Finite Group Databasebeta

← C37×#18415 #22639668

Subgroups — C37×#18415 #22639668

Order 9472.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3534C211yesmaximal, characteristic
2C37×#3196C211yesmaximal, characteristic, complemented
3C37×#3187C211yesmaximal, characteristic, complemented
4C37×#2663C211yesmaximal, characteristic, complemented
5C37×#1618C211yesmaximal, characteristic, complemented
6C37×#1616C211yesmaximal, characteristic, complemented
7C37×#1615C211yesmaximal, characteristic, complemented
8C37×#1613C211yesmaximal, characteristic, complemented
9C37×#1606C211yesmaximal, characteristic, complemented
10C37×#1604C211yesmaximal, characteristic, complemented
11C37×#1603C211yesmaximal, characteristic, complemented
12C37×#1601C211yesmaximal, characteristic, complemented
13C37×#1507C211yesmaximal, characteristic, complemented
14C37×#1501C211yesmaximal, characteristic, complemented
15C37×#1468C211yesmaximal, characteristic, complemented
16C37×#562—21no—
17C37×#560—21no—
18C37×#553—21no—
19C37×#551—21no—
20C37×#546—21no—
21C37×#546—21no—
22C37×#546—21no—
23D42×C37—21no—
24C37×#540—21no—
25C37×#539—21no—
26C37×#539C2211yescharacteristic
27C37×#538—21no—
28C37×#538C2211yescharacteristic
29C37×#537C2211yescharacteristic
30C37×#534—21no—
31C37×#534C2211yescharacteristic
32C37×#525C2211yescharacteristic
33C2×#123×C37C2211yescharacteristic
34C2×C22⋊Q8×C37C2211yescharacteristic, complemented
35C2×#121×C37C2211yescharacteristic
36C37×#485—21no—
37C37×#484C2211yescharacteristic, complemented
38C37×#483—21no—
39C37×#481C2211yescharacteristic
40C37×#481C2211yescharacteristic, complemented
41C37×#481C2211yescharacteristic, complemented
42C37×#470—21no—
43C37×#468—21no—
44C37×#465—21no—
45C37×#465—21no—
46C37×#452—21no—
47C37×#451C2211yescharacteristic, complemented
48C37×#450—21no—
49C37×#448C2211yescharacteristic
50C37×#448C2211yescharacteristic, complemented
51C37×#448C2211yescharacteristic, complemented
52C37×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#400C2211yescharacteristic, complemented
55C37×#399C2211yescharacteristic, complemented
56C37×#397—21no—
57C37×#395C2211yescharacteristic, complemented
58C37×#394—21no—
59C37×#393C2211yescharacteristic, complemented
60C37×#389—21no—
61C37×#388—21no—
62C4×C22⋊C4×C37C2211yescharacteristic, complemented
63C37×#328C2211yescharacteristic, complemented
64C37×#328C2211yescharacteristic, complemented
65C37×#327C2211yescharacteristic
66C37×#327C2211yescharacteristic
67C37×#327C2211yescharacteristic, complemented
68C37×#327C2211yescharacteristic, complemented
69C37×#327C2211yescharacteristic, complemented
70C37×#327C2211yescharacteristic, complemented
71C37×#324C2211yescharacteristic, complemented
72C37×#324C2211yescharacteristic, complemented
73C37×#323C2211yescharacteristic, complemented
74C37×#323C2211yescharacteristic, complemented
75C2×#41×C37—21no—
76C2×#41×C37D411yescharacteristic
77C22×Q8×C37C2311yescharacteristic
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37D411yescharacteristic
82C22×D4×C37D411yescharacteristic
83C23×C4×C37C2311yescharacteristic
84C2×Q16×C37—21no—
85C2×SD16×C37—21no—
86C2×SD16×C37—21no—
87C2×SD16×C37—21no—
88C2×M16×C37—21no—
89C22×C8×C37—21no—
90#127×C37—21no—
91#126×C37—21no—
92#126×C37—21no—
93#126×C37—21no—
94#126×C37—21no—
95#125×C37—21no—
96#125×C37—21no—
97#124×C37—21no—
98#124×C37—21no—
99#124×C37—21no—
100#123×C37—21no—
101#123×C37—21no—
102#123×C37—21no—
103#123×C37—21no—
104#123×C37—21no—
105#123×C37—21no—
106#123×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—
114C22⋊Q8×C37—21no—
115C22⋊Q8×C37—21no—
116C22⋊Q8×C37—21no—
117C22⋊Q8×C37—21no—
118C22⋊Q8×C37—21no—
119C22⋊Q8×C37—21no—
120C22⋊Q8×C37—21no—
121C22⋊Q8×C37—21no—
122C22⋊Q8×C37—21no—
123C22⋊Q8×C37D411yescharacteristic
124C22⋊Q8×C37C2311yescharacteristic
125#121×C37—21no—
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—21no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37—21no—
133#121×C37—21no—
134#121×C37—21no—
135#121×C37—21no—
136#121×C37—21no—
137#121×C37—21no—
138#121×C37—21no—
139#121×C37—21no—
140#121×C37D411yescharacteristic
141#121×C37D411yescharacteristic
142#121×C37D411yescharacteristic
143#121×C37C2311yescharacteristic
144#121×C37C2311yescharacteristic
145#121×C37C2311yescharacteristic
146#120×C37—21no—
147#120×C37—21no—
148#120×C37—21no—
149#120×C37—21no—
150#120×C37—21no—
151#120×C37—21no—
152#120×C37—21no—
153#120×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—
161C4×D4×C37—21no—
162#117×C37—21no—
163#117×C37D411yescharacteristic
164C2×C4⋊C4×C37—21no—
165C2×C4⋊C4×C37—21no—
166C2×C4⋊C4×C37—21no—
167C2×C4⋊C4×C37D411yescharacteristic
168C2×C4⋊C4×C37D411yescharacteristic
169C2×C4⋊C4×C37C2311yescharacteristic
170C2×C4⋊C4×C37C2311yescharacteristic
171C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
179C2×C22⋊C4×C37D411yescharacteristic
180C2×C22⋊C4×C37C2311yescharacteristic
181C2×C42×C37—21no—
182#107×C37—21no—
183#106×C37—21no—
184#106×C37—21no—
185#106×C37—21no—
186#103×C37—21no—
187#103×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—
194C22⋊C8×C37—21no—
195C22⋊C8×C37—21no—
196C22⋊C8×C37C2311yescharacteristic
197C22⋊C8×C37C2311yescharacteristic
198C22⋊C8×C37C2311yescharacteristic
199C22⋊C8×C37C2311yescharacteristic
200#95×C37—21no—
201#95×C37—21no—
202#95×C37—21no—
203#95×C37—21no—
204#95×C37C2311yescharacteristic
205#95×C37C2311yescharacteristic
206C24×C37—21no—
207C24×C37—21no—
208C24×C37C2×D411yescharacteristic
209C24×C37C2×D411yescharacteristic
210#41×C37—81no—
211#41×C37—81no—
212#41×C37—81no—
213C2×Q8×C37—21no—
214C2×Q8×C37—21no—
215C2×Q8×C37—21no—
216C2×Q8×C37—81no—
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—21no—
228C2×D4×C37—21no—
229C2×D4×C37—21no—
230C2×D4×C37—21no—
231C2×D4×C37—21no—
232C2×D4×C37—21no—
233C2×D4×C37—21no—
234C2×D4×C37—21no—
235C2×D4×C37—81no—
236C2×D4×C37—81no—
237C2×D4×C37—81no—
238C2×D4×C37—81no—
239C2×D4×C37—81no—
240C2×D4×C37—81no—
241C2×D4×C37—82no—
242C2×D4×C37C2×D411yescharacteristic
243C2×D4×C37C2×D411yescharacteristic
244C2×D4×C37C2×D411yescharacteristic
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—81no—
257C22×C4×C37C2×D411yescharacteristic
258C22×C4×C37C2×D411yescharacteristic
259C22×C4×C37C2×D411yescharacteristic
260C22×C4×C37C2×D411yescharacteristic
261C22×C4×C37C2×D411yescharacteristic
262C22×C4×C37C2×D411yescharacteristic
263C22×C4×C37C2×D411yescharacteristic
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2411yescharacteristic
266Q16×C37—81no—
267SD16×C37—81no—
268SD16×C37—81no—
269SD16×C37—81no—
270M16×C37—81no—
271C2×C8×C37—21no—
272C2×C8×C37—21no—
273C2×C8×C37—21no—
274C2×C8×C37—21no—
275C2×C8×C37—81no—
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—42no—
292C4⋊C4×C37—41no—
293C4⋊C4×C37—41no—
294C4⋊C4×C37—81no—
295C4⋊C4×C37C2×D411yescharacteristic
296C4⋊C4×C37C2×D411yescharacteristic
297C4⋊C4×C37C2×D411yescharacteristic
298C4⋊C4×C37C2×D411yescharacteristic
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—21no—
321C22⋊C4×C37—21no—
322C22⋊C4×C37—21no—
323C22⋊C4×C37—21no—
324C22⋊C4×C37—42no—
325C22⋊C4×C37—42no—
326C22⋊C4×C37—41no—
327C22⋊C4×C37—41no—
328C22⋊C4×C37—81no—
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—21no—
340C23×C37—21no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—42no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—81no—
347C23×C37—81no—
348C23×C37—81no—
349C23×C37—81no—
350C23×C37—81no—
351C23×C37#12011yescharacteristic
352C23×C37#12011yescharacteristic
353C23×C37C22×D411yescharacteristic
354Q8×C37—41no—
355Q8×C37—41no—
356Q8×C37—41no—
357Q8×C37—41no—
358Q8×C37—41no—
359Q8×C37—81no—
360D4×C37—41no—
361D4×C37—41no—
362D4×C37—41no—
363D4×C37—42no—
364D4×C37—42no—
365D4×C37—41no—
366D4×C37—41no—
367D4×C37—41no—
368D4×C37—41no—
369D4×C37—41no—
370D4×C37—41no—
371D4×C37—81no—
372D4×C37—81no—
373D4×C37—81no—
374D4×C37—81no—
375D4×C37—81no—
376D4×C37—81no—
377D4×C37—81no—
378D4×C37—81no—
379D4×C37—81no—
380D4×C37—81no—
381D4×C37—81no—
382D4×C37—81no—
383C2×C4×C37—22no—
384C2×C4×C37—21no—
385C2×C4×C37—21no—
386C2×C4×C37—21no—
387C2×C4×C37—21no—
388C2×C4×C37—21no—
389C2×C4×C37—21no—
390C2×C4×C37—21no—
391C2×C4×C37—21no—
392C2×C4×C37—21no—
393C2×C4×C37—21no—
394C2×C4×C37—41no—
395C2×C4×C37—41no—
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—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37—41no—
409C2×C4×C37—41no—
410C2×C4×C37—41no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37—81no—
414C2×C4×C37—81no—
415C2×C4×C37—81no—
416C2×C4×C37—81no—
417C2×C4×C37—81no—
418C2×C4×C37—81no—
419C2×C4×C37—81no—
420C2×C4×C37#12011yescharacteristic
421C2×C4×C37#12011yescharacteristic
422C2×C4×C37C22×D411yescharacteristic
423C2×C4×C37C22×D411yescharacteristic
424C8×C37—41no—
425C8×C37—41no—
426C8×C37—41no—
427C8×C37—41no—
428#18415C3711yesmaximal, characteristic, direct product factor, Sylow
429C22×C37—21no—
430C22×C37—21no—
431C22×C37—21no—
432C22×C37—21no—
433C22×C37—21no—
434C22×C37—21no—
435C22×C37—21no—
436C22×C37—21no—
437C22×C37—41no—
438C22×C37—41no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—41no—
443C22×C37—41no—
444C22×C37—41no—
445C22×C37—41no—
446C22×C37—41no—
447C22×C37—41no—
448C22×C37—41no—
449C22×C37—81no—
450C22×C37—81no—
451C22×C37—81no—
452C22×C37—81no—
453C22×C37—162no—
454C22×C37—162no—
455C22×C37C2×#12011yescharacteristic
456C22×C37#57711yescharacteristic
457C22×C37#57711yescharacteristic
458C4×C37—21no—
459C4×C37—21no—
460C4×C37—21no—
461C4×C37—21no—
462C4×C37—42no—
463C4×C37—41no—
464C4×C37—41no—
465C4×C37—41no—
466C4×C37—41no—
467C4×C37—41no—
468C4×C37—41no—
469C4×C37—41no—
470C4×C37—41no—
471C4×C37—81no—
472C4×C37—81no—
473C4×C37—81no—
474#3534C2×C3711yescharacteristic
475#3196C2×C3711yescharacteristic, complemented
476#3187C2×C3711yescharacteristic, complemented
477#2663C2×C3711yescharacteristic, complemented
478#1618C2×C3711yescharacteristic, complemented
479#1616C2×C3711yescharacteristic, complemented
480#1615C2×C3711yescharacteristic, complemented
481#1613C2×C3711yescharacteristic, complemented
482#1606C2×C3711yescharacteristic, complemented
483#1604C2×C3711yescharacteristic, complemented
484#1603C2×C3711yescharacteristic, complemented
485#1601C2×C3711yescharacteristic, complemented
486#1507C2×C3711yescharacteristic, complemented
487#1501C2×C3711yescharacteristic, complemented
488#1468C2×C3711yescharacteristic, complemented
489C2×C37—21no—
490C2×C37—21no—
491C2×C37—41no—
492C2×C37—41no—
493C2×C37—81no—
494C2×C37—81no—
495C2×C37—81no—
496C2×C37—81no—
497C2×C37#300911yescharacteristic
498C2×C37#301811yescharacteristic
499C2×C37#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C3711yescharacteristic
511#538—21no—
512#538C22×C3711yescharacteristic
513#537C22×C3711yescharacteristic
514#534—21no—
515#534C22×C3711yescharacteristic
516#525C22×C3711yescharacteristic
517C2×#123C22×C3711yescharacteristic
518C2×C22⋊Q8C22×C3711yescharacteristic, complemented
519C2×#121C22×C3711yescharacteristic
520#485—21no—
521#484C22×C3711yescharacteristic, complemented
522#483—21no—
523#481C22×C3711yescharacteristic
524#481C22×C3711yescharacteristic, complemented
525#481C22×C3711yescharacteristic, complemented
526#470—21no—
527#468—21no—
528#465—21no—
529#465—21no—
530#452—21no—
531#451C22×C3711yescharacteristic, complemented
532#450—21no—
533#448C22×C3711yescharacteristic
534#448C22×C3711yescharacteristic, complemented
535#448C22×C3711yescharacteristic, complemented
536#407C22×C3711yescharacteristic, complemented
537C2×C22⋊C8C22×C3711yescharacteristic, complemented
538#400C22×C3711yescharacteristic, complemented
539#399C22×C3711yescharacteristic, complemented
540#397—21no—
541#395C22×C3711yescharacteristic, complemented
542#394—21no—
543#393C22×C3711yescharacteristic, complemented
544#389—21no—
545#388—21no—
546C4×C22⋊C4C22×C3711yescharacteristic, complemented
547#328C22×C3711yescharacteristic, complemented
548#328C22×C3711yescharacteristic, complemented
549#327C22×C3711yescharacteristic
550#327C22×C3711yescharacteristic
551#327C22×C3711yescharacteristic, complemented
552#327C22×C3711yescharacteristic, complemented
553#327C22×C3711yescharacteristic, complemented
554#327C22×C3711yescharacteristic, complemented
555#324C22×C3711yescharacteristic, complemented
556#324C22×C3711yescharacteristic, complemented
557#323C22×C3711yescharacteristic, complemented
558#323C22×C3711yescharacteristic, complemented
559C37#1841511yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C3711yescharacteristic
562C22×Q8C23×C3711yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C3711yescharacteristic
567C22×D4D4×C3711yescharacteristic
568C23×C4C23×C3711yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—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—
596#123—21no—
597#123—21no—
598#123—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⋊Q8D4×C3711yescharacteristic
609C22⋊Q8C23×C3711yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
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#121—21no—
625#121D4×C3711yescharacteristic
626#121D4×C3711yescharacteristic
627#121D4×C3711yescharacteristic
628#121C23×C3711yescharacteristic
629#121C23×C3711yescharacteristic
630#121C23×C3711yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C3711yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C3711yescharacteristic
653C2×C4⋊C4D4×C3711yescharacteristic
654C2×C4⋊C4C23×C3711yescharacteristic
655C2×C4⋊C4C23×C3711yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C3711yescharacteristic
664C2×C22⋊C4D4×C3711yescharacteristic
665C2×C22⋊C4C23×C3711yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C3711yescharacteristic
682C22⋊C8C23×C3711yescharacteristic
683C22⋊C8C23×C3711yescharacteristic
684C22⋊C8C23×C3711yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C3711yescharacteristic
690#95C23×C3711yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C3711yescharacteristic
694C24C2×D4×C3711yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C3711yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C3711yescharacteristic
728C2×D4C2×D4×C3711yescharacteristic
729C2×D4C2×D4×C3711yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C3711yescharacteristic
743C22×C4C2×D4×C3711yescharacteristic
744C22×C4C2×D4×C3711yescharacteristic
745C22×C4C2×D4×C3711yescharacteristic
746C22×C4C2×D4×C3711yescharacteristic
747C22×C4C2×D4×C3711yescharacteristic
748C22×C4C2×D4×C3711yescharacteristic
749C22×C4C2×D4×C3711yescharacteristic
750C22×C4C24×C3711yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C3711yescharacteristic
781C4⋊C4C2×D4×C3711yescharacteristic
782C4⋊C4C2×D4×C3711yescharacteristic
783C4⋊C4C2×D4×C3711yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C3711yescharacteristic
837C23#120×C3711yescharacteristic
838C23C22×D4×C3711yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C3711yescharacteristic
906C2×C4#120×C3711yescharacteristic
907C2×C4C22×D4×C3711yescharacteristic
908C2×C4C22×D4×C3711yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C3711yescharacteristic
940C22C37×#57711yescharacteristic
941C22C37×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C37×#300911yescharacteristic
967C2C37×#301811yescharacteristic
968C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3534C2
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
2. C37×#3196C2semidirect
3. C37×#3187C2semidirect
4. C37×#2663C2semidirect
5. C37×#1618C2semidirect
6. C37×#1616C2semidirect
7. C37×#1615C2semidirect
8. C37×#1613C2semidirect
9. C37×#1606C2semidirect
10. C37×#1604C2semidirect
11. C37×#1603C2semidirect
12. C37×#1601C2semidirect
13. C37×#1507C2semidirect
14. C37×#1501C2semidirect
15. C37×#1468C2semidirect
34. C2×C22⋊Q8×C37C22semidirect
37. C37×#484C22semidirect
40. C37×#481C22semidirect
41. C37×#481C22semidirect
47. C37×#451C22semidirect
50. C37×#448C22semidirect
51. C37×#448C22semidirect
52. C37×#407C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C37×#400C22semidirect
55. C37×#399C22semidirect
57. C37×#395C22semidirect
59. C37×#393C22semidirect
62. C4×C22⋊C4×C37C22semidirect
63. C37×#328C22semidirect
64. C37×#328C22semidirect
67. C37×#327C22semidirect
68. C37×#327C22semidirect
69. C37×#327C22semidirect
70. C37×#327C22semidirect
71. C37×#324C22semidirect
72. C37×#324C22semidirect
73. C37×#323C22semidirect
74. C37×#323C22semidirect
428. #18415C37direct (N × H)
475. #3196C2×C37semidirect
476. #3187C2×C37semidirect
477. #2663C2×C37semidirect
478. #1618C2×C37semidirect
479. #1616C2×C37semidirect
480. #1615C2×C37semidirect
481. #1613C2×C37semidirect
482. #1606C2×C37semidirect
483. #1604C2×C37semidirect
484. #1603C2×C37semidirect
485. #1601C2×C37semidirect
486. #1507C2×C37semidirect
487. #1501C2×C37semidirect
488. #1468C2×C37semidirect
518. C2×C22⋊Q8C22×C37semidirect
521. #484C22×C37semidirect
524. #481C22×C37semidirect
525. #481C22×C37semidirect
531. #451C22×C37semidirect
534. #448C22×C37semidirect
535. #448C22×C37semidirect
536. #407C22×C37semidirect
537. C2×C22⋊C8C22×C37semidirect
538. #400C22×C37semidirect
539. #399C22×C37semidirect
541. #395C22×C37semidirect
543. #393C22×C37semidirect
546. C4×C22⋊C4C22×C37semidirect
547. #328C22×C37semidirect
548. #328C22×C37semidirect
551. #327C22×C37semidirect
552. #327C22×C37semidirect
553. #327C22×C37semidirect
554. #327C22×C37semidirect
555. #324C22×C37semidirect
556. #324C22×C37semidirect
557. #323C22×C37semidirect
558. #323C22×C37semidirect
559. C37#18415direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35342
C37×#31962
C37×#31872
C37×#26632
C37×#16182
C37×#16162
C37×#16152
C37×#16132
C37×#16062
C37×#16042
C37×#16032
C37×#16012
C37×#15072
C37×#15012
C37×#14682
#1841537