Finite Group Databasebeta

← C37×#13995 #22635248

Subgroups — C37×#13995 #22635248

Order 9472.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C37C211yesmaximal, characteristic
2C23×C22⋊C4×C37C211yesmaximal, characteristic, complemented
3C2×C37×#390C212yesmaximal, complemented
4C2×C37×#386C211yesmaximal, characteristic, complemented
5C2×C37×#386C211yesmaximal, characteristic, complemented
6C2×C37×#385C211yesmaximal, characteristic, complemented
7C2×C37×#379C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
9C37×#1439C212yesmaximal, complemented
10C37×#1438C212yesmaximal, complemented
11C37×#1437C212yesmaximal, complemented
12C26×C37C2211yescharacteristic
13C23×D4×C37C2211yescharacteristic
14C23×D4×C37C2212yes—
15C24×C4×C37C2211yescharacteristic
16C24×C4×C37C2211yescharacteristic
17C2×#120×C37—24no—
18C2×#120×C37—24no—
19C2×#120×C37C418yescomplemented
20C22×C4⋊C4×C37C2212yescomplemented
21C22×C22⋊C4×C37—24no—
22C22×C22⋊C4×C37—28no—
23C22×C22⋊C4×C37C2212yes—
24C22×C22⋊C4×C37C2211yescharacteristic
25C22×C22⋊C4×C37C2212yes—
26C22×C22⋊C4×C37C2212yes—
27C22×C22⋊C4×C37C2212yes—
28C22×C22⋊C4×C37C2212yes—
29C22×C22⋊C4×C37C2211yescharacteristic
30C22×C22⋊C4×C37C2211yescharacteristic
31C22×C22⋊C4×C37C2211yescharacteristic, complemented
32C22×C22⋊C4×C37C2212yescomplemented
33C22×C22⋊C4×C37C2211yescharacteristic, complemented
34C22×C42×C37C2212yescomplemented
35C37×#390—28no—
36C37×#386—24no—
37C37×#386—24no—
38C37×#385—24no—
39C37×#379—24no—
40C4×C22⋊C4×C37—24no—
41C2×#95×C37C2211yescharacteristic, complemented
42C2×#95×C37C2212yescomplemented
43C2×#95×C37C2212yescomplemented
44C2×#95×C37C2212yescomplemented
45C2×#95×C37C2211yescharacteristic, complemented
46C25×C37—24no—
47C25×C37—22no—
48C25×C37—24no—
49C25×C37—22no—
50C25×C37—22no—
51C25×C37—22no—
52C25×C37—22no—
53C25×C37—22no—
54C25×C37—42no—
55C25×C37—42no—
56C25×C37C2×C414yes—
57C25×C37C2311yescharacteristic
58C25×C37C2312yes—
59C25×C37C2311yescharacteristic
60C22×D4×C37—22no—
61C22×D4×C37—22no—
62C22×D4×C37—22no—
63C22×D4×C37—22no—
64C22×D4×C37—24no—
65C22×D4×C37—24no—
66C22×D4×C37—22no—
67C22×D4×C37—22no—
68C22×D4×C37—24no—
69C22×D4×C37—24no—
70C22×D4×C37—42no—
71C22×D4×C37—42no—
72C22×D4×C37C2×C414yes—
73C22×D4×C37C2×C418yescomplemented
74C23×C4×C37—22no—
75C23×C4×C37—22no—
76C23×C4×C37—22no—
77C23×C4×C37—24no—
78C23×C4×C37—24no—
79C23×C4×C37—22no—
80C23×C4×C37—22no—
81C23×C4×C37—42no—
82C23×C4×C37—42no—
83C23×C4×C37D414yescomplemented
84C23×C4×C37C2311yescharacteristic
85C23×C4×C37C2311yescharacteristic
86C23×C4×C37C2311yescharacteristic
87C23×C4×C37C2311yescharacteristic
88C23×C4×C37C2312yes—
89C23×C4×C37C2312yes—
90C23×C4×C37C2312yes—
91C23×C4×C37C2311yescharacteristic
92#120×C37—232no—
93C2×C4⋊C4×C37—24no—
94C2×C4⋊C4×C37—24no—
95C2×C4⋊C4×C37—42no—
96C2×C22⋊C4×C37—232no—
97C2×C22⋊C4×C37—22no—
98C2×C22⋊C4×C37—24no—
99C2×C22⋊C4×C37—22no—
100C2×C22⋊C4×C37—24no—
101C2×C22⋊C4×C37—24no—
102C2×C22⋊C4×C37—24no—
103C2×C22⋊C4×C37—24no—
104C2×C22⋊C4×C37—24no—
105C2×C22⋊C4×C37—24no—
106C2×C22⋊C4×C37—22no—
107C2×C22⋊C4×C37—22no—
108C2×C22⋊C4×C37—22no—
109C2×C22⋊C4×C37—24no—
110C2×C22⋊C4×C37—24no—
111C2×C22⋊C4×C37—24no—
112C2×C22⋊C4×C37—24no—
113C2×C22⋊C4×C37—24no—
114C2×C22⋊C4×C37—22no—
115C2×C22⋊C4×C37—22no—
116C2×C22⋊C4×C37—24no—
117C2×C22⋊C4×C37—24no—
118C2×C22⋊C4×C37—42no—
119C2×C22⋊C4×C37—42no—
120C2×C22⋊C4×C37—42no—
121C2×C22⋊C4×C37—42no—
122C2×C22⋊C4×C37C2×C414yes—
123C2×C22⋊C4×C37C2×C418yescomplemented
124C2×C22⋊C4×C37D414yes—
125C2×C22⋊C4×C37D414yes—
126C2×C22⋊C4×C37D414yescomplemented
127C2×C22⋊C4×C37D418yescomplemented
128C2×C42×C37—24no—
129C2×C42×C37—24no—
130C2×C42×C37—42no—
131#95×C37—24no—
132#95×C37—24no—
133#95×C37—24no—
134#95×C37—22no—
135#95×C37—22no—
136C24×C37—22no—
137C24×C37—22no—
138C24×C37—22no—
139C24×C37—22no—
140C24×C37—28no—
141C24×C37—28no—
142C24×C37—216no—
143C24×C37—216no—
144C24×C37—28no—
145C24×C37—22no—
146C24×C37—22no—
147C24×C37—22no—
148C24×C37—22no—
149C24×C37—22no—
150C24×C37—22no—
151C24×C37—22no—
152C24×C37—22no—
153C24×C37—22no—
154C24×C37—22no—
155C24×C37—22no—
156C24×C37—22no—
157C24×C37—28no—
158C24×C37—28no—
159C24×C37—21no—
160C24×C37—22no—
161C24×C37—21no—
162C24×C37—21no—
163C24×C37—21no—
164C24×C37—21no—
165C24×C37—21no—
166C24×C37—22no—
167C24×C37—22no—
168C24×C37—22no—
169C24×C37—48no—
170C24×C37—48no—
171C24×C37—48no—
172C24×C37—48no—
173C24×C37—48no—
174C24×C37—48no—
175C24×C37—48no—
176C24×C37—48no—
177C24×C37—48no—
178C24×C37—44no—
179C24×C37—44no—
180C24×C37—48no—
181C24×C37—44no—
182C24×C37—44no—
183C24×C37—44no—
184C24×C37—44no—
185C24×C37C22×C412yes—
186C24×C37C22×C414yes—
187C24×C37C22×C412yes—
188C24×C37C2×D414yes—
189C24×C37C2×D412yes—
190C24×C37C2×D412yes—
191C24×C37C2×D412yes—
192C24×C37C2×D412yes—
193C24×C37#4114yes—
194C24×C37#4112yes—
195C24×C37#4112yes—
196C24×C37C2411yescharacteristic
197C2×D4×C37—28no—
198C2×D4×C37—28no—
199C2×D4×C37—28no—
200C2×D4×C37—216no—
201C2×D4×C37—216no—
202C2×D4×C37—48no—
203C2×D4×C37—48no—
204C2×D4×C37—48no—
205C2×D4×C37—48no—
206C2×D4×C37—48no—
207C2×D4×C37—44no—
208C2×D4×C37—44no—
209C2×D4×C37—44no—
210C2×D4×C37—44no—
211C22×C4×C37—21no—
212C22×C4×C37—22no—
213C22×C4×C37—21no—
214C22×C4×C37—22no—
215C22×C4×C37—22no—
216C22×C4×C37—22no—
217C22×C4×C37—22no—
218C22×C4×C37—28no—
219C22×C4×C37—28no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—22no—
224C22×C4×C37—22no—
225C22×C4×C37—22no—
226C22×C4×C37—22no—
227C22×C4×C37—22no—
228C22×C4×C37—22no—
229C22×C4×C37—22no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—22no—
233C22×C4×C37—22no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—21no—
237C22×C4×C37—22no—
238C22×C4×C37—22no—
239C22×C4×C37—22no—
240C22×C4×C37—22no—
241C22×C4×C37—22no—
242C22×C4×C37—28no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—22no—
249C22×C4×C37—21no—
250C22×C4×C37—22no—
251C22×C4×C37—22no—
252C22×C4×C37—22no—
253C22×C4×C37—44no—
254C22×C4×C37—48no—
255C22×C4×C37—48no—
256C22×C4×C37—48no—
257C22×C4×C37—48no—
258C22×C4×C37—44no—
259C22×C4×C37—44no—
260C22×C4×C37C22×C412yes—
261C22×C4×C37C22×C414yes—
262C22×C4×C37C2×D414yes—
263C22×C4×C37C2×D412yes—
264C22×C4×C37C2×D414yes—
265C22×C4×C37C2×D414yes—
266C22×C4×C37C2×D414yes—
267C22×C4×C37C2×D412yes—
268C22×C4×C37C2×D414yes—
269C4⋊C4×C37—48no—
270C22⋊C4×C37—216no—
271C22⋊C4×C37—28no—
272C22⋊C4×C37—216no—
273C22⋊C4×C37—216no—
274C22⋊C4×C37—48no—
275C22⋊C4×C37—48no—
276C22⋊C4×C37—48no—
277C22⋊C4×C37—44no—
278C22⋊C4×C37—44no—
279C22⋊C4×C37—44no—
280C22⋊C4×C37C22⋊C4116yescomplemented
281C42×C37—48no—
282C23×C37—24no—
283C23×C37—24no—
284C23×C37—22no—
285C23×C37—22no—
286C23×C37—24no—
287C23×C37—22no—
288C23×C37—22no—
289C23×C37—24no—
290C23×C37—24no—
291C23×C37—24no—
292C23×C37—24no—
293C23×C37—24no—
294C23×C37—24no—
295C23×C37—24no—
296C23×C37—24no—
297C23×C37—24no—
298C23×C37—232no—
299C23×C37—24no—
300C23×C37—24no—
301C23×C37—24no—
302C23×C37—24no—
303C23×C37—24no—
304C23×C37—24no—
305C23×C37—24no—
306C23×C37—24no—
307C23×C37—24no—
308C23×C37—24no—
309C23×C37—24no—
310C23×C37—24no—
311C23×C37—24no—
312C23×C37—24no—
313C23×C37—24no—
314C23×C37—24no—
315C23×C37—24no—
316C23×C37—24no—
317C23×C37—22no—
318C23×C37—22no—
319C23×C37—24no—
320C23×C37—22no—
321C23×C37—24no—
322C23×C37—432no—
323C23×C37—432no—
324C23×C37—416no—
325C23×C37—416no—
326C23×C37—416no—
327C23×C37—432no—
328C23×C37—416no—
329C23×C37—432no—
330C23×C37—416no—
331C23×C37—42no—
332C23×C37—42no—
333C23×C37—42no—
334C23×C37—42no—
335C23×C37—42no—
336C23×C37—42no—
337C23×C37—42no—
338C23×C37—42no—
339C23×C37—42no—
340C23×C37—42no—
341C23×C37—42no—
342C23×C37—42no—
343C23×C37—42no—
344C23×C37—42no—
345C23×C37—42no—
346C23×C37—42no—
347C23×C37—416no—
348C23×C37—41no—
349C23×C37—41no—
350C23×C37—41no—
351C23×C37—41no—
352C23×C37—42no—
353C23×C37—41no—
354C23×C37—41no—
355C23×C37—41no—
356C23×C37—41no—
357C23×C37—42no—
358C23×C37—42no—
359C23×C37—42no—
360C23×C37—42no—
361C23×C37—42no—
362C23×C37—42no—
363C23×C37—42no—
364C23×C37—42no—
365C23×C37—42no—
366C23×C37C2×C22⋊C414yes—
367C23×C37C4×D418yes—
368C23×C37C4×D414yes—
369C23×C37C4×D414yes—
370C23×C37#12114yes—
371C23×C37#12114yes—
372C23×C37#12414yes—
373C23×C37#12714yes—
374C23×C37C23×C411yescharacteristic
375C23×C37C22×D411yescharacteristic
376C23×C37C22×D411yescharacteristic
377C23×C37C22×D411yescharacteristic
378C23×C37C22×D412yes—
379C23×C37C22×D411yescharacteristic
380C23×C37C2×#4111yescharacteristic
381C23×C37C2×#4111yescharacteristic
382C23×C37C2×#4112yes—
383C23×C37H(5,𝔽2)12yes—
384C23×C37H(5,𝔽2)12yes—
385D4×C37—432no—
386D4×C37—416no—
387C2×C4×C37—24no—
388C2×C4×C37—24no—
389C2×C4×C37—22no—
390C2×C4×C37—22no—
391C2×C4×C37—24no—
392C2×C4×C37—24no—
393C2×C4×C37—24no—
394C2×C4×C37—24no—
395C2×C4×C37—24no—
396C2×C4×C37—24no—
397C2×C4×C37—22no—
398C2×C4×C37—22no—
399C2×C4×C37—22no—
400C2×C4×C37—22no—
401C2×C4×C37—24no—
402C2×C4×C37—24no—
403C2×C4×C37—22no—
404C2×C4×C37—22no—
405C2×C4×C37—24no—
406C2×C4×C37—24no—
407C2×C4×C37—24no—
408C2×C4×C37—24no—
409C2×C4×C37—416no—
410C2×C4×C37—416no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37—42no—
414C2×C4×C37—41no—
415C2×C4×C37—42no—
416C2×C4×C37—41no—
417C2×C4×C37—42no—
418C2×C4×C37—42no—
419C2×C4×C37—42no—
420C2×C4×C37—42no—
421C2×C4×C37—42no—
422C2×C4×C37—42no—
423C2×C4×C37—42no—
424C2×C4×C37—42no—
425C2×C4×C37—41no—
426C2×C4×C37—41no—
427C2×C4×C37—41no—
428C2×C4×C37—41no—
429C2×C4×C37—41no—
430C2×C4×C37—41no—
431C2×C4×C37—42no—
432C2×C4×C37—42no—
433C2×C4×C37—42no—
434C2×C4×C37—42no—
435C2×C4×C37C2×C22⋊C418yescomplemented
436C2×C4×C37#12014yescomplemented
437#13995C3711yesmaximal, characteristic, direct product factor, Sylow
438C22×C37—24no—
439C22×C37—28no—
440C22×C37—28no—
441C22×C37—24no—
442C22×C37—24no—
443C22×C37—28no—
444C22×C37—24no—
445C22×C37—28no—
446C22×C37—24no—
447C22×C37—24no—
448C22×C37—28no—
449C22×C37—28no—
450C22×C37—28no—
451C22×C37—464no—
452C22×C37—44no—
453C22×C37—44no—
454C22×C37—44no—
455C22×C37—44no—
456C22×C37—44no—
457C22×C37—44no—
458C22×C37—44no—
459C22×C37—44no—
460C22×C37—44no—
461C22×C37—44no—
462C22×C37—44no—
463C22×C37—44no—
464C22×C37—42no—
465C22×C37—44no—
466C22×C37—44no—
467C22×C37—42no—
468C22×C37—42no—
469C22×C37—81no—
470C22×C37—81no—
471C22×C37—82no—
472C22×C37—81no—
473C22×C37—82no—
474C22×C37—81no—
475C22×C37#39018yescomplemented
476C22×C37C22×C22⋊C411yescharacteristic
477C22×C37C2×C4×D411yescharacteristic
478C22×C37C2×C4×D412yes—
479C22×C37C2×C4×D411yescharacteristic
480C22×C37#51812yes—
481C22×C37C2×#12011yescharacteristic
482C22×C37C2×#12111yescharacteristic
483C22×C37C2×#12111yescharacteristic
484C22×C37#52511yescharacteristic
485C22×C37#52512yes—
486C22×C37C2×#12411yescharacteristic
487C22×C37C2×#12711yescharacteristic
488C22×C37#53411yescharacteristic
489C22×C37#53511yescharacteristic
490C22×C37#53812yes—
491C22×C37D4212yes—
492C22×C37D4212yes—
493C22×C37D4212yes—
494C22×C37#54612yes—
495C22×C37#54612yes—
496C22×C37#54612yes—
497C22×C37#54612yes—
498C22×C37#55112yes—
499C4×C37—28no—
500C4×C37—24no—
501C4×C37—42no—
502C4×C37—44no—
503C4×C37—44no—
504C4×C37—42no—
505C4×C37—81no—
506C4×C37—81no—
507C22×#120C2×C3711yescharacteristic
508C23×C22⋊C4C2×C3711yescharacteristic, complemented
509C2×#390C2×C3712yescomplemented
510C2×#386C2×C3711yescharacteristic, complemented
511C2×#386C2×C3711yescharacteristic, complemented
512C2×#385C2×C3711yescharacteristic, complemented
513C2×#379C2×C3711yescharacteristic, complemented
514C2×C4×C22⋊C4C2×C3711yescharacteristic, complemented
515#1439C2×C3712yescomplemented
516#1438C2×C3712yescomplemented
517#1437C2×C3712yescomplemented
518C2×C37—28no—
519C2×C37—48no—
520C2×C37—82no—
521C2×C37C2×#39011yescharacteristic
522C2×C37C4×#12011yescharacteristic
523C2×C37#232111yescharacteristic
524C2×C37D4×C22⋊C412yes—
525C2×C37#235812yes—
526C2×C37#241011yescharacteristic
527C2×C37#241111yescharacteristic
528C2×C37#242412yes—
529C2×C37#243311yescharacteristic
530C2×C37#247212yes—
531C2×C37#253911yescharacteristic
532C26C22×C3711yescharacteristic
533C23×D4C22×C3711yescharacteristic
534C23×D4C22×C3712yes—
535C24×C4C22×C3711yescharacteristic
536C24×C4C22×C3711yescharacteristic
537C2×#120—24no—
538C2×#120—24no—
539C2×#120C4×C3718yescomplemented
540C22×C4⋊C4C22×C3712yescomplemented
541C22×C22⋊C4—24no—
542C22×C22⋊C4—28no—
543C22×C22⋊C4C22×C3712yes—
544C22×C22⋊C4C22×C3711yescharacteristic
545C22×C22⋊C4C22×C3712yes—
546C22×C22⋊C4C22×C3712yes—
547C22×C22⋊C4C22×C3712yes—
548C22×C22⋊C4C22×C3712yes—
549C22×C22⋊C4C22×C3711yescharacteristic
550C22×C22⋊C4C22×C3711yescharacteristic
551C22×C22⋊C4C22×C3711yescharacteristic, complemented
552C22×C22⋊C4C22×C3712yescomplemented
553C22×C22⋊C4C22×C3711yescharacteristic, complemented
554C22×C42C22×C3712yescomplemented
555#390—28no—
556#386—24no—
557#386—24no—
558#385—24no—
559#379—24no—
560C4×C22⋊C4—24no—
561C2×#95C22×C3711yescharacteristic, complemented
562C2×#95C22×C3712yescomplemented
563C2×#95C22×C3712yescomplemented
564C2×#95C22×C3712yescomplemented
565C2×#95C22×C3711yescharacteristic, complemented
566C37#1399511yescharacteristic, direct product factor, Sylow
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C3714yes—
578C25C23×C3711yescharacteristic
579C25C23×C3712yes—
580C25C23×C3711yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C3714yes—
594C22×D4C2×C4×C3718yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C3714yescomplemented
605C23×C4C23×C3711yescharacteristic
606C23×C4C23×C3711yescharacteristic
607C23×C4C23×C3711yescharacteristic
608C23×C4C23×C3712yes—
609C23×C4C23×C3712yes—
610C23×C4C23×C3711yescharacteristic
611C23×C4C23×C3712yes—
612C23×C4C23×C3711yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C3714yes—
644C2×C22⋊C4C2×C4×C3718yescomplemented
645C2×C22⋊C4D4×C3714yes—
646C2×C22⋊C4D4×C3714yes—
647C2×C22⋊C4D4×C3718yescomplemented
648C2×C22⋊C4D4×C3714yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C3712yes—
707C24C22×C4×C3714yes—
708C24C22×C4×C3712yes—
709C24C2×D4×C3714yes—
710C24C2×D4×C3712yes—
711C24C2×D4×C3712yes—
712C24C2×D4×C3712yes—
713C24C2×D4×C3712yes—
714C24#41×C3714yes—
715C24#41×C3712yes—
716C24#41×C3712yes—
717C24C24×C3711yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C3712yes—
782C22×C4C22×C4×C3714yes—
783C22×C4C2×D4×C3714yes—
784C22×C4C2×D4×C3712yes—
785C22×C4C2×D4×C3714yes—
786C22×C4C2×D4×C3714yes—
787C22×C4C2×D4×C3714yes—
788C22×C4C2×D4×C3712yes—
789C22×C4C2×D4×C3714yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C37116yescomplemented
802C42—48no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—432no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C3714yes—
888C23C4×D4×C3718yes—
889C23C4×D4×C3714yes—
890C23C4×D4×C3714yes—
891C23#121×C3714yes—
892C23#121×C3714yes—
893C23#124×C3714yes—
894C23#127×C3714yes—
895C23C23×C4×C3711yescharacteristic
896C23C22×D4×C3711yescharacteristic
897C23C22×D4×C3712yes—
898C23C22×D4×C3711yescharacteristic
899C23C22×D4×C3711yescharacteristic
900C23C22×D4×C3711yescharacteristic
901C23C2×#41×C3711yescharacteristic
902C23C2×#41×C3711yescharacteristic
903C23C2×#41×C3712yes—
904C23H(5,𝔽2)×C3712yes—
905C23H(5,𝔽2)×C3712yes—
906D4—432no—
907D4—416no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C3718yescomplemented
957C2×C4#120×C3714yescomplemented
958C22—28no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—24no—
963C22—28no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—82no—
992C22—81no—
993C22—82no—
994C22—81no—
995C22C37×#39018yescomplemented
996C22C22×C22⋊C4×C3711yescharacteristic
997C22C2×C4×D4×C3711yescharacteristic
998C22C2×C4×D4×C3712yes—
999C22C2×C4×D4×C3711yescharacteristic
1000C22C37×#51812yes—
1001C22C2×#120×C3711yescharacteristic
1002C22C2×#121×C3711yescharacteristic
1003C22C2×#121×C3711yescharacteristic
1004C22C37×#52511yescharacteristic
1005C22C37×#52512yes—
1006C22C2×#124×C3711yescharacteristic
1007C22C2×#127×C3711yescharacteristic
1008C22C37×#53411yescharacteristic
1009C22C37×#53511yescharacteristic
1010C22C37×#53812yes—
1011C22D42×C3712yes—
1012C22D42×C3712yes—
1013C22D42×C3712yes—
1014C22C37×#54612yes—
1015C22C37×#54612yes—
1016C22C37×#54612yes—
1017C22C37×#54612yes—
1018C22C37×#55112yes—
1019C4—24no—
1020C4—28no—
1021C4—42no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×C37×#39011yescharacteristic
1031C2C4×#120×C3711yescharacteristic
1032C2C37×#232111yescharacteristic
1033C2D4×C22⋊C4×C3712yes—
1034C2C37×#235812yes—
1035C2C37×#241011yescharacteristic
1036C2C37×#241111yescharacteristic
1037C2C37×#242412yes—
1038C2C37×#243311yescharacteristic
1039C2C37×#247212yes—
1040C2C37×#253911yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC22×#120×C37C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C37C2semidirect
3. C2×C37×#390C2semidirect
4. C2×C37×#386C2semidirect
5. C2×C37×#386C2semidirect
6. C2×C37×#385C2semidirect
7. C2×C37×#379C2semidirect
8. C2×C4×C22⋊C4×C37C2semidirect
9. C37×#1439C2semidirect
10. C37×#1438C2semidirect
11. C37×#1437C2semidirect
19. C2×#120×C37C4semidirect
20. C22×C4⋊C4×C37C22semidirect
31. C22×C22⋊C4×C37C22semidirect
32. C22×C22⋊C4×C37C22semidirect
33. C22×C22⋊C4×C37C22semidirect
34. C22×C42×C37C22semidirect
41. C2×#95×C37C22semidirect
42. C2×#95×C37C22semidirect
43. C2×#95×C37C22semidirect
44. C2×#95×C37C22semidirect
45. C2×#95×C37C22semidirect
73. C22×D4×C37C2×C4semidirect
83. C23×C4×C37D4semidirect
123. C2×C22⋊C4×C37C2×C4semidirect
126. C2×C22⋊C4×C37D4semidirect
127. C2×C22⋊C4×C37D4semidirect
280. C22⋊C4×C37C22⋊C4semidirect
435. C2×C4×C37C2×C22⋊C4semidirect
436. C2×C4×C37#120semidirect
437. #13995C37direct (N × H)
475. C22×C37#390semidirect
508. C23×C22⋊C4C2×C37semidirect
509. C2×#390C2×C37semidirect
510. C2×#386C2×C37semidirect
511. C2×#386C2×C37semidirect
512. C2×#385C2×C37semidirect
513. C2×#379C2×C37semidirect
514. C2×C4×C22⋊C4C2×C37semidirect
515. #1439C2×C37semidirect
516. #1438C2×C37semidirect
517. #1437C2×C37semidirect
539. C2×#120C4×C37semidirect
540. C22×C4⋊C4C22×C37semidirect
551. C22×C22⋊C4C22×C37semidirect
552. C22×C22⋊C4C22×C37semidirect
553. C22×C22⋊C4C22×C37semidirect
554. C22×C42C22×C37semidirect
561. C2×#95C22×C37semidirect
562. C2×#95C22×C37semidirect
563. C2×#95C22×C37semidirect
564. C2×#95C22×C37semidirect
565. C2×#95C22×C37semidirect
566. C37#13995direct (N × H)
594. C22×D4C2×C4×C37semidirect
604. C23×C4D4×C37semidirect
644. C2×C22⋊C4C2×C4×C37semidirect
647. C2×C22⋊C4D4×C37semidirect
648. C2×C22⋊C4D4×C37semidirect
801. C22⋊C4C22⋊C4×C37semidirect
956. C2×C4C2×C22⋊C4×C37semidirect
957. C2×C4#120×C37semidirect
995. C22C37×#390semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C372
C23×C22⋊C4×C372
C2×C37×#3902
C2×C37×#3862
C2×C37×#3852
C2×C37×#3792
C2×C4×C22⋊C4×C372
C37×#14392
C37×#14382
C37×#14372
#1399537