Finite Group Databasebeta

← C37×#26401 #22647654

Subgroups — C37×#26401 #22647654

Order 9472.

714 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3084C211yesmaximal, characteristic
2C37×#3082C211yesmaximal, characteristic, complemented
3C37×#2947C211yesmaximal, characteristic
4C37×#2912C211yesmaximal, characteristic
5C37×#2096C211yesmaximal, characteristic, complemented
6C37×#2090C211yesmaximal, characteristic, complemented
7C37×#2064C211yesmaximal, characteristic, complemented
8C37×#2060C211yesmaximal, characteristic, complemented
9C37×#1951C211yesmaximal, characteristic, complemented
10C37×#1922C211yesmaximal, characteristic, complemented
11C37×#1908C211yesmaximal, characteristic
12C37×#1882C211yesmaximal, characteristic
13C37×#1866C211yesmaximal, characteristic
14C37×#1859C211yesmaximal, characteristic
15C37×#1857C211yesmaximal, characteristic, complemented
16C2×#137×C37C2211yescharacteristic
17C2×#131×C37C2211yescharacteristic
18C37×#544C2211yescharacteristic
19C37×#520C2211yescharacteristic
20C37×#520C2211yescharacteristic
21C37×#519C2211yescharacteristic
22C37×#479—21no—
23C37×#479—21no—
24C37×#479—21no—
25C37×#478—21no—
26C37×#477—21no—
27C37×#476—21no—
28C37×#475—21no—
29C37×#475—21no—
30C37×#441—21no—
31C37×#440—21no—
32C4×Q16×C37—21no—
33C4×SD16×C37—21no—
34C2×#108×C37C2211yescharacteristic
35C37×#428—21no—
36C37×#428—21no—
37C37×#428C2211yescharacteristic
38C37×#428C2211yescharacteristic
39C37×#428C2211yescharacteristic
40C37×#428C2211yescharacteristic
41C37×#428C2211yescharacteristic
42C37×#427—21no—
43C37×#427C2211yescharacteristic
44C2×#106×C37—21no—
45C2×#106×C37C2211yescharacteristic
46C2×#106×C37C2211yescharacteristic
47C37×#424C2211yescharacteristic
48C37×#424C2211yescharacteristic
49C2×#104×C37C2211yescharacteristic
50C37×#419C2211yescharacteristic
51C37×#417C2211yescharacteristic
52C37×#416C2211yescharacteristic
53C2×#103×C37C2211yescharacteristic
54C2×#103×C37C2211yescharacteristic
55C2×#101×C37C2211yescharacteristic
56C37×#405C2211yescharacteristic
57C37×#391C2211yescharacteristic
58C37×#384C2211yescharacteristic
59C37×#343C2211yescharacteristic
60C37×#343C2211yescharacteristic
61C37×#343C2211yescharacteristic
62C37×#341C2211yescharacteristic
63C37×#339C2211yescharacteristic
64C37×#339C2211yescharacteristic
65C37×#339C2211yescharacteristic
66C37×#336C2211yescharacteristic
67C2×#41×C37C2311yescharacteristic
68C22×Q8×C37C2311yescharacteristic
69#137×C37—22no—
70#137×C37Q814yescomplemented
71C2×Q16×C37—21no—
72C2×SD16×C37—21no—
73#131×C37—22no—
74#131×C37—22no—
75C2×M16×C37—21no—
76C2×M16×C37C2311yescharacteristic
77C2×M16×C37C2311yescharacteristic
78C2×M16×C37C2311yescharacteristic
79C2×M16×C37C2311yescharacteristic
80C22×C8×C37—21no—
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C4⋊Q8×C37—21no—
84C4⋊Q8×C37—21no—
85#125×C37—21no—
86#125×C37—21no—
87C22⋊Q8×C37—41no—
88C4×Q8×C37—21no—
89C4×Q8×C37—21no—
90C4×Q8×C37—21no—
91C4×Q8×C37—21no—
92C4×Q8×C37—21no—
93C4×Q8×C37—21no—
94C4×D4×C37—21no—
95C4×D4×C37—21no—
96C4×D4×C37—41no—
97C4×D4×C37—41no—
98#117×C37—21no—
99#117×C37—21no—
100#117×C37—41no—
101#117×C37C2311yescharacteristic
102#117×C37C2311yescharacteristic
103#117×C37C2311yescharacteristic
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—41no—
107C2×C4⋊C4×C37C2311yescharacteristic
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C4⋊C4×C37C2311yescharacteristic
110C2×C42×C37C2311yescharacteristic
111#108×C37—22no—
112#107×C37—21no—
113#107×C37—21no—
114#107×C37—21no—
115#107×C37—21no—
116#107×C37—21no—
117#107×C37D411yescharacteristic
118#107×C37D411yescharacteristic
119#106×C37—21no—
120#106×C37—21no—
121#106×C37—21no—
122#106×C37—21no—
123#106×C37—21no—
124#106×C37—21no—
125#106×C37—21no—
126#106×C37—21no—
127#106×C37—21no—
128#106×C37D411yescharacteristic
129#106×C37D411yescharacteristic
130C4⋊C8×C37—21no—
131C4⋊C8×C37—21no—
132C4⋊C8×C37—21no—
133C4⋊C8×C37—21no—
134#104×C37—22no—
135#103×C37—21no—
136#103×C37—21no—
137#103×C37—21no—
138#103×C37—21no—
139#103×C37—21no—
140#103×C37—21no—
141#103×C37—21no—
142#103×C37D411yescharacteristic
143#103×C37D411yescharacteristic
144#102×C37—21no—
145#102×C37D411yescharacteristic
146#102×C37D411yescharacteristic
147#101×C37—22no—
148#97×C37—21no—
149C4×C8×C37—21no—
150#95×C37—41no—
151#41×C37—21no—
152#41×C37—21no—
153#41×C37C2×Q812yes—
154#41×C37#4112yes—
155C2×Q8×C37—21no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—21no—
159C2×Q8×C37—21no—
160C2×Q8×C37—41no—
161C2×Q8×C37C2×D411yescharacteristic
162C2×Q8×C37C2×Q812yes—
163C2×D4×C37—21no—
164C2×D4×C37C2×D411yescharacteristic
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—41no—
172C22×C4×C37—41no—
173C22×C4×C37C2411yescharacteristic
174Q16×C37—24no—
175SD16×C37—24no—
176M16×C37—24no—
177M16×C37—21no—
178M16×C37—21no—
179M16×C37—21no—
180M16×C37—21no—
181M16×C37—21no—
182M16×C37—21no—
183M16×C37C2×Q812yes—
184M16×C37#4112yes—
185C2×C8×C37—24no—
186C2×C8×C37—21no—
187C2×C8×C37—21no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37C2×D411yescharacteristic
195C2×C8×C37C2×D411yescharacteristic
196C2×C8×C37C2×D411yescharacteristic
197C2×C8×C37C2×D411yescharacteristic
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—41no—
205C4⋊C4×C37—41no—
206C4⋊C4×C37—41no—
207C4⋊C4×C37—41no—
208C4⋊C4×C37—41no—
209C4⋊C4×C37—41no—
210C4⋊C4×C37—41no—
211C4⋊C4×C37—82no—
212C4⋊C4×C37C2×D411yescharacteristic
213C4⋊C4×C37C2×D411yescharacteristic
214C4⋊C4×C37C2×D411yescharacteristic
215C4⋊C4×C37C2×D411yescharacteristic
216C4⋊C4×C37C2×D411yescharacteristic
217C4⋊C4×C37C2×D411yescharacteristic
218C22⋊C4×C37—21no—
219C22⋊C4×C37—21no—
220C22⋊C4×C37—21no—
221C22⋊C4×C37—41no—
222C22⋊C4×C37—41no—
223C42×C37—21no—
224C42×C37—21no—
225C42×C37—21no—
226C42×C37—21no—
227C42×C37—21no—
228C42×C37—41no—
229C42×C37—41no—
230C42×C37—41no—
231C42×C37—41no—
232C23×C37—21no—
233C23×C37H(5,𝔽2)11yescharacteristic
234Q8×C37—21no—
235Q8×C37—22no—
236Q8×C37—22no—
237Q8×C37—41no—
238Q8×C37—41no—
239Q8×C37—161no—
240Q8×C37C22⋊Q812yes—
241D4×C37—22no—
242D4×C37—22no—
243D4×C37—21no—
244D4×C37C22⋊Q812yes—
245C2×C4×C37—21no—
246C2×C4×C37—22no—
247C2×C4×C37—22no—
248C2×C4×C37—22no—
249C2×C4×C37—21no—
250C2×C4×C37—21no—
251C2×C4×C37—21no—
252C2×C4×C37—21no—
253C2×C4×C37—21no—
254C2×C4×C37—21no—
255C2×C4×C37—22no—
256C2×C4×C37—41no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—41no—
260C2×C4×C37—41no—
261C2×C4×C37—41no—
262C2×C4×C37—41no—
263C2×C4×C37—81no—
264C2×C4×C37—81no—
265C2×C4×C37—81no—
266C2×C4×C37—161no—
267C2×C4×C37—161no—
268C2×C4×C37C22×D411yescharacteristic
269C2×C4×C37C22×D411yescharacteristic
270C2×C4×C37C22×Q811yescharacteristic
271C2×C4×C37C2×#4111yescharacteristic
272C2×C4×C37C2×#4111yescharacteristic
273C2×C4×C372−1+411yescharacteristic
274C8×C37—22no—
275C8×C37—21no—
276C8×C37—22no—
277C8×C37—21no—
278C8×C37—21no—
279C8×C37—21no—
280C8×C37—41no—
281C8×C37—41no—
282#26401C3711yesmaximal, characteristic, direct product factor, Sylow
283C22×C37—21no—
284C22×C37—21no—
285C22×C37—22no—
286C22×C37—41no—
287C22×C37—41no—
288C22×C37#53911yescharacteristic
289C22×C37D4211yescharacteristic
290C22×C37#55411yescharacteristic
291C4×C37—22no—
292C4×C37—42no—
293C4×C37—42no—
294C4×C37—41no—
295C4×C37—41no—
296C4×C37—41no—
297C4×C37—41no—
298C4×C37—41no—
299C4×C37—41no—
300C4×C37—81no—
301C4×C37—81no—
302C4×C37—81no—
303C4×C37C2×C22⋊Q811yescharacteristic
304C4×C37#52511yescharacteristic
305C4×C37#54711yescharacteristic
306C4×C37D4×Q811yescharacteristic
307#3084C2×C3711yescharacteristic
308#3082C2×C3711yescharacteristic, complemented
309#2947C2×C3711yescharacteristic
310#2912C2×C3711yescharacteristic
311#2096C2×C3711yescharacteristic, complemented
312#2090C2×C3711yescharacteristic, complemented
313#2064C2×C3711yescharacteristic, complemented
314#2060C2×C3711yescharacteristic, complemented
315#1951C2×C3711yescharacteristic, complemented
316#1922C2×C3711yescharacteristic, complemented
317#1908C2×C3711yescharacteristic
318#1882C2×C3711yescharacteristic
319#1866C2×C3711yescharacteristic
320#1859C2×C3711yescharacteristic
321#1857C2×C3711yescharacteristic, complemented
322C2×C37—21no—
323C2×C37—21no—
324C2×C37—42no—
325C2×C37#244911yescharacteristic
326C2×C37#328911yescharacteristic
327C2×C37#329111yescharacteristic
328C2×#137C22×C3711yescharacteristic
329C2×#131C22×C3711yescharacteristic
330#544C22×C3711yescharacteristic
331#520C22×C3711yescharacteristic
332#520C22×C3711yescharacteristic
333#519C22×C3711yescharacteristic
334#479—21no—
335#479—21no—
336#479—21no—
337#478—21no—
338#477—21no—
339#476—21no—
340#475—21no—
341#475—21no—
342#441—21no—
343#440—21no—
344C4×Q16—21no—
345C4×SD16—21no—
346C2×#108C22×C3711yescharacteristic
347#428—21no—
348#428—21no—
349#428C22×C3711yescharacteristic
350#428C22×C3711yescharacteristic
351#428C22×C3711yescharacteristic
352#428C22×C3711yescharacteristic
353#428C22×C3711yescharacteristic
354#427—21no—
355#427C22×C3711yescharacteristic
356C2×#106—21no—
357C2×#106C22×C3711yescharacteristic
358C2×#106C22×C3711yescharacteristic
359#424C22×C3711yescharacteristic
360#424C22×C3711yescharacteristic
361C2×#104C22×C3711yescharacteristic
362#419C22×C3711yescharacteristic
363#417C22×C3711yescharacteristic
364#416C22×C3711yescharacteristic
365C2×#103C22×C3711yescharacteristic
366C2×#103C22×C3711yescharacteristic
367C2×#101C22×C3711yescharacteristic
368#405C22×C3711yescharacteristic
369#391C22×C3711yescharacteristic
370#384C22×C3711yescharacteristic
371#343C22×C3711yescharacteristic
372#343C22×C3711yescharacteristic
373#343C22×C3711yescharacteristic
374#341C22×C3711yescharacteristic
375#339C22×C3711yescharacteristic
376#339C22×C3711yescharacteristic
377#339C22×C3711yescharacteristic
378#336C22×C3711yescharacteristic
379C37#2640111yescharacteristic, direct product factor, Sylow
380C2×#41C23×C3711yescharacteristic
381C22×Q8C23×C3711yescharacteristic
382#137—22no—
383#137Q8×C3714yescomplemented
384C2×Q16—21no—
385C2×SD16—21no—
386#131—22no—
387#131—22no—
388C2×M16—21no—
389C2×M16C23×C3711yescharacteristic
390C2×M16C23×C3711yescharacteristic
391C2×M16C23×C3711yescharacteristic
392C2×M16C23×C3711yescharacteristic
393C22×C8—21no—
394C22×C8C23×C3711yescharacteristic
395C22×C8C23×C3711yescharacteristic
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398#125—21no—
399#125—21no—
400C22⋊Q8—41no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—41no—
410C4×D4—41no—
411#117—21no—
412#117—21no—
413#117—41no—
414#117C23×C3711yescharacteristic
415#117C23×C3711yescharacteristic
416#117C23×C3711yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4C23×C3711yescharacteristic
421C2×C4⋊C4C23×C3711yescharacteristic
422C2×C4⋊C4C23×C3711yescharacteristic
423C2×C42C23×C3711yescharacteristic
424#108—22no—
425#107—21no—
426#107—21no—
427#107—21no—
428#107—21no—
429#107—21no—
430#107D4×C3711yescharacteristic
431#107D4×C3711yescharacteristic
432#106—21no—
433#106—21no—
434#106—21no—
435#106—21no—
436#106—21no—
437#106—21no—
438#106—21no—
439#106—21no—
440#106—21no—
441#106D4×C3711yescharacteristic
442#106D4×C3711yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447#104—22no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—21no—
453#103—21no—
454#103—21no—
455#103D4×C3711yescharacteristic
456#103D4×C3711yescharacteristic
457#102—21no—
458#102D4×C3711yescharacteristic
459#102D4×C3711yescharacteristic
460#101—22no—
461#97—21no—
462C4×C8—21no—
463#95—41no—
464#41—21no—
465#41—21no—
466#41C2×Q8×C3712yes—
467#41#41×C3712yes—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—41no—
474C2×Q8C2×D4×C3711yescharacteristic
475C2×Q8C2×Q8×C3712yes—
476C2×D4—21no—
477C2×D4C2×D4×C3711yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4C24×C3711yescharacteristic
487Q16—24no—
488SD16—24no—
489M16—24no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16C2×Q8×C3712yes—
497M16#41×C3712yes—
498C2×C8—24no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8C2×D4×C3711yescharacteristic
508C2×C8C2×D4×C3711yescharacteristic
509C2×C8C2×D4×C3711yescharacteristic
510C2×C8C2×D4×C3711yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—82no—
525C4⋊C4C2×D4×C3711yescharacteristic
526C4⋊C4C2×D4×C3711yescharacteristic
527C4⋊C4C2×D4×C3711yescharacteristic
528C4⋊C4C2×D4×C3711yescharacteristic
529C4⋊C4C2×D4×C3711yescharacteristic
530C4⋊C4C2×D4×C3711yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—41no—
542C42—41no—
543C42—41no—
544C42—41no—
545C23—21no—
546C23H(5,𝔽2)×C3711yescharacteristic
547Q8—21no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—161no—
553Q8C22⋊Q8×C3712yes—
554D4—22no—
555D4—22no—
556D4—21no—
557D4C22⋊Q8×C3712yes—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—161no—
580C2×C4—161no—
581C2×C4C22×D4×C3711yescharacteristic
582C2×C4C22×D4×C3711yescharacteristic
583C2×C4C22×Q8×C3711yescharacteristic
584C2×C4C2×#41×C3711yescharacteristic
585C2×C4C2×#41×C3711yescharacteristic
586C2×C42−1+4×C3711yescharacteristic
587C8—22no—
588C8—21no—
589C8—22no—
590C8—21no—
591C8—21no—
592C8—21no—
593C8—41no—
594C8—41no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22C37×#53911yescharacteristic
601C22D42×C3711yescharacteristic
602C22C37×#55411yescharacteristic
603C4—22no—
604C4—42no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×C22⋊Q8×C3711yescharacteristic
616C4C37×#52511yescharacteristic
617C4C37×#54711yescharacteristic
618C4D4×Q8×C3711yescharacteristic
619C2—21no—
620C2—21no—
621C2—42no—
622C2C37×#244911yescharacteristic
623C2C37×#328911yescharacteristic
624C2C37×#329111yescharacteristic
subgroupG/H
center, socleC22×C37D42
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#41×C37C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3082C2semidirect
5. C37×#2096C2semidirect
6. C37×#2090C2semidirect
7. C37×#2064C2semidirect
8. C37×#2060C2semidirect
9. C37×#1951C2semidirect
10. C37×#1922C2semidirect
15. C37×#1857C2semidirect
70. #137×C37Q8semidirect
282. #26401C37direct (N × H)
308. #3082C2×C37semidirect
311. #2096C2×C37semidirect
312. #2090C2×C37semidirect
313. #2064C2×C37semidirect
314. #2060C2×C37semidirect
315. #1951C2×C37semidirect
316. #1922C2×C37semidirect
321. #1857C2×C37semidirect
379. C37#26401direct (N × H)
383. #137Q8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#30842
C37×#30822
C37×#29472
C37×#29122
C37×#20962
C37×#20902
C37×#20642
C37×#20602
C37×#19512
C37×#19222
C37×#19082
C37×#18822
C37×#18662
C37×#18592
C37×#18572
#2640137