Finite Group Databasebeta

← C37×#32793 #22654046

Subgroups — C37×#32793 #22654046

Order 9472.

592 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2629C211yesmaximal, characteristic
2C37×#2628C211yesmaximal, characteristic
3C37×#2101C211yesmaximal, characteristic, complemented
4C37×#2101C211yesmaximal, characteristic, complemented
5C37×#2100C211yesmaximal, characteristic, complemented
6C37×#2099C211yesmaximal, characteristic, complemented
7C37×#2077C211yesmaximal, characteristic
8C37×#2077C211yesmaximal, characteristic
9C37×#2076C211yesmaximal, characteristic
10C37×#2075C211yesmaximal, characteristic
11C37×#2059C211yesmaximal, characteristic, complemented
12C37×#2059C211yesmaximal, characteristic, complemented
13C37×#2058C211yesmaximal, characteristic, complemented
14C37×#2057C211yesmaximal, characteristic, complemented
15C37×#1818C211yesmaximal, characteristic
16C2×C4⋊Q8×C37C2211yescharacteristic
17C2×#125×C37C2211yescharacteristic
18C2×#117×C37C2211yescharacteristic
19C2×#107×C37C2211yescharacteristic
20C2×#107×C37C2211yescharacteristic
21C2×#106×C37C2211yescharacteristic
22C2×#106×C37C2211yescharacteristic
23C2×C22⋊C8×C37C2211yescharacteristic
24C2×C22⋊C8×C37C2211yescharacteristic
25C37×#400—21no—
26C37×#399—21no—
27C37×#398—21no—
28C37×#398—21no—
29C37×#396—21no—
30C37×#396—21no—
31C37×#395—21no—
32C37×#393—21no—
33C37×#389C2211yescharacteristic
34C37×#389C2211yescharacteristic
35C37×#389C2211yescharacteristic
36C37×#389C2211yescharacteristic
37C37×#384C2211yescharacteristic
38C37×#382C2211yescharacteristic
39C37×#380C2211yescharacteristic
40C37×#380C2211yescharacteristic
41C37×#380C2211yescharacteristic
42C37×#380C2211yescharacteristic
43C37×#340C2211yescharacteristic
44C37×#340C2211yescharacteristic
45C37×#340C2211yescharacteristic
46C37×#340C2211yescharacteristic
47C37×#340C2211yescharacteristic
48C37×#340C2211yescharacteristic
49C37×#340C2211yescharacteristic
50C37×#340C2211yescharacteristic
51C37×#340C2211yescharacteristic
52C37×#340C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#336C2211yescharacteristic
56C37×#336C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C22×Q8×C37—21no—
60C23×C4×C37C2311yescharacteristic
61C22×C8×C37C2311yescharacteristic
62C22×C8×C37C2311yescharacteristic
63C22×C8×C37C2311yescharacteristic
64C22×C8×C37C2311yescharacteristic
65C4⋊Q8×C37—41no—
66C4⋊Q8×C37—41no—
67#125×C37—41no—
68#125×C37—41no—
69#117×C37—41no—
70#117×C37—41no—
71C2×C4⋊C4×C37—21no—
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×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37D411yescharacteristic
81C2×C4⋊C4×C37D411yescharacteristic
82C2×C4⋊C4×C37C2311yescharacteristic
83C2×C4⋊C4×C37C2311yescharacteristic
84C2×C4⋊C4×C37C2311yescharacteristic
85C2×C4⋊C4×C37C2311yescharacteristic
86C2×C4⋊C4×C37C2311yescharacteristic
87C2×C4⋊C4×C37C2311yescharacteristic
88C2×C4⋊C4×C37C2311yescharacteristic
89C2×C4⋊C4×C37C2311yescharacteristic
90C2×C22⋊C4×C37—21no—
91C2×C22⋊C4×C37—21no—
92C2×C22⋊C4×C37—21no—
93C2×C22⋊C4×C37—21no—
94C2×C22⋊C4×C37D411yescharacteristic
95C2×C22⋊C4×C37D411yescharacteristic
96C2×C42×C37C2311yescharacteristic
97C2×C42×C37C2311yescharacteristic
98#107×C37—41no—
99#107×C37—41no—
100#106×C37—41no—
101#106×C37—41no—
102C22⋊C8×C37—41no—
103C22⋊C8×C37—41no—
104#95×C37—21no—
105#95×C37—21no—
106#95×C37—21no—
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—
114C24×C37C2×D411yescharacteristic
115C2×Q8×C37—42no—
116C2×Q8×C37—81no—
117C2×Q8×C37—81no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—21no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37C2×D411yescharacteristic
133C22×C4×C37C2×D411yescharacteristic
134C22×C4×C37C2×D411yescharacteristic
135C22×C4×C37C2×D411yescharacteristic
136C22×C4×C37C2×D411yescharacteristic
137C22×C4×C37C2411yescharacteristic
138C2×C8×C37—21no—
139C2×C8×C37—21no—
140C2×C8×C37—21no—
141C2×C8×C37—21no—
142C2×C8×C37—21no—
143C2×C8×C37—21no—
144C2×C8×C37—21no—
145C2×C8×C37—21no—
146C2×C8×C37—21no—
147C2×C8×C37—21no—
148C2×C8×C37—21no—
149C2×C8×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—21no—
159C4⋊C4×C37—21no—
160C4⋊C4×C37—21no—
161C4⋊C4×C37—21no—
162C4⋊C4×C37—21no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—21no—
165C4⋊C4×C37—21no—
166C4⋊C4×C37—41no—
167C4⋊C4×C37—41no—
168C4⋊C4×C37—42no—
169C4⋊C4×C37—42no—
170C4⋊C4×C37—42no—
171C4⋊C4×C37—81no—
172C4⋊C4×C37—81no—
173C4⋊C4×C37—81no—
174C4⋊C4×C37—81no—
175C4⋊C4×C37—81no—
176C4⋊C4×C37—81no—
177C22⋊C4×C37—41no—
178C22⋊C4×C37—41no—
179C22⋊C4×C37—81no—
180C22⋊C4×C37—81no—
181C22⋊C4×C37—81no—
182C22⋊C4×C37—81no—
183C42×C37—21no—
184C42×C37—21no—
185C42×C37—21no—
186C42×C37—21no—
187C23×C37—21no—
188C23×C37—21no—
189C23×C37—21no—
190C23×C37—21no—
191C23×C37—21no—
192C23×C37—21no—
193C23×C37—21no—
194C23×C37C22×D411yescharacteristic
195Q8×C37—84no—
196C2×C4×C37—21no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—21no—
200C2×C4×C37—21no—
201C2×C4×C37—21no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—21no—
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—41no—
212C2×C4×C37—41no—
213C2×C4×C37—41no—
214C2×C4×C37—41no—
215C2×C4×C37—41no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—41no—
219C2×C4×C37—41no—
220C2×C4×C37—41no—
221C2×C4×C37—41no—
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×C37H(5,𝔽2)11yescharacteristic
240C2×C4×C37H(5,𝔽2)11yescharacteristic
241C2×C4×C372−1+411yescharacteristic
242C2×C4×C372−1+411yescharacteristic
243C2×C4×C372−1+411yescharacteristic
244C2×C4×C372−1+411yescharacteristic
245C8×C37—41no—
246C8×C37—41no—
247C8×C37—41no—
248C8×C37—41no—
249#32793C3711yesmaximal, characteristic, direct product factor, Sylow
250C22×C37—41no—
251C22×C37—41no—
252C22×C37—41no—
253C22×C37—41no—
254C22×C37—41no—
255C22×C37—41no—
256C22×C37—41no—
257C22×C37#53411yescharacteristic
258C22×C37#53611yescharacteristic
259C22×C37#53611yescharacteristic
260C22×C37#57611yescharacteristic
261C22×C37#57711yescharacteristic
262C22×C37#57711yescharacteristic
263C22×C37#57811yescharacteristic
264C4×C37—41no—
265C4×C37—41no—
266C4×C37—41no—
267C4×C37—41no—
268C4×C37—41no—
269C4×C37—81no—
270C4×C37—81no—
271C4×C37—81no—
272C4×C37—81no—
273C4×C37—81no—
274C4×C37—81no—
275C4×C37—81no—
276C4×C37—81no—
277C4×C37#56311yescharacteristic
278C4×C37#56311yescharacteristic
279C4×C37#56311yescharacteristic
280C4×C37#56311yescharacteristic
281#2629C2×C3711yescharacteristic
282#2628C2×C3711yescharacteristic
283#2101C2×C3711yescharacteristic, complemented
284#2101C2×C3711yescharacteristic, complemented
285#2100C2×C3711yescharacteristic, complemented
286#2099C2×C3711yescharacteristic, complemented
287#2077C2×C3711yescharacteristic
288#2077C2×C3711yescharacteristic
289#2076C2×C3711yescharacteristic
290#2075C2×C3711yescharacteristic
291#2059C2×C3711yescharacteristic, complemented
292#2059C2×C3711yescharacteristic, complemented
293#2058C2×C3711yescharacteristic, complemented
294#2057C2×C3711yescharacteristic, complemented
295#1818C2×C3711yescharacteristic
296C2×C37—81no—
297C2×C37#281711yescharacteristic
298C2×C37#319811yescharacteristic
299C2×C37#320111yescharacteristic
300C2×C37#324111yescharacteristic
301C2×C37#324211yescharacteristic
302C2×C37#324311yescharacteristic
303C2×C37#324411yescharacteristic
304C2×C4⋊Q8C22×C3711yescharacteristic
305C2×#125C22×C3711yescharacteristic
306C2×#117C22×C3711yescharacteristic
307C2×#107C22×C3711yescharacteristic
308C2×#107C22×C3711yescharacteristic
309C2×#106C22×C3711yescharacteristic
310C2×#106C22×C3711yescharacteristic
311C2×C22⋊C8C22×C3711yescharacteristic
312C2×C22⋊C8C22×C3711yescharacteristic
313#400—21no—
314#399—21no—
315#398—21no—
316#398—21no—
317#396—21no—
318#396—21no—
319#395—21no—
320#393—21no—
321#389C22×C3711yescharacteristic
322#389C22×C3711yescharacteristic
323#389C22×C3711yescharacteristic
324#389C22×C3711yescharacteristic
325#384C22×C3711yescharacteristic
326#382C22×C3711yescharacteristic
327#380C22×C3711yescharacteristic
328#380C22×C3711yescharacteristic
329#380C22×C3711yescharacteristic
330#380C22×C3711yescharacteristic
331#340C22×C3711yescharacteristic
332#340C22×C3711yescharacteristic
333#340C22×C3711yescharacteristic
334#340C22×C3711yescharacteristic
335#340C22×C3711yescharacteristic
336#340C22×C3711yescharacteristic
337#340C22×C3711yescharacteristic
338#340C22×C3711yescharacteristic
339#340C22×C3711yescharacteristic
340#340C22×C3711yescharacteristic
341#340C22×C3711yescharacteristic
342#340C22×C3711yescharacteristic
343#336C22×C3711yescharacteristic
344#336C22×C3711yescharacteristic
345#336C22×C3711yescharacteristic
346#336C22×C3711yescharacteristic
347C37#3279311yescharacteristic, direct product factor, Sylow
348C22×Q8—21no—
349C23×C4C23×C3711yescharacteristic
350C22×C8C23×C3711yescharacteristic
351C22×C8C23×C3711yescharacteristic
352C22×C8C23×C3711yescharacteristic
353C22×C8C23×C3711yescharacteristic
354C4⋊Q8—41no—
355C4⋊Q8—41no—
356#125—41no—
357#125—41no—
358#117—41no—
359#117—41no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C3711yescharacteristic
370C2×C4⋊C4D4×C3711yescharacteristic
371C2×C4⋊C4C23×C3711yescharacteristic
372C2×C4⋊C4C23×C3711yescharacteristic
373C2×C4⋊C4C23×C3711yescharacteristic
374C2×C4⋊C4C23×C3711yescharacteristic
375C2×C4⋊C4C23×C3711yescharacteristic
376C2×C4⋊C4C23×C3711yescharacteristic
377C2×C4⋊C4C23×C3711yescharacteristic
378C2×C4⋊C4C23×C3711yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4D4×C3711yescharacteristic
384C2×C22⋊C4D4×C3711yescharacteristic
385C2×C42C23×C3711yescharacteristic
386C2×C42C23×C3711yescharacteristic
387#107—41no—
388#107—41no—
389#106—41no—
390#106—41no—
391C22⋊C8—41no—
392C22⋊C8—41no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403C24C2×D4×C3711yescharacteristic
404C2×Q8—42no—
405C2×Q8—81no—
406C2×Q8—81no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4C2×D4×C3711yescharacteristic
422C22×C4C2×D4×C3711yescharacteristic
423C22×C4C2×D4×C3711yescharacteristic
424C22×C4C2×D4×C3711yescharacteristic
425C22×C4C2×D4×C3711yescharacteristic
426C22×C4C24×C3711yescharacteristic
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C22⋊C4—81no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23C22×D4×C3711yescharacteristic
484Q8—84no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
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—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
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—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4H(5,𝔽2)×C3711yescharacteristic
529C2×C4H(5,𝔽2)×C3711yescharacteristic
530C2×C42−1+4×C3711yescharacteristic
531C2×C42−1+4×C3711yescharacteristic
532C2×C42−1+4×C3711yescharacteristic
533C2×C42−1+4×C3711yescharacteristic
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22C37×#53411yescharacteristic
546C22C37×#53611yescharacteristic
547C22C37×#53611yescharacteristic
548C22C37×#57611yescharacteristic
549C22C37×#57711yescharacteristic
550C22C37×#57711yescharacteristic
551C22C37×#57811yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C37×#56311yescharacteristic
566C4C37×#56311yescharacteristic
567C4C37×#56311yescharacteristic
568C4C37×#56311yescharacteristic
569C2—81no—
570C2C37×#281711yescharacteristic
571C2C37×#319811yescharacteristic
572C2C37×#320111yescharacteristic
573C2C37×#324111yescharacteristic
574C2C37×#324211yescharacteristic
575C2C37×#324311yescharacteristic
576C2C37×#324411yescharacteristic
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×#2101C2semidirect
4. C37×#2101C2semidirect
5. C37×#2100C2semidirect
6. C37×#2099C2semidirect
11. C37×#2059C2semidirect
12. C37×#2059C2semidirect
13. C37×#2058C2semidirect
14. C37×#2057C2semidirect
249. #32793C37direct (N × H)
283. #2101C2×C37semidirect
284. #2101C2×C37semidirect
285. #2100C2×C37semidirect
286. #2099C2×C37semidirect
291. #2059C2×C37semidirect
292. #2059C2×C37semidirect
293. #2058C2×C37semidirect
294. #2057C2×C37semidirect
347. C37#32793direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#26292
C37×#26282
C37×#21012
C37×#21002
C37×#20992
C37×#20772
C37×#20762
C37×#20752
C37×#20592
C37×#20582
C37×#20572
C37×#18182
#3279337