Finite Group Databasebeta

← C37×#29668 #22650921

Subgroups — C37×#29668 #22650921

Order 9472.

1158 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#533C211yesmaximal, characteristic, complemented
2C2×C37×#464C212yesmaximal, complemented
3C37×#2850C211yesmaximal, characteristic
4C37×#2024C211yesmaximal, characteristic, complemented
5C37×#2023C211yesmaximal, characteristic, complemented
6C37×#2016C211yesmaximal, characteristic, complemented
7C37×#2013C211yesmaximal, characteristic, complemented
8C37×#2001C212yesmaximal, complemented
9C37×#2000C212yesmaximal
10C37×#1805C212yesmaximal, complemented
11C37×#1797C211yesmaximal, characteristic, complemented
12C22×Q16×C37C2212yes—
13C22×SD16×C37C2212yes—
14C37×#533—28no—
15C2×C4⋊Q8×C37C2211yescharacteristic
16C2×C4⋊Q8×C37C2211yescharacteristic
17C2×#125×C37—21no—
18C2×#124×C37C2211yescharacteristic
19C2×C22⋊Q8×C37—21no—
20C2×C22⋊Q8×C37C2212yes—
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×C4×Q8×C37—21no—
24C2×C4×Q8×C37C2212yes—
25C2×#117×C37—21no—
26C22×C42×C37C2211yescharacteristic
27C37×#464—28no—
28C2×C4⋊C8×C37C2212yes—
29C2×#103×C37C2212yes—
30C2×#103×C37C2212yes—
31C2×#103×C37C2212yes—
32C2×#102×C37C2212yes—
33C2×C22⋊C8×C37C2212yes—
34C37×#391C2211yescharacteristic
35C37×#390C2211yescharacteristic
36C37×#388—21no—
37C37×#388—21no—
38C37×#386—21no—
39C37×#386—21no—
40C37×#382C2211yescharacteristic
41C37×#340C2212yes—
42C37×#340C2212yes—
43C37×#336C2211yescharacteristic
44C37×#336C2211yescharacteristic
45C22×Q8×C37—21no—
46C22×Q8×C37C2311yescharacteristic
47C22×Q8×C37C2312yes—
48C22×D4×C37—21no—
49C22×D4×C37C2311yescharacteristic
50C23×C4×C37D411yescharacteristic
51C23×C4×C37D411yescharacteristic
52C23×C4×C37C2311yescharacteristic
53C2×Q16×C37—24no—
54C2×Q16×C37—42no—
55C2×Q16×C37—42no—
56C2×SD16×C37—24no—
57C2×SD16×C37—42no—
58C2×SD16×C37—42no—
59C22×C8×C37C2312yes—
60C22×C8×C37C2312yes—
61C4⋊Q8×C37—24no—
62C4⋊Q8×C37—24no—
63#125×C37—28no—
64#124×C37—24no—
65C22⋊Q8×C37—28no—
66C22⋊Q8×C37—24no—
67C22⋊Q8×C37—24no—
68C22⋊Q8×C37—42no—
69#121×C37—42no—
70C4×Q8×C37—28no—
71C4×Q8×C37—24no—
72C4×Q8×C37D418yescomplemented
73#117×C37—28no—
74C2×C4⋊C4×C37—22no—
75C2×C4⋊C4×C37—21no—
76C2×C4⋊C4×C37—22no—
77C2×C4⋊C4×C37—21no—
78C2×C4⋊C4×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37C2311yescharacteristic
81C2×C4⋊C4×C37C2311yescharacteristic
82C2×C4⋊C4×C37C2312yes—
83C2×C22⋊C4×C37—22no—
84C2×C22⋊C4×C37—21no—
85C2×C22⋊C4×C37—21no—
86C2×C22⋊C4×C37—21no—
87C2×C22⋊C4×C37—21no—
88C2×C22⋊C4×C37—21no—
89C2×C22⋊C4×C37—21no—
90C2×C42×C37—22no—
91C2×C42×C37—24no—
92C2×C42×C37D411yescharacteristic
93C2×C42×C37D411yescharacteristic
94C2×C42×C37C2311yescharacteristic
95C2×C42×C37C2311yescharacteristic
96C4⋊C8×C37—24no—
97#103×C37—24no—
98#103×C37—42no—
99#103×C37—42no—
100#102×C37—24no—
101C22⋊C8×C37—42no—
102#95×C37—21no—
103#95×C37—21no—
104#95×C37—21no—
105#95×C37—21no—
106C24×C37—21no—
107C24×C37C2×D411yescharacteristic
108C2×Q8×C37—24no—
109C2×Q8×C37—22no—
110C2×Q8×C37—22no—
111C2×Q8×C37—22no—
112C2×Q8×C37—22no—
113C2×Q8×C37—22no—
114C2×Q8×C37—22no—
115C2×Q8×C37—21no—
116C2×Q8×C37—22no—
117C2×Q8×C37—21no—
118C2×Q8×C37—42no—
119C2×Q8×C37—42no—
120C2×Q8×C37C2×D414yes—
121C2×D4×C37—22no—
122C2×D4×C37—22no—
123C2×D4×C37—21no—
124C2×D4×C37—21no—
125C2×D4×C37—42no—
126C2×D4×C37—42no—
127C2×D4×C37—42no—
128C22×C4×C37—22no—
129C22×C4×C37—22no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—22no—
136C22×C4×C37—21no—
137C22×C4×C37—22no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—41no—
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146C22×C4×C37C2×D411yescharacteristic
147C22×C4×C37C2×D411yescharacteristic
148C22×C4×C37C2411yescharacteristic
149Q16×C37—48no—
150SD16×C37—48no—
151C2×C8×C37—22no—
152C2×C8×C37—22no—
153C2×C8×C37—22no—
154C2×C8×C37—22no—
155C2×C8×C37—22no—
156C2×C8×C37—22no—
157C4⋊C4×C37—24no—
158C4⋊C4×C37—24no—
159C4⋊C4×C37—28no—
160C4⋊C4×C37—24no—
161C4⋊C4×C37—28no—
162C4⋊C4×C37—22no—
163C4⋊C4×C37—22no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—42no—
166C4⋊C4×C37C2×D414yes—
167C22⋊C4×C37—28no—
168C22⋊C4×C37—42no—
169C22⋊C4×C37—42no—
170C22⋊C4×C37—42no—
171C22⋊C4×C37—42no—
172C22⋊C4×C37—42no—
173C22⋊C4×C37—42no—
174C42×C37—22no—
175C42×C37—22no—
176C42×C37—28no—
177C42×C37—22no—
178C42×C37C2×D414yes—
179C23×C37—21no—
180C23×C37—21no—
181C23×C37—21no—
182C23×C37—21no—
183C23×C37—21no—
184C23×C37—21no—
185C23×C37—41no—
186C23×C37—41no—
187C23×C37—41no—
188C23×C37—41no—
189C23×C37—41no—
190C23×C37—41no—
191C23×C37—41no—
192C23×C37#13712yes—
193C23×C37C22×D411yescharacteristic
194Q8×C37—24no—
195Q8×C37—24no—
196Q8×C37—48no—
197Q8×C37—42no—
198Q8×C37—42no—
199Q8×C37—42no—
200Q8×C37—42no—
201D4×C37—42no—
202D4×C37—42no—
203D4×C37—84no—
204C2×C4×C37—28no—
205C2×C4×C37—21no—
206C2×C4×C37—21no—
207C2×C4×C37—21no—
208C2×C4×C37—21no—
209C2×C4×C37—21no—
210C2×C4×C37—21no—
211C2×C4×C37—21no—
212C2×C4×C37—21no—
213C2×C4×C37—21no—
214C2×C4×C37—24no—
215C2×C4×C37—24no—
216C2×C4×C37—21no—
217C2×C4×C37—21no—
218C2×C4×C37—44no—
219C2×C4×C37—42no—
220C2×C4×C37—42no—
221C2×C4×C37—42no—
222C2×C4×C37—42no—
223C2×C4×C37—42no—
224C2×C4×C37—42no—
225C2×C4×C37—41no—
226C2×C4×C37—41no—
227C2×C4×C37—41no—
228C2×C4×C37—41no—
229C2×C4×C37—41no—
230C2×C4×C37—41no—
231C2×C4×C37—41no—
232C2×C4×C37—41no—
233C2×C4×C37—41no—
234C2×C4×C37#12012yes—
235C2×C4×C37#12012yes—
236C2×C4×C37#13512yes—
237C2×C4×C37#13712yes—
238C2×C4×C37C22×D412yes—
239C2×C4×C37H(5,𝔽2)11yescharacteristic
240C2×C4×C37H(5,𝔽2)12yes—
241C2×C4×C372−1+411yescharacteristic
242C8×C37—42no—
243C8×C37—42no—
244#29668C3711yesmaximal, characteristic, direct product factor, Sylow
245C22×C37—22no—
246C22×C37—22no—
247C22×C37—22no—
248C22×C37—41no—
249C22×C37—41no—
250C22×C37—41no—
251C22×C37—41no—
252C22×C37—81no—
253C22×C37—81no—
254C22×C37—81no—
255C22×C37—81no—
256C22×C37—81no—
257C22×C37—81no—
258C22×C37—81no—
259C22×C37C2×#12011yescharacteristic
260C22×C37#53511yescharacteristic
261C22×C37#53711yescharacteristic
262C22×C37C2×#13511yescharacteristic
263C22×C37C2×#13711yescharacteristic
264C22×C37C2×#13711yescharacteristic
265C22×C37#57511yescharacteristic
266C4×C37—22no—
267C4×C37—22no—
268C4×C37—22no—
269C4×C37—22no—
270C4×C37—41no—
271C4×C37—44no—
272C4×C37—44no—
273C4×C37—81no—
274C4×C37—81no—
275C4×C37—81no—
276C4×C37#53512yes—
277C4×C37#53712yes—
278C2×#533C2×C3711yescharacteristic, complemented
279C2×#464C2×C3712yescomplemented
280#2850C2×C3711yescharacteristic
281#2024C2×C3711yescharacteristic, complemented
282#2023C2×C3711yescharacteristic, complemented
283#2016C2×C3711yescharacteristic, complemented
284#2013C2×C3711yescharacteristic, complemented
285#2001C2×C3712yescomplemented
286#2000C2×C3712yes—
287#1805C2×C3712yescomplemented
288#1797C2×C3711yescharacteristic, complemented
289C2×C37—42no—
290C2×C37—161no—
291C2×C37#261511yescharacteristic
292C2×C37#300211yescharacteristic
293C2×C37#300411yescharacteristic
294C2×C37#321011yescharacteristic
295C2×C37#321511yescharacteristic
296C2×C37#324811yescharacteristic
297C2×C37#325211yescharacteristic
298C22×Q16C22×C3712yes—
299C22×SD16C22×C3712yes—
300#533—28no—
301C2×C4⋊Q8C22×C3711yescharacteristic
302C2×C4⋊Q8C22×C3711yescharacteristic
303C2×#125—21no—
304C2×#124C22×C3711yescharacteristic
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8C22×C3712yes—
307C2×C22⋊Q8C22×C3711yescharacteristic
308C2×#121C22×C3711yescharacteristic
309C2×C4×Q8—21no—
310C2×C4×Q8C22×C3712yes—
311C2×#117—21no—
312C22×C42C22×C3711yescharacteristic
313#464—28no—
314C2×C4⋊C8C22×C3712yes—
315C2×#103C22×C3712yes—
316C2×#103C22×C3712yes—
317C2×#103C22×C3712yes—
318C2×#102C22×C3712yes—
319C2×C22⋊C8C22×C3712yes—
320#391C22×C3711yescharacteristic
321#390C22×C3711yescharacteristic
322#388—21no—
323#388—21no—
324#386—21no—
325#386—21no—
326#382C22×C3711yescharacteristic
327#340C22×C3712yes—
328#340C22×C3712yes—
329#336C22×C3711yescharacteristic
330#336C22×C3711yescharacteristic
331C37#2966811yescharacteristic, direct product factor, Sylow
332C22×Q8—21no—
333C22×Q8C23×C3711yescharacteristic
334C22×Q8C23×C3712yes—
335C22×D4—21no—
336C22×D4C23×C3711yescharacteristic
337C23×C4D4×C3711yescharacteristic
338C23×C4D4×C3711yescharacteristic
339C23×C4C23×C3711yescharacteristic
340C2×Q16—24no—
341C2×Q16—42no—
342C2×Q16—42no—
343C2×SD16—24no—
344C2×SD16—42no—
345C2×SD16—42no—
346C22×C8C23×C3712yes—
347C22×C8C23×C3712yes—
348C4⋊Q8—24no—
349C4⋊Q8—24no—
350#125—28no—
351#124—24no—
352C22⋊Q8—28no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—42no—
356#121—42no—
357C4×Q8—28no—
358C4×Q8—24no—
359C4×Q8D4×C3718yescomplemented
360#117—28no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C3711yescharacteristic
368C2×C4⋊C4C23×C3711yescharacteristic
369C2×C4⋊C4C23×C3712yes—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42D4×C3711yescharacteristic
380C2×C42D4×C3711yescharacteristic
381C2×C42C23×C3711yescharacteristic
382C2×C42C23×C3711yescharacteristic
383C4⋊C8—24no—
384#103—24no—
385#103—42no—
386#103—42no—
387#102—24no—
388C22⋊C8—42no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393C24—21no—
394C24C2×D4×C3711yescharacteristic
395C2×Q8—24no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—21no—
405C2×Q8—42no—
406C2×Q8—42no—
407C2×Q8C2×D4×C3714yes—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—42no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—41no—
430C22×C4C2×D4×C3711yescharacteristic
431C22×C4C2×D4×C3711yescharacteristic
432C22×C4C2×D4×C3711yescharacteristic
433C22×C4C2×D4×C3711yescharacteristic
434C22×C4C2×D4×C3711yescharacteristic
435C22×C4C24×C3711yescharacteristic
436Q16—48no—
437SD16—48no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—28no—
447C4⋊C4—24no—
448C4⋊C4—28no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—42no—
453C4⋊C4C2×D4×C3714yes—
454C22⋊C4—28no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C42—22no—
462C42—22no—
463C42—28no—
464C42—22no—
465C42C2×D4×C3714yes—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23#137×C3712yes—
480C23C22×D4×C3711yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—48no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488D4—42no—
489D4—42no—
490D4—84no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4#120×C3712yes—
522C2×C4#120×C3712yes—
523C2×C4#135×C3712yes—
524C2×C4#137×C3712yes—
525C2×C4C22×D4×C3712yes—
526C2×C4H(5,𝔽2)×C3711yescharacteristic
527C2×C4H(5,𝔽2)×C3712yes—
528C2×C42−1+4×C3711yescharacteristic
529C8—42no—
530C8—42no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22C2×#120×C3711yescharacteristic
546C22C37×#53511yescharacteristic
547C22C37×#53711yescharacteristic
548C22C2×#135×C3711yescharacteristic
549C22C2×#137×C3711yescharacteristic
550C22C2×#137×C3711yescharacteristic
551C22C37×#57511yescharacteristic
552C4—22no—
553C4—22no—
554C4—22no—
555C4—22no—
556C4—41no—
557C4—44no—
558C4—44no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C37×#53512yes—
563C4C37×#53712yes—
564C2—42no—
565C2—161no—
566C2C37×#261511yescharacteristic
567C2C37×#300211yescharacteristic
568C2C37×#300411yescharacteristic
569C2C37×#321011yescharacteristic
570C2C37×#321511yescharacteristic
571C2C37×#324811yescharacteristic
572C2C37×#325211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#533C2semidirect
2. C2×C37×#464C2semidirect
4. C37×#2024C2semidirect
5. C37×#2023C2semidirect
6. C37×#2016C2semidirect
7. C37×#2013C2semidirect
8. C37×#2001C2semidirect
10. C37×#1805C2semidirect
11. C37×#1797C2semidirect
72. C4×Q8×C37D4semidirect
244. #29668C37direct (N × H)
278. C2×#533C2×C37semidirect
279. C2×#464C2×C37semidirect
281. #2024C2×C37semidirect
282. #2023C2×C37semidirect
283. #2016C2×C37semidirect
284. #2013C2×C37semidirect
285. #2001C2×C37semidirect
287. #1805C2×C37semidirect
288. #1797C2×C37semidirect
331. C37#29668direct (N × H)
359. C4×Q8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5332
C2×C37×#4642
C37×#28502
C37×#20242
C37×#20232
C37×#20162
C37×#20132
C37×#20012
C37×#20002
C37×#18052
C37×#17972
#2966837