Finite Group Databasebeta

← C37×#25151 #22646404

Subgroups — C37×#25151 #22646404

Order 9472.

1078 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#462C211yesmaximal, characteristic, complemented
2C2×C37×#452C211yesmaximal, characteristic
3C2×C37×#452C211yesmaximal, characteristic
4C2×C4×Q16×C37C211yesmaximal, characteristic, complemented
5C37×#2429C211yesmaximal, characteristic, complemented
6C37×#2341C211yesmaximal, characteristic
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2036C211yesmaximal, characteristic, complemented
9C37×#2035C211yesmaximal, characteristic, complemented
10C37×#2013C211yesmaximal, characteristic, complemented
11C37×#1968C211yesmaximal, characteristic, complemented
12C37×#1923C211yesmaximal, characteristic, complemented
13C37×#1880C211yesmaximal, characteristic, complemented
14C37×#1878C211yesmaximal, characteristic, complemented
15C37×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×Q16×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C2×C4⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic
25C2×C4×Q8×C37C2211yescharacteristic
26C2×C4×Q8×C37C2211yescharacteristic
27C37×#462—24no—
28C37×#452—24no—
29C37×#452—24no—
30C4×Q16×C37—24no—
31C2×#107×C37C2211yescharacteristic
32C2×#106×C37C2211yescharacteristic
33C2×C4⋊C8×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#103×C37C2211yescharacteristic
38C2×#103×C37C2211yescharacteristic
39C2×#103×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×C22⋊C8×C37C2211yescharacteristic
43C2×C22⋊C8×C37C2211yescharacteristic
44C2×C4×C8×C37C2211yescharacteristic
45C37×#398—21no—
46C37×#396—21no—
47C37×#391C2211yescharacteristic
48C37×#390—21no—
49C37×#390—21no—
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#389—21no—
53C37×#389C2211yescharacteristic
54C37×#388—21no—
55C37×#380—21no—
56C37×#380C2211yescharacteristic
57C4×C22⋊C4×C37—21no—
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×Q8×C37C2311yescharacteristic
71C22×Q8×C37C2311yescharacteristic
72C22×D4×C37—21no—
73C22×D4×C37C2311yescharacteristic
74C23×C4×C37—21no—
75C23×C4×C37C2311yescharacteristic
76C2×Q16×C37—22no—
77C2×Q16×C37—22no—
78C2×Q16×C37—22no—
79C2×Q16×C37—22no—
80C2×Q16×C37—22no—
81C2×Q16×C37D414yes—
82C2×SD16×C37—22no—
83C2×SD16×C37—22no—
84C2×SD16×C37—22no—
85C2×SD16×C37—22no—
86C2×SD16×C37—41no—
87C2×SD16×C37—41no—
88C22×C8×C37C2311yescharacteristic
89C22×C8×C37C2311yescharacteristic
90C22×C8×C37C2311yescharacteristic
91C22×C8×C37C2311yescharacteristic
92C4⋊Q8×C37—22no—
93C4⋊Q8×C37—41no—
94C22⋊Q8×C37—22no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—41no—
97C22⋊Q8×C37—41no—
98C4×Q8×C37—22no—
99C4×Q8×C37—22no—
100C4×Q8×C37—22no—
101C4×Q8×C37—41no—
102C4×Q8×C37—41no—
103C4×Q8×C37—41no—
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
124C2×C22⋊C4×C37D411yescharacteristic
125C2×C42×C37—21no—
126C2×C42×C37—21no—
127C2×C42×C37—21no—
128C2×C42×C37C2311yescharacteristic
129C2×C42×C37C2311yescharacteristic
130#107×C37—22no—
131#106×C37—41no—
132C4⋊C8×C37—22no—
133#103×C37—22no—
134#103×C37—22no—
135#103×C37—22no—
136#103×C37—22no—
137#103×C37—41no—
138#103×C37D414yes—
139#102×C37—22no—
140#102×C37—22no—
141C22⋊C8×C37—22no—
142C22⋊C8×C37—22no—
143C4×C8×C37—22no—
144#95×C37—21no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37D411yescharacteristic
149#95×C37D411yescharacteristic
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152#41×C37—44no—
153#41×C37—44no—
154#41×C37—44no—
155#41×C37—44no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—21no—
159C2×Q8×C37—21no—
160C2×Q8×C37—21no—
161C2×Q8×C37—21no—
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37—21no—
165C2×Q8×C37—21no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×Q8×C37—21no—
169C2×Q8×C37—21no—
170C2×Q8×C37C2×D412yes—
171C2×Q8×C37C2×D412yes—
172C2×Q8×C37C2×D412yes—
173C2×Q8×C37#4112yes—
174C2×D4×C37—24no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—42no—
181C2×D4×C37—42no—
182C2×D4×C37#4112yes—
183C22×C4×C37—21no—
184C22×C4×C37—24no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—42no—
198C22×C4×C37—42no—
199C22×C4×C37C2×D411yescharacteristic
200C22×C4×C37C2×D411yescharacteristic
201C22×C4×C37C2×D411yescharacteristic
202C22×C4×C37C2×D411yescharacteristic
203C22×C4×C37C2×D411yescharacteristic
204C22×C4×C37C2411yescharacteristic
205Q16×C37—28no—
206Q16×C37—44no—
207SD16×C37—44no—
208SD16×C37—44no—
209C2×C8×C37—21no—
210C2×C8×C37—21no—
211C2×C8×C37—21no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37C2×D412yes—
220C2×C8×C37C2×D412yes—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—21no—
225C4⋊C4×C37—21no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—42no—
229C4⋊C4×C37—42no—
230C4⋊C4×C37—42no—
231C4⋊C4×C37—42no—
232C4⋊C4×C37—42no—
233C4⋊C4×C37—42no—
234C4⋊C4×C37—42no—
235C4⋊C4×C37—42no—
236C4⋊C4×C37C2×D412yes—
237C22⋊C4×C37—22no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—42no—
240C22⋊C4×C37—42no—
241C22⋊C4×C37—42no—
242C22⋊C4×C37—42no—
243C22⋊C4×C37—81no—
244C22⋊C4×C37—81no—
245C22⋊C4×C37—81no—
246C42×C37—21no—
247C42×C37—21no—
248C42×C37—21no—
249C42×C37—21no—
250C42×C37—42no—
251C42×C37—42no—
252C42×C37—42no—
253C23×C37—21no—
254C23×C37—22no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—41no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37C22×D411yescharacteristic
268Q8×C37—22no—
269Q8×C37—22no—
270Q8×C37—22no—
271Q8×C37—22no—
272Q8×C37—22no—
273Q8×C37—41no—
274Q8×C37—41no—
275Q8×C37—41no—
276Q8×C37—41no—
277Q8×C37—41no—
278Q8×C37—41no—
279Q8×C37#12114yes—
280D4×C37—22no—
281D4×C37—22no—
282D4×C37—48no—
283D4×C37—41no—
284D4×C37—41no—
285C2×C4×C37—22no—
286C2×C4×C37—21no—
287C2×C4×C37—21no—
288C2×C4×C37—22no—
289C2×C4×C37—22no—
290C2×C4×C37—21no—
291C2×C4×C37—21no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—22no—
296C2×C4×C37—22no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—48no—
304C2×C4×C37—41no—
305C2×C4×C37—41no—
306C2×C4×C37—41no—
307C2×C4×C37—41no—
308C2×C4×C37—41no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37#13512yes—
325C2×C4×C37#13712yes—
326C2×C4×C37C22×D411yescharacteristic
327C2×C4×C37C22×D411yescharacteristic
328C2×C4×C37C2×#4111yescharacteristic
329C2×C4×C37C2×#4111yescharacteristic
330C2×C4×C37H(5,𝔽2)11yescharacteristic
331C2×C4×C37H(5,𝔽2)11yescharacteristic
332C8×C37—22no—
333C8×C37—22no—
334C8×C37—41no—
335C8×C37—41no—
336#25151C3711yesmaximal, characteristic, direct product factor, Sylow
337C22×C37—41no—
338C22×C37—42no—
339C22×C37—41no—
340C22×C37—42no—
341C22×C37—42no—
342C22×C37—41no—
343C22×C37—41no—
344C22×C37—41no—
345C22×C37—41no—
346C22×C37—41no—
347C22×C37—81no—
348C22×C37—81no—
349C22×C37—81no—
350C22×C37—81no—
351C22×C37#52511yescharacteristic
352C22×C37D4211yescharacteristic
353C22×C37D4211yescharacteristic
354C22×C37C2×#13511yescharacteristic
355C22×C37C2×#13711yescharacteristic
356C22×C37#57711yescharacteristic
357C22×C37#57811yescharacteristic
358C4×C37—24no—
359C4×C37—22no—
360C4×C37—22no—
361C4×C37—41no—
362C4×C37—42no—
363C4×C37—41no—
364C4×C37—41no—
365C4×C37—42no—
366C4×C37—81no—
367C4×C37—81no—
368C4×C37—81no—
369C4×C37—81no—
370C4×C37C2×#12111yescharacteristic
371C4×C37#53811yescharacteristic
372C4×C37#54611yescharacteristic
373C4×C37#54611yescharacteristic
374C2×#462C2×C3711yescharacteristic, complemented
375C2×#452C2×C3711yescharacteristic
376C2×#452C2×C3711yescharacteristic
377C2×C4×Q16C2×C3711yescharacteristic, complemented
378#2429C2×C3711yescharacteristic, complemented
379#2341C2×C3711yescharacteristic
380#2067C2×C3711yescharacteristic, complemented
381#2036C2×C3711yescharacteristic, complemented
382#2035C2×C3711yescharacteristic, complemented
383#2013C2×C3711yescharacteristic, complemented
384#1968C2×C3711yescharacteristic, complemented
385#1923C2×C3711yescharacteristic, complemented
386#1880C2×C3711yescharacteristic, complemented
387#1878C2×C3711yescharacteristic, complemented
388#1865C2×C3711yescharacteristic, complemented
389C2×C37—81no—
390C2×C37—82no—
391C2×C37#242411yescharacteristic
392C2×C37#310711yescharacteristic
393C2×C37#312011yescharacteristic
394C2×C37#327011yescharacteristic
395C2×C37#327811yescharacteristic
396C2×C37#328411yescharacteristic
397C2×C37#328511yescharacteristic
398C22×#41C22×C3711yescharacteristic
399C22×Q16C22×C3711yescharacteristic
400C22×Q16C22×C3711yescharacteristic
401C22×SD16C22×C3711yescharacteristic
402C22×SD16C22×C3711yescharacteristic
403C2×C4⋊Q8C22×C3711yescharacteristic
404C2×C22⋊Q8C22×C3711yescharacteristic
405C2×C22⋊Q8C22×C3711yescharacteristic
406C2×C4×Q8C22×C3711yescharacteristic
407C2×C4×Q8C22×C3711yescharacteristic
408C2×C4×Q8C22×C3711yescharacteristic
409#462—24no—
410#452—24no—
411#452—24no—
412C4×Q16—24no—
413C2×#107C22×C3711yescharacteristic
414C2×#106C22×C3711yescharacteristic
415C2×C4⋊C8C22×C3711yescharacteristic
416C2×#103C22×C3711yescharacteristic
417C2×#103C22×C3711yescharacteristic
418C2×#103C22×C3711yescharacteristic
419C2×#103C22×C3711yescharacteristic
420C2×#103C22×C3711yescharacteristic
421C2×#103C22×C3711yescharacteristic
422C2×#102C22×C3711yescharacteristic
423C2×#102C22×C3711yescharacteristic
424C2×C22⋊C8C22×C3711yescharacteristic
425C2×C22⋊C8C22×C3711yescharacteristic
426C2×C4×C8C22×C3711yescharacteristic
427#398—21no—
428#396—21no—
429#391C22×C3711yescharacteristic
430#390—21no—
431#390—21no—
432#390C22×C3711yescharacteristic
433#390C22×C3711yescharacteristic
434#389—21no—
435#389C22×C3711yescharacteristic
436#388—21no—
437#380—21no—
438#380C22×C3711yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4C22×C3711yescharacteristic
441#340C22×C3711yescharacteristic
442#340C22×C3711yescharacteristic
443#336C22×C3711yescharacteristic
444#336C22×C3711yescharacteristic
445C37#2515111yescharacteristic, direct product factor, Sylow
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C22×Q8C23×C3711yescharacteristic
453C22×Q8C23×C3711yescharacteristic
454C22×Q8C23×C3711yescharacteristic
455C22×D4—21no—
456C22×D4C23×C3711yescharacteristic
457C23×C4—21no—
458C23×C4C23×C3711yescharacteristic
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×Q16—22no—
464C2×Q16D4×C3714yes—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—41no—
470C2×SD16—41no—
471C22×C8C23×C3711yescharacteristic
472C22×C8C23×C3711yescharacteristic
473C22×C8C23×C3711yescharacteristic
474C22×C8C23×C3711yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8—41no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—41no—
480C22⋊Q8—41no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—41no—
485C4×Q8—41no—
486C4×Q8—41no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C3711yescharacteristic
496C2×C4⋊C4C23×C3711yescharacteristic
497C2×C4⋊C4C23×C3711yescharacteristic
498C2×C4⋊C4C23×C3711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4D4×C3711yescharacteristic
507C2×C22⋊C4D4×C3711yescharacteristic
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42C23×C3711yescharacteristic
512C2×C42C23×C3711yescharacteristic
513#107—22no—
514#106—41no—
515C4⋊C8—22no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103—22no—
520#103—41no—
521#103D4×C3714yes—
522#102—22no—
523#102—22no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C4×C8—22no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C3711yescharacteristic
532#95D4×C3711yescharacteristic
533C24—21no—
534C24C2×D4×C3711yescharacteristic
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×D4×C3712yes—
554C2×Q8C2×D4×C3712yes—
555C2×Q8C2×D4×C3712yes—
556C2×Q8#41×C3712yes—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4#41×C3712yes—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4C2×D4×C3711yescharacteristic
583C22×C4C2×D4×C3711yescharacteristic
584C22×C4C2×D4×C3711yescharacteristic
585C22×C4C2×D4×C3711yescharacteristic
586C22×C4C2×D4×C3711yescharacteristic
587C22×C4C24×C3711yescharacteristic
588Q16—28no—
589Q16—44no—
590SD16—44no—
591SD16—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×D4×C3712yes—
603C2×C8C2×D4×C3712yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4C2×D4×C3712yes—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—42no—
634C42—42no—
635C42—42no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C22×D4×C3711yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8#121×C3714yes—
663D4—22no—
664D4—22no—
665D4—48no—
666D4—41no—
667D4—41no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—48no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4#135×C3712yes—
708C2×C4#137×C3712yes—
709C2×C4C22×D4×C3711yescharacteristic
710C2×C4C22×D4×C3711yescharacteristic
711C2×C4C2×#41×C3711yescharacteristic
712C2×C4C2×#41×C3711yescharacteristic
713C2×C4H(5,𝔽2)×C3711yescharacteristic
714C2×C4H(5,𝔽2)×C3711yescharacteristic
715C8—22no—
716C8—22no—
717C8—41no—
718C8—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C37×#52511yescharacteristic
734C22D42×C3711yescharacteristic
735C22D42×C3711yescharacteristic
736C22C2×#135×C3711yescharacteristic
737C22C2×#137×C3711yescharacteristic
738C22C37×#57711yescharacteristic
739C22C37×#57811yescharacteristic
740C4—24no—
741C4—22no—
742C4—22no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4C2×#121×C3711yescharacteristic
753C4C37×#53811yescharacteristic
754C4C37×#54611yescharacteristic
755C4C37×#54611yescharacteristic
756C2—81no—
757C2—82no—
758C2C37×#242411yescharacteristic
759C2C37×#310711yescharacteristic
760C2C37×#312011yescharacteristic
761C2C37×#327011yescharacteristic
762C2C37×#327811yescharacteristic
763C2C37×#328411yescharacteristic
764C2C37×#328511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×#41×C37C22
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×#462C2semidirect
4. C2×C4×Q16×C37C2semidirect
5. C37×#2429C2semidirect
7. C37×#2067C2semidirect
8. C37×#2036C2semidirect
9. C37×#2035C2semidirect
10. C37×#2013C2semidirect
11. C37×#1968C2semidirect
12. C37×#1923C2semidirect
13. C37×#1880C2semidirect
14. C37×#1878C2semidirect
15. C37×#1865C2semidirect
336. #25151C37direct (N × H)
374. C2×#462C2×C37semidirect
377. C2×C4×Q16C2×C37semidirect
378. #2429C2×C37semidirect
380. #2067C2×C37semidirect
381. #2036C2×C37semidirect
382. #2035C2×C37semidirect
383. #2013C2×C37semidirect
384. #1968C2×C37semidirect
385. #1923C2×C37semidirect
386. #1880C2×C37semidirect
387. #1878C2×C37semidirect
388. #1865C2×C37semidirect
445. C37#25151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4622
C2×C37×#4522
C2×C4×Q16×C372
C37×#24292
C37×#23412
C37×#20672
C37×#20362
C37×#20352
C37×#20132
C37×#19682
C37×#19232
C37×#18802
C37×#18782
C37×#18652
#2515137