Finite Group Databasebeta

← C37×#23983 #22645236

Subgroups — C37×#23983 #22645236

Order 9472.

1228 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#552C211yesmaximal, characteristic
2C2×C37×#451C211yesmaximal, characteristic, complemented
3C2×C37×#419C211yesmaximal, characteristic, complemented
4C37×#2409C211yesmaximal, characteristic
5C37×#2026C212yesmaximal, complemented
6C37×#2001C212yesmaximal, complemented
7C37×#1894C211yesmaximal, characteristic, complemented
8C37×#1878C212yesmaximal, complemented
9C37×#1872C212yesmaximal, complemented
10C37×#1870C211yesmaximal, characteristic
11C37×#1825C211yesmaximal, characteristic, complemented
12C23×Q8×C37C2211yescharacteristic
13C22×Q16×C37C2212yes—
14C22×M16×C37C2211yescharacteristic
15C37×#552—24no—
16C37×#552—24no—
17C2×#126×C37—21no—
18C2×#125×C37—21no—
19C2×#125×C37C2211yescharacteristic
20C2×#123×C37—21no—
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2212yes—
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C2×#117×C37—21no—
27C2×#117×C37C2211yescharacteristic
28C22×C4⋊C4×C37C2211yescharacteristic
29C37×#451—24no—
30C37×#419—24no—
31C2×#103×C37C2212yes—
32C2×#103×C37C2212yes—
33C2×#103×C37C2212yes—
34C2×#103×C37C2212yes—
35C2×C22⋊C8×C37C2211yescharacteristic
36C2×C22⋊C8×C37C2212yes—
37C37×#395—21no—
38C37×#393—21no—
39C37×#391C2212yes—
40C37×#386—21no—
41C37×#385—21no—
42C37×#380C2211yescharacteristic
43C37×#340C2212yes—
44C37×#340C2212yes—
45C37×#340C2212yes—
46C37×#336C2212yes—
47C22×Q8×C37—21no—
48C22×Q8×C37—24no—
49C22×Q8×C37—22no—
50C22×Q8×C37—22no—
51C22×Q8×C37—42no—
52C22×Q8×C37C2311yescharacteristic
53C22×Q8×C37C2312yes—
54C22×D4×C37D411yescharacteristic
55C23×C4×C37—21no—
56C23×C4×C37—21no—
57C23×C4×C37C2311yescharacteristic
58C23×C4×C37C2311yescharacteristic
59C2×Q16×C37—24no—
60C2×Q16×C37—24no—
61C2×Q16×C37—42no—
62C2×M16×C37—22no—
63C2×M16×C37—42no—
64C22×C8×C37C2312yes—
65C22×C8×C37C2312yes—
66#126×C37—28no—
67#125×C37—28no—
68#125×C37—22no—
69#125×C37—22no—
70#123×C37—28no—
71C22⋊Q8×C37—22no—
72C22⋊Q8×C37—22no—
73C22⋊Q8×C37—22no—
74C22⋊Q8×C37—24no—
75C22⋊Q8×C37—42no—
76C22⋊Q8×C37D414yes—
77C4×Q8×C37—22no—
78C4×Q8×C37—22no—
79C4×D4×C37—22no—
80C4×D4×C37—22no—
81#117×C37—28no—
82#117×C37—22no—
83#117×C37D414yes—
84C2×C4⋊C4×C37—21no—
85C2×C4⋊C4×C37—21no—
86C2×C4⋊C4×C37—21no—
87C2×C4⋊C4×C37—21no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—22no—
91C2×C4⋊C4×C37—22no—
92C2×C4⋊C4×C37—22no—
93C2×C4⋊C4×C37D411yescharacteristic
94C2×C4⋊C4×C37C2312yes—
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C22⋊C4×C37—21no—
99C2×C22⋊C4×C37—21no—
100C2×C22⋊C4×C37—21no—
101C2×C22⋊C4×C37—22no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37D411yescharacteristic
104C2×C22⋊C4×C37D411yescharacteristic
105C2×C42×C37—21no—
106C2×C42×C37—21no—
107C2×C42×C37C2311yescharacteristic
108#103×C37—24no—
109#103×C37—24no—
110#103×C37—24no—
111#103×C37—42no—
112C22⋊C8×C37—22no—
113C22⋊C8×C37—42no—
114#95×C37—21no—
115#95×C37—22no—
116#95×C37—22no—
117C24×C37C2×D411yescharacteristic
118C24×C37C2×D411yescharacteristic
119C2×Q8×C37—21no—
120C2×Q8×C37—22no—
121C2×Q8×C37—28no—
122C2×Q8×C37—22no—
123C2×Q8×C37—22no—
124C2×Q8×C37—22no—
125C2×Q8×C37—22no—
126C2×Q8×C37—22no—
127C2×Q8×C37—22no—
128C2×Q8×C37—44no—
129C2×Q8×C37—48no—
130C2×Q8×C37—44no—
131C2×Q8×C37—42no—
132C2×Q8×C37C2×D412yes—
133C2×Q8×C37#4114yes—
134C2×D4×C37—22no—
135C2×D4×C37—22no—
136C2×D4×C37—41no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—24no—
140C22×C4×C37—22no—
141C22×C4×C37—21no—
142C22×C4×C37—21no—
143C22×C4×C37—21no—
144C22×C4×C37—21no—
145C22×C4×C37—21no—
146C22×C4×C37—21no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—44no—
151C22×C4×C37—42no—
152C22×C4×C37—42no—
153C22×C4×C37—42no—
154C22×C4×C37C2×D411yescharacteristic
155C22×C4×C37C2×D411yescharacteristic
156C22×C4×C37C2×D411yescharacteristic
157C22×C4×C37C2×D411yescharacteristic
158C22×C4×C37C2×D412yes—
159C22×C4×C37C2×D412yes—
160C22×C4×C37C2411yescharacteristic
161Q16×C37—48no—
162M16×C37—44no—
163C2×C8×C37—22no—
164C2×C8×C37—22no—
165C2×C8×C37—22no—
166C2×C8×C37—22no—
167C2×C8×C37—22no—
168C2×C8×C37—22no—
169C4⋊C4×C37—24no—
170C4⋊C4×C37—24no—
171C4⋊C4×C37—24no—
172C4⋊C4×C37—24no—
173C4⋊C4×C37—24no—
174C4⋊C4×C37—24no—
175C4⋊C4×C37—22no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—21no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—22no—
180C4⋊C4×C37—22no—
181C4⋊C4×C37—44no—
182C4⋊C4×C37C2×D412yes—
183C4⋊C4×C37C2×D412yes—
184C4⋊C4×C37C2×D412yes—
185C22⋊C4×C37—24no—
186C22⋊C4×C37—24no—
187C22⋊C4×C37—24no—
188C22⋊C4×C37—22no—
189C22⋊C4×C37—22no—
190C22⋊C4×C37—44no—
191C22⋊C4×C37—42no—
192C42×C37—24no—
193C42×C37—24no—
194C42×C37—21no—
195C42×C37—21no—
196C23×C37—21no—
197C23×C37—22no—
198C23×C37—22no—
199C23×C37—21no—
200C23×C37—21no—
201C23×C37—21no—
202C23×C37—22no—
203C23×C37—22no—
204C23×C37#12012yes—
205C23×C37#13712yes—
206C23×C37C22×D411yescharacteristic
207Q8×C37—24no—
208Q8×C37—24no—
209Q8×C37—24no—
210Q8×C37—48no—
211Q8×C37—41no—
212Q8×C37—41no—
213Q8×C37—42no—
214Q8×C37—42no—
215D4×C37—44no—
216C2×C4×C37—22no—
217C2×C4×C37—22no—
218C2×C4×C37—22no—
219C2×C4×C37—24no—
220C2×C4×C37—21no—
221C2×C4×C37—22no—
222C2×C4×C37—22no—
223C2×C4×C37—22no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—22no—
227C2×C4×C37—24no—
228C2×C4×C37—22no—
229C2×C4×C37—21no—
230C2×C4×C37—21no—
231C2×C4×C37—22no—
232C2×C4×C37—48no—
233C2×C4×C37—48no—
234C2×C4×C37—42no—
235C2×C4×C37—42no—
236C2×C4×C37—42no—
237C2×C4×C37—41no—
238C2×C4×C37—41no—
239C2×C4×C37—41no—
240C2×C4×C37—41no—
241C2×C4×C37—42no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—42no—
245C2×C4×C37—42no—
246C2×C4×C37—42no—
247C2×C4×C37—42no—
248C2×C4×C37#12012yes—
249C2×C4×C37C22×D411yescharacteristic
250C2×C4×C37C22×D411yescharacteristic
251C2×C4×C37C2×#4112yes—
252C2×C4×C37H(5,𝔽2)12yes—
253C8×C37—42no—
254C8×C37—42no—
255#23983C3711yesmaximal, characteristic, direct product factor, Sylow
256C22×C37—22no—
257C22×C37—22no—
258C22×C37—22no—
259C22×C37—22no—
260C22×C37—24no—
261C22×C37—41no—
262C22×C37—41no—
263C22×C37—42no—
264C22×C37—42no—
265C22×C37—42no—
266C22×C37C2×#12011yescharacteristic
267C22×C37#54612yes—
268C22×C37C2×#13711yescharacteristic
269C22×C37#57511yescharacteristic
270C22×C37#57812yes—
271C4×C37—22no—
272C4×C37—41no—
273C4×C37—44no—
274C4×C37—42no—
275C4×C37—41no—
276C4×C37—42no—
277C4×C37—42no—
278C4×C37—41no—
279C4×C37—42no—
280C4×C37—82no—
281C4×C37#52511yescharacteristic
282C4×C37#53511yescharacteristic
283C4×C37#54612yes—
284C2×#552C2×C3711yescharacteristic
285C2×#451C2×C3711yescharacteristic, complemented
286C2×#419C2×C3711yescharacteristic, complemented
287#2409C2×C3711yescharacteristic
288#2026C2×C3712yescomplemented
289#2001C2×C3712yescomplemented
290#1894C2×C3711yescharacteristic, complemented
291#1878C2×C3712yescomplemented
292#1872C2×C3712yescomplemented
293#1870C2×C3711yescharacteristic
294#1825C2×C3711yescharacteristic, complemented
295C2×C37—42no—
296C2×C37—42no—
297C2×C37#240411yescharacteristic
298C2×C37#300711yescharacteristic
299C2×C37#301111yescharacteristic
300C2×C37#331212yes—
301C2×C37#332712yes—
302C23×Q8C22×C3711yescharacteristic
303C22×Q16C22×C3712yes—
304C22×M16C22×C3711yescharacteristic
305#552—24no—
306#552—24no—
307C2×#126—21no—
308C2×#125—21no—
309C2×#125C22×C3711yescharacteristic
310C2×#123—21no—
311C2×C22⋊Q8C22×C3711yescharacteristic
312C2×C22⋊Q8C22×C3712yes—
313C2×C22⋊Q8C22×C3711yescharacteristic
314C2×C4×Q8C22×C3711yescharacteristic
315C2×C4×D4C22×C3711yescharacteristic
316C2×#117—21no—
317C2×#117C22×C3711yescharacteristic
318C22×C4⋊C4C22×C3711yescharacteristic
319#451—24no—
320#419—24no—
321C2×#103C22×C3712yes—
322C2×#103C22×C3712yes—
323C2×#103C22×C3712yes—
324C2×#103C22×C3712yes—
325C2×C22⋊C8C22×C3711yescharacteristic
326C2×C22⋊C8C22×C3712yes—
327#395—21no—
328#393—21no—
329#391C22×C3712yes—
330#386—21no—
331#385—21no—
332#380C22×C3711yescharacteristic
333#340C22×C3712yes—
334#340C22×C3712yes—
335#340C22×C3712yes—
336#336C22×C3712yes—
337C37#2398311yescharacteristic, direct product factor, Sylow
338C22×Q8—21no—
339C22×Q8—24no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—42no—
343C22×Q8C23×C3711yescharacteristic
344C22×Q8C23×C3712yes—
345C22×D4D4×C3711yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4C23×C3711yescharacteristic
349C23×C4C23×C3711yescharacteristic
350C2×Q16—24no—
351C2×Q16—24no—
352C2×Q16—42no—
353C2×M16—22no—
354C2×M16—42no—
355C22×C8C23×C3712yes—
356C22×C8C23×C3712yes—
357#126—28no—
358#125—28no—
359#125—22no—
360#125—22no—
361#123—28no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—24no—
366C22⋊Q8—42no—
367C22⋊Q8D4×C3714yes—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×D4—22no—
371C4×D4—22no—
372#117—28no—
373#117—22no—
374#117D4×C3714yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4D4×C3711yescharacteristic
385C2×C4⋊C4C23×C3712yes—
386C2×C4⋊C4C23×C3711yescharacteristic
387C2×C4⋊C4C23×C3711yescharacteristic
388C2×C4⋊C4C23×C3711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4D4×C3711yescharacteristic
395C2×C22⋊C4D4×C3711yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C3711yescharacteristic
399#103—24no—
400#103—24no—
401#103—24no—
402#103—42no—
403C22⋊C8—22no—
404C22⋊C8—42no—
405#95—21no—
406#95—22no—
407#95—22no—
408C24C2×D4×C3711yescharacteristic
409C24C2×D4×C3711yescharacteristic
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—28no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—44no—
420C2×Q8—48no—
421C2×Q8—44no—
422C2×Q8—42no—
423C2×Q8C2×D4×C3712yes—
424C2×Q8#41×C3714yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—41no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C2×D4×C3711yescharacteristic
446C22×C4C2×D4×C3711yescharacteristic
447C22×C4C2×D4×C3711yescharacteristic
448C22×C4C2×D4×C3711yescharacteristic
449C22×C4C2×D4×C3712yes—
450C22×C4C2×D4×C3712yes—
451C22×C4C24×C3711yescharacteristic
452Q16—48no—
453M16—44no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—44no—
473C4⋊C4C2×D4×C3712yes—
474C4⋊C4C2×D4×C3712yes—
475C4⋊C4C2×D4×C3712yes—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—44no—
482C22⋊C4—42no—
483C42—24no—
484C42—24no—
485C42—21no—
486C42—21no—
487C23—21no—
488C23—22no—
489C23—22no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—22no—
494C23—22no—
495C23#120×C3712yes—
496C23#137×C3712yes—
497C23C22×D4×C3711yescharacteristic
498Q8—24no—
499Q8—24no—
500Q8—24no—
501Q8—48no—
502Q8—41no—
503Q8—42no—
504Q8—41no—
505Q8—42no—
506D4—44no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—48no—
524C2×C4—48no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4#120×C3712yes—
540C2×C4C22×D4×C3711yescharacteristic
541C2×C4C22×D4×C3711yescharacteristic
542C2×C4C2×#41×C3712yes—
543C2×C4H(5,𝔽2)×C3712yes—
544C8—42no—
545C8—42no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—41no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22C2×#120×C3711yescharacteristic
557C22C37×#54612yes—
558C22C2×#137×C3711yescharacteristic
559C22C37×#57511yescharacteristic
560C22C37×#57812yes—
561C4—22no—
562C4—41no—
563C4—44no—
564C4—42no—
565C4—41no—
566C4—42no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—82no—
571C4C37×#52511yescharacteristic
572C4C37×#53511yescharacteristic
573C4C37×#54612yes—
574C2—42no—
575C2—42no—
576C2C37×#240411yescharacteristic
577C2C37×#300711yescharacteristic
578C2C37×#301111yescharacteristic
579C2C37×#331212yes—
580C2C37×#332712yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×D4×C37D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#451C2semidirect
3. C2×C37×#419C2semidirect
5. C37×#2026C2semidirect
6. C37×#2001C2semidirect
7. C37×#1894C2semidirect
8. C37×#1878C2semidirect
9. C37×#1872C2semidirect
11. C37×#1825C2semidirect
255. #23983C37direct (N × H)
285. C2×#451C2×C37semidirect
286. C2×#419C2×C37semidirect
288. #2026C2×C37semidirect
289. #2001C2×C37semidirect
290. #1894C2×C37semidirect
291. #1878C2×C37semidirect
292. #1872C2×C37semidirect
294. #1825C2×C37semidirect
337. C37#23983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5522
C2×C37×#4512
C2×C37×#4192
C37×#24092
C37×#20262
C37×#20012
C37×#18942
C37×#18782
C37×#18722
C37×#18702
C37×#18252
#2398337