Finite Group Databasebeta

← C37×#13899 #22635152

Subgroups — C37×#13899 #22635152

Order 9472.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C37C211yesmaximal, characteristic
2C2×C37×#386C212yesmaximal
3C2×C37×#385C212yesmaximal, complemented
4C2×C37×#380C211yesmaximal, characteristic, complemented
5C22×#95×C37C211yesmaximal, characteristic, complemented
6C37×#1441C212yesmaximal, complemented
7C37×#1439C212yesmaximal, complemented
8C37×C4⋊#95C211yesmaximal, characteristic, complemented
9C37×#1434C211yesmaximal, characteristic, complemented
10C37×C22⋊#95C211yesmaximal, characteristic, complemented
11C37×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C37C2211yescharacteristic
13C24×C4×C37C2212yes—
14C24×C4×C37C2211yescharacteristic
15C24×C4×C37C2211yescharacteristic
16C2×C4×D4×C37—28no—
17C2×C4×D4×C37C418yescomplemented
18C22×C4⋊C4×C37C2212yes—
19C22×C4⋊C4×C37C2212yes—
20C22×C4⋊C4×C37C2211yescharacteristic
21C22×C22⋊C4×C37C2212yes—
22C22×C22⋊C4×C37C2212yes—
23C22×C22⋊C4×C37C2212yes—
24C22×C22⋊C4×C37C2211yescharacteristic
25C22×C22⋊C4×C37C2211yescharacteristic
26C22×C42×C37C2211yescharacteristic
27C37×#386—28no—
28C37×#385—28no—
29C37×#380—24no—
30C2×#95×C37—24no—
31C2×#95×C37C2211yescharacteristic
32C2×#95×C37C2211yescharacteristic
33C2×#95×C37C2211yescharacteristic
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2212yes—
37C2×#95×C37C2212yes—
38C2×#95×C37C2212yes—
39C2×#95×C37C2212yes—
40C2×#95×C37C2211yescharacteristic
41C25×C37C2311yescharacteristic
42C25×C37C2311yescharacteristic
43C22×D4×C37—24no—
44C22×D4×C37—24no—
45C22×D4×C37C2×C414yes—
46C22×D4×C37D414yes—
47C22×D4×C37Q814yes—
48C23×C4×C37—24no—
49C23×C4×C37—24no—
50C23×C4×C37—24no—
51C23×C4×C37—22no—
52C23×C4×C37—22no—
53C23×C4×C37—24no—
54C23×C4×C37—22no—
55C23×C4×C37—24no—
56C23×C4×C37—22no—
57C23×C4×C37—24no—
58C23×C4×C37—24no—
59C23×C4×C37—42no—
60C23×C4×C37—42no—
61C23×C4×C37—42no—
62C23×C4×C37—42no—
63C23×C4×C37C2×C414yes—
64C23×C4×C37C2×C414yescomplemented
65C23×C4×C37C2312yes—
66C23×C4×C37C2312yes—
67C23×C4×C37C2311yescharacteristic
68C23×C4×C37C2312yes—
69C23×C4×C37C2312yes—
70C23×C4×C37C2311yescharacteristic
71C23×C4×C37C2311yescharacteristic
72C23×C4×C37C2311yescharacteristic
73C23×C4×C37C2311yescharacteristic
74C4×D4×C37—232no—
75C2×C4⋊C4×C37—24no—
76C2×C4⋊C4×C37—24no—
77C2×C4⋊C4×C37—24no—
78C2×C4⋊C4×C37—24no—
79C2×C4⋊C4×C37—24no—
80C2×C4⋊C4×C37—42no—
81C2×C4⋊C4×C37—42no—
82C2×C4⋊C4×C37C2×C414yescomplemented
83C2×C22⋊C4×C37—24no—
84C2×C22⋊C4×C37—24no—
85C2×C22⋊C4×C37—24no—
86C2×C22⋊C4×C37—24no—
87C2×C22⋊C4×C37—24no—
88C2×C22⋊C4×C37—24no—
89C2×C22⋊C4×C37—24no—
90C2×C22⋊C4×C37—24no—
91C2×C22⋊C4×C37—42no—
92C2×C22⋊C4×C37—42no—
93C2×C22⋊C4×C37C2×C414yes—
94C2×C22⋊C4×C37C2×C414yescomplemented
95C2×C22⋊C4×C37D418yes—
96C2×C42×C37—24no—
97C2×C42×C37C2×C414yescomplemented
98#95×C37—24no—
99#95×C37—22no—
100#95×C37—22no—
101#95×C37—24no—
102#95×C37—24no—
103#95×C37—24no—
104#95×C37—24no—
105#95×C37—22no—
106#95×C37—42no—
107#95×C37D414yescomplemented
108C24×C37—21no—
109C24×C37—21no—
110C24×C37—22no—
111C24×C37—22no—
112C24×C37—21no—
113C24×C37—21no—
114C24×C37—21no—
115C24×C37—22no—
116C24×C37—22no—
117C24×C37—21no—
118C24×C37—22no—
119C24×C37—21no—
120C24×C37—22no—
121C24×C37—21no—
122C24×C37C22×C412yes—
123C24×C37C22×C412yes—
124C24×C37C2×D412yes—
125C24×C37C2×D414yes—
126C24×C37C2×D412yes—
127C24×C37C2×Q812yes—
128C24×C37C2×Q812yes—
129C24×C37#4114yes—
130C24×C37C2411yescharacteristic
131C2×D4×C37—28no—
132C2×D4×C37—28no—
133C2×D4×C37—216no—
134C2×D4×C37—216no—
135C2×D4×C37C4⋊C4116yescomplemented
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37—21no—
139C22×C4×C37—22no—
140C22×C4×C37—21no—
141C22×C4×C37—22no—
142C22×C4×C37—21no—
143C22×C4×C37—22no—
144C22×C4×C37—22no—
145C22×C4×C37—21no—
146C22×C4×C37—216no—
147C22×C4×C37—28no—
148C22×C4×C37—21no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—21no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—22no—
159C22×C4×C37—22no—
160C22×C4×C37—22no—
161C22×C4×C37—22no—
162C22×C4×C37—22no—
163C22×C4×C37—22no—
164C22×C4×C37—28no—
165C22×C4×C37—28no—
166C22×C4×C37—28no—
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—22no—
171C22×C4×C37—22no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—22no—
175C22×C4×C37—22no—
176C22×C4×C37—22no—
177C22×C4×C37—22no—
178C22×C4×C37—22no—
179C22×C4×C37—22no—
180C22×C4×C37—22no—
181C22×C4×C37—44no—
182C22×C4×C37—44no—
183C22×C4×C37—48no—
184C22×C4×C37—48no—
185C22×C4×C37—48no—
186C22×C4×C37—48no—
187C22×C4×C37—48no—
188C22×C4×C37—48no—
189C22×C4×C37—48no—
190C22×C4×C37—48no—
191C22×C4×C37—48no—
192C22×C4×C37—48no—
193C22×C4×C37C22×C412yes—
194C22×C4×C37C22×C412yes—
195C22×C4×C37C22×C412yes—
196C22×C4×C37C22×C412yes—
197C22×C4×C37C22×C412yes—
198C22×C4×C37C2×D414yes—
199C22×C4×C37C2×D414yes—
200C22×C4×C37C2×D414yes—
201C22×C4×C37C2×D412yes—
202C22×C4×C37C2×D412yes—
203C22×C4×C37C2×Q812yes—
204C22×C4×C37#4114yes—
205C22×C4×C37#4112yes—
206C4⋊C4×C37—28no—
207C4⋊C4×C37—48no—
208C4⋊C4×C37—48no—
209C22⋊C4×C37—28no—
210C22⋊C4×C37—48no—
211C22⋊C4×C37—48no—
212C22⋊C4×C37—48no—
213C22⋊C4×C37C22⋊C4116yescomplemented
214C42×C37—28no—
215C23×C37—22no—
216C23×C37—22no—
217C23×C37—22no—
218C23×C37—22no—
219C23×C37—24no—
220C23×C37—24no—
221C23×C37—24no—
222C23×C37—24no—
223C23×C37—24no—
224C23×C37—22no—
225C23×C37—24no—
226C23×C37—24no—
227C23×C37—24no—
228C23×C37—24no—
229C23×C37—22no—
230C23×C37—22no—
231C23×C37—22no—
232C23×C37—24no—
233C23×C37—22no—
234C23×C37—22no—
235C23×C37—22no—
236C23×C37—22no—
237C23×C37—22no—
238C23×C37—22no—
239C23×C37—24no—
240C23×C37—24no—
241C23×C37—22no—
242C23×C37—24no—
243C23×C37—22no—
244C23×C37—22no—
245C23×C37—22no—
246C23×C37—24no—
247C23×C37—42no—
248C23×C37—42no—
249C23×C37—42no—
250C23×C37—42no—
251C23×C37—42no—
252C23×C37—42no—
253C23×C37—42no—
254C23×C37—42no—
255C23×C37C2×C22⋊C414yes—
256C23×C37C2×C4⋊C414yes—
257C23×C37C2×C4⋊C414yes—
258C23×C37#11714yes—
259C23×C37#12118yes—
260C23×C37C22⋊Q818yes—
261C23×C37C23×C411yescharacteristic
262C23×C37C22×D412yes—
263C23×C37C22×D411yescharacteristic
264C23×C37C22×D411yescharacteristic
265C23×C37C22×Q811yescharacteristic
266C23×C37C2×#4112yes—
267C23×C37C2×#4111yescharacteristic
268C23×C37C2×#4112yes—
269C23×C37H(5,𝔽2)12yes—
270C23×C37H(5,𝔽2)11yescharacteristic
271C23×C372−1+411yescharacteristic
272D4×C37—232no—
273C2×C4×C37—22no—
274C2×C4×C37—22no—
275C2×C4×C37—22no—
276C2×C4×C37—22no—
277C2×C4×C37—22no—
278C2×C4×C37—22no—
279C2×C4×C37—22no—
280C2×C4×C37—22no—
281C2×C4×C37—24no—
282C2×C4×C37—24no—
283C2×C4×C37—24no—
284C2×C4×C37—24no—
285C2×C4×C37—24no—
286C2×C4×C37—24no—
287C2×C4×C37—24no—
288C2×C4×C37—24no—
289C2×C4×C37—22no—
290C2×C4×C37—22no—
291C2×C4×C37—22no—
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—416no—
299C2×C4×C37—416no—
300C2×C4×C37—432no—
301C2×C4×C37—42no—
302C2×C4×C37—42no—
303C2×C4×C37—42no—
304C2×C4×C37—42no—
305C2×C4×C37—42no—
306C2×C4×C37—42no—
307C2×C4×C37—42no—
308C2×C4×C37—42no—
309C2×C4×C37—42no—
310C2×C4×C37—42no—
311C2×C4×C37—42no—
312C2×C4×C37—42no—
313C2×C4×C37—42no—
314C2×C4×C37—42no—
315C2×C4×C37—42no—
316C2×C4×C37—42no—
317C2×C4×C37—42no—
318C2×C4×C37—42no—
319C2×C4×C37—42no—
320C2×C4×C37—42no—
321C2×C4×C37—42no—
322C2×C4×C37—42no—
323C2×C4×C37—42no—
324C2×C4×C37—42no—
325C2×C4×C37C2×C22⋊C414yes—
326C2×C4×C37C2×C22⋊C414yes—
327C2×C4×C37C2×C4⋊C414yes—
328C2×C4×C37C4×D414yes—
329#13899C3711yesmaximal, characteristic, direct product factor, Sylow
330C22×C37—24no—
331C22×C37—24no—
332C22×C37—24no—
333C22×C37—24no—
334C22×C37—24no—
335C22×C37—28no—
336C22×C37—28no—
337C22×C37—28no—
338C22×C37—28no—
339C22×C37—24no—
340C22×C37—24no—
341C22×C37—24no—
342C22×C37—24no—
343C22×C37—42no—
344C22×C37—42no—
345C22×C37—42no—
346C22×C37—44no—
347C22×C37—44no—
348C22×C37—44no—
349C22×C37—44no—
350C22×C37—42no—
351C22×C37#38018yescomplemented
352C22×C37C22×C22⋊C411yescharacteristic
353C22×C37C22×C4⋊C411yescharacteristic
354C22×C37C2×#11711yescharacteristic
355C22×C37C2×C4×D411yescharacteristic
356C22×C37C4×#4111yescharacteristic
357C22×C37#51811yescharacteristic
358C22×C37#52011yescharacteristic
359C22×C37C2×#12112yes—
360C22×C37C2×C22⋊Q812yes—
361C22×C37#52512yes—
362C22×C37#52912yes—
363C22×C37#53812yes—
364C22×C37#53912yes—
365C22×C37D4212yes—
366C22×C37D4211yescharacteristic
367C22×C37#54612yes—
368C22×C37#54612yes—
369C22×C37#54612yes—
370C22×C37#54712yes—
371C22×C37#54711yescharacteristic
372C22×C37D4×Q811yescharacteristic
373C22×C37#55411yescharacteristic
374C22×C37#55412yes—
375C4×C37—24no—
376C4×C37—24no—
377C4×C37—24no—
378C4×C37—24no—
379C4×C37—42no—
380C4×C37—44no—
381C4×C37—44no—
382C4×C37—82no—
383C4×C37—82no—
384C22×C4×D4C2×C3711yescharacteristic
385C2×#386C2×C3712yes—
386C2×#385C2×C3712yescomplemented
387C2×#380C2×C3711yescharacteristic, complemented
388C22×#95C2×C3711yescharacteristic, complemented
389#1441C2×C3712yescomplemented
390#1439C2×C3712yescomplemented
391C4⋊#95C2×C3711yescharacteristic, complemented
392#1434C2×C3711yescharacteristic, complemented
393C22⋊#95C2×C3711yescharacteristic, complemented
394C22⋊#95C2×C3711yescharacteristic, complemented
395C2×C37—28no—
396C2×C37—44no—
397C2×C37C2×#38011yescharacteristic
398C2×C37#229011yescharacteristic
399C2×C37#231811yescharacteristic
400C2×C37D4×C22⋊C411yescharacteristic
401C2×C37#233911yescharacteristic
402C2×C37D4×C4⋊C411yescharacteristic
403C2×C37#234911yescharacteristic
404C2×C37#242412yes—
405C2×C37#242512yes—
406C2×C37#244912yes—
407C2×C37#245012yes—
408C23×D4C22×C3711yescharacteristic
409C24×C4C22×C3712yes—
410C24×C4C22×C3711yescharacteristic
411C24×C4C22×C3711yescharacteristic
412C2×C4×D4—28no—
413C2×C4×D4C4×C3718yescomplemented
414C22×C4⋊C4C22×C3712yes—
415C22×C4⋊C4C22×C3712yes—
416C22×C4⋊C4C22×C3711yescharacteristic
417C22×C22⋊C4C22×C3712yes—
418C22×C22⋊C4C22×C3712yes—
419C22×C22⋊C4C22×C3712yes—
420C22×C22⋊C4C22×C3711yescharacteristic
421C22×C22⋊C4C22×C3711yescharacteristic
422C22×C42C22×C3711yescharacteristic
423#386—28no—
424#385—28no—
425#380—24no—
426C2×#95—24no—
427C2×#95C22×C3711yescharacteristic
428C2×#95C22×C3711yescharacteristic
429C2×#95C22×C3711yescharacteristic
430C2×#95C22×C3712yes—
431C2×#95C22×C3712yes—
432C2×#95C22×C3712yes—
433C2×#95C22×C3712yes—
434C2×#95C22×C3712yes—
435C2×#95C22×C3712yes—
436C2×#95C22×C3711yescharacteristic
437C37#1389911yescharacteristic, direct product factor, Sylow
438C25C23×C3711yescharacteristic
439C25C23×C3711yescharacteristic
440C22×D4—24no—
441C22×D4—24no—
442C22×D4C2×C4×C3714yes—
443C22×D4D4×C3714yes—
444C22×D4Q8×C3714yes—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—24no—
453C23×C4—22no—
454C23×C4—24no—
455C23×C4—24no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4—42no—
460C23×C4C2×C4×C3714yes—
461C23×C4C2×C4×C3714yescomplemented
462C23×C4C23×C3712yes—
463C23×C4C23×C3712yes—
464C23×C4C23×C3711yescharacteristic
465C23×C4C23×C3712yes—
466C23×C4C23×C3712yes—
467C23×C4C23×C3711yescharacteristic
468C23×C4C23×C3711yescharacteristic
469C23×C4C23×C3711yescharacteristic
470C23×C4C23×C3711yescharacteristic
471C4×D4—232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4C2×C4×C3714yescomplemented
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4C2×C4×C3714yes—
491C2×C22⋊C4C2×C4×C3714yescomplemented
492C2×C22⋊C4D4×C3718yes—
493C2×C42—24no—
494C2×C42C2×C4×C3714yescomplemented
495#95—24no—
496#95—22no—
497#95—22no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95—24no—
502#95—22no—
503#95—42no—
504#95D4×C3714yescomplemented
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—22no—
518C24—21no—
519C24C22×C4×C3712yes—
520C24C22×C4×C3712yes—
521C24C2×D4×C3712yes—
522C24C2×D4×C3714yes—
523C24C2×D4×C3712yes—
524C24C2×Q8×C3712yes—
525C24C2×Q8×C3712yes—
526C24#41×C3714yes—
527C24C24×C3711yescharacteristic
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4C4⋊C4×C37116yescomplemented
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—216no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4C22×C4×C3712yes—
591C22×C4C22×C4×C3712yes—
592C22×C4C22×C4×C3712yes—
593C22×C4C22×C4×C3712yes—
594C22×C4C22×C4×C3712yes—
595C22×C4C2×D4×C3714yes—
596C22×C4C2×D4×C3714yes—
597C22×C4C2×D4×C3714yes—
598C22×C4C2×D4×C3712yes—
599C22×C4C2×D4×C3712yes—
600C22×C4C2×Q8×C3712yes—
601C22×C4#41×C3714yes—
602C22×C4#41×C3712yes—
603C4⋊C4—28no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C22⋊C4—28no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4C22⋊C4×C37116yescomplemented
611C42—28no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C2×C22⋊C4×C3714yes—
653C23C2×C4⋊C4×C3714yes—
654C23C2×C4⋊C4×C3714yes—
655C23#117×C3714yes—
656C23#121×C3718yes—
657C23C22⋊Q8×C3718yes—
658C23C23×C4×C3711yescharacteristic
659C23C22×D4×C3711yescharacteristic
660C23C22×D4×C3712yes—
661C23C22×D4×C3711yescharacteristic
662C23C22×Q8×C3711yescharacteristic
663C23C2×#41×C3712yes—
664C23C2×#41×C3712yes—
665C23C2×#41×C3711yescharacteristic
666C23H(5,𝔽2)×C3711yescharacteristic
667C23H(5,𝔽2)×C3712yes—
668C232−1+4×C3711yescharacteristic
669D4—232no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—416no—
696C2×C4—416no—
697C2×C4—432no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C2×C22⋊C4×C3714yes—
723C2×C4C2×C22⋊C4×C3714yes—
724C2×C4C2×C4⋊C4×C3714yes—
725C2×C4C4×D4×C3714yes—
726C22—28no—
727C22—28no—
728C22—28no—
729C22—28no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22C37×#38018yescomplemented
748C22C22×C22⋊C4×C3711yescharacteristic
749C22C22×C4⋊C4×C3711yescharacteristic
750C22C2×#117×C3711yescharacteristic
751C22C2×C4×D4×C3711yescharacteristic
752C22C4×#41×C3711yescharacteristic
753C22C37×#51811yescharacteristic
754C22C37×#52011yescharacteristic
755C22C2×#121×C3712yes—
756C22C2×C22⋊Q8×C3712yes—
757C22C37×#52512yes—
758C22C37×#52912yes—
759C22C37×#53812yes—
760C22C37×#53912yes—
761C22D42×C3711yescharacteristic
762C22D42×C3712yes—
763C22C37×#54612yes—
764C22C37×#54612yes—
765C22C37×#54612yes—
766C22C37×#54711yescharacteristic
767C22C37×#54712yes—
768C22D4×Q8×C3711yescharacteristic
769C22C37×#55412yes—
770C22C37×#55411yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—44no—
776C4—44no—
777C4—42no—
778C4—82no—
779C4—82no—
780C2—28no—
781C2—44no—
782C2C2×C37×#38011yescharacteristic
783C2C37×#229011yescharacteristic
784C2C37×#231811yescharacteristic
785C2D4×C22⋊C4×C3711yescharacteristic
786C2C37×#233911yescharacteristic
787C2D4×C4⋊C4×C3711yescharacteristic
788C2C37×#234911yescharacteristic
789C2C37×#242412yes—
790C2C37×#242512yes—
791C2C37×#244912yes—
792C2C37×#245012yes—
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
3. C2×C37×#385C2semidirect
4. C2×C37×#380C2semidirect
5. C22×#95×C37C2semidirect
6. C37×#1441C2semidirect
7. C37×#1439C2semidirect
8. C37×C4⋊#95C2semidirect
9. C37×#1434C2semidirect
10. C37×C22⋊#95C2semidirect
11. C37×C22⋊#95C2semidirect
17. C2×C4×D4×C37C4semidirect
64. C23×C4×C37C2×C4semidirect
82. C2×C4⋊C4×C37C2×C4semidirect
94. C2×C22⋊C4×C37C2×C4semidirect
97. C2×C42×C37C2×C4semidirect
107. #95×C37D4semidirect
135. C2×D4×C37C4⋊C4semidirect
213. C22⋊C4×C37C22⋊C4semidirect
329. #13899C37direct (N × H)
351. C22×C37#380semidirect
386. C2×#385C2×C37semidirect
387. C2×#380C2×C37semidirect
388. C22×#95C2×C37semidirect
389. #1441C2×C37semidirect
390. #1439C2×C37semidirect
391. C4⋊#95C2×C37semidirect
392. #1434C2×C37semidirect
393. C22⋊#95C2×C37semidirect
394. C22⋊#95C2×C37semidirect
413. C2×C4×D4C4×C37semidirect
437. C37#13899direct (N × H)
461. C23×C4C2×C4×C37semidirect
479. C2×C4⋊C4C2×C4×C37semidirect
491. C2×C22⋊C4C2×C4×C37semidirect
494. C2×C42C2×C4×C37semidirect
504. #95D4×C37semidirect
532. C2×D4C4⋊C4×C37semidirect
610. C22⋊C4C22⋊C4×C37semidirect
747. C22C37×#380semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C372
C2×C37×#3862
C2×C37×#3852
C2×C37×#3802
C22×#95×C372
C37×#14412
C37×#14392
C37×C4⋊#952
C37×#14342
C37×C22⋊#952
#1389937