Finite Group Databasebeta

← C37×#18961 #22640214

Subgroups — C37×#18961 #22640214

Order 9472.

818 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3555C211yesmaximal, characteristic
2C37×#3238C211yesmaximal, characteristic
3C37×#3230C211yesmaximal, characteristic, complemented
4C37×#3209C211yesmaximal, characteristic, complemented
5C37×#1638C212yesmaximal, complemented
6C37×#1636C212yesmaximal, complemented
7C37×#1633C212yesmaximal, complemented
8C37×#1632C212yesmaximal, complemented
9C37×#1554C211yesmaximal, characteristic, complemented
10C37×#1497C211yesmaximal, characteristic, complemented
11C37×#1482C211yesmaximal, characteristic
12C37×#563—22no—
13Q82×C37C2211yescharacteristic
14C37×#557—21no—
15C37×#557C2211yescharacteristic
16C37×#556—21no—
17C37×#556—21no—
18C37×#556C2211yescharacteristic
19C37×#554C2211yescharacteristic
20C37×#552—21no—
21C37×#544—21no—
22C37×#542—21no—
23C37×#541—21no—
24C37×#541—21no—
25C37×#541—22no—
26C37×#533C2211yescharacteristic
27C37×#533C2211yescharacteristic
28C2×C4⋊Q8×C37C2211yescharacteristic
29C37×#529C2211yescharacteristic
30C37×#501—21no—
31C37×#500—21no—
32C37×#494C2212yes—
33C37×#489—21no—
34C37×#487—21no—
35C37×#487C2212yes—
36C37×#484—21no—
37C37×#484—21no—
38C37×#483—21no—
39C37×#480—21no—
40C37×#477C2212yes—
41C37×#477C2212yes—
42C37×#477C2212yes—
43C37×#476C2212yes—
44C37×#462—22no—
45C37×#451—22no—
46C37×#432C2211yescharacteristic
47C37×#431C2211yescharacteristic
48C37×#431C2211yescharacteristic
49C37×#333C2212yes—
50C37×#332C2212yes—
51C37×Q8⋊C8C2212yes—
52C37×Q8⋊C8C2212yes—
53C37×Q8⋊C8C2212yes—
54C37×D4⋊C8C2212yes—
55C22×Q8×C37—21no—
56C2×Q16×C37—24no—
57C4⋊Q8×C37—22no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—22no—
60C4⋊Q8×C37—21no—
61C4⋊Q8×C37—21no—
62C4⋊Q8×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37—21no—
65C4⋊Q8×C37D411yescharacteristic
66C4⋊Q8×C37D411yescharacteristic
67C4⋊Q8×C37C2312yes—
68C4⋊Q8×C37C2311yescharacteristic
69C4⋊Q8×C37C2311yescharacteristic
70#126×C37—22no—
71#126×C37—22no—
72#126×C37—22no—
73#126×C37—22no—
74#126×C37—22no—
75#126×C37—22no—
76#126×C37—21no—
77#125×C37—22no—
78#125×C37—22no—
79#125×C37—22no—
80#125×C37—22no—
81#125×C37—21no—
82#125×C37—22no—
83#125×C37—21no—
84#125×C37—21no—
85#125×C37—21no—
86#125×C37D411yescharacteristic
87#124×C37—22no—
88#124×C37—21no—
89#124×C37D411yescharacteristic
90#123×C37—22no—
91#123×C37—21no—
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—21no—
95C22⋊Q8×C37—21no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37D411yescharacteristic
100C22⋊Q8×C37D411yescharacteristic
101C22⋊Q8×C37D411yescharacteristic
102C22⋊Q8×C37D412yes—
103#121×C37D411yescharacteristic
104C4×Q8×C37—22no—
105C4×Q8×C37—21no—
106C4×Q8×C37—21no—
107C4×Q8×C37—21no—
108C4×Q8×C37—21no—
109C4×Q8×C37—21no—
110C4×Q8×C37—21no—
111C4×Q8×C37—21no—
112C4×Q8×C37D412yes—
113C4×Q8×C37C2311yescharacteristic
114C4×Q8×C37C2311yescharacteristic
115C4×Q8×C37C2311yescharacteristic
116C4×D4×C37—21no—
117C4×D4×C37—21no—
118C4×D4×C37C2311yescharacteristic
119#117×C37—22no—
120#117×C37—21no—
121#117×C37—21no—
122#117×C37—21no—
123#117×C37—21no—
124C2×C4⋊C4×C37—21no—
125C2×C4⋊C4×C37—21no—
126C2×C4⋊C4×C37—21no—
127C2×C42×C37C2311yescharacteristic
128#107×C37—22no—
129#107×C37—22no—
130#107×C37—22no—
131#106×C37—22no—
132C4⋊C8×C37—21no—
133C4⋊C8×C37C2312yes—
134C4⋊C8×C37C2312yes—
135#103×C37—22no—
136#103×C37—22no—
137#103×C37—22no—
138#103×C37—24no—
139#102×C37—22no—
140C22⋊C8×C37—21no—
141C22⋊C8×C37—21no—
142C22⋊C8×C37—21no—
143#97×C37—21no—
144C4×C8×C37—21no—
145C4×C8×C37C2312yes—
146C2×Q8×C37—22no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—22no—
150C2×Q8×C37—41no—
151C2×Q8×C37—82no—
152C2×Q8×C37C2×D411yescharacteristic
153C2×Q8×C37C2×D411yescharacteristic
154C2×Q8×C37C2×D411yescharacteristic
155C2×Q8×C37C2×D412yes—
156C2×D4×C37—21no—
157C2×D4×C37C2×D411yescharacteristic
158C22×C4×C37—22no—
159C22×C4×C37—21no—
160C22×C4×C37—41no—
161C22×C4×C37C2×D411yescharacteristic
162C22×C4×C37C2×D411yescharacteristic
163C22×C4×C37C2×D411yescharacteristic
164Q16×C37—84no—
165C2×C8×C37—22no—
166C2×C8×C37—22no—
167C2×C8×C37—22no—
168C4⋊C4×C37—22no—
169C4⋊C4×C37—22no—
170C4⋊C4×C37—22no—
171C4⋊C4×C37—22no—
172C4⋊C4×C37—22no—
173C4⋊C4×C37—22no—
174C4⋊C4×C37—22no—
175C4⋊C4×C37—22no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—21no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—21no—
181C4⋊C4×C37—21no—
182C4⋊C4×C37—21no—
183C4⋊C4×C37—22no—
184C4⋊C4×C37—21no—
185C4⋊C4×C37—22no—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—21no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—22no—
194C4⋊C4×C37—41no—
195C4⋊C4×C37—41no—
196C4⋊C4×C37C2×D412yes—
197C4⋊C4×C37C2×D411yescharacteristic
198C4⋊C4×C37C2×D411yescharacteristic
199C4⋊C4×C37C2×D411yescharacteristic
200C4⋊C4×C37C2×D411yescharacteristic
201C22⋊C4×C37—22no—
202C22⋊C4×C37—22no—
203C22⋊C4×C37—22no—
204C22⋊C4×C37—21no—
205C22⋊C4×C37—22no—
206C22⋊C4×C37—21no—
207C22⋊C4×C37—21no—
208C22⋊C4×C37—21no—
209C22⋊C4×C37—21no—
210C22⋊C4×C37—21no—
211C22⋊C4×C37—21no—
212C42×C37—22no—
213C42×C37—22no—
214C42×C37—22no—
215C42×C37—22no—
216C42×C37—21no—
217C42×C37—21no—
218C42×C37—21no—
219C42×C37C2×D411yescharacteristic
220C42×C37C2×D411yescharacteristic
221C42×C37C2×D411yescharacteristic
222C42×C37C2411yescharacteristic
223C23×C37—21no—
224C23×C37#12011yescharacteristic
225Q8×C37—22no—
226Q8×C37—22no—
227Q8×C37—22no—
228Q8×C37—42no—
229Q8×C37—44no—
230Q8×C37—42no—
231Q8×C37—81no—
232Q8×C37—82no—
233Q8×C37—82no—
234D4×C37—22no—
235D4×C37—81no—
236C2×C4×C37—22no—
237C2×C4×C37—22no—
238C2×C4×C37—21no—
239C2×C4×C37—21no—
240C2×C4×C37—21no—
241C2×C4×C37—22no—
242C2×C4×C37—21no—
243C2×C4×C37—21no—
244C2×C4×C37—21no—
245C2×C4×C37—22no—
246C2×C4×C37—21no—
247C2×C4×C37—41no—
248C2×C4×C37—42no—
249C2×C4×C37—42no—
250C2×C4×C37—82no—
251C2×C4×C37—82no—
252C2×C4×C37#12011yescharacteristic
253C2×C4×C37#12011yescharacteristic
254C2×C4×C37#12011yescharacteristic
255C2×C4×C37C22×D411yescharacteristic
256C2×C4×C37C22×D411yescharacteristic
257C2×C4×C37C22×D411yescharacteristic
258C8×C37—42no—
259C8×C37—42no—
260C8×C37—42no—
261#18961C3711yesmaximal, characteristic, direct product factor, Sylow
262C22×C37—21no—
263C22×C37—21no—
264C22×C37—21no—
265C22×C37—41no—
266C22×C37—41no—
267C22×C37—41no—
268C22×C37C2×#12011yescharacteristic
269C4×C37—21no—
270C4×C37—21no—
271C4×C37—21no—
272C4×C37—21no—
273C4×C37—41no—
274C4×C37—41no—
275C4×C37—41no—
276C4×C37—41no—
277C4×C37—42no—
278C4×C37—41no—
279C4×C37—42no—
280C4×C37—41no—
281C4×C37—41no—
282C4×C37—82no—
283C4×C37#57812yes—
284C4×C37#57812yes—
285#3555C2×C3711yescharacteristic
286#3238C2×C3711yescharacteristic
287#3230C2×C3711yescharacteristic, complemented
288#3209C2×C3711yescharacteristic, complemented
289#1638C2×C3712yescomplemented
290#1636C2×C3712yescomplemented
291#1633C2×C3712yescomplemented
292#1632C2×C3712yescomplemented
293#1554C2×C3711yescharacteristic, complemented
294#1497C2×C3711yescharacteristic, complemented
295#1482C2×C3711yescharacteristic
296C2×C37—41no—
297C2×C37—81no—
298C2×C37#301111yescharacteristic
299C2×C37#301111yescharacteristic
300C2×C37#302111yescharacteristic
301#563—22no—
302Q82C22×C3711yescharacteristic
303#557—21no—
304#557C22×C3711yescharacteristic
305#556—21no—
306#556—21no—
307#556C22×C3711yescharacteristic
308#554C22×C3711yescharacteristic
309#552—21no—
310#544—21no—
311#542—21no—
312#541—21no—
313#541—21no—
314#541—22no—
315#533C22×C3711yescharacteristic
316#533C22×C3711yescharacteristic
317C2×C4⋊Q8C22×C3711yescharacteristic
318#529C22×C3711yescharacteristic
319#501—21no—
320#500—21no—
321#494C22×C3712yes—
322#489—21no—
323#487—21no—
324#487C22×C3712yes—
325#484—21no—
326#484—21no—
327#483—21no—
328#480—21no—
329#477C22×C3712yes—
330#477C22×C3712yes—
331#477C22×C3712yes—
332#476C22×C3712yes—
333#462—22no—
334#451—22no—
335#432C22×C3711yescharacteristic
336#431C22×C3711yescharacteristic
337#431C22×C3711yescharacteristic
338#333C22×C3712yes—
339#332C22×C3712yes—
340Q8⋊C8C22×C3712yes—
341Q8⋊C8C22×C3712yes—
342Q8⋊C8C22×C3712yes—
343D4⋊C8C22×C3712yes—
344C37#1896111yescharacteristic, direct product factor, Sylow
345C22×Q8—21no—
346C2×Q16—24no—
347C4⋊Q8—22no—
348C4⋊Q8—21no—
349C4⋊Q8—22no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8D4×C3711yescharacteristic
356C4⋊Q8D4×C3711yescharacteristic
357C4⋊Q8C23×C3712yes—
358C4⋊Q8C23×C3711yescharacteristic
359C4⋊Q8C23×C3711yescharacteristic
360#126—22no—
361#126—22no—
362#126—22no—
363#126—22no—
364#126—22no—
365#126—22no—
366#126—21no—
367#125—22no—
368#125—22no—
369#125—22no—
370#125—22no—
371#125—21no—
372#125—22no—
373#125—21no—
374#125—21no—
375#125—21no—
376#125D4×C3711yescharacteristic
377#124—22no—
378#124—21no—
379#124D4×C3711yescharacteristic
380#123—22no—
381#123—21no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8D4×C3711yescharacteristic
390C22⋊Q8D4×C3711yescharacteristic
391C22⋊Q8D4×C3711yescharacteristic
392C22⋊Q8D4×C3712yes—
393#121D4×C3711yescharacteristic
394C4×Q8—22no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8D4×C3712yes—
403C4×Q8C23×C3711yescharacteristic
404C4×Q8C23×C3711yescharacteristic
405C4×Q8C23×C3711yescharacteristic
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C3711yescharacteristic
409#117—22no—
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C42C23×C3711yescharacteristic
418#107—22no—
419#107—22no—
420#107—22no—
421#106—22no—
422C4⋊C8—21no—
423C4⋊C8C23×C3712yes—
424C4⋊C8C23×C3712yes—
425#103—22no—
426#103—22no—
427#103—22no—
428#103—24no—
429#102—22no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C3712yes—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—41no—
441C2×Q8—82no—
442C2×Q8C2×D4×C3711yescharacteristic
443C2×Q8C2×D4×C3711yescharacteristic
444C2×Q8C2×D4×C3711yescharacteristic
445C2×Q8C2×D4×C3712yes—
446C2×D4—21no—
447C2×D4C2×D4×C3711yescharacteristic
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C3711yescharacteristic
452C22×C4C2×D4×C3711yescharacteristic
453C22×C4C2×D4×C3711yescharacteristic
454Q16—84no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C3712yes—
487C4⋊C4C2×D4×C3711yescharacteristic
488C4⋊C4C2×D4×C3711yescharacteristic
489C4⋊C4C2×D4×C3711yescharacteristic
490C4⋊C4C2×D4×C3711yescharacteristic
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42C2×D4×C3711yescharacteristic
510C42C2×D4×C3711yescharacteristic
511C42C2×D4×C3711yescharacteristic
512C42C24×C3711yescharacteristic
513C23—21no—
514C23#120×C3711yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—44no—
520Q8—42no—
521Q8—81no—
522Q8—82no—
523Q8—82no—
524D4—22no—
525D4—81no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4#120×C3711yescharacteristic
543C2×C4#120×C3711yescharacteristic
544C2×C4#120×C3711yescharacteristic
545C2×C4C22×D4×C3711yescharacteristic
546C2×C4C22×D4×C3711yescharacteristic
547C2×C4C22×D4×C3711yescharacteristic
548C8—42no—
549C8—42no—
550C8—42no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×#120×C3711yescharacteristic
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—82no—
572C4C37×#57812yes—
573C4C37×#57812yes—
574C2—41no—
575C2—81no—
576C2C37×#301111yescharacteristic
577C2C37×#301111yescharacteristic
578C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radical#121×C37D4
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
3. C37×#3230C2semidirect
4. C37×#3209C2semidirect
5. C37×#1638C2semidirect
6. C37×#1636C2semidirect
7. C37×#1633C2semidirect
8. C37×#1632C2semidirect
9. C37×#1554C2semidirect
10. C37×#1497C2semidirect
261. #18961C37direct (N × H)
287. #3230C2×C37semidirect
288. #3209C2×C37semidirect
289. #1638C2×C37semidirect
290. #1636C2×C37semidirect
291. #1633C2×C37semidirect
292. #1632C2×C37semidirect
293. #1554C2×C37semidirect
294. #1497C2×C37semidirect
344. C37#18961direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35552
C37×#32382
C37×#32302
C37×#32092
C37×#16382
C37×#16362
C37×#16332
C37×#16322
C37×#15542
C37×#14972
C37×#14822
#1896137