Finite Group Databasebeta

← C37×#13996 #22635249

Subgroups — C37×#13996 #22635249

Order 9472.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C37C211yesmaximal, characteristic
2C2×C37×#386C211yesmaximal, characteristic
3C2×C37×#386C211yesmaximal, characteristic
4C2×C37×#385C211yesmaximal, characteristic, complemented
5C2×C37×#381C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
7C22×#95×C37C211yesmaximal, characteristic, complemented
8C37×#1445C212yesmaximal, complemented
9C37×#1439C212yesmaximal, complemented
10C37×#1437C212yesmaximal, complemented
11C37×C4⋊#95C212yesmaximal, complemented
12C23×D4×C37C2211yescharacteristic
13C24×C4×C37C2211yescharacteristic
14C24×C4×C37C2211yescharacteristic
15C24×C4×C37C2211yescharacteristic
16C2×#123×C37—24no—
17C2×#123×C37—24no—
18C2×#123×C37C418yescomplemented
19C22×C4⋊C4×C37C2212yes—
20C22×C4⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2211yescharacteristic
22C22×C22⋊C4×C37C2211yescharacteristic
23C22×C22⋊C4×C37C2212yes—
24C22×C22⋊C4×C37C2212yes—
25C22×C22⋊C4×C37C2211yescharacteristic
26C22×C22⋊C4×C37C2211yescharacteristic
27C22×C22⋊C4×C37C2211yescharacteristic
28C22×C42×C37C2212yes—
29C37×#386—24no—
30C37×#386—24no—
31C37×#385—24no—
32C37×#381—24no—
33C4×C22⋊C4×C37—24no—
34C2×#95×C37—24no—
35C2×#95×C37C2211yescharacteristic
36C2×#95×C37C2212yes—
37C2×#95×C37C2212yes—
38C2×#95×C37C2212yes—
39C2×#95×C37C2212yes—
40C2×#95×C37C2212yes—
41C2×#95×C37C2212yes—
42C2×#95×C37C2212yes—
43C2×#95×C37C2211yescharacteristic
44C25×C37C2311yescharacteristic
45C25×C37C2311yescharacteristic
46C22×D4×C37—22no—
47C22×D4×C37—22no—
48C22×D4×C37—22no—
49C22×D4×C37—22no—
50C22×D4×C37—22no—
51C22×D4×C37—22no—
52C22×D4×C37C2×C414yes—
53C23×C4×C37—22no—
54C23×C4×C37—22no—
55C23×C4×C37—22no—
56C23×C4×C37—22no—
57C23×C4×C37—22no—
58C23×C4×C37—22no—
59C23×C4×C37—22no—
60C23×C4×C37—22no—
61C23×C4×C37—22no—
62C23×C4×C37—24no—
63C23×C4×C37—24no—
64C23×C4×C37—22no—
65C23×C4×C37—22no—
66C23×C4×C37—42no—
67C23×C4×C37—42no—
68C23×C4×C37C2×C414yes—
69C23×C4×C37D414yes—
70C23×C4×C37C2311yescharacteristic
71C23×C4×C37C2311yescharacteristic
72C23×C4×C37C2312yes—
73C23×C4×C37C2311yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C23×C4×C37C2312yes—
76C23×C4×C37C2312yes—
77C23×C4×C37C2312yes—
78C23×C4×C37C2311yescharacteristic
79#123×C37—232no—
80C2×C4⋊C4×C37—24no—
81C2×C4⋊C4×C37—24no—
82C2×C4⋊C4×C37—24no—
83C2×C4⋊C4×C37—24no—
84C2×C4⋊C4×C37—42no—
85C2×C4⋊C4×C37C2×C418yescomplemented
86C2×C22⋊C4×C37—22no—
87C2×C22⋊C4×C37—22no—
88C2×C22⋊C4×C37—24no—
89C2×C22⋊C4×C37—24no—
90C2×C22⋊C4×C37—22no—
91C2×C22⋊C4×C37—22no—
92C2×C22⋊C4×C37—22no—
93C2×C22⋊C4×C37—24no—
94C2×C22⋊C4×C37—22no—
95C2×C22⋊C4×C37—22no—
96C2×C22⋊C4×C37—24no—
97C2×C22⋊C4×C37—24no—
98C2×C22⋊C4×C37—42no—
99C2×C22⋊C4×C37—42no—
100C2×C22⋊C4×C37C2×C414yes—
101C2×C22⋊C4×C37C2×C418yescomplemented
102C2×C22⋊C4×C37D414yes—
103C2×C22⋊C4×C37D414yes—
104C2×C22⋊C4×C37D414yes—
105C2×C42×C37—24no—
106C2×C42×C37—24no—
107C2×C42×C37—42no—
108#95×C37—24no—
109#95×C37—24no—
110#95×C37—24no—
111#95×C37—24no—
112#95×C37—24no—
113#95×C37—24no—
114#95×C37—24no—
115#95×C37—22no—
116#95×C37—22no—
117C24×C37—22no—
118C24×C37—22no—
119C24×C37—22no—
120C24×C37—22no—
121C24×C37—21no—
122C24×C37—21no—
123C24×C37—21no—
124C24×C37—21no—
125C24×C37—22no—
126C24×C37—22no—
127C24×C37—21no—
128C24×C37—21no—
129C24×C37—22no—
130C24×C37—22no—
131C24×C37C22×C412yes—
132C24×C37C22×C412yes—
133C24×C37C2×D412yes—
134C24×C37C2×D412yes—
135C24×C37C2×D412yes—
136C24×C37C2×D412yes—
137C24×C37#4112yes—
138C24×C37#4112yes—
139C24×C37C2411yescharacteristic
140C2×D4×C37—28no—
141C2×D4×C37—28no—
142C2×D4×C37—28no—
143C2×D4×C37—44no—
144C2×D4×C37—44no—
145C2×D4×C37—44no—
146C2×D4×C37—44no—
147C22×C4×C37—21no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—21no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37—22no—
154C22×C4×C37—28no—
155C22×C4×C37—28no—
156C22×C4×C37—28no—
157C22×C4×C37—28no—
158C22×C4×C37—28no—
159C22×C4×C37—22no—
160C22×C4×C37—22no—
161C22×C4×C37—21no—
162C22×C4×C37—22no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—22no—
175C22×C4×C37—22no—
176C22×C4×C37—22no—
177C22×C4×C37—21no—
178C22×C4×C37—22no—
179C22×C4×C37—22no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—22no—
183C22×C4×C37—22no—
184C22×C4×C37—22no—
185C22×C4×C37—22no—
186C22×C4×C37—22no—
187C22×C4×C37—28no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—22no—
195C22×C4×C37—22no—
196C22×C4×C37—22no—
197C22×C4×C37—22no—
198C22×C4×C37—44no—
199C22×C4×C37—48no—
200C22×C4×C37—48no—
201C22×C4×C37—48no—
202C22×C4×C37—48no—
203C22×C4×C37—44no—
204C22×C4×C37—44no—
205C22×C4×C37—44no—
206C22×C4×C37—44no—
207C22×C4×C37—44no—
208C22×C4×C37—44no—
209C22×C4×C37C22×C414yes—
210C22×C4×C37C22×C412yes—
211C22×C4×C37C22×C414yes—
212C22×C4×C37C2×D414yes—
213C22×C4×C37C2×D412yes—
214C22×C4×C37C2×D414yes—
215C22×C4×C37C2×D414yes—
216C22×C4×C37C2×D412yes—
217C22×C4×C37#4114yes—
218C22×C4×C37#4114yes—
219C4⋊C4×C37—216no—
220C4⋊C4×C37—48no—
221C22⋊C4×C37—28no—
222C22⋊C4×C37—216no—
223C22⋊C4×C37—48no—
224C22⋊C4×C37—44no—
225C22⋊C4×C37—44no—
226C22⋊C4×C37—44no—
227C22⋊C4×C37C22⋊C4116yescomplemented
228C42×C37—48no—
229C23×C37—24no—
230C23×C37—24no—
231C23×C37—22no—
232C23×C37—22no—
233C23×C37—24no—
234C23×C37—22no—
235C23×C37—22no—
236C23×C37—24no—
237C23×C37—24no—
238C23×C37—24no—
239C23×C37—24no—
240C23×C37—24no—
241C23×C37—24no—
242C23×C37—24no—
243C23×C37—24no—
244C23×C37—24no—
245C23×C37—22no—
246C23×C37—22no—
247C23×C37—22no—
248C23×C37—24no—
249C23×C37—24no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37—42no—
256C23×C37—41no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—42no—
260C23×C37—42no—
261C23×C37—42no—
262C23×C37—42no—
263C23×C37—42no—
264C23×C37—42no—
265C23×C37—42no—
266C23×C37—42no—
267C23×C37—42no—
268C23×C37C2×C22⋊C414yes—
269C23×C37C4×D414yes—
270C23×C37C4×D414yes—
271C23×C37#12114yes—
272C23×C37#12114yes—
273C23×C37#12414yes—
274C23×C37#12714yes—
275C23×C37C23×C411yescharacteristic
276C23×C37C22×D411yescharacteristic
277C23×C37C22×D411yescharacteristic
278C23×C37C22×D411yescharacteristic
279C23×C37C22×D411yescharacteristic
280C23×C37C2×#4111yescharacteristic
281C23×C37C2×#4111yescharacteristic
282C23×C37C2×#4112yes—
283C23×C37C2×#4112yes—
284C23×C37H(5,𝔽2)12yes—
285C23×C372−1+412yes—
286D4×C37—416no—
287C2×C4×C37—24no—
288C2×C4×C37—24no—
289C2×C4×C37—22no—
290C2×C4×C37—22no—
291C2×C4×C37—24no—
292C2×C4×C37—24no—
293C2×C4×C37—24no—
294C2×C4×C37—24no—
295C2×C4×C37—24no—
296C2×C4×C37—24no—
297C2×C4×C37—24no—
298C2×C4×C37—22no—
299C2×C4×C37—24no—
300C2×C4×C37—24no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—24no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—24no—
307C2×C4×C37—22no—
308C2×C4×C37—24no—
309C2×C4×C37—24no—
310C2×C4×C37—24no—
311C2×C4×C37—24no—
312C2×C4×C37—416no—
313C2×C4×C37—416no—
314C2×C4×C37—42no—
315C2×C4×C37—42no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—42no—
319C2×C4×C37—41no—
320C2×C4×C37—42no—
321C2×C4×C37—42no—
322C2×C4×C37—42no—
323C2×C4×C37—41no—
324C2×C4×C37—42no—
325C2×C4×C37—42no—
326C2×C4×C37—42no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329C2×C4×C37—42no—
330C2×C4×C37—42no—
331C2×C4×C37—42no—
332C2×C4×C37—416no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—42no—
340C2×C4×C37—42no—
341C2×C4×C37—42no—
342C2×C4×C37—42no—
343C2×C4×C37C2×C22⋊C418yes—
344C2×C4×C37#12314yescomplemented
345#13996C3711yesmaximal, characteristic, direct product factor, Sylow
346C22×C37—24no—
347C22×C37—28no—
348C22×C37—28no—
349C22×C37—24no—
350C22×C37—24no—
351C22×C37—28no—
352C22×C37—28no—
353C22×C37—24no—
354C22×C37—24no—
355C22×C37—24no—
356C22×C37—42no—
357C22×C37—44no—
358C22×C37—44no—
359C22×C37—42no—
360C22×C37—42no—
361C22×C37—81no—
362C22×C37—81no—
363C22×C37—82no—
364C22×C37—82no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37#39018yes—
368C22×C37C22×C22⋊C411yescharacteristic
369C22×C37C2×C4×D411yescharacteristic
370C22×C37C2×C4×D411yescharacteristic
371C22×C37C4×#4112yes—
372C22×C37#52012yes—
373C22×C37C2×#12111yescharacteristic
374C22×C37C2×#12111yescharacteristic
375C22×C37C2×#12311yescharacteristic
376C22×C37#52511yescharacteristic
377C22×C37C2×#12411yescharacteristic
378C22×C37#52912yes—
379C22×C37C2×#12711yescharacteristic
380C22×C37#53411yescharacteristic
381C22×C37#53611yescharacteristic
382C22×C37#53912yes—
383C22×C37#54612yes—
384C22×C37#54612yes—
385C22×C37#54612yes—
386C22×C37#54712yes—
387C22×C37#54712yes—
388C22×C37#54712yes—
389C22×C37#55112yes—
390C22×C37#55212yes—
391C4×C37—28no—
392C4×C37—24no—
393C4×C37—42no—
394C4×C37—44no—
395C4×C37—44no—
396C4×C37—44no—
397C4×C37—42no—
398C4×C37—81no—
399C4×C37—81no—
400C22×#123C2×C3711yescharacteristic
401C2×#386C2×C3711yescharacteristic
402C2×#386C2×C3711yescharacteristic
403C2×#385C2×C3711yescharacteristic, complemented
404C2×#381C2×C3711yescharacteristic, complemented
405C2×C4×C22⋊C4C2×C3711yescharacteristic, complemented
406C22×#95C2×C3711yescharacteristic, complemented
407#1445C2×C3712yescomplemented
408#1439C2×C3712yescomplemented
409#1437C2×C3712yescomplemented
410C4⋊#95C2×C3712yescomplemented
411C2×C37—28no—
412C2×C37—82no—
413C2×C37C2×#39011yescharacteristic
414C2×C37C4×#12311yescharacteristic
415C2×C37#232211yescharacteristic
416C2×C37#233912yes—
417C2×C37#235912yes—
418C2×C37#241211yescharacteristic
419C2×C37#241311yescharacteristic
420C2×C37#242512yes—
421C2×C37#248812yes—
422C2×C37#250111yescharacteristic
423C2×C37#253911yescharacteristic
424C23×D4C22×C3711yescharacteristic
425C24×C4C22×C3711yescharacteristic
426C24×C4C22×C3711yescharacteristic
427C24×C4C22×C3711yescharacteristic
428C2×#123—24no—
429C2×#123—24no—
430C2×#123C4×C3718yescomplemented
431C22×C4⋊C4C22×C3712yes—
432C22×C4⋊C4C22×C3712yes—
433C22×C22⋊C4C22×C3711yescharacteristic
434C22×C22⋊C4C22×C3711yescharacteristic
435C22×C22⋊C4C22×C3712yes—
436C22×C22⋊C4C22×C3712yes—
437C22×C22⋊C4C22×C3711yescharacteristic
438C22×C22⋊C4C22×C3711yescharacteristic
439C22×C22⋊C4C22×C3711yescharacteristic
440C22×C42C22×C3712yes—
441#386—24no—
442#386—24no—
443#385—24no—
444#381—24no—
445C4×C22⋊C4—24no—
446C2×#95—24no—
447C2×#95C22×C3711yescharacteristic
448C2×#95C22×C3712yes—
449C2×#95C22×C3712yes—
450C2×#95C22×C3712yes—
451C2×#95C22×C3712yes—
452C2×#95C22×C3712yes—
453C2×#95C22×C3712yes—
454C2×#95C22×C3712yes—
455C2×#95C22×C3711yescharacteristic
456C37#1399611yescharacteristic, direct product factor, Sylow
457C25C23×C3711yescharacteristic
458C25C23×C3711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C3714yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C3714yes—
482C23×C4D4×C3714yes—
483C23×C4C23×C3711yescharacteristic
484C23×C4C23×C3711yescharacteristic
485C23×C4C23×C3712yes—
486C23×C4C23×C3711yescharacteristic
487C23×C4C23×C3712yes—
488C23×C4C23×C3711yescharacteristic
489C23×C4C23×C3712yes—
490C23×C4C23×C3712yes—
491C23×C4C23×C3711yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C3718yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C3714yes—
514C2×C22⋊C4C2×C4×C3718yescomplemented
515C2×C22⋊C4D4×C3714yes—
516C2×C22⋊C4D4×C3714yes—
517C2×C22⋊C4D4×C3714yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C3712yes—
545C24C22×C4×C3712yes—
546C24C2×D4×C3712yes—
547C24C2×D4×C3712yes—
548C24C2×D4×C3712yes—
549C24C2×D4×C3712yes—
550C24#41×C3712yes—
551C24#41×C3712yes—
552C24C24×C3711yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C3714yes—
623C22×C4C22×C4×C3712yes—
624C22×C4C22×C4×C3714yes—
625C22×C4C2×D4×C3714yes—
626C22×C4C2×D4×C3712yes—
627C22×C4C2×D4×C3714yes—
628C22×C4C2×D4×C3714yes—
629C22×C4C2×D4×C3712yes—
630C22×C4#41×C3714yes—
631C22×C4#41×C3714yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C37116yescomplemented
641C42—48no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C3714yes—
682C23C4×D4×C3714yes—
683C23C4×D4×C3714yes—
684C23#121×C3714yes—
685C23#121×C3714yes—
686C23#124×C3714yes—
687C23#127×C3714yes—
688C23C23×C4×C3711yescharacteristic
689C23C22×D4×C3711yescharacteristic
690C23C22×D4×C3711yescharacteristic
691C23C22×D4×C3711yescharacteristic
692C23C22×D4×C3711yescharacteristic
693C23C2×#41×C3711yescharacteristic
694C23C2×#41×C3711yescharacteristic
695C23C2×#41×C3712yes—
696C23C2×#41×C3712yes—
697C23H(5,𝔽2)×C3712yes—
698C232−1+4×C3712yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C3718yes—
757C2×C4#123×C3714yescomplemented
758C22—28no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22C37×#39018yes—
780C22C22×C22⋊C4×C3711yescharacteristic
781C22C2×C4×D4×C3711yescharacteristic
782C22C2×C4×D4×C3711yescharacteristic
783C22C4×#41×C3712yes—
784C22C37×#52012yes—
785C22C2×#121×C3711yescharacteristic
786C22C2×#121×C3711yescharacteristic
787C22C2×#123×C3711yescharacteristic
788C22C37×#52511yescharacteristic
789C22C2×#124×C3711yescharacteristic
790C22C37×#52912yes—
791C22C2×#127×C3711yescharacteristic
792C22C37×#53411yescharacteristic
793C22C37×#53611yescharacteristic
794C22C37×#53912yes—
795C22C37×#54612yes—
796C22C37×#54612yes—
797C22C37×#54612yes—
798C22C37×#54712yes—
799C22C37×#54712yes—
800C22C37×#54712yes—
801C22C37×#55112yes—
802C22C37×#55212yes—
803C4—24no—
804C4—28no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C37×#39011yescharacteristic
815C2C4×#123×C3711yescharacteristic
816C2C37×#232211yescharacteristic
817C2C37×#233912yes—
818C2C37×#235912yes—
819C2C37×#241211yescharacteristic
820C2C37×#241311yescharacteristic
821C2C37×#242512yes—
822C2C37×#248812yes—
823C2C37×#250111yescharacteristic
824C2C37×#253911yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC23×D4×C37C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C37×#385C2semidirect
5. C2×C37×#381C2semidirect
6. C2×C4×C22⋊C4×C37C2semidirect
7. C22×#95×C37C2semidirect
8. C37×#1445C2semidirect
9. C37×#1439C2semidirect
10. C37×#1437C2semidirect
11. C37×C4⋊#95C2semidirect
18. C2×#123×C37C4semidirect
85. C2×C4⋊C4×C37C2×C4semidirect
101. C2×C22⋊C4×C37C2×C4semidirect
227. C22⋊C4×C37C22⋊C4semidirect
344. C2×C4×C37#123semidirect
345. #13996C37direct (N × H)
403. C2×#385C2×C37semidirect
404. C2×#381C2×C37semidirect
405. C2×C4×C22⋊C4C2×C37semidirect
406. C22×#95C2×C37semidirect
407. #1445C2×C37semidirect
408. #1439C2×C37semidirect
409. #1437C2×C37semidirect
410. C4⋊#95C2×C37semidirect
430. C2×#123C4×C37semidirect
456. C37#13996direct (N × H)
498. C2×C4⋊C4C2×C4×C37semidirect
514. C2×C22⋊C4C2×C4×C37semidirect
640. C22⋊C4C22⋊C4×C37semidirect
757. C2×C4#123×C37semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C372
C2×C37×#3862
C2×C37×#3852
C2×C37×#3812
C2×C4×C22⋊C4×C372
C22×#95×C372
C37×#14452
C37×#14392
C37×#14372
C37×C4⋊#952
#1399637