Finite Group Databasebeta

← C37×#25106 #22646359

Subgroups — C37×#25106 #22646359

Order 9472.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#469C211yesmaximal, characteristic, complemented
2C2×C37×#463C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C2×C37×#417C211yesmaximal, characteristic, complemented
5C37×#2431C211yesmaximal, characteristic, complemented
6C37×#2361C211yesmaximal, characteristic, complemented
7C37×#2065C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2042C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1982C211yesmaximal, characteristic, complemented
12C37×#1927C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1874C211yesmaximal, characteristic, complemented
15C37×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#124×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×C4×D4×C37—21no—
26C2×C4×D4×C37C2211yescharacteristic
27C22×C4⋊C4×C37C2211yescharacteristic
28C37×#469—24no—
29C37×#463—24no—
30C37×#449—24no—
31C2×#106×C37C2211yescharacteristic
32C2×C4⋊C8×C37C2211yescharacteristic
33C2×C4⋊C8×C37C2211yescharacteristic
34C37×#417—24no—
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#103×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic
46C37×#392—21no—
47C37×#392—21no—
48C37×#391C2211yescharacteristic
49C37×#390C2211yescharacteristic
50C37×#390C2211yescharacteristic
51C37×#389C2211yescharacteristic
52C37×#388—21no—
53C37×#386—21no—
54C37×#386—21no—
55C37×#386—21no—
56C37×#385—21no—
57C4×C4⋊C4×C37C2211yescharacteristic
58C4×C22⋊C4×C37C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C2×#41×C37—22no—
64C2×#41×C37—22no—
65C2×#41×C37—22no—
66C2×#41×C37—22no—
67C2×#41×C37—41no—
68C2×#41×C37—41no—
69C22×Q8×C37C2311yescharacteristic
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37C2311yescharacteristic
76C22×D4×C37C2311yescharacteristic
77C22×D4×C37C2311yescharacteristic
78C23×C4×C37—21no—
79C23×C4×C37—21no—
80C23×C4×C37—21no—
81C23×C4×C37C2311yescharacteristic
82C2×SD16×C37—22no—
83C2×SD16×C37—22no—
84C2×SD16×C37—41no—
85C2×D8×C37—22no—
86C2×D8×C37—22no—
87C2×D8×C37—22no—
88C2×D8×C37—22no—
89C2×D8×C37—41no—
90C2×D8×C37—41no—
91C2×M16×C37—22no—
92C2×M16×C37—22no—
93C2×M16×C37—41no—
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97C22×C8×C37C2311yescharacteristic
98#127×C37—22no—
99#127×C37—41no—
100#124×C37—22no—
101#124×C37—41no—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37—22no—
105#121×C37D414yescomplemented
106C4×D4×C37—22no—
107C4×D4×C37—41no—
108C4×D4×C37—44no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—41no—
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37D411yescharacteristic
127C2×C22⋊C4×C37D411yescharacteristic
128C2×C42×C37—21no—
129C2×C42×C37C2311yescharacteristic
130C2×C42×C37C2311yescharacteristic
131#106×C37—22no—
132C4⋊C8×C37—22no—
133C4⋊C8×C37—41no—
134#103×C37—22no—
135#103×C37—22no—
136#103×C37D414yescomplemented
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—41no—
144C22⋊C8×C37—22no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37D411yescharacteristic
150#95×C37D411yescharacteristic
151C24×C37—21no—
152C24×C37—21no—
153C24×C37—21no—
154C24×C37C2×D411yescharacteristic
155#41×C37—28no—
156#41×C37—44no—
157#41×C37—44no—
158#41×C37—44no—
159C2×Q8×C37—21no—
160C2×Q8×C37—21no—
161C2×Q8×C37—21no—
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37C2×D412yes—
165C2×D4×C37—24no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—21no—
181C2×D4×C37—21no—
182C2×D4×C37—42no—
183C2×D4×C37—42no—
184C2×D4×C37—42no—
185C2×D4×C37—42no—
186C2×D4×C37—42no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
191C2×D4×C37—42no—
192C2×D4×C37—81no—
193C2×D4×C37—81no—
194C2×D4×C37—81no—
195C2×D4×C37—81no—
196C2×D4×C37C2×D412yes—
197C2×D4×C37#4112yes—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—42no—
208C22×C4×C37—42no—
209C22×C4×C37—42no—
210C22×C4×C37—42no—
211C22×C4×C37—42no—
212C22×C4×C37—42no—
213C22×C4×C37—42no—
214C22×C4×C37—81no—
215C22×C4×C37—81no—
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2×D411yescharacteristic
220C22×C4×C37C2×D412yes—
221C22×C4×C37C2×D411yescharacteristic
222C22×C4×C37#4112yes—
223C22×C4×C37C2411yescharacteristic
224SD16×C37—44no—
225D8×C37—44no—
226D8×C37—44no—
227M16×C37—44no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—21no—
235C2×C8×C37—21no—
236C2×C8×C37—21no—
237C2×C8×C37—21no—
238C2×C8×C37—21no—
239C2×C8×C37C2×D412yes—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—21no—
243C4⋊C4×C37—21no—
244C4⋊C4×C37—21no—
245C4⋊C4×C37—21no—
246C4⋊C4×C37—42no—
247C4⋊C4×C37—42no—
248C4⋊C4×C37C2×D412yes—
249C4⋊C4×C37C2×D412yes—
250C22⋊C4×C37—24no—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—41no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—42no—
257C22⋊C4×C37—42no—
258C22⋊C4×C37—81no—
259C22⋊C4×C37—81no—
260C22⋊C4×C37—81no—
261C42×C37—21no—
262C42×C37—21no—
263C42×C37—21no—
264C42×C37—21no—
265C42×C37—42no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—21no—
272C23×C37—22no—
273C23×C37—22no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37—41no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—41no—
289C23×C37—41no—
290C23×C37—41no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37#12112yes—
294C23×C37C22×D411yescharacteristic
295Q8×C37—22no—
296Q8×C37—22no—
297Q8×C37—41no—
298Q8×C37—41no—
299D4×C37—22no—
300D4×C37—22no—
301D4×C37—22no—
302D4×C37—22no—
303D4×C37—48no—
304D4×C37—48no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—41no—
309D4×C37—41no—
310D4×C37—41no—
311D4×C37—41no—
312D4×C37—41no—
313D4×C37—84no—
314D4×C37—84no—
315D4×C37—84no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—21no—
320C2×C4×C37—22no—
321C2×C4×C37—22no—
322C2×C4×C37—22no—
323C2×C4×C37—22no—
324C2×C4×C37—22no—
325C2×C4×C37—21no—
326C2×C4×C37—21no—
327C2×C4×C37—22no—
328C2×C4×C37—22no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—21no—
335C2×C4×C37—21no—
336C2×C4×C37—48no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
346C2×C4×C37—41no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—84no—
350C2×C4×C37—84no—
351C2×C4×C37#12112yes—
352C2×C4×C37AGL(1,ℤ/8)12yes—
353C2×C4×C37C22×D411yescharacteristic
354C2×C4×C37C22×D411yescharacteristic
355C2×C4×C37C2×#4111yescharacteristic
356C2×C4×C37C2×#4111yescharacteristic
357C2×C4×C37H(5,𝔽2)11yescharacteristic
358C2×C4×C37H(5,𝔽2)11yescharacteristic
359C8×C37—22no—
360C8×C37—41no—
361C8×C37—41no—
362C8×C37—41no—
363#25106C3711yesmaximal, characteristic, direct product factor, Sylow
364C22×C37—22no—
365C22×C37—22no—
366C22×C37—22no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—41no—
371C22×C37—42no—
372C22×C37—42no—
373C22×C37—42no—
374C22×C37—42no—
375C22×C37—42no—
376C22×C37—42no—
377C22×C37—81no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37—81no—
382C22×C37—81no—
383C22×C37—81no—
384C22×C37—81no—
385C22×C37—81no—
386C22×C37—81no—
387C22×C37—81no—
388C22×C37—81no—
389C22×C37—81no—
390C22×C37—81no—
391C22×C37—81no—
392C22×C37C2×#12111yescharacteristic
393C22×C37D4211yescharacteristic
394C22×C37#54611yescharacteristic
395C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C37#57511yescharacteristic
397C22×C37#57611yescharacteristic
398C22×C37#57711yescharacteristic
399C4×C37—22no—
400C4×C37—22no—
401C4×C37—42no—
402C4×C37—41no—
403C4×C37—41no—
404C4×C37—42no—
405C4×C37—42no—
406C4×C37—41no—
407C4×C37—81no—
408C4×C37—81no—
409C4×C37#52511yescharacteristic
410C4×C37#53811yescharacteristic
411C4×C37D4211yescharacteristic
412C4×C37#54611yescharacteristic
413C2×#469C2×C3711yescharacteristic, complemented
414C2×#463C2×C3711yescharacteristic, complemented
415C2×#449C2×C3711yescharacteristic, complemented
416C2×#417C2×C3711yescharacteristic, complemented
417#2431C2×C3711yescharacteristic, complemented
418#2361C2×C3711yescharacteristic, complemented
419#2065C2×C3711yescharacteristic, complemented
420#2055C2×C3711yescharacteristic, complemented
421#2042C2×C3711yescharacteristic, complemented
422#2011C2×C3711yescharacteristic, complemented
423#1982C2×C3711yescharacteristic, complemented
424#1927C2×C3711yescharacteristic, complemented
425#1879C2×C3711yescharacteristic, complemented
426#1874C2×C3711yescharacteristic, complemented
427#1851C2×C3711yescharacteristic, complemented
428C2×C37—42no—
429C2×C37—82no—
430C2×C37—82no—
431C2×C37—161no—
432C2×C37#242411yescharacteristic
433C2×C37#303611yescharacteristic
434C2×C37#304511yescharacteristic
435C2×C37#327111yescharacteristic
436C2×C37#327411yescharacteristic
437C2×C37#330611yescharacteristic
438C2×C37#332211yescharacteristic
439C22×#41C22×C3711yescharacteristic
440C22×SD16C22×C3711yescharacteristic
441C22×D8C22×C3711yescharacteristic
442C22×D8C22×C3711yescharacteristic
443C22×M16C22×C3711yescharacteristic
444C2×#127C22×C3711yescharacteristic
445C2×#124C22×C3711yescharacteristic
446C2×#121C22×C3711yescharacteristic
447C2×#121C22×C3711yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C22×C3711yescharacteristic
450C22×C4⋊C4C22×C3711yescharacteristic
451#469—24no—
452#463—24no—
453#449—24no—
454C2×#106C22×C3711yescharacteristic
455C2×C4⋊C8C22×C3711yescharacteristic
456C2×C4⋊C8C22×C3711yescharacteristic
457#417—24no—
458C2×#103C22×C3711yescharacteristic
459C2×#103C22×C3711yescharacteristic
460C2×#103C22×C3711yescharacteristic
461C2×#102C22×C3711yescharacteristic
462C2×#102C22×C3711yescharacteristic
463C2×#102C22×C3711yescharacteristic
464C2×#102C22×C3711yescharacteristic
465C2×#102C22×C3711yescharacteristic
466C2×#102C22×C3711yescharacteristic
467C2×#102C22×C3711yescharacteristic
468C2×C22⋊C8C22×C3711yescharacteristic
469#392—21no—
470#392—21no—
471#391C22×C3711yescharacteristic
472#390C22×C3711yescharacteristic
473#390C22×C3711yescharacteristic
474#389C22×C3711yescharacteristic
475#388—21no—
476#386—21no—
477#386—21no—
478#386—21no—
479#385—21no—
480C4×C4⋊C4C22×C3711yescharacteristic
481C4×C22⋊C4C22×C3711yescharacteristic
482#340C22×C3711yescharacteristic
483#340C22×C3711yescharacteristic
484#336C22×C3711yescharacteristic
485#336C22×C3711yescharacteristic
486C37#2510611yescharacteristic, direct product factor, Sylow
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C3711yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C3711yescharacteristic
500C22×D4C23×C3711yescharacteristic
501C22×D4C23×C3711yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C3711yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C3711yescharacteristic
519C22×C8C23×C3711yescharacteristic
520C22×C8C23×C3711yescharacteristic
521C22×C8C23×C3711yescharacteristic
522#127—22no—
523#127—41no—
524#124—22no—
525#124—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121D4×C3714yescomplemented
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4C23×C3711yescharacteristic
538C2×C4⋊C4C23×C3711yescharacteristic
539C2×C4⋊C4C23×C3711yescharacteristic
540C2×C4⋊C4C23×C3711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C3711yescharacteristic
551C2×C22⋊C4D4×C3711yescharacteristic
552C2×C42—21no—
553C2×C42C23×C3711yescharacteristic
554C2×C42C23×C3711yescharacteristic
555#106—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103D4×C3714yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C3711yescharacteristic
574#95D4×C3711yescharacteristic
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C3711yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8C2×D4×C3712yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C3712yes—
621C2×D4#41×C3712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C3711yescharacteristic
641C22×C4C2×D4×C3711yescharacteristic
642C22×C4C2×D4×C3711yescharacteristic
643C22×C4C2×D4×C3711yescharacteristic
644C22×C4C2×D4×C3712yes—
645C22×C4C2×D4×C3711yescharacteristic
646C22×C4#41×C3712yes—
647C22×C4C24×C3711yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C3712yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C3712yes—
673C4⋊C4C2×D4×C3712yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23#121×C3712yes—
718C23C22×D4×C3711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4#121×C3712yes—
776C2×C4AGL(1,ℤ/8)×C3712yes—
777C2×C4C22×D4×C3711yescharacteristic
778C2×C4C22×D4×C3711yescharacteristic
779C2×C4C2×#41×C3711yescharacteristic
780C2×C4C2×#41×C3711yescharacteristic
781C2×C4H(5,𝔽2)×C3711yescharacteristic
782C2×C4H(5,𝔽2)×C3711yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C3711yescharacteristic
816C22D42×C3711yescharacteristic
817C22C37×#54611yescharacteristic
818C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
819C22C37×#57511yescharacteristic
820C22C37×#57611yescharacteristic
821C22C37×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4C37×#52511yescharacteristic
833C4C37×#53811yescharacteristic
834C4D42×C3711yescharacteristic
835C4C37×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2C37×#242411yescharacteristic
841C2C37×#303611yescharacteristic
842C2C37×#304511yescharacteristic
843C2C37×#327111yescharacteristic
844C2C37×#327411yescharacteristic
845C2C37×#330611yescharacteristic
846C2C37×#332211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#469C2semidirect
2. C2×C37×#463C2semidirect
3. C2×C37×#449C2semidirect
4. C2×C37×#417C2semidirect
5. C37×#2431C2semidirect
6. C37×#2361C2semidirect
7. C37×#2065C2semidirect
8. C37×#2055C2semidirect
9. C37×#2042C2semidirect
10. C37×#2011C2semidirect
11. C37×#1982C2semidirect
12. C37×#1927C2semidirect
13. C37×#1879C2semidirect
14. C37×#1874C2semidirect
15. C37×#1851C2semidirect
105. #121×C37D4semidirect
136. #103×C37D4semidirect
363. #25106C37direct (N × H)
413. C2×#469C2×C37semidirect
414. C2×#463C2×C37semidirect
415. C2×#449C2×C37semidirect
416. C2×#417C2×C37semidirect
417. #2431C2×C37semidirect
418. #2361C2×C37semidirect
419. #2065C2×C37semidirect
420. #2055C2×C37semidirect
421. #2042C2×C37semidirect
422. #2011C2×C37semidirect
423. #1982C2×C37semidirect
424. #1927C2×C37semidirect
425. #1879C2×C37semidirect
426. #1874C2×C37semidirect
427. #1851C2×C37semidirect
486. C37#25106direct (N × H)
529. #121D4×C37semidirect
560. #103D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4692
C2×C37×#4632
C2×C37×#4492
C2×C37×#4172
C37×#24312
C37×#23612
C37×#20652
C37×#20552
C37×#20422
C37×#20112
C37×#19822
C37×#19272
C37×#18792
C37×#18742
C37×#18512
#2510637