Finite Group Databasebeta

← C37×#13873 #22635126

Subgroups — C37×#13873 #22635126

Order 9472.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C37C211yesmaximal, characteristic
2C2×C37×#388C212yesmaximal, complemented
3C2×C37×#380C211yesmaximal, characteristic, complemented
4C2×C37×#379C211yesmaximal, characteristic
5C2×C37×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
7C37×#1440C212yesmaximal, complemented
8C37×#1439C212yesmaximal, complemented
9C37×#1437C212yesmaximal, complemented
10C37×C22⋊#95C211yesmaximal, characteristic, complemented
11C37×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C37C2211yescharacteristic
13C24×C4×C37C2211yescharacteristic
14C24×C4×C37C2211yescharacteristic
15C22×C4⋊C4×C37C2212yescomplemented
16C22×C22⋊C4×C37—28no—
17C22×C22⋊C4×C37C418yescomplemented
18C22×C22⋊C4×C37C2211yescharacteristic
19C22×C22⋊C4×C37C2211yescharacteristic
20C22×C22⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2212yes—
22C22×C22⋊C4×C37C2212yes—
23C22×C22⋊C4×C37C2212yes—
24C22×C22⋊C4×C37C2211yescharacteristic
25C22×C22⋊C4×C37C2211yescharacteristic
26C22×C22⋊C4×C37C2211yescharacteristic
27C22×C22⋊C4×C37C2211yescharacteristic
28C22×C22⋊C4×C37C2211yescharacteristic
29C22×C22⋊C4×C37C2211yescharacteristic
30C22×C42×C37C2212yescomplemented
31C37×#388—28no—
32C37×#380—24no—
33C37×#379—24no—
34C37×#379—24no—
35C4×C22⋊C4×C37—24no—
36C2×#95×C37C2212yescomplemented
37C2×#95×C37C2212yescomplemented
38C2×#95×C37C2212yescomplemented
39C2×#95×C37C2212yescomplemented
40C2×#95×C37C2212yescomplemented
41C2×#95×C37C2212yescomplemented
42C25×C37—24no—
43C25×C37—24no—
44C25×C37—22no—
45C25×C37—22no—
46C25×C37—22no—
47C25×C37—22no—
48C25×C37—22no—
49C25×C37—22no—
50C25×C37—42no—
51C25×C37—42no—
52C25×C37C2×C414yes—
53C25×C37C2311yescharacteristic
54C25×C37C2311yescharacteristic
55C25×C37C2311yescharacteristic
56C23×C4×C37—22no—
57C23×C4×C37—22no—
58C23×C4×C37—22no—
59C23×C4×C37—22no—
60C23×C4×C37—24no—
61C23×C4×C37—24no—
62C23×C4×C37—42no—
63C23×C4×C37—42no—
64C23×C4×C37C2×C414yes—
65C23×C4×C37C2×C414yes—
66C23×C4×C37C2312yes—
67C23×C4×C37C2312yes—
68C23×C4×C37C2311yescharacteristic
69C23×C4×C37C2311yescharacteristic
70C23×C4×C37C2312yes—
71C23×C4×C37C2312yes—
72C23×C4×C37C2311yescharacteristic
73C23×C4×C37C2311yescharacteristic
74C2×C4⋊C4×C37—24no—
75C2×C4⋊C4×C37—24no—
76C2×C4⋊C4×C37—42no—
77C2×C22⋊C4×C37—22no—
78C2×C22⋊C4×C37—24no—
79C2×C22⋊C4×C37—22no—
80C2×C22⋊C4×C37—22no—
81C2×C22⋊C4×C37—22no—
82C2×C22⋊C4×C37—24no—
83C2×C22⋊C4×C37—24no—
84C2×C22⋊C4×C37—232no—
85C2×C22⋊C4×C37—22no—
86C2×C22⋊C4×C37—22no—
87C2×C22⋊C4×C37—22no—
88C2×C22⋊C4×C37—24no—
89C2×C22⋊C4×C37—24no—
90C2×C22⋊C4×C37—24no—
91C2×C22⋊C4×C37—24no—
92C2×C22⋊C4×C37—22no—
93C2×C22⋊C4×C37—22no—
94C2×C22⋊C4×C37—22no—
95C2×C22⋊C4×C37—24no—
96C2×C22⋊C4×C37—24no—
97C2×C22⋊C4×C37—24no—
98C2×C22⋊C4×C37—24no—
99C2×C22⋊C4×C37—42no—
100C2×C22⋊C4×C37—42no—
101C2×C22⋊C4×C37—42no—
102C2×C22⋊C4×C37—42no—
103C2×C22⋊C4×C37C2×C414yes—
104C2×C22⋊C4×C37C2×C414yes—
105C2×C22⋊C4×C37C2×C414yes—
106C2×C22⋊C4×C37C2×C414yes—
107C2×C22⋊C4×C37D414yes—
108C2×C22⋊C4×C37D414yes—
109C2×C22⋊C4×C37D418yes—
110C2×C42×C37—24no—
111C2×C42×C37—24no—
112C2×C42×C37—42no—
113#95×C37—24no—
114#95×C37—24no—
115#95×C37—24no—
116#95×C37—24no—
117#95×C37—42no—
118#95×C37—42no—
119C24×C37—22no—
120C24×C37—22no—
121C24×C37—22no—
122C24×C37—22no—
123C24×C37—216no—
124C24×C37—216no—
125C24×C37—28no—
126C24×C37—28no—
127C24×C37—28no—
128C24×C37—22no—
129C24×C37—21no—
130C24×C37—21no—
131C24×C37—21no—
132C24×C37—21no—
133C24×C37—21no—
134C24×C37—21no—
135C24×C37—22no—
136C24×C37—21no—
137C24×C37—21no—
138C24×C37—21no—
139C24×C37—21no—
140C24×C37—21no—
141C24×C37—21no—
142C24×C37—22no—
143C24×C37—22no—
144C24×C37—22no—
145C24×C37—22no—
146C24×C37—28no—
147C24×C37—28no—
148C24×C37—44no—
149C24×C37—44no—
150C24×C37—48no—
151C24×C37—48no—
152C24×C37—48no—
153C24×C37—48no—
154C24×C37—48no—
155C24×C37—48no—
156C24×C37—48no—
157C24×C37—48no—
158C24×C37—48no—
159C24×C37—48no—
160C24×C37—44no—
161C24×C37—44no—
162C24×C37—44no—
163C24×C37—44no—
164C24×C37C22×C412yes—
165C24×C37C22×C412yes—
166C24×C37C22×C412yes—
167C24×C37C2×D414yes—
168C24×C37C2×D412yes—
169C24×C37C2×D412yes—
170C24×C37#4114yes—
171C24×C37#4112yes—
172C24×C37#4112yes—
173C24×C37#4112yes—
174C24×C37#4112yes—
175C24×C37C2411yescharacteristic
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—22no—
181C22×C4×C37—22no—
182C22×C4×C37—28no—
183C22×C4×C37—28no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—22no—
187C22×C4×C37—22no—
188C22×C4×C37—22no—
189C22×C4×C37—22no—
190C22×C4×C37—22no—
191C22×C4×C37—22no—
192C22×C4×C37—22no—
193C22×C4×C37—22no—
194C22×C4×C37—22no—
195C22×C4×C37—22no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—22no—
199C22×C4×C37—22no—
200C22×C4×C37—22no—
201C22×C4×C37—22no—
202C22×C4×C37—22no—
203C22×C4×C37—22no—
204C22×C4×C37—28no—
205C22×C4×C37—28no—
206C22×C4×C37—22no—
207C22×C4×C37—22no—
208C22×C4×C37—22no—
209C22×C4×C37—22no—
210C22×C4×C37—22no—
211C22×C4×C37—22no—
212C22×C4×C37—22no—
213C22×C4×C37—22no—
214C22×C4×C37—22no—
215C22×C4×C37—22no—
216C22×C4×C37—22no—
217C22×C4×C37—22no—
218C22×C4×C37—22no—
219C22×C4×C37—22no—
220C22×C4×C37—44no—
221C22×C4×C37—44no—
222C22×C4×C37—48no—
223C22×C4×C37—48no—
224C22×C4×C37—48no—
225C22×C4×C37—48no—
226C22×C4×C37C22×C412yes—
227C22×C4×C37C22×C412yes—
228C22×C4×C37C22×C412yes—
229C22×C4×C37C22×C412yes—
230C22×C4×C37C2×D414yes—
231C22×C4×C37C2×D414yes—
232C22×C4×C37C2×D414yes—
233C22×C4×C37C2×D414yes—
234C4⋊C4×C37—48no—
235C22⋊C4×C37—28no—
236C22⋊C4×C37—28no—
237C22⋊C4×C37—28no—
238C22⋊C4×C37—28no—
239C22⋊C4×C37—28no—
240C22⋊C4×C37—48no—
241C22⋊C4×C37—48no—
242C22⋊C4×C37—48no—
243C22⋊C4×C37—48no—
244C22⋊C4×C37—44no—
245C22⋊C4×C37—44no—
246C22⋊C4×C37C22⋊C4116yescomplemented
247C42×C37—48no—
248C23×C37—22no—
249C23×C37—22no—
250C23×C37—22no—
251C23×C37—22no—
252C23×C37—24no—
253C23×C37—24no—
254C23×C37—24no—
255C23×C37—24no—
256C23×C37—24no—
257C23×C37—24no—
258C23×C37—24no—
259C23×C37—24no—
260C23×C37—24no—
261C23×C37—24no—
262C23×C37—24no—
263C23×C37—24no—
264C23×C37—232no—
265C23×C37—22no—
266C23×C37—22no—
267C23×C37—22no—
268C23×C37—22no—
269C23×C37—22no—
270C23×C37—22no—
271C23×C37—22no—
272C23×C37—22no—
273C23×C37—22no—
274C23×C37—22no—
275C23×C37—22no—
276C23×C37—22no—
277C23×C37—24no—
278C23×C37—24no—
279C23×C37—24no—
280C23×C37—24no—
281C23×C37—24no—
282C23×C37—24no—
283C23×C37—24no—
284C23×C37—24no—
285C23×C37—24no—
286C23×C37—24no—
287C23×C37—24no—
288C23×C37—24no—
289C23×C37—416no—
290C23×C37—416no—
291C23×C37—416no—
292C23×C37—416no—
293C23×C37—416no—
294C23×C37—432no—
295C23×C37—432no—
296C23×C37—432no—
297C23×C37—432no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37—41no—
301C23×C37—41no—
302C23×C37—41no—
303C23×C37—41no—
304C23×C37—41no—
305C23×C37—41no—
306C23×C37—42no—
307C23×C37—42no—
308C23×C37—42no—
309C23×C37—42no—
310C23×C37—42no—
311C23×C37—42no—
312C23×C37—42no—
313C23×C37—42no—
314C23×C37—42no—
315C23×C37—42no—
316C23×C37—42no—
317C23×C37—42no—
318C23×C37—416no—
319C23×C37C2×C22⋊C414yes—
320C23×C37#11714yes—
321C23×C37#11714yes—
322C23×C37C4×D414yes—
323C23×C37C4×D414yes—
324C23×C37#12114yes—
325C23×C37#12314yes—
326C23×C37#12414yes—
327C23×C37#12614yes—
328C23×C37C23×C411yescharacteristic
329C23×C37C22×D412yes—
330C23×C37C22×D411yescharacteristic
331C23×C37C22×D411yescharacteristic
332C23×C37C2×#4111yescharacteristic
333C23×C37C2×#4111yescharacteristic
334C23×C37C2×#4112yes—
335C23×C37C2×#4111yescharacteristic
336C23×C37C2×#4111yescharacteristic
337C23×C37H(5,𝔽2)12yes—
338C23×C37H(5,𝔽2)12yes—
339C2×C4×C37—22no—
340C2×C4×C37—22no—
341C2×C4×C37—22no—
342C2×C4×C37—22no—
343C2×C4×C37—24no—
344C2×C4×C37—24no—
345C2×C4×C37—24no—
346C2×C4×C37—24no—
347C2×C4×C37—22no—
348C2×C4×C37—22no—
349C2×C4×C37—22no—
350C2×C4×C37—22no—
351C2×C4×C37—22no—
352C2×C4×C37—22no—
353C2×C4×C37—24no—
354C2×C4×C37—24no—
355C2×C4×C37—24no—
356C2×C4×C37—24no—
357C2×C4×C37—24no—
358C2×C4×C37—24no—
359C2×C4×C37—416no—
360C2×C4×C37—416no—
361C2×C4×C37—42no—
362C2×C4×C37—42no—
363C2×C4×C37—42no—
364C2×C4×C37—42no—
365C2×C4×C37—42no—
366C2×C4×C37—42no—
367C2×C4×C37—42no—
368C2×C4×C37—42no—
369C2×C4×C37—42no—
370C2×C4×C37—42no—
371C2×C4×C37—42no—
372C2×C4×C37—42no—
373C2×C4×C37—42no—
374C2×C4×C37—42no—
375C2×C4×C37—42no—
376C2×C4×C37—42no—
377C2×C4×C37—42no—
378C2×C4×C37—42no—
379C2×C4×C37—42no—
380C2×C4×C37—42no—
381C2×C4×C37—42no—
382C2×C4×C37—42no—
383C2×C4×C37—42no—
384C2×C4×C37—42no—
385C2×C4×C37—42no—
386C2×C4×C37—42no—
387C2×C4×C37C2×C22⋊C414yes—
388C2×C4×C37C2×C22⋊C414yes—
389#13873C3711yesmaximal, characteristic, direct product factor, Sylow
390C22×C37—24no—
391C22×C37—24no—
392C22×C37—24no—
393C22×C37—24no—
394C22×C37—24no—
395C22×C37—28no—
396C22×C37—28no—
397C22×C37—28no—
398C22×C37—28no—
399C22×C37—24no—
400C22×C37—24no—
401C22×C37—24no—
402C22×C37—24no—
403C22×C37—24no—
404C22×C37—24no—
405C22×C37—24no—
406C22×C37—464no—
407C22×C37—42no—
408C22×C37—42no—
409C22×C37—42no—
410C22×C37—42no—
411C22×C37—42no—
412C22×C37—42no—
413C22×C37—44no—
414C22×C37—44no—
415C22×C37—44no—
416C22×C37—44no—
417C22×C37—44no—
418C22×C37—44no—
419C22×C37—44no—
420C22×C37—44no—
421C22×C37—42no—
422C22×C37—42no—
423C22×C37#38818yescomplemented
424C22×C37C22×C22⋊C411yescharacteristic
425C22×C37C2×#11711yescharacteristic
426C22×C37C2×#11711yescharacteristic
427C22×C37C2×C4×D411yescharacteristic
428C22×C37C2×C4×D411yescharacteristic
429C22×C37#51811yescharacteristic
430C22×C37#51811yescharacteristic
431C22×C37C2×#12111yescharacteristic
432C22×C37C2×#12311yescharacteristic
433C22×C37#52512yes—
434C22×C37#52512yes—
435C22×C37C2×#12411yescharacteristic
436C22×C37C2×#12611yescharacteristic
437C22×C37#53812yes—
438C22×C37#53812yes—
439C22×C37D4212yes—
440C22×C37D4212yes—
441C22×C37#54612yes—
442C22×C37#54612yes—
443C22×C37#54612yes—
444C22×C37#54612yes—
445C22×C37#55112yes—
446C22×C37#55112yes—
447C4×C37—24no—
448C4×C37—24no—
449C4×C37—42no—
450C4×C37—42no—
451C4×C37—44no—
452C4×C37—44no—
453C4×C37—82no—
454C4×C37—82no—
455C23×C22⋊C4C2×C3711yescharacteristic
456C2×#388C2×C3712yescomplemented
457C2×#380C2×C3711yescharacteristic, complemented
458C2×#379C2×C3711yescharacteristic
459C2×#379C2×C3711yescharacteristic
460C2×C4×C22⋊C4C2×C3711yescharacteristic, complemented
461#1440C2×C3712yescomplemented
462#1439C2×C3712yescomplemented
463#1437C2×C3712yescomplemented
464C22⋊#95C2×C3711yescharacteristic, complemented
465C22⋊#95C2×C3711yescharacteristic, complemented
466C2×C37—28no—
467C2×C37—44no—
468C2×C37—44no—
469C2×C37#228011yescharacteristic
470C2×C37C2×#38811yescharacteristic
471C2×C37#231211yescharacteristic
472C2×C37D4×C22⋊C411yescharacteristic
473C2×C37D4×C22⋊C411yescharacteristic
474C2×C37#234211yescharacteristic
475C2×C37#234211yescharacteristic
476C2×C37#241812yes—
477C2×C37#242412yes—
478C2×C37#247212yes—
479C2×C37#248012yes—
480C26C22×C3711yescharacteristic
481C24×C4C22×C3711yescharacteristic
482C24×C4C22×C3711yescharacteristic
483C22×C4⋊C4C22×C3712yescomplemented
484C22×C22⋊C4—28no—
485C22×C22⋊C4C4×C3718yescomplemented
486C22×C22⋊C4C22×C3711yescharacteristic
487C22×C22⋊C4C22×C3711yescharacteristic
488C22×C22⋊C4C22×C3712yes—
489C22×C22⋊C4C22×C3712yes—
490C22×C22⋊C4C22×C3712yes—
491C22×C22⋊C4C22×C3712yes—
492C22×C22⋊C4C22×C3711yescharacteristic
493C22×C22⋊C4C22×C3711yescharacteristic
494C22×C22⋊C4C22×C3711yescharacteristic
495C22×C22⋊C4C22×C3711yescharacteristic
496C22×C22⋊C4C22×C3711yescharacteristic
497C22×C22⋊C4C22×C3711yescharacteristic
498C22×C42C22×C3712yescomplemented
499#388—28no—
500#380—24no—
501#379—24no—
502#379—24no—
503C4×C22⋊C4—24no—
504C2×#95C22×C3712yescomplemented
505C2×#95C22×C3712yescomplemented
506C2×#95C22×C3712yescomplemented
507C2×#95C22×C3712yescomplemented
508C2×#95C22×C3712yescomplemented
509C2×#95C22×C3712yescomplemented
510C37#1387311yescharacteristic, direct product factor, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C3714yes—
522C25C23×C3711yescharacteristic
523C25C23×C3711yescharacteristic
524C25C23×C3711yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C3714yes—
534C23×C4C2×C4×C3714yes—
535C23×C4C23×C3712yes—
536C23×C4C23×C3712yes—
537C23×C4C23×C3711yescharacteristic
538C23×C4C23×C3711yescharacteristic
539C23×C4C23×C3712yes—
540C23×C4C23×C3712yes—
541C23×C4C23×C3711yescharacteristic
542C23×C4C23×C3711yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C3714yes—
573C2×C22⋊C4C2×C4×C3714yes—
574C2×C22⋊C4C2×C4×C3714yes—
575C2×C22⋊C4C2×C4×C3714yes—
576C2×C22⋊C4D4×C3714yes—
577C2×C22⋊C4D4×C3714yes—
578C2×C22⋊C4D4×C3718yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C3712yes—
634C24C22×C4×C3712yes—
635C24C22×C4×C3712yes—
636C24C2×D4×C3714yes—
637C24C2×D4×C3712yes—
638C24C2×D4×C3712yes—
639C24#41×C3714yes—
640C24#41×C3712yes—
641C24#41×C3712yes—
642C24#41×C3712yes—
643C24#41×C3712yes—
644C24C24×C3711yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C3712yes—
696C22×C4C22×C4×C3712yes—
697C22×C4C22×C4×C3712yes—
698C22×C4C22×C4×C3712yes—
699C22×C4C2×D4×C3714yes—
700C22×C4C2×D4×C3714yes—
701C22×C4C2×D4×C3714yes—
702C22×C4C2×D4×C3714yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C37116yescomplemented
716C42—48no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—232no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—416no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C3714yes—
789C23#117×C3714yes—
790C23#117×C3714yes—
791C23C4×D4×C3714yes—
792C23C4×D4×C3714yes—
793C23#121×C3714yes—
794C23#123×C3714yes—
795C23#124×C3714yes—
796C23#126×C3714yes—
797C23C23×C4×C3711yescharacteristic
798C23C22×D4×C3711yescharacteristic
799C23C22×D4×C3711yescharacteristic
800C23C22×D4×C3712yes—
801C23C2×#41×C3711yescharacteristic
802C23C2×#41×C3711yescharacteristic
803C23C2×#41×C3711yescharacteristic
804C23C2×#41×C3712yes—
805C23C2×#41×C3711yescharacteristic
806C23H(5,𝔽2)×C3712yes—
807C23H(5,𝔽2)×C3712yes—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C3714yes—
857C2×C4C2×C22⋊C4×C3714yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22C37×#38818yescomplemented
892C22C22×C22⋊C4×C3711yescharacteristic
893C22C2×#117×C3711yescharacteristic
894C22C2×#117×C3711yescharacteristic
895C22C2×C4×D4×C3711yescharacteristic
896C22C2×C4×D4×C3711yescharacteristic
897C22C37×#51811yescharacteristic
898C22C37×#51811yescharacteristic
899C22C2×#121×C3711yescharacteristic
900C22C2×#123×C3711yescharacteristic
901C22C37×#52512yes—
902C22C37×#52512yes—
903C22C2×#124×C3711yescharacteristic
904C22C2×#126×C3711yescharacteristic
905C22C37×#53812yes—
906C22C37×#53812yes—
907C22D42×C3712yes—
908C22D42×C3712yes—
909C22C37×#54612yes—
910C22C37×#54612yes—
911C22C37×#54612yes—
912C22C37×#54612yes—
913C22C37×#55112yes—
914C22C37×#55112yes—
915C4—24no—
916C4—24no—
917C4—44no—
918C4—44no—
919C4—42no—
920C4—42no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C37×#228011yescharacteristic
927C2C2×C37×#38811yescharacteristic
928C2C37×#231211yescharacteristic
929C2D4×C22⋊C4×C3711yescharacteristic
930C2D4×C22⋊C4×C3711yescharacteristic
931C2C37×#234211yescharacteristic
932C2C37×#234211yescharacteristic
933C2C37×#241812yes—
934C2C37×#242412yes—
935C2C37×#247212yes—
936C2C37×#248012yes—
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC26×C37C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#388C2semidirect
3. C2×C37×#380C2semidirect
6. C2×C4×C22⋊C4×C37C2semidirect
7. C37×#1440C2semidirect
8. C37×#1439C2semidirect
9. C37×#1437C2semidirect
10. C37×C22⋊#95C2semidirect
11. C37×C22⋊#95C2semidirect
15. C22×C4⋊C4×C37C22semidirect
17. C22×C22⋊C4×C37C4semidirect
30. C22×C42×C37C22semidirect
36. C2×#95×C37C22semidirect
37. C2×#95×C37C22semidirect
38. C2×#95×C37C22semidirect
39. C2×#95×C37C22semidirect
40. C2×#95×C37C22semidirect
41. C2×#95×C37C22semidirect
246. C22⋊C4×C37C22⋊C4semidirect
389. #13873C37direct (N × H)
423. C22×C37#388semidirect
456. C2×#388C2×C37semidirect
457. C2×#380C2×C37semidirect
460. C2×C4×C22⋊C4C2×C37semidirect
461. #1440C2×C37semidirect
462. #1439C2×C37semidirect
463. #1437C2×C37semidirect
464. C22⋊#95C2×C37semidirect
465. C22⋊#95C2×C37semidirect
483. C22×C4⋊C4C22×C37semidirect
485. C22×C22⋊C4C4×C37semidirect
498. C22×C42C22×C37semidirect
504. C2×#95C22×C37semidirect
505. C2×#95C22×C37semidirect
506. C2×#95C22×C37semidirect
507. C2×#95C22×C37semidirect
508. C2×#95C22×C37semidirect
509. C2×#95C22×C37semidirect
510. C37#13873direct (N × H)
715. C22⋊C4C22⋊C4×C37semidirect
891. C22C37×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C372
C2×C37×#3882
C2×C37×#3802
C2×C37×#3792
C2×C4×C22⋊C4×C372
C37×#14402
C37×#14392
C37×#14372
C37×C22⋊#952
#1387337