469C4⋊C4C2×D4×C3712yes—
470C4⋊C4C2×D4×C3711yescharacteristic
471C4⋊C4C2×D4×C3711yescharacteristic
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C22⋊C4—22no—
484C42—24no—
485C42—22no—
486C42—21no—
487C42C2×D4×C3711yescharacteristic
488C42C2×D4×C3711yescharacteristic
489C42C2×D4×C3711yescharacteristic
490C42C2×D4×C3711yescharacteristic
491C23—21no—
492C23—22no—
493C23C22×D4×C3711yescharacteristic
494Q8—41no—
495Q8—44no—
496Q8—42no—
497Q8—42no—
498Q8—81no—
499Q8—82no—
500D4—42no—
501D4—41no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—81no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4#120×C3711yescharacteristic
530C2×C4#120×C3711yescharacteristic
531C2×C4#120×C3711yescharacteristic
532C2×C4#120×C3711yescharacteristic
533C2×C4C22×D4×C3711yescharacteristic
534C2×C4C22×D4×C3711yescharacteristic
535C8—42no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—41no—
545C22C2×#120×C3711yescharacteristic
546C22C37×#57712yes—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—41no—
556C4—41no—
557C4—42no—
558C4—41no—
559C4—82no—
560C4C37×#45612yes—
561C2—22no—
562C2—81no—
563C2—82no—
564C2C37×#300911yescharacteristic
565C2C2×C37×#45611yescharacteristic
566C2C37×#302711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3559C2
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
2. C37×#3218C2semidirect
3. C37×#3206C2semidirect
4. C37×#2660C2semidirect
5. C37×#1604C2semidirect
6. C37×#1603C2semidirect
7. C37×#1505C2semidirect
8. C37×#1500C2semidirect
9. C37×#1470C2semidirect
253. #18431C37direct (N × H)
279. #3218C2×C37semidirect
280. #3206C2×C37semidirect
281. #2660C2×C37semidirect
282. #1604C2×C37semidirect
283. #1603C2×C37semidirect
284. #1505C2×C37semidirect
285. #1500C2×C37semidirect
286. #1470C2×C37semidirect
330. C37#18431direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35592
C37×#32182
C37×#32062
C37×#26602
C37×#16042
C37×#16032
C37×#15052
C37×#15002
C37×#14702
#1843137