Finite Group Databasebeta

← C37×#32752 #22654005

Subgroups — C37×#32752 #22654005

Order 9472.

614 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2628C211yesmaximal, characteristic
2C37×#2625C211yesmaximal, characteristic
3C37×#2088C211yesmaximal, characteristic, complemented
4C37×#2088C211yesmaximal, characteristic, complemented
5C37×#2085C211yesmaximal, characteristic, complemented
6C37×#2077C211yesmaximal, characteristic
7C37×#2076C211yesmaximal, characteristic
8C37×#2074C211yesmaximal, characteristic, complemented
9C37×#2068C211yesmaximal, characteristic, complemented
10C37×#2066C211yesmaximal, characteristic, complemented
11C37×#2058C211yesmaximal, characteristic, complemented
12C37×#2035C211yesmaximal, characteristic
13C37×#2035C211yesmaximal, characteristic
14C37×#2024C211yesmaximal, characteristic, complemented
15C37×#1798C211yesmaximal, characteristic
16C2×C4⋊Q8×C37C2211yescharacteristic
17C2×C22⋊Q8×C37C2211yescharacteristic
18C2×#117×C37C2211yescharacteristic
19C2×#107×C37C2211yescharacteristic
20C2×#106×C37C2211yescharacteristic
21C2×#106×C37C2211yescharacteristic
22C2×#106×C37C2211yescharacteristic
23C2×C4⋊C8×C37C2211yescharacteristic
24C2×C4⋊C8×C37C2211yescharacteristic
25C2×#103×C37C2211yescharacteristic
26C2×#103×C37C2211yescharacteristic
27C2×#103×C37C2211yescharacteristic
28C2×#103×C37C2211yescharacteristic
29C2×C22⋊C8×C37C2211yescharacteristic
30C2×C22⋊C8×C37C2211yescharacteristic
31C37×#400—21no—
32C37×#400—21no—
33C37×#399—21no—
34C37×#398—21no—
35C37×#397—21no—
36C37×#397—21no—
37C37×#395—21no—
38C37×#393—21no—
39C37×#391C2211yescharacteristic
40C37×#391C2211yescharacteristic
41C37×#389C2211yescharacteristic
42C37×#389C2211yescharacteristic
43C37×#389C2211yescharacteristic
44C37×#389C2211yescharacteristic
45C37×#382C2211yescharacteristic
46C37×#380C2211yescharacteristic
47C37×#380C2211yescharacteristic
48C37×#380C2211yescharacteristic
49C37×#340C2211yescharacteristic
50C37×#340C2211yescharacteristic
51C37×#340C2211yescharacteristic
52C37×#340C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C22×Q8×C37—21no—
60C22×Q8×C37C2311yescharacteristic
61C23×C4×C37C2311yescharacteristic
62C22×C8×C37C2311yescharacteristic
63C22×C8×C37C2311yescharacteristic
64C22×C8×C37C2311yescharacteristic
65C22×C8×C37C2311yescharacteristic
66C4⋊Q8×C37—41no—
67C4⋊Q8×C37—41no—
68C22⋊Q8×C37—41no—
69C22⋊Q8×C37—41no—
70#117×C37—41no—
71#117×C37—41no—
72C2×C4⋊C4×C37—21no—
73C2×C4⋊C4×C37—21no—
74C2×C4⋊C4×C37—21no—
75C2×C4⋊C4×C37—21no—
76C2×C4⋊C4×C37—21no—
77C2×C4⋊C4×C37—21no—
78C2×C4⋊C4×C37D411yescharacteristic
79C2×C4⋊C4×C37D411yescharacteristic
80C2×C4⋊C4×C37C2311yescharacteristic
81C2×C4⋊C4×C37C2311yescharacteristic
82C2×C4⋊C4×C37C2311yescharacteristic
83C2×C4⋊C4×C37C2311yescharacteristic
84C2×C4⋊C4×C37C2311yescharacteristic
85C2×C4⋊C4×C37C2311yescharacteristic
86C2×C4⋊C4×C37C2311yescharacteristic
87C2×C22⋊C4×C37—21no—
88C2×C22⋊C4×C37—21no—
89C2×C22⋊C4×C37—21no—
90C2×C22⋊C4×C37—21no—
91C2×C22⋊C4×C37D411yescharacteristic
92C2×C22⋊C4×C37D411yescharacteristic
93C2×C42×C37C2311yescharacteristic
94C2×C42×C37C2311yescharacteristic
95#107×C37—41no—
96#106×C37—41no—
97#106×C37—41no—
98#106×C37—41no—
99C4⋊C8×C37—41no—
100C4⋊C8×C37—41no—
101#103×C37—41no—
102#103×C37—41no—
103#103×C37—41no—
104#103×C37—41no—
105C22⋊C8×C37—41no—
106C22⋊C8×C37—41no—
107#95×C37—21no—
108#95×C37—21no—
109#95×C37—21no—
110#95×C37—21no—
111#95×C37—21no—
112#95×C37—21no—
113#95×C37—21no—
114#95×C37—21no—
115#95×C37—21no—
116#95×C37—21no—
117#95×C37—21no—
118#95×C37—21no—
119#95×C37—21no—
120C24×C37C2×D411yescharacteristic
121C2×Q8×C37—21no—
122C2×Q8×C37—21no—
123C2×Q8×C37—21no—
124C2×Q8×C37—21no—
125C2×Q8×C37—21no—
126C2×Q8×C37—21no—
127C2×Q8×C37—42no—
128C2×Q8×C37—81no—
129C2×Q8×C37—81no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—21no—
135C22×C4×C37—21no—
136C22×C4×C37—21no—
137C22×C4×C37—21no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—21no—
143C22×C4×C37—21no—
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146C22×C4×C37C2×D411yescharacteristic
147C22×C4×C37C2×D411yescharacteristic
148C22×C4×C37C2×D411yescharacteristic
149C22×C4×C37C2411yescharacteristic
150C2×C8×C37—21no—
151C2×C8×C37—21no—
152C2×C8×C37—21no—
153C2×C8×C37—21no—
154C2×C8×C37—21no—
155C2×C8×C37—21no—
156C2×C8×C37—21no—
157C2×C8×C37—21no—
158C2×C8×C37—21no—
159C2×C8×C37—21no—
160C2×C8×C37—21no—
161C2×C8×C37—21no—
162C4⋊C4×C37—21no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—21no—
165C4⋊C4×C37—21no—
166C4⋊C4×C37—21no—
167C4⋊C4×C37—21no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—21no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—21no—
173C4⋊C4×C37—21no—
174C4⋊C4×C37—21no—
175C4⋊C4×C37—21no—
176C4⋊C4×C37—41no—
177C4⋊C4×C37—41no—
178C4⋊C4×C37—42no—
179C4⋊C4×C37—42no—
180C4⋊C4×C37—81no—
181C4⋊C4×C37—81no—
182C4⋊C4×C37—81no—
183C4⋊C4×C37—81no—
184C22⋊C4×C37—41no—
185C22⋊C4×C37—41no—
186C22⋊C4×C37—42no—
187C22⋊C4×C37—81no—
188C22⋊C4×C37—81no—
189C22⋊C4×C37—81no—
190C42×C37—21no—
191C42×C37—21no—
192C42×C37—21no—
193C42×C37—21no—
194C23×C37—21no—
195C23×C37—21no—
196C23×C37—21no—
197C23×C37—21no—
198C23×C37—21no—
199C23×C37—21no—
200C23×C37—21no—
201C23×C37C22×D411yescharacteristic
202Q8×C37—41no—
203Q8×C37—41no—
204Q8×C37—41no—
205Q8×C37—41no—
206Q8×C37—84no—
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—21no—
215C2×C4×C37—21no—
216C2×C4×C37—21no—
217C2×C4×C37—21no—
218C2×C4×C37—21no—
219C2×C4×C37—21no—
220C2×C4×C37—21no—
221C2×C4×C37—21no—
222C2×C4×C37—41no—
223C2×C4×C37—41no—
224C2×C4×C37—41no—
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—41no—
235C2×C4×C37—41no—
236C2×C4×C37—41no—
237C2×C4×C37—41no—
238C2×C4×C37—41no—
239C2×C4×C37—41no—
240C2×C4×C37—41no—
241C2×C4×C37—41no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—41no—
245C2×C4×C37—41no—
246C2×C4×C37—41no—
247C2×C4×C37—41no—
248C2×C4×C37—41no—
249C2×C4×C37—41no—
250C2×C4×C37H(5,𝔽2)11yescharacteristic
251C2×C4×C37H(5,𝔽2)11yescharacteristic
252C2×C4×C37H(5,𝔽2)11yescharacteristic
253C2×C4×C372−1+411yescharacteristic
254C2×C4×C372−1+411yescharacteristic
255C2×C4×C372−1+411yescharacteristic
256C8×C37—41no—
257C8×C37—41no—
258C8×C37—41no—
259C8×C37—41no—
260#32752C3711yesmaximal, characteristic, direct product factor, Sylow
261C22×C37—41no—
262C22×C37—41no—
263C22×C37—41no—
264C22×C37—41no—
265C22×C37—41no—
266C22×C37—41no—
267C22×C37—41no—
268C22×C37#53411yescharacteristic
269C22×C37#53611yescharacteristic
270C22×C37#53711yescharacteristic
271C22×C37#57711yescharacteristic
272C22×C37#57711yescharacteristic
273C22×C37#57711yescharacteristic
274C22×C37#57811yescharacteristic
275C4×C37—41no—
276C4×C37—41no—
277C4×C37—41no—
278C4×C37—41no—
279C4×C37—41no—
280C4×C37—81no—
281C4×C37—81no—
282C4×C37—81no—
283C4×C37—81no—
284C4×C37—81no—
285C4×C37—81no—
286C4×C37—81no—
287C4×C37—81no—
288C4×C37#56211yescharacteristic
289C4×C37#56211yescharacteristic
290C4×C37#56311yescharacteristic
291C4×C37#56311yescharacteristic
292#2628C2×C3711yescharacteristic
293#2625C2×C3711yescharacteristic
294#2088C2×C3711yescharacteristic, complemented
295#2088C2×C3711yescharacteristic, complemented
296#2085C2×C3711yescharacteristic, complemented
297#2077C2×C3711yescharacteristic
298#2076C2×C3711yescharacteristic
299#2074C2×C3711yescharacteristic, complemented
300#2068C2×C3711yescharacteristic, complemented
301#2066C2×C3711yescharacteristic, complemented
302#2058C2×C3711yescharacteristic, complemented
303#2035C2×C3711yescharacteristic
304#2035C2×C3711yescharacteristic
305#2024C2×C3711yescharacteristic, complemented
306#1798C2×C3711yescharacteristic
307C2×C37—81no—
308C2×C37#281411yescharacteristic
309C2×C37#320011yescharacteristic
310C2×C37#320111yescharacteristic
311C2×C37#324211yescharacteristic
312C2×C37#324411yescharacteristic
313C2×C37#325811yescharacteristic
314C2×C37#326311yescharacteristic
315C2×C4⋊Q8C22×C3711yescharacteristic
316C2×C22⋊Q8C22×C3711yescharacteristic
317C2×#117C22×C3711yescharacteristic
318C2×#107C22×C3711yescharacteristic
319C2×#106C22×C3711yescharacteristic
320C2×#106C22×C3711yescharacteristic
321C2×#106C22×C3711yescharacteristic
322C2×C4⋊C8C22×C3711yescharacteristic
323C2×C4⋊C8C22×C3711yescharacteristic
324C2×#103C22×C3711yescharacteristic
325C2×#103C22×C3711yescharacteristic
326C2×#103C22×C3711yescharacteristic
327C2×#103C22×C3711yescharacteristic
328C2×C22⋊C8C22×C3711yescharacteristic
329C2×C22⋊C8C22×C3711yescharacteristic
330#400—21no—
331#400—21no—
332#399—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#395—21no—
337#393—21no—
338#391C22×C3711yescharacteristic
339#391C22×C3711yescharacteristic
340#389C22×C3711yescharacteristic
341#389C22×C3711yescharacteristic
342#389C22×C3711yescharacteristic
343#389C22×C3711yescharacteristic
344#382C22×C3711yescharacteristic
345#380C22×C3711yescharacteristic
346#380C22×C3711yescharacteristic
347#380C22×C3711yescharacteristic
348#340C22×C3711yescharacteristic
349#340C22×C3711yescharacteristic
350#340C22×C3711yescharacteristic
351#340C22×C3711yescharacteristic
352#340C22×C3711yescharacteristic
353#340C22×C3711yescharacteristic
354#340C22×C3711yescharacteristic
355#340C22×C3711yescharacteristic
356#336C22×C3711yescharacteristic
357#336C22×C3711yescharacteristic
358C37#3275211yescharacteristic, direct product factor, Sylow
359C22×Q8—21no—
360C22×Q8C23×C3711yescharacteristic
361C23×C4C23×C3711yescharacteristic
362C22×C8C23×C3711yescharacteristic
363C22×C8C23×C3711yescharacteristic
364C22×C8C23×C3711yescharacteristic
365C22×C8C23×C3711yescharacteristic
366C4⋊Q8—41no—
367C4⋊Q8—41no—
368C22⋊Q8—41no—
369C22⋊Q8—41no—
370#117—41no—
371#117—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C3711yescharacteristic
379C2×C4⋊C4D4×C3711yescharacteristic
380C2×C4⋊C4C23×C3711yescharacteristic
381C2×C4⋊C4C23×C3711yescharacteristic
382C2×C4⋊C4C23×C3711yescharacteristic
383C2×C4⋊C4C23×C3711yescharacteristic
384C2×C4⋊C4C23×C3711yescharacteristic
385C2×C4⋊C4C23×C3711yescharacteristic
386C2×C4⋊C4C23×C3711yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4D4×C3711yescharacteristic
392C2×C22⋊C4D4×C3711yescharacteristic
393C2×C42C23×C3711yescharacteristic
394C2×C42C23×C3711yescharacteristic
395#107—41no—
396#106—41no—
397#106—41no—
398#106—41no—
399C4⋊C8—41no—
400C4⋊C8—41no—
401#103—41no—
402#103—41no—
403#103—41no—
404#103—41no—
405C22⋊C8—41no—
406C22⋊C8—41no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420C24C2×D4×C3711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—42no—
428C2×Q8—81no—
429C2×Q8—81no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×D4×C3711yescharacteristic
445C22×C4C2×D4×C3711yescharacteristic
446C22×C4C2×D4×C3711yescharacteristic
447C22×C4C2×D4×C3711yescharacteristic
448C22×C4C2×D4×C3711yescharacteristic
449C22×C4C24×C3711yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23C22×D4×C3711yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—84no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4H(5,𝔽2)×C3711yescharacteristic
551C2×C4H(5,𝔽2)×C3711yescharacteristic
552C2×C4H(5,𝔽2)×C3711yescharacteristic
553C2×C42−1+4×C3711yescharacteristic
554C2×C42−1+4×C3711yescharacteristic
555C2×C42−1+4×C3711yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C37×#53411yescharacteristic
568C22C37×#53611yescharacteristic
569C22C37×#53711yescharacteristic
570C22C37×#57711yescharacteristic
571C22C37×#57711yescharacteristic
572C22C37×#57711yescharacteristic
573C22C37×#57811yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C37×#56211yescharacteristic
588C4C37×#56211yescharacteristic
589C4C37×#56311yescharacteristic
590C4C37×#56311yescharacteristic
591C2—81no—
592C2C37×#281411yescharacteristic
593C2C37×#320011yescharacteristic
594C2C37×#320111yescharacteristic
595C2C37×#324211yescharacteristic
596C2C37×#324411yescharacteristic
597C2C37×#325811yescharacteristic
598C2C37×#326311yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#2088C2semidirect
4. C37×#2088C2semidirect
5. C37×#2085C2semidirect
8. C37×#2074C2semidirect
9. C37×#2068C2semidirect
10. C37×#2066C2semidirect
11. C37×#2058C2semidirect
14. C37×#2024C2semidirect
260. #32752C37direct (N × H)
294. #2088C2×C37semidirect
295. #2088C2×C37semidirect
296. #2085C2×C37semidirect
299. #2074C2×C37semidirect
300. #2068C2×C37semidirect
301. #2066C2×C37semidirect
302. #2058C2×C37semidirect
305. #2024C2×C37semidirect
358. C37#32752direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#26282
C37×#26252
C37×#20882
C37×#20852
C37×#20772
C37×#20762
C37×#20742
C37×#20682
C37×#20662
C37×#20582
C37×#20352
C37×#20242
C37×#17982
#3275237