Finite Group Databasebeta

← C37×#33347 #22654600

Subgroups — C37×#33347 #22654600

Order 9472.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3449C211yesmaximal, characteristic
2C2×C37×#413C211yesmaximal, characteristic, complemented
3C2×C37×#410C211yesmaximal, characteristic, complemented
4C37×#2123C212yesmaximal, complemented
5C37×#2122C212yesmaximal, complemented
6C37×#2121C214yesmaximal, complemented
7C37×#2120C214yesmaximal, complemented
8C22×#41×C37C411yescharacteristic, complemented
9C22×#41×C37C2211yescharacteristic
10C22×M16×C37—21no—
11C37×#537—21no—
12C37×#537—21no—
13C37×#536—21no—
14C37×#536C411yescharacteristic, complemented
15C37×#536C2211yescharacteristic
16C37×#535—21no—
17C37×#535C411yescharacteristic, complemented
18C37×#535C2211yescharacteristic
19C37×#534C412yescomplemented
20C37×#534C2212yes—
21C37×#532—21no—
22C37×#532—21no—
23C37×#525—21no—
24C37×#525—21no—
25C37×#525C412yescomplemented
26C37×#525C2212yes—
27C2×#117×C37—21no—
28C2×#117×C37C411yescharacteristic, complemented
29C37×#413—21no—
30C37×#413—21no—
31C37×#413C2212yes—
32C37×#413C2212yes—
33C2×#101×C37—21no—
34C2×#100×C37C2212yes—
35C37×#410—21no—
36C37×#410—21no—
37C37×#410C2212yes—
38C37×#410C2212yes—
39C2×#99×C37—21no—
40C2×#99×C37C2212yes—
41C37×#352C2218yescomplemented
42C37×AΣL(1,𝔽16)C2218yescomplemented
43C2×#41×C37—21no—
44C2×#41×C37—21no—
45C2×#41×C37—21no—
46C2×#41×C37—21no—
47C2×#41×C37—41no—
48C2×#41×C37—41no—
49C2×#41×C37—41no—
50C2×#41×C37—41no—
51C2×#41×C37—41no—
52C2×#41×C37—41no—
53C2×#41×C37—41no—
54C2×#41×C37—41no—
55C2×#41×C37C2×C411yescharacteristic
56C2×#41×C37C2×C411yescharacteristic
57C2×#41×C37D411yescharacteristic
58C2×#41×C37D411yescharacteristic
59C2×#41×C37D411yescharacteristic
60C2×#41×C37D411yescharacteristic
61C2×#41×C37C2311yescharacteristic
62C2×#41×C37C2311yescharacteristic
63C22×Q8×C37C2×C411yescharacteristic, complemented
64C22×Q8×C37D411yescharacteristic
65C22×D4×C37C2×C411yescharacteristic
66C22×D4×C37C2×C412yes—
67C22×D4×C37C2×C411yescharacteristic, complemented
68C22×D4×C37D411yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C23×C4×C37C2×C411yescharacteristic
71C23×C4×C37C2×C412yescomplemented
72C23×C4×C37D411yescharacteristic
73C23×C4×C37D411yescharacteristic
74C2×M16×C37—22no—
75C2×M16×C37—22no—
76C2×M16×C37—22no—
77C2×M16×C37—41no—
78C2×M16×C37—41no—
79C2×M16×C37—41no—
80C22×C8×C37—41no—
81C4⋊Q8×C37—21no—
82C4⋊Q8×C37—21no—
83#127×C37—21no—
84#127×C37—21no—
85#124×C37—21no—
86#124×C37—21no—
87#124×C37—21no—
88#124×C37—21no—
89#123×C37—22no—
90#123×C37—22no—
91#123×C37C2×C412yes—
92#123×C37C2×C412yescomplemented
93#123×C37C2×C412yescomplemented
94#123×C37C2312yes—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37—21no—
100C22⋊Q8×C37—21no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37—22no—
105#121×C37—22no—
106#121×C37—22no—
107#121×C37—21no—
108#121×C37—21no—
109#121×C37—21no—
110#121×C37—21no—
111#120×C37—22no—
112#120×C37—22no—
113#120×C37C2×C412yes—
114#120×C37C2×C412yescomplemented
115#120×C37C2×C412yescomplemented
116#120×C37C2312yes—
117C4×D4×C37—22no—
118C4×D4×C37—22no—
119C4×D4×C37—22no—
120C4×D4×C37—22no—
121#117×C37—21no—
122#117×C37—21no—
123#117×C37—22no—
124#117×C37—22no—
125#117×C37—41no—
126#117×C37—41no—
127#117×C37C2×C412yescomplemented
128#117×C37C2×C411yescharacteristic, complemented
129#117×C37C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C37—21no—
131C2×C4⋊C4×C37—41no—
132C2×C22⋊C4×C37—22no—
133C2×C22⋊C4×C37C2×C412yes—
134C2×C42×C37—21no—
135C2×C42×C37—41no—
136#101×C37—22no—
137#101×C37—22no—
138#100×C37—22no—
139#100×C37C2314yes—
140#99×C37—22no—
141#99×C37—22no—
142#99×C37—22no—
143#99×C37C2314yes—
144C24×C37C22⋊C411yescharacteristic
145C24×C37C22×C411yescharacteristic
146C24×C37C22×C412yes—
147C24×C37C2×D411yescharacteristic
148#41×C37—41no—
149#41×C37—41no—
150#41×C37—41no—
151#41×C37—41no—
152#41×C37—41no—
153#41×C37—41no—
154#41×C37—41no—
155#41×C37—41no—
156#41×C37—41no—
157#41×C37—41no—
158#41×C37—41no—
159#41×C37—41no—
160#41×C37—41no—
161#41×C37—41no—
162#41×C37—41no—
163#41×C37—41no—
164#41×C37—42no—
165#41×C37—42no—
166#41×C37—42no—
167#41×C37—42no—
168#41×C37—42no—
169#41×C37—42no—
170#41×C37—41no—
171#41×C37—41no—
172#41×C37—41no—
173#41×C37—41no—
174C2×Q8×C37—21no—
175C2×Q8×C37—21no—
176C2×Q8×C37—41no—
177C2×Q8×C37—41no—
178C2×Q8×C37—41no—
179C2×Q8×C37—41no—
180C2×Q8×C37C22⋊C411yescharacteristic
181C2×Q8×C37C22⋊C411yescharacteristic
182C2×Q8×C37C2×D411yescharacteristic
183C2×Q8×C37C2×D411yescharacteristic
184C2×D4×C37—22no—
185C2×D4×C37—22no—
186C2×D4×C37—22no—
187C2×D4×C37—22no—
188C2×D4×C37—22no—
189C2×D4×C37—22no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—41no—
193C2×D4×C37—41no—
194C2×D4×C37—41no—
195C2×D4×C37—41no—
196C2×D4×C37—41no—
197C2×D4×C37—41no—
198C2×D4×C37—41no—
199C2×D4×C37—41no—
200C2×D4×C37—42no—
201C2×D4×C37—42no—
202C2×D4×C37C22⋊C411yescharacteristic
203C2×D4×C37C22⋊C411yescharacteristic
204C2×D4×C37C22⋊C411yescharacteristic
205C2×D4×C37C22⋊C411yescharacteristic
206C2×D4×C37C22×C411yescharacteristic
207C2×D4×C37C22×C411yescharacteristic
208C2×D4×C37C22×C411yescharacteristic
209C2×D4×C37C2×D411yescharacteristic
210C2×D4×C37C2×D411yescharacteristic
211C2×D4×C37C2×D411yescharacteristic
212C2×D4×C37C2×D411yescharacteristic
213C2×D4×C37C2411yescharacteristic
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—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—22no—
227C22×C4×C37—22no—
228C22×C4×C37—22no—
229C22×C4×C37—42no—
230C22×C4×C37—42no—
231C22×C4×C37—42no—
232C22×C4×C37C22⋊C411yescharacteristic
233C22×C4×C37C22⋊C411yescharacteristic
234C22×C4×C37C22⋊C411yescharacteristic
235C22×C4×C37C22⋊C411yescharacteristic
236C22×C4×C37C22⋊C411yescharacteristic
237C22×C4×C37C22⋊C411yescharacteristic
238C22×C4×C37C22⋊C411yescharacteristic
239C22×C4×C37C22⋊C411yescharacteristic
240C22×C4×C37C22⋊C411yescharacteristic
241C22×C4×C37C22×C411yescharacteristic
242C22×C4×C37C22×C411yescharacteristic
243C22×C4×C37C22×C412yes—
244C22×C4×C37C2×D411yescharacteristic
245C22×C4×C37C2×D411yescharacteristic
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249M16×C37—24no—
250M16×C37—42no—
251M16×C37—42no—
252M16×C37—42no—
253C2×C8×C37—42no—
254C2×C8×C37—42no—
255C2×C8×C37—42no—
256C4⋊C4×C37—22no—
257C4⋊C4×C37—21no—
258C4⋊C4×C37—21no—
259C4⋊C4×C37—22no—
260C4⋊C4×C37—22no—
261C4⋊C4×C37—22no—
262C4⋊C4×C37—22no—
263C4⋊C4×C37—42no—
264C4⋊C4×C37—42no—
265C22⋊C4×C37—22no—
266C22⋊C4×C37—22no—
267C22⋊C4×C37—22no—
268C22⋊C4×C37—22no—
269C22⋊C4×C37—22no—
270C22⋊C4×C37—22no—
271C22⋊C4×C37—22no—
272C22⋊C4×C37—22no—
273C22⋊C4×C37—22no—
274C22⋊C4×C37—24no—
275C22⋊C4×C37—42no—
276C22⋊C4×C37C22×C412yes—
277C22⋊C4×C37C22×C412yes—
278C42×C37—22no—
279C42×C37—21no—
280C42×C37—21no—
281C42×C37—42no—
282C42×C37—42no—
283C23×C37—21no—
284C23×C37—21no—
285C23×C37—21no—
286C23×C37—21no—
287C23×C37—21no—
288C23×C37—21no—
289C23×C37—22no—
290C23×C37—42no—
291C23×C37—81no—
292C23×C37—81no—
293C23×C37—81no—
294C23×C37—82no—
295C23×C37C2×C22⋊C411yescharacteristic
296C23×C37C2×C22⋊C411yescharacteristic
297C23×C37C2×C22⋊C411yescharacteristic
298C23×C37C2×C22⋊C411yescharacteristic
299C23×C37C2×C22⋊C411yescharacteristic
300C23×C37C23×C411yescharacteristic
301C23×C37C22×D411yescharacteristic
302Q8×C37—41no—
303Q8×C37—41no—
304Q8×C37—41no—
305Q8×C37—41no—
306Q8×C37—42no—
307Q8×C37—41no—
308Q8×C37—41no—
309D4×C37—41no—
310D4×C37—41no—
311D4×C37—41no—
312D4×C37—41no—
313D4×C37—41no—
314D4×C37—41no—
315D4×C37—41no—
316D4×C37—41no—
317D4×C37—41no—
318D4×C37—41no—
319D4×C37—41no—
320D4×C37—41no—
321D4×C37—42no—
322D4×C37—44no—
323D4×C37—42no—
324D4×C37—42no—
325D4×C37—41no—
326D4×C37—41no—
327D4×C37—82no—
328D4×C37—82no—
329D4×C37—82no—
330D4×C37—82no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—21no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—21no—
339C2×C4×C37—21no—
340C2×C4×C37—21no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—21no—
354C2×C4×C37—21no—
355C2×C4×C37—21no—
356C2×C4×C37—21no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—21no—
360C2×C4×C37—21no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—22no—
364C2×C4×C37—44no—
365C2×C4×C37—42no—
366C2×C4×C37—42no—
367C2×C4×C37—42no—
368C2×C4×C37—44no—
369C2×C4×C37—82no—
370C2×C4×C37—84no—
371C2×C4×C37#9911yescharacteristic
372C2×C4×C37#9911yescharacteristic
373C2×C4×C37#9911yescharacteristic
374C2×C4×C37#9911yescharacteristic
375C2×C4×C37C2×C22⋊C411yescharacteristic
376C2×C4×C37C2×C22⋊C411yescharacteristic
377C2×C4×C37C2×C22⋊C411yescharacteristic
378C2×C4×C37C2×C22⋊C411yescharacteristic
379C2×C4×C37C2×C22⋊C411yescharacteristic
380C2×C4×C37C2×C22⋊C411yescharacteristic
381C2×C4×C37C2×C22⋊C411yescharacteristic
382C2×C4×C37C22×D411yescharacteristic
383C8×C37—44no—
384#33347C3711yesmaximal, characteristic, direct product factor, Sylow
385C22×C37—21no—
386C22×C37—21no—
387C22×C37—21no—
388C22×C37—21no—
389C22×C37—21no—
390C22×C37—21no—
391C22×C37—41no—
392C22×C37—41no—
393C22×C37—41no—
394C22×C37—41no—
395C22×C37—41no—
396C22×C37—41no—
397C22×C37—41no—
398C22×C37—42no—
399C22×C37—42no—
400C22×C37—42no—
401C22×C37—42no—
402C22×C37—42no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37—81no—
406C22×C37—81no—
407C22×C37—84no—
408C22×C37C2×#9911yescharacteristic
409C22×C37C2×#9911yescharacteristic
410C22×C37C22×C22⋊C411yescharacteristic
411C4×C37—21no—
412C4×C37—21no—
413C4×C37—21no—
414C4×C37—21no—
415C4×C37—21no—
416C4×C37—21no—
417C4×C37—42no—
418C4×C37—42no—
419C4×C37—42no—
420C4×C37—84no—
421C4×C37C2×#9911yescharacteristic
422C4×C37C2×#9911yescharacteristic
423C4×C37C2×#9911yescharacteristic
424C4×C37C2×#9911yescharacteristic
425#3449C2×C3711yescharacteristic
426C2×#413C2×C3711yescharacteristic, complemented
427C2×#410C2×C3711yescharacteristic, complemented
428#2123C2×C3712yescomplemented
429#2122C2×C3712yescomplemented
430#2121C2×C3714yescomplemented
431#2120C2×C3714yescomplemented
432C2×C37—21no—
433C2×C37—21no—
434C2×C37—21no—
435C2×C37—41no—
436C2×C37—41no—
437C2×C37—41no—
438C2×C37—41no—
439C2×C37—41no—
440C2×C37—41no—
441C2×C37—82no—
442C2×C37C22×#9911yescharacteristic
443C22×#41C4×C3711yescharacteristic, complemented
444C22×#41C22×C3711yescharacteristic
445C22×M16—21no—
446#537—21no—
447#537—21no—
448#536—21no—
449#536C4×C3711yescharacteristic, complemented
450#536C22×C3711yescharacteristic
451#535—21no—
452#535C4×C3711yescharacteristic, complemented
453#535C22×C3711yescharacteristic
454#534C4×C3712yescomplemented
455#534C22×C3712yes—
456#532—21no—
457#532—21no—
458#525—21no—
459#525—21no—
460#525C4×C3712yescomplemented
461#525C22×C3712yes—
462C2×#117—21no—
463C2×#117C4×C3711yescharacteristic, complemented
464#413—21no—
465#413—21no—
466#413C22×C3712yes—
467#413C22×C3712yes—
468C2×#101—21no—
469C2×#100C22×C3712yes—
470#410—21no—
471#410—21no—
472#410C22×C3712yes—
473#410C22×C3712yes—
474C2×#99—21no—
475C2×#99C22×C3712yes—
476#352C22×C3718yescomplemented
477AΣL(1,𝔽16)C22×C3718yescomplemented
478C37#3334711yescharacteristic, direct product factor, Sylow
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C3711yescharacteristic
492C2×#41C2×C4×C3711yescharacteristic
493C2×#41D4×C3711yescharacteristic
494C2×#41D4×C3711yescharacteristic
495C2×#41D4×C3711yescharacteristic
496C2×#41D4×C3711yescharacteristic
497C2×#41C23×C3711yescharacteristic
498C2×#41C23×C3711yescharacteristic
499C22×Q8C2×C4×C3711yescharacteristic, complemented
500C22×Q8D4×C3711yescharacteristic
501C22×D4C2×C4×C3711yescharacteristic
502C22×D4C2×C4×C3712yes—
503C22×D4C2×C4×C3711yescharacteristic, complemented
504C22×D4D4×C3711yescharacteristic
505C22×D4C23×C3711yescharacteristic
506C23×C4C2×C4×C3711yescharacteristic
507C23×C4C2×C4×C3712yescomplemented
508C23×C4D4×C3711yescharacteristic
509C23×C4D4×C3711yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C3712yes—
528#123C2×C4×C3712yescomplemented
529#123C2×C4×C3712yescomplemented
530#123C23×C3712yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C3712yes—
550#120C2×C4×C3712yescomplemented
551#120C2×C4×C3712yescomplemented
552#120C23×C3712yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C3712yescomplemented
564#117C2×C4×C3711yescharacteristic, complemented
565#117C2×C4×C3711yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C3712yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C3714yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C3714yes—
580C24C22⋊C4×C3711yescharacteristic
581C24C22×C4×C3711yescharacteristic
582C24C22×C4×C3712yes—
583C24C2×D4×C3711yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C3711yescharacteristic
617C2×Q8C22⋊C4×C3711yescharacteristic
618C2×Q8C2×D4×C3711yescharacteristic
619C2×Q8C2×D4×C3711yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C3711yescharacteristic
639C2×D4C22⋊C4×C3711yescharacteristic
640C2×D4C22⋊C4×C3711yescharacteristic
641C2×D4C22⋊C4×C3711yescharacteristic
642C2×D4C22×C4×C3711yescharacteristic
643C2×D4C22×C4×C3711yescharacteristic
644C2×D4C22×C4×C3711yescharacteristic
645C2×D4C2×D4×C3711yescharacteristic
646C2×D4C2×D4×C3711yescharacteristic
647C2×D4C2×D4×C3711yescharacteristic
648C2×D4C2×D4×C3711yescharacteristic
649C2×D4C24×C3711yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C3711yescharacteristic
669C22×C4C22⋊C4×C3711yescharacteristic
670C22×C4C22⋊C4×C3711yescharacteristic
671C22×C4C22⋊C4×C3711yescharacteristic
672C22×C4C22⋊C4×C3711yescharacteristic
673C22×C4C22⋊C4×C3711yescharacteristic
674C22×C4C22⋊C4×C3711yescharacteristic
675C22×C4C22⋊C4×C3711yescharacteristic
676C22×C4C22⋊C4×C3711yescharacteristic
677C22×C4C22×C4×C3711yescharacteristic
678C22×C4C22×C4×C3711yescharacteristic
679C22×C4C22×C4×C3712yes—
680C22×C4C2×D4×C3711yescharacteristic
681C22×C4C2×D4×C3711yescharacteristic
682C22×C4C2×D4×C3711yescharacteristic
683C22×C4C2×D4×C3711yescharacteristic
684C22×C4C2×D4×C3711yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C3712yes—
713C22⋊C4C22×C4×C3712yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C3711yescharacteristic
732C23C2×C22⋊C4×C3711yescharacteristic
733C23C2×C22⋊C4×C3711yescharacteristic
734C23C2×C22⋊C4×C3711yescharacteristic
735C23C2×C22⋊C4×C3711yescharacteristic
736C23C23×C4×C3711yescharacteristic
737C23C22×D4×C3711yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C3711yescharacteristic
808C2×C4#99×C3711yescharacteristic
809C2×C4#99×C3711yescharacteristic
810C2×C4#99×C3711yescharacteristic
811C2×C4C2×C22⋊C4×C3711yescharacteristic
812C2×C4C2×C22⋊C4×C3711yescharacteristic
813C2×C4C2×C22⋊C4×C3711yescharacteristic
814C2×C4C2×C22⋊C4×C3711yescharacteristic
815C2×C4C2×C22⋊C4×C3711yescharacteristic
816C2×C4C2×C22⋊C4×C3711yescharacteristic
817C2×C4C2×C22⋊C4×C3711yescharacteristic
818C2×C4C22×D4×C3711yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C3711yescharacteristic
844C22C2×#99×C3711yescharacteristic
845C22C22×C22⋊C4×C3711yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C3711yescharacteristic
857C4C2×#99×C3711yescharacteristic
858C4C2×#99×C3711yescharacteristic
859C4C2×#99×C3711yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C3711yescharacteristic
subgroupG/H
centerC4×C37C2×#99
commutatorC23C23×C4×C37
Frattini, cosocleC2×D4C24×C37
socleC2×C37C22×#99
prime radicalC37×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C37 ◁ C22×C4×C37 ◁ C22×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#413C2semidirect
3. C2×C37×#410C2semidirect
4. C37×#2123C2semidirect
5. C37×#2122C2semidirect
6. C37×#2121C2semidirect
7. C37×#2120C2semidirect
8. C22×#41×C37C4semidirect
14. C37×#536C4semidirect
17. C37×#535C4semidirect
19. C37×#534C4semidirect
25. C37×#525C4semidirect
28. C2×#117×C37C4semidirect
41. C37×#352C22semidirect
42. C37×AΣL(1,𝔽16)C22semidirect
63. C22×Q8×C37C2×C4semidirect
67. C22×D4×C37C2×C4semidirect
71. C23×C4×C37C2×C4semidirect
92. #123×C37C2×C4semidirect
93. #123×C37C2×C4semidirect
114. #120×C37C2×C4semidirect
115. #120×C37C2×C4semidirect
127. #117×C37C2×C4semidirect
128. #117×C37C2×C4semidirect
129. #117×C37C2×C4semidirect
384. #33347C37direct (N × H)
426. C2×#413C2×C37semidirect
427. C2×#410C2×C37semidirect
428. #2123C2×C37semidirect
429. #2122C2×C37semidirect
430. #2121C2×C37semidirect
431. #2120C2×C37semidirect
443. C22×#41C4×C37semidirect
449. #536C4×C37semidirect
452. #535C4×C37semidirect
454. #534C4×C37semidirect
460. #525C4×C37semidirect
463. C2×#117C4×C37semidirect
476. #352C22×C37semidirect
477. AΣL(1,𝔽16)C22×C37semidirect
478. C37#33347direct (N × H)
499. C22×Q8C2×C4×C37semidirect
503. C22×D4C2×C4×C37semidirect
507. C23×C4C2×C4×C37semidirect
528. #123C2×C4×C37semidirect
529. #123C2×C4×C37semidirect
550. #120C2×C4×C37semidirect
551. #120C2×C4×C37semidirect
563. #117C2×C4×C37semidirect
564. #117C2×C4×C37semidirect
565. #117C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34492
C2×C37×#4132
C2×C37×#4102
C37×#21232
C37×#21222
C37×#21212
C37×#21202
#3334737