Finite Group Databasebeta

← C37×#24894 #22646147

Subgroups — C37×#24894 #22646147

Order 9472.

988 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#448C211yesmaximal, characteristic
2C2×C4×SD16×C37C211yesmaximal, characteristic, complemented
3C37×#2420C211yesmaximal, characteristic
4Q8×C22⋊C4×C37C211yesmaximal, characteristic, complemented
5C37×#2097C211yesmaximal, characteristic, complemented
6C37×#2077C211yesmaximal, characteristic, complemented
7C37×#2055C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic
9C37×#1933C211yesmaximal, characteristic, complemented
10C37×#1923C211yesmaximal, characteristic, complemented
11C37×#1880C211yesmaximal, characteristic, complemented
12C37×#1877C211yesmaximal, characteristic, complemented
13C37×#1863C211yesmaximal, characteristic, complemented
14C37×#1805C211yesmaximal, characteristic, complemented
15C37×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×C4×Q8×C37C2211yescharacteristic
21C2×C4×Q8×C37C2211yescharacteristic
22C2×C4×D4×C37C2211yescharacteristic
23C37×#448—24no—
24C4×SD16×C37—24no—
25C2×#107×C37C2211yescharacteristic
26C2×#106×C37C2211yescharacteristic
27C2×C4⋊C8×C37C2211yescharacteristic
28C2×#103×C37C2211yescharacteristic
29C2×#103×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×C22⋊C8×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C4×C8×C37C2211yescharacteristic
39C37×#397—21no—
40C37×#394—21no—
41C37×#391—21no—
42C37×#391—21no—
43C37×#391C2211yescharacteristic
44C37×#391C2211yescharacteristic
45C37×#390C2211yescharacteristic
46C37×#389C2211yescharacteristic
47C37×#386—21no—
48C37×#382C2211yescharacteristic
49C37×#381—21no—
50C37×#380—21no—
51C37×#380C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C4×C22⋊C4×C37—21no—
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37—22no—
62C22×Q8×C37—22no—
63C22×Q8×C37—21no—
64C22×Q8×C37—22no—
65C22×Q8×C37—22no—
66C22×Q8×C37—41no—
67C22×Q8×C37—41no—
68C22×Q8×C37C2311yescharacteristic
69C22×Q8×C37C2311yescharacteristic
70C22×D4×C37—21no—
71C22×D4×C37C2311yescharacteristic
72C23×C4×C37—21no—
73C23×C4×C37—21no—
74C23×C4×C37C2311yescharacteristic
75C2×SD16×C37—22no—
76C2×SD16×C37—22no—
77C2×SD16×C37—22no—
78C2×SD16×C37—22no—
79C2×SD16×C37—41no—
80C2×SD16×C37D414yes—
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85#121×C37—22no—
86#121×C37—41no—
87C4×Q8×C37—22no—
88C4×Q8×C37—22no—
89C4×Q8×C37—41no—
90C4×Q8×C37—41no—
91C4×D4×C37—22no—
92C4×D4×C37—41no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37D411yescharacteristic
108C2×C22⋊C4×C37D411yescharacteristic
109C2×C42×C37—21no—
110C2×C42×C37—21no—
111C2×C42×C37C2311yescharacteristic
112C2×C42×C37C2311yescharacteristic
113#107×C37—41no—
114#106×C37—22no—
115C4⋊C8×C37—41no—
116#103×C37—22no—
117#103×C37—22no—
118#103×C37—22no—
119#103×C37—22no—
120#103×C37—22no—
121#103×C37—41no—
122#102×C37—22no—
123#102×C37—41no—
124C22⋊C8×C37—22no—
125C22⋊C8×C37—41no—
126C4×C8×C37—22no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37D411yescharacteristic
137#95×C37D411yescharacteristic
138C24×C37—21no—
139C24×C37C2×D411yescharacteristic
140C2×Q8×C37—24no—
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—42no—
150C2×Q8×C37—42no—
151C2×Q8×C37—44no—
152C2×Q8×C37—44no—
153C2×Q8×C37—44no—
154C2×Q8×C37—44no—
155C2×Q8×C37C2×D412yes—
156C2×Q8×C37#4112yes—
157C2×Q8×C37#4112yes—
158C2×Q8×C37#4112yes—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—21no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—81no—
167C2×D4×C37C2×D412yes—
168C22×C4×C37—21no—
169C22×C4×C37—24no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—42no—
183C22×C4×C37—42no—
184C22×C4×C37—42no—
185C22×C4×C37—42no—
186C22×C4×C37—81no—
187C22×C4×C37C2×D411yescharacteristic
188C22×C4×C37C2×D411yescharacteristic
189C22×C4×C37C2×D411yescharacteristic
190C22×C4×C37C2×D411yescharacteristic
191C22×C4×C37C2×D411yescharacteristic
192C22×C4×C37C2411yescharacteristic
193SD16×C37—28no—
194SD16×C37—44no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37—21no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
205C2×C8×C37—21no—
206C2×C8×C37C2×D412yes—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—42no—
218C4⋊C4×C37—42no—
219C4⋊C4×C37—81no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—22no—
222C22⋊C4×C37—42no—
223C22⋊C4×C37—42no—
224C22⋊C4×C37—42no—
225C22⋊C4×C37—81no—
226C22⋊C4×C37—81no—
227C22⋊C4×C37—81no—
228C42×C37—21no—
229C42×C37—21no—
230C42×C37—21no—
231C42×C37—21no—
232C42×C37—42no—
233C42×C37—42no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—22no—
241C23×C37—41no—
242C23×C37—41no—
243C23×C37—41no—
244C23×C37—41no—
245C23×C37—41no—
246C23×C37—41no—
247C23×C37#13512yes—
248C23×C37C22×D411yescharacteristic
249Q8×C37—22no—
250Q8×C37—22no—
251Q8×C37—22no—
252Q8×C37—22no—
253Q8×C37—22no—
254Q8×C37—48no—
255Q8×C37—41no—
256Q8×C37—41no—
257Q8×C37#12314yes—
258D4×C37—22no—
259D4×C37—22no—
260D4×C37—41no—
261D4×C37—41no—
262D4×C37—84no—
263C2×C4×C37—22no—
264C2×C4×C37—21no—
265C2×C4×C37—22no—
266C2×C4×C37—22no—
267C2×C4×C37—21no—
268C2×C4×C37—22no—
269C2×C4×C37—21no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
272C2×C4×C37—21no—
273C2×C4×C37—21no—
274C2×C4×C37—21no—
275C2×C4×C37—21no—
276C2×C4×C37—21no—
277C2×C4×C37—21no—
278C2×C4×C37—21no—
279C2×C4×C37—21no—
280C2×C4×C37—21no—
281C2×C4×C37—48no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—41no—
285C2×C4×C37—41no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—41no—
295C2×C4×C37—41no—
296C2×C4×C37—41no—
297C2×C4×C37—41no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37—41no—
301C2×C4×C37—41no—
302C2×C4×C37—41no—
303C2×C4×C37—84no—
304C2×C4×C37#13712yes—
305C2×C4×C37C22×D411yescharacteristic
306C2×C4×C37C2×#4111yescharacteristic
307C2×C4×C37C2×#4111yescharacteristic
308C2×C4×C37C2×#4111yescharacteristic
309C2×C4×C37H(5,𝔽2)11yescharacteristic
310C2×C4×C37H(5,𝔽2)11yescharacteristic
311C8×C37—22no—
312C8×C37—41no—
313C8×C37—41no—
314C8×C37—41no—
315#24894C3711yesmaximal, characteristic, direct product factor, Sylow
316C22×C37—22no—
317C22×C37—22no—
318C22×C37—22no—
319C22×C37—41no—
320C22×C37—41no—
321C22×C37—41no—
322C22×C37—41no—
323C22×C37—42no—
324C22×C37—42no—
325C22×C37—42no—
326C22×C37—81no—
327C22×C37—81no—
328C22×C37—81no—
329C22×C37—81no—
330C22×C37#52511yescharacteristic
331C22×C37D4211yescharacteristic
332C22×C37#54611yescharacteristic
333C22×C37C2×#13511yescharacteristic
334C22×C37C2×#13711yescharacteristic
335C22×C37#57711yescharacteristic
336C22×C37#57711yescharacteristic
337C4×C37—24no—
338C4×C37—22no—
339C4×C37—41no—
340C4×C37—41no—
341C4×C37—42no—
342C4×C37—41no—
343C4×C37—41no—
344C4×C37—81no—
345C4×C37—81no—
346C4×C37—81no—
347C4×C37—81no—
348C4×C37—81no—
349C4×C37C2×#12311yescharacteristic
350C4×C37#53811yescharacteristic
351C4×C37#54611yescharacteristic
352C4×C37#55111yescharacteristic
353C2×#448C2×C3711yescharacteristic
354C2×C4×SD16C2×C3711yescharacteristic, complemented
355#2420C2×C3711yescharacteristic
356Q8×C22⋊C4C2×C3711yescharacteristic, complemented
357#2097C2×C3711yescharacteristic, complemented
358#2077C2×C3711yescharacteristic, complemented
359#2055C2×C3711yescharacteristic, complemented
360#2033C2×C3711yescharacteristic
361#1933C2×C3711yescharacteristic, complemented
362#1923C2×C3711yescharacteristic, complemented
363#1880C2×C3711yescharacteristic, complemented
364#1877C2×C3711yescharacteristic, complemented
365#1863C2×C3711yescharacteristic, complemented
366#1805C2×C3711yescharacteristic, complemented
367#1787C2×C3711yescharacteristic, complemented
368C2×C37—42no—
369C2×C37—82no—
370C2×C37#241811yescharacteristic
371C2×C37#310811yescharacteristic
372C2×C37#312611yescharacteristic
373C2×C37#326611yescharacteristic
374C2×C37#328211yescharacteristic
375C2×C37#330111yescharacteristic
376C2×C37#332911yescharacteristic
377C23×Q8C22×C3711yescharacteristic
378C22×SD16C22×C3711yescharacteristic
379C22×SD16C22×C3711yescharacteristic
380C2×#121C22×C3711yescharacteristic
381C2×C4×Q8C22×C3711yescharacteristic
382C2×C4×Q8C22×C3711yescharacteristic
383C2×C4×D4C22×C3711yescharacteristic
384#448—24no—
385C4×SD16—24no—
386C2×#107C22×C3711yescharacteristic
387C2×#106C22×C3711yescharacteristic
388C2×C4⋊C8C22×C3711yescharacteristic
389C2×#103C22×C3711yescharacteristic
390C2×#103C22×C3711yescharacteristic
391C2×#103C22×C3711yescharacteristic
392C2×#103C22×C3711yescharacteristic
393C2×#103C22×C3711yescharacteristic
394C2×#103C22×C3711yescharacteristic
395C2×#102C22×C3711yescharacteristic
396C2×#102C22×C3711yescharacteristic
397C2×C22⋊C8C22×C3711yescharacteristic
398C2×C22⋊C8C22×C3711yescharacteristic
399C2×C4×C8C22×C3711yescharacteristic
400#397—21no—
401#394—21no—
402#391—21no—
403#391—21no—
404#391C22×C3711yescharacteristic
405#391C22×C3711yescharacteristic
406#390C22×C3711yescharacteristic
407#389C22×C3711yescharacteristic
408#386—21no—
409#382C22×C3711yescharacteristic
410#381—21no—
411#380—21no—
412#380C22×C3711yescharacteristic
413#380C22×C3711yescharacteristic
414C4×C22⋊C4—21no—
415C4×C22⋊C4C22×C3711yescharacteristic
416#340C22×C3711yescharacteristic
417#340C22×C3711yescharacteristic
418#340C22×C3711yescharacteristic
419#340C22×C3711yescharacteristic
420#336C22×C3711yescharacteristic
421#336C22×C3711yescharacteristic
422C37#2489411yescharacteristic, direct product factor, Sylow
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—21no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—41no—
429C22×Q8—41no—
430C22×Q8C23×C3711yescharacteristic
431C22×Q8C23×C3711yescharacteristic
432C22×D4—21no—
433C22×D4C23×C3711yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C3711yescharacteristic
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—41no—
442C2×SD16D4×C3714yes—
443C22×C8C23×C3711yescharacteristic
444C22×C8C23×C3711yescharacteristic
445C22×C8C23×C3711yescharacteristic
446C22×C8C23×C3711yescharacteristic
447#121—22no—
448#121—41no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—41no—
452C4×Q8—41no—
453C4×D4—22no—
454C4×D4—41no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4C23×C3711yescharacteristic
459C2×C4⋊C4C23×C3711yescharacteristic
460C2×C4⋊C4C23×C3711yescharacteristic
461C2×C4⋊C4C23×C3711yescharacteristic
462C2×C4⋊C4C23×C3711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C3711yescharacteristic
470C2×C22⋊C4D4×C3711yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C3711yescharacteristic
474C2×C42C23×C3711yescharacteristic
475#107—41no—
476#106—22no—
477C4⋊C8—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#102—22no—
485#102—41no—
486C22⋊C8—22no—
487C22⋊C8—41no—
488C4×C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C3711yescharacteristic
499#95D4×C3711yescharacteristic
500C24—21no—
501C24C2×D4×C3711yescharacteristic
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8C2×D4×C3712yes—
518C2×Q8#41×C3712yes—
519C2×Q8#41×C3712yes—
520C2×Q8#41×C3712yes—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4C2×D4×C3712yes—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4C2×D4×C3711yescharacteristic
550C22×C4C2×D4×C3711yescharacteristic
551C22×C4C2×D4×C3711yescharacteristic
552C22×C4C2×D4×C3711yescharacteristic
553C22×C4C2×D4×C3711yescharacteristic
554C22×C4C24×C3711yescharacteristic
555SD16—28no—
556SD16—44no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8C2×D4×C3712yes—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—42no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23#135×C3712yes—
610C23C22×D4×C3711yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—48no—
617Q8—41no—
618Q8—41no—
619Q8#123×C3714yes—
620D4—22no—
621D4—22no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4#137×C3712yes—
667C2×C4C22×D4×C3711yescharacteristic
668C2×C4C2×#41×C3711yescharacteristic
669C2×C4C2×#41×C3711yescharacteristic
670C2×C4C2×#41×C3711yescharacteristic
671C2×C4H(5,𝔽2)×C3711yescharacteristic
672C2×C4H(5,𝔽2)×C3711yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C37×#52511yescharacteristic
692C22D42×C3711yescharacteristic
693C22C37×#54611yescharacteristic
694C22C2×#135×C3711yescharacteristic
695C22C2×#137×C3711yescharacteristic
696C22C37×#57711yescharacteristic
697C22C37×#57711yescharacteristic
698C4—24no—
699C4—22no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×#123×C3711yescharacteristic
711C4C37×#53811yescharacteristic
712C4C37×#54611yescharacteristic
713C4C37×#55111yescharacteristic
714C2—42no—
715C2—82no—
716C2C37×#241811yescharacteristic
717C2C37×#310811yescharacteristic
718C2C37×#312611yescharacteristic
719C2C37×#326611yescharacteristic
720C2C37×#328211yescharacteristic
721C2C37×#330111yescharacteristic
722C2C37×#332911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×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
2. C2×C4×SD16×C37C2semidirect
4. Q8×C22⋊C4×C37C2semidirect
5. C37×#2097C2semidirect
6. C37×#2077C2semidirect
7. C37×#2055C2semidirect
9. C37×#1933C2semidirect
10. C37×#1923C2semidirect
11. C37×#1880C2semidirect
12. C37×#1877C2semidirect
13. C37×#1863C2semidirect
14. C37×#1805C2semidirect
15. C37×#1787C2semidirect
315. #24894C37direct (N × H)
354. C2×C4×SD16C2×C37semidirect
356. Q8×C22⋊C4C2×C37semidirect
357. #2097C2×C37semidirect
358. #2077C2×C37semidirect
359. #2055C2×C37semidirect
361. #1933C2×C37semidirect
362. #1923C2×C37semidirect
363. #1880C2×C37semidirect
364. #1877C2×C37semidirect
365. #1863C2×C37semidirect
366. #1805C2×C37semidirect
367. #1787C2×C37semidirect
422. C37#24894direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4482
C2×C4×SD16×C372
C37×#24202
Q8×C22⋊C4×C372
C37×#20972
C37×#20772
C37×#20552
C37×#20332
C37×#19332
C37×#19232
C37×#18802
C37×#18772
C37×#18632
C37×#18052
C37×#17872
#2489437