Finite Group Databasebeta

← C37×#24034 #22645287

Subgroups — C37×#24034 #22645287

Order 9472.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#550C211yesmaximal, characteristic
2C2×C37×#482C211yesmaximal, characteristic, complemented
3C2×C37×#416C211yesmaximal, characteristic, complemented
4C37×#2485C211yesmaximal, characteristic, complemented
5C37×#2041C211yesmaximal, characteristic, complemented
6C37×#2041C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#1893C211yesmaximal, characteristic, complemented
10C37×#1869C211yesmaximal, characteristic, complemented
11C37×#1865C211yesmaximal, characteristic, complemented
12C37×#1863C211yesmaximal, characteristic, complemented
13C37×#1788C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C23×C8×C37C2211yescharacteristic
19C37×#550—24no—
20C37×#550—24no—
21C2×#127×C37—21no—
22C2×#127×C37C2211yescharacteristic
23C2×#121×C37—21no—
24C2×#121×C37—21no—
25C2×#121×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×C4×Q8×C37C2211yescharacteristic
28C2×C4×D4×C37—21no—
29C2×C4×D4×C37C2211yescharacteristic
30C2×#117×C37C2211yescharacteristic
31C37×#482—24no—
32C2×#107×C37C2211yescharacteristic
33C2×#106×C37C2211yescharacteristic
34C37×#416—24no—
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#103×C37C2211yescharacteristic
38C2×#103×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C2×C22⋊C8×C37C2211yescharacteristic
50C37×#397—21no—
51C37×#394—21no—
52C37×#389C2211yescharacteristic
53C37×#389C2211yescharacteristic
54C37×#388—21no—
55C37×#387—21no—
56C37×#380C2211yescharacteristic
57C37×#380C2211yescharacteristic
58C37×#380C2211yescharacteristic
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—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C2×#41×C37—41no—
73C2×#41×C37—41no—
74C2×#41×C37D414yes—
75C22×Q8×C37C2311yescharacteristic
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37D411yescharacteristic
83C22×D4×C37C2311yescharacteristic
84C22×D4×C37C2311yescharacteristic
85C23×C4×C37—21no—
86C23×C4×C37—21no—
87C23×C4×C37C2311yescharacteristic
88C23×C4×C37C2311yescharacteristic
89C22×C8×C37—22no—
90C22×C8×C37—41no—
91C22×C8×C37—41no—
92C22×C8×C37C2311yescharacteristic
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96#127×C37—28no—
97#127×C37—22no—
98#127×C37—22no—
99#121×C37—28no—
100#121×C37—28no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37D414yes—
105C4×Q8×C37—22no—
106C4×Q8×C37—22no—
107C4×D4×C37—28no—
108C4×D4×C37—22no—
109C4×D4×C37—22no—
110#117×C37—22no—
111#117×C37—22no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37D411yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
127C2×C22⋊C4×C37D411yescharacteristic
128C2×C22⋊C4×C37D411yescharacteristic
129C2×C42×C37—21no—
130C2×C42×C37—21no—
131C2×C42×C37C2311yescharacteristic
132#107×C37—22no—
133#106×C37—22no—
134#103×C37—22no—
135#103×C37—22no—
136#103×C37—22no—
137#103×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—41no—
143#102×C37—41no—
144#102×C37—41no—
145#102×C37—41no—
146C22⋊C8×C37—22no—
147C22⋊C8×C37—41no—
148C22⋊C8×C37—41no—
149#95×C37—21no—
150#95×C37—21no—
151#95×C37—21no—
152#95×C37—21no—
153#95×C37—21no—
154C24×C37—21no—
155C24×C37—21no—
156C24×C37C2×D411yescharacteristic
157C24×C37C2×D411yescharacteristic
158#41×C37—28no—
159#41×C37—44no—
160#41×C37—44no—
161#41×C37—44no—
162#41×C37—44no—
163#41×C37—44no—
164#41×C37—44no—
165#41×C37—44no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×Q8×C37—21no—
169C2×Q8×C37C2×D412yes—
170C2×Q8×C37#4112yes—
171C2×Q8×C37#4112yes—
172C2×D4×C37—24no—
173C2×D4×C37—24no—
174C2×D4×C37—22no—
175C2×D4×C37—24no—
176C2×D4×C37—24no—
177C2×D4×C37—24no—
178C2×D4×C37—24no—
179C2×D4×C37—22no—
180C2×D4×C37—21no—
181C2×D4×C37—21no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—21no—
189C2×D4×C37—21no—
190C2×D4×C37—41no—
191C2×D4×C37—42no—
192C2×D4×C37—42no—
193C2×D4×C37—42no—
194C2×D4×C37—42no—
195C2×D4×C37—42no—
196C2×D4×C37—42no—
197C2×D4×C37—81no—
198C2×D4×C37—81no—
199C2×D4×C37—81no—
200C2×D4×C37—81no—
201C2×D4×C37—81no—
202C2×D4×C37—81no—
203C2×D4×C37C2×D412yes—
204C2×D4×C37C2×D412yes—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—21no—
208C22×C4×C37—21no—
209C22×C4×C37—21no—
210C22×C4×C37—24no—
211C22×C4×C37—21no—
212C22×C4×C37—24no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—42no—
224C22×C4×C37—42no—
225C22×C4×C37—42no—
226C22×C4×C37—42no—
227C22×C4×C37C2×D411yescharacteristic
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D411yescharacteristic
230C22×C4×C37C2×D412yes—
231C22×C4×C37C2×D412yes—
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37C2411yescharacteristic
234C2×C8×C37—21no—
235C2×C8×C37—21no—
236C2×C8×C37—21no—
237C2×C8×C37—21no—
238C2×C8×C37—21no—
239C2×C8×C37—21no—
240C2×C8×C37—21no—
241C2×C8×C37—21no—
242C2×C8×C37—21no—
243C2×C8×C37—21no—
244C2×C8×C37—21no—
245C2×C8×C37—21no—
246C2×C8×C37—44no—
247C4⋊C4×C37—24no—
248C4⋊C4×C37—22no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—21no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37—21no—
255C4⋊C4×C37—21no—
256C4⋊C4×C37—21no—
257C4⋊C4×C37—21no—
258C4⋊C4×C37—42no—
259C4⋊C4×C37—81no—
260C4⋊C4×C37C2×D412yes—
261C22⋊C4×C37—24no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—24no—
264C22⋊C4×C37—22no—
265C22⋊C4×C37—42no—
266C22⋊C4×C37—42no—
267C22⋊C4×C37—81no—
268C22⋊C4×C37—81no—
269C42×C37—24no—
270C42×C37—21no—
271C42×C37—21no—
272C42×C37—42no—
273C23×C37—21no—
274C23×C37—21no—
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
279C23×C37—21no—
280C23×C37—22no—
281C23×C37—22no—
282C23×C37—21no—
283C23×C37—21no—
284C23×C37—21no—
285C23×C37—21no—
286C23×C37—21no—
287C23×C37—21no—
288C23×C37—41no—
289C23×C37—41no—
290C23×C37—41no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37—41no—
294C23×C37—41no—
295C23×C37—41no—
296C23×C37—41no—
297C23×C37—41no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37#12012yes—
301C23×C37C22×D411yescharacteristic
302Q8×C37—22no—
303Q8×C37—22no—
304Q8×C37—22no—
305Q8×C37#12314yes—
306D4×C37—22no—
307D4×C37—22no—
308D4×C37—22no—
309D4×C37—22no—
310D4×C37—44no—
311D4×C37—48no—
312D4×C37—48no—
313D4×C37—48no—
314D4×C37—41no—
315D4×C37—41no—
316D4×C37—41no—
317D4×C37—41no—
318D4×C37—84no—
319D4×C37—84no—
320D4×C37—84no—
321C2×C4×C37—21no—
322C2×C4×C37—22no—
323C2×C4×C37—21no—
324C2×C4×C37—21no—
325C2×C4×C37—22no—
326C2×C4×C37—22no—
327C2×C4×C37—21no—
328C2×C4×C37—22no—
329C2×C4×C37—22no—
330C2×C4×C37—22no—
331C2×C4×C37—22no—
332C2×C4×C37—21no—
333C2×C4×C37—22no—
334C2×C4×C37—21no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—21no—
339C2×C4×C37—48no—
340C2×C4×C37—48no—
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—41no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37—41no—
354C2×C4×C37—41no—
355C2×C4×C37—41no—
356C2×C4×C37—41no—
357C2×C4×C37—41no—
358C2×C4×C37—41no—
359C2×C4×C37#12012yes—
360C2×C4×C37#13512yes—
361C2×C4×C37C22×D411yescharacteristic
362C2×C4×C37C22×D411yescharacteristic
363C2×C4×C37C2×#4111yescharacteristic
364C2×C4×C37C2×#4111yescharacteristic
365C2×C4×C37H(5,𝔽2)11yescharacteristic
366C2×C4×C37H(5,𝔽2)11yescharacteristic
367C8×C37—41no—
368C8×C37—41no—
369C8×C37—41no—
370C8×C37—41no—
371#24034C3711yesmaximal, characteristic, direct product factor, Sylow
372C22×C37—22no—
373C22×C37—22no—
374C22×C37—22no—
375C22×C37—41no—
376C22×C37—41no—
377C22×C37—41no—
378C22×C37—41no—
379C22×C37—42no—
380C22×C37—42no—
381C22×C37—41no—
382C22×C37—41no—
383C22×C37—42no—
384C22×C37—42no—
385C22×C37—41no—
386C22×C37—42no—
387C22×C37—42no—
388C22×C37—41no—
389C22×C37—41no—
390C22×C37—41no—
391C22×C37—41no—
392C22×C37—81no—
393C22×C37—81no—
394C22×C37—81no—
395C22×C37—81no—
396C22×C37—81no—
397C22×C37—81no—
398C22×C37—81no—
399C22×C37—81no—
400C22×C37C2×#12011yescharacteristic
401C22×C37#54611yescharacteristic
402C22×C37#54611yescharacteristic
403C22×C37C2×#13511yescharacteristic
404C22×C37#57511yescharacteristic
405C22×C37#57611yescharacteristic
406C22×C37#57711yescharacteristic
407C4×C37—22no—
408C4×C37—24no—
409C4×C37—22no—
410C4×C37—41no—
411C4×C37—41no—
412C4×C37—42no—
413C4×C37—81no—
414C4×C37—81no—
415C4×C37—81no—
416C4×C37—81no—
417C4×C37C2×#12311yescharacteristic
418C4×C37#53411yescharacteristic
419C4×C37#54611yescharacteristic
420C4×C37#54611yescharacteristic
421C2×#550C2×C3711yescharacteristic
422C2×#482C2×C3711yescharacteristic, complemented
423C2×#416C2×C3711yescharacteristic, complemented
424#2485C2×C3711yescharacteristic, complemented
425#2041C2×C3711yescharacteristic, complemented
426#2041C2×C3711yescharacteristic, complemented
427#2034C2×C3711yescharacteristic, complemented
428#2033C2×C3711yescharacteristic, complemented
429#1893C2×C3711yescharacteristic, complemented
430#1869C2×C3711yescharacteristic, complemented
431#1865C2×C3711yescharacteristic, complemented
432#1863C2×C3711yescharacteristic, complemented
433#1788C2×C3711yescharacteristic, complemented
434#1788C2×C3711yescharacteristic, complemented
435#1788C2×C3711yescharacteristic, complemented
436C2×C37—42no—
437C2×C37—81no—
438C2×C37—82no—
439C2×C37—82no—
440C2×C37#240511yescharacteristic
441C2×C37#300211yescharacteristic
442C2×C37#301211yescharacteristic
443C2×C37#330411yescharacteristic
444C2×C37#330511yescharacteristic
445C2×C37#330911yescharacteristic
446C2×C37#331711yescharacteristic
447C22×#41C22×C3711yescharacteristic
448C22×#41C22×C3711yescharacteristic
449C23×C8C22×C3711yescharacteristic
450#550—24no—
451#550—24no—
452C2×#127—21no—
453C2×#127C22×C3711yescharacteristic
454C2×#121—21no—
455C2×#121—21no—
456C2×#121C22×C3711yescharacteristic
457C2×#121C22×C3711yescharacteristic
458C2×C4×Q8C22×C3711yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C3711yescharacteristic
461C2×#117C22×C3711yescharacteristic
462#482—24no—
463C2×#107C22×C3711yescharacteristic
464C2×#106C22×C3711yescharacteristic
465#416—24no—
466C2×#103C22×C3711yescharacteristic
467C2×#103C22×C3711yescharacteristic
468C2×#103C22×C3711yescharacteristic
469C2×#103C22×C3711yescharacteristic
470C2×#102C22×C3711yescharacteristic
471C2×#102C22×C3711yescharacteristic
472C2×#102C22×C3711yescharacteristic
473C2×#102C22×C3711yescharacteristic
474C2×#102C22×C3711yescharacteristic
475C2×#102C22×C3711yescharacteristic
476C2×#102C22×C3711yescharacteristic
477C2×#102C22×C3711yescharacteristic
478C2×C22⋊C8C22×C3711yescharacteristic
479C2×C22⋊C8C22×C3711yescharacteristic
480C2×C22⋊C8C22×C3711yescharacteristic
481#397—21no—
482#394—21no—
483#389C22×C3711yescharacteristic
484#389C22×C3711yescharacteristic
485#388—21no—
486#387—21no—
487#380C22×C3711yescharacteristic
488#380C22×C3711yescharacteristic
489#380C22×C3711yescharacteristic
490#340C22×C3711yescharacteristic
491#340C22×C3711yescharacteristic
492#336C22×C3711yescharacteristic
493#336C22×C3711yescharacteristic
494C37#2403411yescharacteristic, direct product factor, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C3714yes—
507C22×Q8C23×C3711yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C3711yescharacteristic
515C22×D4C23×C3711yescharacteristic
516C22×D4C23×C3711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C3711yescharacteristic
520C23×C4C23×C3711yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C3711yescharacteristic
525C22×C8C23×C3711yescharacteristic
526C22×C8C23×C3711yescharacteristic
527C22×C8C23×C3711yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C3714yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C3711yescharacteristic
548C2×C4⋊C4C23×C3711yescharacteristic
549C2×C4⋊C4C23×C3711yescharacteristic
550C2×C4⋊C4C23×C3711yescharacteristic
551C2×C4⋊C4C23×C3711yescharacteristic
552C2×C4⋊C4C23×C3711yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C3711yescharacteristic
560C2×C22⋊C4D4×C3711yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C3711yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C3711yescharacteristic
589C24C2×D4×C3711yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C3712yes—
602C2×Q8#41×C3712yes—
603C2×Q8#41×C3712yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C3712yes—
636C2×D4C2×D4×C3712yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C3711yescharacteristic
660C22×C4C2×D4×C3711yescharacteristic
661C22×C4C2×D4×C3711yescharacteristic
662C22×C4C2×D4×C3712yes—
663C22×C4C2×D4×C3712yes—
664C22×C4C2×D4×C3711yescharacteristic
665C22×C4C24×C3711yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C3712yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C3712yes—
733C23C22×D4×C3711yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C3714yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C3712yes—
792C2×C4#135×C3712yes—
793C2×C4C22×D4×C3711yescharacteristic
794C2×C4C22×D4×C3711yescharacteristic
795C2×C4C2×#41×C3711yescharacteristic
796C2×C4C2×#41×C3711yescharacteristic
797C2×C4H(5,𝔽2)×C3711yescharacteristic
798C2×C4H(5,𝔽2)×C3711yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C3711yescharacteristic
832C22C37×#54611yescharacteristic
833C22C37×#54611yescharacteristic
834C22C2×#135×C3711yescharacteristic
835C22C37×#57511yescharacteristic
836C22C37×#57611yescharacteristic
837C22C37×#57711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C3711yescharacteristic
849C4C37×#53411yescharacteristic
850C4C37×#54611yescharacteristic
851C4C37×#54611yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C37×#240511yescharacteristic
857C2C37×#300211yescharacteristic
858C2C37×#301211yescharacteristic
859C2C37×#330411yescharacteristic
860C2C37×#330511yescharacteristic
861C2C37×#330911yescharacteristic
862C2C37×#331711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#482C2semidirect
3. C2×C37×#416C2semidirect
4. C37×#2485C2semidirect
5. C37×#2041C2semidirect
6. C37×#2041C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#1893C2semidirect
10. C37×#1869C2semidirect
11. C37×#1865C2semidirect
12. C37×#1863C2semidirect
13. C37×#1788C2semidirect
14. C37×#1788C2semidirect
15. C37×#1788C2semidirect
371. #24034C37direct (N × H)
422. C2×#482C2×C37semidirect
423. C2×#416C2×C37semidirect
424. #2485C2×C37semidirect
425. #2041C2×C37semidirect
426. #2041C2×C37semidirect
427. #2034C2×C37semidirect
428. #2033C2×C37semidirect
429. #1893C2×C37semidirect
430. #1869C2×C37semidirect
431. #1865C2×C37semidirect
432. #1863C2×C37semidirect
433. #1788C2×C37semidirect
434. #1788C2×C37semidirect
435. #1788C2×C37semidirect
494. C37#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5502
C2×C37×#4822
C2×C37×#4162
C37×#24852
C37×#20412
C37×#20342
C37×#20332
C37×#18932
C37×#18692
C37×#18652
C37×#18632
C37×#17882
#2403437