Finite Group Databasebeta

← C37×#18416 #22639669

Subgroups — C37×#18416 #22639669

Order 9472.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3535C211yesmaximal, characteristic, complemented
2C37×#3194C211yesmaximal, characteristic, complemented
3C37×#3187C211yesmaximal, characteristic, complemented
4C37×#2661C211yesmaximal, characteristic, complemented
5C37×#1612C211yesmaximal, characteristic, complemented
6C37×#1611C211yesmaximal, characteristic, complemented
7C37×#1609C211yesmaximal, characteristic, complemented
8C37×#1608C211yesmaximal, characteristic, complemented
9C37×#1600C211yesmaximal, characteristic, complemented
10C37×#1599C211yesmaximal, characteristic, complemented
11C37×#1597C211yesmaximal, characteristic, complemented
12C37×#1596C211yesmaximal, characteristic, complemented
13C37×#1508C211yesmaximal, characteristic, complemented
14C37×#1501C211yesmaximal, characteristic, complemented
15C37×#1468C211yesmaximal, characteristic, complemented
16C37×#563—21no—
17C37×#562—21no—
18C37×#554—21no—
19C37×#552—21no—
20C37×#551—21no—
21C37×#551—21no—
22C37×#547—21no—
23C37×#546—21no—
24C37×#544C2211yescharacteristic
25C37×#543C2211yescharacteristic
26C37×#542—21no—
27C37×#539—21no—
28C37×#539—21no—
29C37×#539C2211yescharacteristic
30C37×#538C2211yescharacteristic
31C37×#536—21no—
32C37×#525C2211yescharacteristic
33C2×#123×C37C2211yescharacteristic
34C2×C22⋊Q8×C37C2211yescharacteristic
35C2×#121×C37C2211yescharacteristic
36C37×#483C2211yescharacteristic
37C37×#483C2211yescharacteristic
38C37×#483C2211yescharacteristic
39C37×#482—21no—
40C37×#481—21no—
41C37×#480C2211yescharacteristic
42C37×#469—21no—
43C37×#468—21no—
44C37×#465—21no—
45C37×#465—21no—
46C37×#450C2211yescharacteristic
47C37×#450C2211yescharacteristic
48C37×#450C2211yescharacteristic
49C37×#449—21no—
50C37×#448—21no—
51C37×#447C2211yescharacteristic
52C37×#407C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C37×#398C2211yescharacteristic
55C37×#397C2211yescharacteristic
56C37×#394—21no—
57C37×#394C2211yescharacteristic
58C37×#392—21no—
59C37×#392C2211yescharacteristic
60C37×#390—21no—
61C37×#388—21no—
62C4×C22⋊C4×C37C2211yescharacteristic
63C37×#328C2211yescharacteristic
64C37×#328C2211yescharacteristic
65C37×#328C2211yescharacteristic
66C37×#328C2211yescharacteristic
67C37×#328C2211yescharacteristic
68C37×#328C2211yescharacteristic
69C37×#327C2211yescharacteristic
70C37×#327C2211yescharacteristic
71C37×#324C2211yescharacteristic
72C37×#324C2211yescharacteristic
73C37×#323C2211yescharacteristic
74C37×#323C2211yescharacteristic
75C2×#41×C37—21no—
76C2×#41×C37D411yescharacteristic, complemented
77C22×Q8×C37D411yescharacteristic, complemented
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37D411yescharacteristic
81C22×D4×C37C2311yescharacteristic
82C23×C4×C37C2311yescharacteristic
83C2×SD16×C37—21no—
84C2×SD16×C37—21no—
85C2×SD16×C37—21no—
86C2×D8×C37—21no—
87C2×M16×C37—21no—
88C22×C8×C37—21no—
89C4⋊Q8×C37—21no—
90C4⋊Q8×C37—21no—
91C4⋊Q8×C37—21no—
92#126×C37—21no—
93#126×C37—21no—
94#126×C37—21no—
95#126×C37—21no—
96#126×C37—21no—
97#126×C37—21no—
98#125×C37—21no—
99#125×C37—21no—
100#125×C37—21no—
101#125×C37—21no—
102#125×C37—21no—
103#124×C37—21no—
104#124×C37—21no—
105#124×C37—21no—
106#124×C37—21no—
107#123×C37—21no—
108#123×C37—21no—
109#123×C37—21no—
110#123×C37—21no—
111#123×C37—21no—
112#123×C37—21no—
113#123×C37—21no—
114#123×C37—21no—
115#123×C37—21no—
116#123×C37—21no—
117#123×C37—21no—
118#123×C37—21no—
119#123×C37—21no—
120#123×C37—21no—
121C22⋊Q8×C37—21no—
122C22⋊Q8×C37—21no—
123C22⋊Q8×C37—21no—
124C22⋊Q8×C37—21no—
125C22⋊Q8×C37—21no—
126C22⋊Q8×C37—21no—
127C22⋊Q8×C37—21no—
128C22⋊Q8×C37—21no—
129C22⋊Q8×C37—21no—
130C22⋊Q8×C37—21no—
131C22⋊Q8×C37—21no—
132C22⋊Q8×C37—21no—
133C22⋊Q8×C37—21no—
134C22⋊Q8×C37—21no—
135C22⋊Q8×C37D411yescharacteristic, complemented
136C22⋊Q8×C37D411yescharacteristic, complemented
137C22⋊Q8×C37D411yescharacteristic, complemented
138C22⋊Q8×C37C2311yescharacteristic
139C22⋊Q8×C37C2311yescharacteristic
140C22⋊Q8×C37C2311yescharacteristic
141#121×C37—21no—
142#121×C37—21no—
143#121×C37—21no—
144#121×C37—21no—
145#121×C37—21no—
146#121×C37—21no—
147#121×C37—21no—
148#121×C37—21no—
149#121×C37D411yescharacteristic, complemented
150#121×C37C2311yescharacteristic
151#120×C37—21no—
152#120×C37—21no—
153C4×Q8×C37—21no—
154C4×D4×C37—21no—
155C4×D4×C37—21no—
156C4×D4×C37—21no—
157C4×D4×C37—21no—
158C4×D4×C37—21no—
159C4×D4×C37—21no—
160C4×D4×C37—21no—
161#117×C37—21no—
162#117×C37—21no—
163#117×C37—21no—
164#117×C37D411yescharacteristic, complemented
165C2×C4⋊C4×C37—21no—
166C2×C4⋊C4×C37—21no—
167C2×C4⋊C4×C37—21no—
168C2×C4⋊C4×C37D411yescharacteristic
169C2×C4⋊C4×C37D411yescharacteristic, complemented
170C2×C4⋊C4×C37C2311yescharacteristic
171C2×C4⋊C4×C37C2311yescharacteristic
172C2×C22⋊C4×C37—21no—
173C2×C22⋊C4×C37—21no—
174C2×C22⋊C4×C37—21no—
175C2×C22⋊C4×C37—21no—
176C2×C22⋊C4×C37—21no—
177C2×C22⋊C4×C37—21no—
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—21no—
180C2×C22⋊C4×C37D411yescharacteristic
181C2×C22⋊C4×C37D411yescharacteristic
182C2×C22⋊C4×C37C2311yescharacteristic
183C2×C42×C37—21no—
184#107×C37—21no—
185#106×C37—21no—
186#106×C37—21no—
187#106×C37—21no—
188#103×C37—21no—
189#103×C37—21no—
190#103×C37—21no—
191#102×C37—21no—
192#102×C37—21no—
193#102×C37—21no—
194#102×C37—21no—
195#102×C37—21no—
196C22⋊C8×C37—21no—
197C22⋊C8×C37—21no—
198C22⋊C8×C37C2311yescharacteristic
199C22⋊C8×C37C2311yescharacteristic
200C22⋊C8×C37C2311yescharacteristic
201C22⋊C8×C37C2311yescharacteristic
202#95×C37—21no—
203#95×C37—21no—
204#95×C37C2311yescharacteristic
205#95×C37C2311yescharacteristic
206C24×C37—21no—
207C24×C37C2×D411yescharacteristic
208C24×C37C2×D411yescharacteristic
209#41×C37—82no—
210#41×C37—81no—
211C2×Q8×C37—21no—
212C2×Q8×C37—21no—
213C2×Q8×C37—21no—
214C2×Q8×C37—81no—
215C2×Q8×C37C2×D411yescharacteristic
216C2×Q8×C37C2×D411yescharacteristic
217C2×Q8×C37C2×D411yescharacteristic
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—42no—
228C2×D4×C37—41no—
229C2×D4×C37—41no—
230C2×D4×C37—81no—
231C2×D4×C37—81no—
232C2×D4×C37—81no—
233C2×D4×C37—81no—
234C2×D4×C37—81no—
235C2×D4×C37—81no—
236C2×D4×C37C2×D411yescharacteristic
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—81no—
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D411yescharacteristic
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37C2×D411yescharacteristic
253C22×C4×C37C2×D411yescharacteristic
254C22×C4×C37C2×D411yescharacteristic
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2411yescharacteristic
257SD16×C37—81no—
258SD16×C37—81no—
259SD16×C37—81no—
260D8×C37—81no—
261M16×C37—81no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—81no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—21no—
285C4⋊C4×C37—21no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—21no—
291C4⋊C4×C37—21no—
292C4⋊C4×C37—81no—
293C4⋊C4×C37C2×D411yescharacteristic
294C4⋊C4×C37C2×D411yescharacteristic
295C4⋊C4×C37C2×D411yescharacteristic
296C4⋊C4×C37C2×D411yescharacteristic
297C22⋊C4×C37—21no—
298C22⋊C4×C37—21no—
299C22⋊C4×C37—21no—
300C22⋊C4×C37—21no—
301C22⋊C4×C37—21no—
302C22⋊C4×C37—21no—
303C22⋊C4×C37—21no—
304C22⋊C4×C37—21no—
305C22⋊C4×C37—21no—
306C22⋊C4×C37—21no—
307C22⋊C4×C37—21no—
308C22⋊C4×C37—21no—
309C22⋊C4×C37—21no—
310C22⋊C4×C37—21no—
311C22⋊C4×C37—21no—
312C22⋊C4×C37—21no—
313C22⋊C4×C37—21no—
314C22⋊C4×C37—21no—
315C22⋊C4×C37—21no—
316C22⋊C4×C37—21no—
317C22⋊C4×C37—21no—
318C22⋊C4×C37—21no—
319C22⋊C4×C37—21no—
320C22⋊C4×C37—42no—
321C22⋊C4×C37—42no—
322C22⋊C4×C37—41no—
323C22⋊C4×C37—41no—
324C22⋊C4×C37—81no—
325C22⋊C4×C37—81no—
326C22⋊C4×C37—81no—
327C42×C37—21no—
328C42×C37—21no—
329C42×C37—21no—
330C42×C37—21no—
331C42×C37—21no—
332C42×C37—81no—
333C23×C37—21no—
334C23×C37—21no—
335C23×C37—21no—
336C23×C37—21no—
337C23×C37—21no—
338C23×C37—21no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—41no—
348C23×C37—41no—
349C23×C37—41no—
350C23×C37#12011yescharacteristic
351C23×C37#12011yescharacteristic
352C23×C37C22×D411yescharacteristic
353Q8×C37—41no—
354Q8×C37—41no—
355Q8×C37—41no—
356Q8×C37—81no—
357Q8×C37—81no—
358Q8×C37—81no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—41no—
362D4×C37—41no—
363D4×C37—41no—
364D4×C37—42no—
365D4×C37—42no—
366D4×C37—41no—
367D4×C37—41no—
368D4×C37—81no—
369D4×C37—81no—
370D4×C37—81no—
371D4×C37—81no—
372D4×C37—84no—
373D4×C37—82no—
374D4×C37—82no—
375C2×C4×C37—22no—
376C2×C4×C37—21no—
377C2×C4×C37—21no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—21no—
384C2×C4×C37—21no—
385C2×C4×C37—21no—
386C2×C4×C37—21no—
387C2×C4×C37—21no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—42no—
396C2×C4×C37—41no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—81no—
406C2×C4×C37—81no—
407C2×C4×C37—81no—
408C2×C4×C37—81no—
409C2×C4×C37—81no—
410C2×C4×C37—81no—
411C2×C4×C37#12011yescharacteristic
412C2×C4×C37#12011yescharacteristic
413C2×C4×C37C22×D411yescharacteristic
414C2×C4×C37C22×D411yescharacteristic
415C8×C37—41no—
416C8×C37—41no—
417C8×C37—41no—
418C8×C37—41no—
419#18416C3711yesmaximal, characteristic, direct product factor, Sylow
420C22×C37—21no—
421C22×C37—21no—
422C22×C37—21no—
423C22×C37—21no—
424C22×C37—21no—
425C22×C37—21no—
426C22×C37—21no—
427C22×C37—21no—
428C22×C37—41no—
429C22×C37—41no—
430C22×C37—41no—
431C22×C37—41no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—81no—
435C22×C37—81no—
436C22×C37—81no—
437C22×C37—81no—
438C22×C37—81no—
439C22×C37—81no—
440C22×C37—81no—
441C22×C37—81no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37C2×#12011yescharacteristic
446C22×C37#57711yescharacteristic
447C22×C37#57711yescharacteristic
448C4×C37—21no—
449C4×C37—21no—
450C4×C37—21no—
451C4×C37—21no—
452C4×C37—42no—
453C4×C37—41no—
454C4×C37—41no—
455C4×C37—41no—
456C4×C37—41no—
457C4×C37—41no—
458C4×C37—41no—
459C4×C37—41no—
460C4×C37—41no—
461C4×C37—41no—
462C4×C37—41no—
463C4×C37—81no—
464C4×C37—81no—
465#3535C2×C3711yescharacteristic, complemented
466#3194C2×C3711yescharacteristic, complemented
467#3187C2×C3711yescharacteristic, complemented
468#2661C2×C3711yescharacteristic, complemented
469#1612C2×C3711yescharacteristic, complemented
470#1611C2×C3711yescharacteristic, complemented
471#1609C2×C3711yescharacteristic, complemented
472#1608C2×C3711yescharacteristic, complemented
473#1600C2×C3711yescharacteristic, complemented
474#1599C2×C3711yescharacteristic, complemented
475#1597C2×C3711yescharacteristic, complemented
476#1596C2×C3711yescharacteristic, complemented
477#1508C2×C3711yescharacteristic, complemented
478#1501C2×C3711yescharacteristic, complemented
479#1468C2×C3711yescharacteristic, complemented
480C2×C37—21no—
481C2×C37—21no—
482C2×C37—41no—
483C2×C37—41no—
484C2×C37—81no—
485C2×C37—81no—
486C2×C37—161no—
487C2×C37#301011yescharacteristic
488C2×C37#301811yescharacteristic
489C2×C37#302611yescharacteristic
490#563—21no—
491#562—21no—
492#554—21no—
493#552—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#544C22×C3711yescharacteristic
499#543C22×C3711yescharacteristic
500#542—21no—
501#539—21no—
502#539—21no—
503#539C22×C3711yescharacteristic
504#538C22×C3711yescharacteristic
505#536—21no—
506#525C22×C3711yescharacteristic
507C2×#123C22×C3711yescharacteristic
508C2×C22⋊Q8C22×C3711yescharacteristic
509C2×#121C22×C3711yescharacteristic
510#483C22×C3711yescharacteristic
511#483C22×C3711yescharacteristic
512#483C22×C3711yescharacteristic
513#482—21no—
514#481—21no—
515#480C22×C3711yescharacteristic
516#469—21no—
517#468—21no—
518#465—21no—
519#465—21no—
520#450C22×C3711yescharacteristic
521#450C22×C3711yescharacteristic
522#450C22×C3711yescharacteristic
523#449—21no—
524#448—21no—
525#447C22×C3711yescharacteristic
526#407C22×C3711yescharacteristic
527C2×C22⋊C8C22×C3711yescharacteristic
528#398C22×C3711yescharacteristic
529#397C22×C3711yescharacteristic
530#394—21no—
531#394C22×C3711yescharacteristic
532#392—21no—
533#392C22×C3711yescharacteristic
534#390—21no—
535#388—21no—
536C4×C22⋊C4C22×C3711yescharacteristic
537#328C22×C3711yescharacteristic
538#328C22×C3711yescharacteristic
539#328C22×C3711yescharacteristic
540#328C22×C3711yescharacteristic
541#328C22×C3711yescharacteristic
542#328C22×C3711yescharacteristic
543#327C22×C3711yescharacteristic
544#327C22×C3711yescharacteristic
545#324C22×C3711yescharacteristic
546#324C22×C3711yescharacteristic
547#323C22×C3711yescharacteristic
548#323C22×C3711yescharacteristic
549C37#1841611yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41D4×C3711yescharacteristic, complemented
552C22×Q8D4×C3711yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C3711yescharacteristic
556C22×D4C23×C3711yescharacteristic
557C23×C4C23×C3711yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C3711yescharacteristic, complemented
611C22⋊Q8D4×C3711yescharacteristic, complemented
612C22⋊Q8D4×C3711yescharacteristic, complemented
613C22⋊Q8C23×C3711yescharacteristic
614C22⋊Q8C23×C3711yescharacteristic
615C22⋊Q8C23×C3711yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C3711yescharacteristic, complemented
625#121C23×C3711yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C3711yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C3711yescharacteristic
644C2×C4⋊C4D4×C3711yescharacteristic, complemented
645C2×C4⋊C4C23×C3711yescharacteristic
646C2×C4⋊C4C23×C3711yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C3711yescharacteristic
656C2×C22⋊C4D4×C3711yescharacteristic
657C2×C22⋊C4C23×C3711yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C3711yescharacteristic
674C22⋊C8C23×C3711yescharacteristic
675C22⋊C8C23×C3711yescharacteristic
676C22⋊C8C23×C3711yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C3711yescharacteristic
680#95C23×C3711yescharacteristic
681C24—21no—
682C24C2×D4×C3711yescharacteristic
683C24C2×D4×C3711yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C3711yescharacteristic
691C2×Q8C2×D4×C3711yescharacteristic
692C2×Q8C2×D4×C3711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C3711yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C3711yescharacteristic
724C22×C4C2×D4×C3711yescharacteristic
725C22×C4C2×D4×C3711yescharacteristic
726C22×C4C2×D4×C3711yescharacteristic
727C22×C4C2×D4×C3711yescharacteristic
728C22×C4C2×D4×C3711yescharacteristic
729C22×C4C2×D4×C3711yescharacteristic
730C22×C4C2×D4×C3711yescharacteristic
731C22×C4C24×C3711yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C3711yescharacteristic
769C4⋊C4C2×D4×C3711yescharacteristic
770C4⋊C4C2×D4×C3711yescharacteristic
771C4⋊C4C2×D4×C3711yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C3711yescharacteristic
826C23#120×C3711yescharacteristic
827C23C22×D4×C3711yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C3711yescharacteristic
887C2×C4#120×C3711yescharacteristic
888C2×C4C22×D4×C3711yescharacteristic
889C2×C4C22×D4×C3711yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C3711yescharacteristic
920C22C37×#57711yescharacteristic
921C22C37×#57711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C37×#301011yescharacteristic
947C2C37×#301811yescharacteristic
948C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3535C2semidirect
2. C37×#3194C2semidirect
3. C37×#3187C2semidirect
4. C37×#2661C2semidirect
5. C37×#1612C2semidirect
6. C37×#1611C2semidirect
7. C37×#1609C2semidirect
8. C37×#1608C2semidirect
9. C37×#1600C2semidirect
10. C37×#1599C2semidirect
11. C37×#1597C2semidirect
12. C37×#1596C2semidirect
13. C37×#1508C2semidirect
14. C37×#1501C2semidirect
15. C37×#1468C2semidirect
76. C2×#41×C37D4semidirect
77. C22×Q8×C37D4semidirect
135. C22⋊Q8×C37D4semidirect
136. C22⋊Q8×C37D4semidirect
137. C22⋊Q8×C37D4semidirect
149. #121×C37D4semidirect
164. #117×C37D4semidirect
169. C2×C4⋊C4×C37D4semidirect
419. #18416C37direct (N × H)
465. #3535C2×C37semidirect
466. #3194C2×C37semidirect
467. #3187C2×C37semidirect
468. #2661C2×C37semidirect
469. #1612C2×C37semidirect
470. #1611C2×C37semidirect
471. #1609C2×C37semidirect
472. #1608C2×C37semidirect
473. #1600C2×C37semidirect
474. #1599C2×C37semidirect
475. #1597C2×C37semidirect
476. #1596C2×C37semidirect
477. #1508C2×C37semidirect
478. #1501C2×C37semidirect
479. #1468C2×C37semidirect
549. C37#18416direct (N × H)
551. C2×#41D4×C37semidirect
552. C22×Q8D4×C37semidirect
610. C22⋊Q8D4×C37semidirect
611. C22⋊Q8D4×C37semidirect
612. C22⋊Q8D4×C37semidirect
624. #121D4×C37semidirect
639. #117D4×C37semidirect
644. C2×C4⋊C4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35352
C37×#31942
C37×#31872
C37×#26612
C37×#16122
C37×#16112
C37×#16092
C37×#16082
C37×#16002
C37×#15992
C37×#15972
C37×#15962
C37×#15082
C37×#15012
C37×#14682
#1841637