Finite Group Databasebeta

← C37×#18225 #22639478

Subgroups — C37×#18225 #22639478

Order 9472.

1194 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3534C211yesmaximal, characteristic
2C37×#3004C211yesmaximal, characteristic, complemented
3C2×C37×#448C211yesmaximal, characteristic, complemented
4C37×#2614C211yesmaximal, characteristic, complemented
5C37×#1606C212yesmaximal, complemented
6C37×#1604C212yesmaximal, complemented
7C37×#1603C212yesmaximal, complemented
8C37×#1601C212yesmaximal, complemented
9C37×#1516C211yesmaximal, characteristic, complemented
10C37×#1510C211yesmaximal, characteristic, complemented
11C37×#1468C211yesmaximal, characteristic, complemented
12C23×Q8×C37C2211yescharacteristic, complemented
13C2×#137×C37—21no—
14C22×SD16×C37—21no—
15C37×#562—21no—
16C37×#560—21no—
17C37×#553—21no—
18C37×#551—21no—
19C37×#546—21no—
20C37×#546—21no—
21C37×#546—21no—
22D42×C37—21no—
23C37×#540—21no—
24C37×#539—21no—
25C37×#539C2211yescharacteristic
26C37×#538—21no—
27C37×#538C2211yescharacteristic
28C37×#537C2211yescharacteristic
29C37×#534—21no—
30C37×#534C2211yescharacteristic
31C37×#525C2211yescharacteristic
32C2×#123×C37—21no—
33C2×#123×C37C2211yescharacteristic
34C2×#121×C37C2211yescharacteristic
35C37×#451—21no—
36C37×#451C2212yescomplemented
37C37×#448—21no—
38C37×#448—21no—
39C37×#448—21no—
40C37×#448C2212yes—
41C37×#448C2212yescomplemented
42C37×#448C2212yescomplemented
43C37×#419—21no—
44C2×#103×C37—21no—
45C37×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C37C2211yescharacteristic, complemented
47C37×#395—21no—
48C37×#395C2212yescomplemented
49C37×#393—21no—
50C37×#393C2212yescomplemented
51C37×#381—21no—
52C37×#381C2211yescharacteristic, complemented
53C37×#328C2212yescomplemented
54C37×#327C2212yes—
55C37×#327C2212yescomplemented
56C37×#327C2212yescomplemented
57C37×#324C2212yescomplemented
58C37×#323C2212yescomplemented
59C2×#41×C37—21no—
60C2×#41×C37D411yescharacteristic
61C22×Q8×C37—21no—
62C22×Q8×C37—21no—
63C22×Q8×C37—21no—
64C22×Q8×C37—21no—
65C22×Q8×C37—21no—
66C22×Q8×C37—44no—
67C22×Q8×C37C2312yes—
68C22×D4×C37—21no—
69C22×D4×C37—21no—
70C22×D4×C37—21no—
71C22×D4×C37D411yescharacteristic
72C22×D4×C37D411yescharacteristic
73C23×C4×C37—21no—
74C23×C4×C37C2311yescharacteristic
75#137×C37—44no—
76C2×Q16×C37—22no—
77C2×SD16×C37—22no—
78C2×SD16×C37—22no—
79C2×SD16×C37—22no—
80C2×SD16×C37—44no—
81C2×M16×C37—21no—
82C22×C8×C37—21no—
83#127×C37—21no—
84#126×C37—21no—
85#126×C37—21no—
86#126×C37—21no—
87#126×C37—21no—
88#125×C37—21no—
89#125×C37—21no—
90#124×C37—21no—
91#124×C37—21no—
92#124×C37—21no—
93#123×C37—21no—
94#123×C37—21no—
95#123×C37—21no—
96#123×C37—21no—
97#123×C37—21no—
98#123×C37—21no—
99#123×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—44no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37—21no—
113C22⋊Q8×C37D411yescharacteristic
114C22⋊Q8×C37C2311yescharacteristic
115#121×C37—21no—
116#121×C37—21no—
117#121×C37—21no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37—21no—
125#121×C37—21no—
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—21no—
130#121×C37D411yescharacteristic
131#121×C37D411yescharacteristic
132#121×C37D411yescharacteristic
133#121×C37C2311yescharacteristic
134#121×C37C2311yescharacteristic
135#121×C37C2311yescharacteristic
136#120×C37—21no—
137#120×C37—21no—
138#120×C37—21no—
139#120×C37—21no—
140#120×C37—21no—
141#120×C37—21no—
142#120×C37—21no—
143#120×C37—21no—
144C4×D4×C37—21no—
145C4×D4×C37—21no—
146C4×D4×C37—21no—
147C4×D4×C37—21no—
148C4×D4×C37—21no—
149C4×D4×C37—21no—
150C4×D4×C37—21no—
151C4×D4×C37—21no—
152#117×C37—21no—
153#117×C37D411yescharacteristic
154C2×C4⋊C4×C37—22no—
155C2×C4⋊C4×C37D411yescharacteristic
156C2×C4⋊C4×C37D411yescharacteristic
157C2×C4⋊C4×C37C2311yescharacteristic
158C2×C22⋊C4×C37—21no—
159C2×C22⋊C4×C37—21no—
160C2×C22⋊C4×C37—21no—
161C2×C22⋊C4×C37—21no—
162C2×C22⋊C4×C37—22no—
163C2×C22⋊C4×C37D411yescharacteristic
164C2×C22⋊C4×C37D411yescharacteristic
165C2×C22⋊C4×C37C2311yescharacteristic
166#103×C37—22no—
167#103×C37—22no—
168#103×C37—22no—
169#103×C37—22no—
170C22⋊C8×C37—21no—
171C22⋊C8×C37—21no—
172C22⋊C8×C37C2312yes—
173C22⋊C8×C37C2312yes—
174#95×C37—22no—
175#95×C37—22no—
176#95×C37—21no—
177#95×C37C2312yes—
178C24×C37—21no—
179C24×C37—21no—
180C24×C37C2×D411yescharacteristic
181C24×C37C2×D411yescharacteristic
182#41×C37—42no—
183#41×C37—82no—
184C2×Q8×C37—21no—
185C2×Q8×C37—24no—
186C2×Q8×C37—24no—
187C2×Q8×C37—22no—
188C2×Q8×C37—22no—
189C2×Q8×C37—44no—
190C2×Q8×C37—42no—
191C2×Q8×C37—42no—
192C2×Q8×C37—44no—
193C2×Q8×C37—44no—
194C2×Q8×C37—44no—
195C2×Q8×C37—41no—
196C2×Q8×C37—41no—
197C2×Q8×C37C2×D411yescharacteristic
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—21no—
213C2×D4×C37—21no—
214C2×D4×C37—21no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—82no—
218C2×D4×C37—82no—
219C2×D4×C37—82no—
220C2×D4×C37C2×D411yescharacteristic
221C2×D4×C37C2×D411yescharacteristic
222C2×D4×C37C2×D411yescharacteristic
223C22×C4×C37—24no—
224C22×C4×C37—22no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—22no—
233C22×C4×C37—42no—
234C22×C4×C37—42no—
235C22×C4×C37—41no—
236C22×C4×C37—41no—
237C22×C4×C37C2×D411yescharacteristic
238C22×C4×C37C2×D411yescharacteristic
239C22×C4×C37C2×D411yescharacteristic
240C22×C4×C37C2×D411yescharacteristic
241C22×C4×C37C2×D411yescharacteristic
242C22×C4×C37C2×D411yescharacteristic
243C22×C4×C37C2×D411yescharacteristic
244C22×C4×C37C2×D411yescharacteristic
245C22×C4×C37C2411yescharacteristic
246Q16×C37—44no—
247SD16×C37—44no—
248SD16×C37—44no—
249SD16×C37—44no—
250M16×C37—42no—
251C2×C8×C37—22no—
252C2×C8×C37—22no—
253C2×C8×C37—42no—
254C4⋊C4×C37—21no—
255C4⋊C4×C37—21no—
256C4⋊C4×C37—21no—
257C4⋊C4×C37—21no—
258C4⋊C4×C37—21no—
259C4⋊C4×C37—21no—
260C4⋊C4×C37—21no—
261C4⋊C4×C37—21no—
262C4⋊C4×C37—21no—
263C4⋊C4×C37—21no—
264C4⋊C4×C37—21no—
265C4⋊C4×C37—21no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—44no—
268C4⋊C4×C37C2×D411yescharacteristic
269C4⋊C4×C37C2×D411yescharacteristic
270C4⋊C4×C37C2×D411yescharacteristic
271C4⋊C4×C37C2×D411yescharacteristic
272C22⋊C4×C37—21no—
273C22⋊C4×C37—21no—
274C22⋊C4×C37—21no—
275C22⋊C4×C37—21no—
276C22⋊C4×C37—21no—
277C22⋊C4×C37—21no—
278C22⋊C4×C37—21no—
279C22⋊C4×C37—21no—
280C22⋊C4×C37—21no—
281C22⋊C4×C37—21no—
282C22⋊C4×C37—21no—
283C22⋊C4×C37—21no—
284C22⋊C4×C37—21no—
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—21no—
292C22⋊C4×C37—21no—
293C22⋊C4×C37—21no—
294C22⋊C4×C37—21no—
295C22⋊C4×C37—21no—
296C22⋊C4×C37—21no—
297C22⋊C4×C37—44no—
298C22⋊C4×C37—42no—
299C42×C37—21no—
300C42×C37—21no—
301C42×C37—21no—
302C23×C37—22no—
303C23×C37—22no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—22no—
309C23×C37—41no—
310C23×C37—41no—
311C23×C37—41no—
312C23×C37—42no—
313C23×C37—81no—
314C23×C37—81no—
315C23×C37—81no—
316C23×C37—81no—
317C23×C37—81no—
318C23×C37#12011yescharacteristic
319C23×C37#12011yescharacteristic
320C23×C37C22×D411yescharacteristic
321Q8×C37—24no—
322Q8×C37—24no—
323Q8×C37—41no—
324Q8×C37—42no—
325Q8×C37—42no—
326Q8×C37—44no—
327Q8×C37—44no—
328Q8×C37—81no—
329D4×C37—41no—
330D4×C37—41no—
331D4×C37—41no—
332D4×C37—42no—
333D4×C37—42no—
334D4×C37—42no—
335D4×C37—42no—
336D4×C37—42no—
337D4×C37—81no—
338D4×C37—81no—
339D4×C37—81no—
340D4×C37—81no—
341D4×C37—81no—
342D4×C37—81no—
343D4×C37—81no—
344D4×C37—81no—
345D4×C37—81no—
346D4×C37—81no—
347D4×C37—81no—
348D4×C37—81no—
349C2×C4×C37—22no—
350C2×C4×C37—22no—
351C2×C4×C37—24no—
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—22no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—42no—
366C2×C4×C37—44no—
367C2×C4×C37—42no—
368C2×C4×C37—44no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
371C2×C4×C37—42no—
372C2×C4×C37—42no—
373C2×C4×C37—42no—
374C2×C4×C37—81no—
375C2×C4×C37—81no—
376C2×C4×C37—81no—
377C2×C4×C37—81no—
378C2×C4×C37—81no—
379C2×C4×C37—81no—
380C2×C4×C37—81no—
381C2×C4×C37#12011yescharacteristic
382C2×C4×C37#12011yescharacteristic
383C2×C4×C37C22×D411yescharacteristic
384C2×C4×C37C22×D411yescharacteristic
385C8×C37—42no—
386C8×C37—42no—
387#18225C3711yesmaximal, characteristic, direct product factor, Sylow
388C22×C37—21no—
389C22×C37—21no—
390C22×C37—21no—
391C22×C37—21no—
392C22×C37—21no—
393C22×C37—21no—
394C22×C37—21no—
395C22×C37—44no—
396C22×C37—41no—
397C22×C37—41no—
398C22×C37—41no—
399C22×C37—41no—
400C22×C37—41no—
401C22×C37—41no—
402C22×C37—41no—
403C22×C37—41no—
404C22×C37—41no—
405C22×C37—41no—
406C22×C37—41no—
407C22×C37—41no—
408C22×C37—82no—
409C22×C37—162no—
410C22×C37—162no—
411C22×C37B(4,𝔽2)12yes—
412C22×C37C2×#12011yescharacteristic
413C22×C37#57712yes—
414C4×C37—21no—
415C4×C37—21no—
416C4×C37—21no—
417C4×C37—21no—
418C4×C37—41no—
419C4×C37—41no—
420C4×C37—41no—
421C4×C37—41no—
422C4×C37—41no—
423C4×C37—41no—
424C4×C37—44no—
425C4×C37—41no—
426C4×C37—41no—
427C4×C37—82no—
428#3534C2×C3711yescharacteristic
429#3004C2×C3711yescharacteristic, complemented
430C2×#448C2×C3711yescharacteristic, complemented
431#2614C2×C3711yescharacteristic, complemented
432#1606C2×C3712yescomplemented
433#1604C2×C3712yescomplemented
434#1603C2×C3712yescomplemented
435#1601C2×C3712yescomplemented
436#1516C2×C3711yescharacteristic, complemented
437#1510C2×C3711yescharacteristic, complemented
438#1468C2×C3711yescharacteristic, complemented
439C2×C37—22no—
440C2×C37—22no—
441C2×C37—41no—
442C2×C37—81no—
443C2×C37—81no—
444C2×C37—81no—
445C2×C37—81no—
446C2×C37#300911yescharacteristic
447C2×C37#302211yescharacteristic
448C2×C37C2×B(4,𝔽2)11yescharacteristic
449C23×Q8C22×C3711yescharacteristic, complemented
450C2×#137—21no—
451C22×SD16—21no—
452#562—21no—
453#560—21no—
454#553—21no—
455#551—21no—
456#546—21no—
457#546—21no—
458#546—21no—
459D42—21no—
460#540—21no—
461#539—21no—
462#539C22×C3711yescharacteristic
463#538—21no—
464#538C22×C3711yescharacteristic
465#537C22×C3711yescharacteristic
466#534—21no—
467#534C22×C3711yescharacteristic
468#525C22×C3711yescharacteristic
469C2×#123—21no—
470C2×#123C22×C3711yescharacteristic
471C2×#121C22×C3711yescharacteristic
472#451—21no—
473#451C22×C3712yescomplemented
474#448—21no—
475#448—21no—
476#448—21no—
477#448C22×C3712yes—
478#448C22×C3712yescomplemented
479#448C22×C3712yescomplemented
480#419—21no—
481C2×#103—21no—
482#407C22×C3711yescharacteristic, complemented
483C2×C22⋊C8C22×C3711yescharacteristic, complemented
484#395—21no—
485#395C22×C3712yescomplemented
486#393—21no—
487#393C22×C3712yescomplemented
488#381—21no—
489#381C22×C3711yescharacteristic, complemented
490#328C22×C3712yescomplemented
491#327C22×C3712yes—
492#327C22×C3712yescomplemented
493#327C22×C3712yescomplemented
494#324C22×C3712yescomplemented
495#323C22×C3712yescomplemented
496C37#1822511yescharacteristic, direct product factor, Sylow
497C2×#41—21no—
498C2×#41D4×C3711yescharacteristic
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8—44no—
505C22×Q8C23×C3712yes—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C3711yescharacteristic
510C22×D4D4×C3711yescharacteristic
511C23×C4—21no—
512C23×C4C23×C3711yescharacteristic
513#137—44no—
514C2×Q16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—44no—
519C2×M16—21no—
520C22×C8—21no—
521#127—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#125—21no—
527#125—21no—
528#124—21no—
529#124—21no—
530#124—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—44no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8D4×C3711yescharacteristic
552C22⋊Q8C23×C3711yescharacteristic
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121D4×C3711yescharacteristic
569#121D4×C3711yescharacteristic
570#121D4×C3711yescharacteristic
571#121C23×C3711yescharacteristic
572#121C23×C3711yescharacteristic
573#121C23×C3711yescharacteristic
574#120—21no—
575#120—21no—
576#120—21no—
577#120—21no—
578#120—21no—
579#120—21no—
580#120—21no—
581#120—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590#117—21no—
591#117D4×C3711yescharacteristic
592C2×C4⋊C4—22no—
593C2×C4⋊C4D4×C3711yescharacteristic
594C2×C4⋊C4D4×C3711yescharacteristic
595C2×C4⋊C4C23×C3711yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4D4×C3711yescharacteristic
602C2×C22⋊C4D4×C3711yescharacteristic
603C2×C22⋊C4C23×C3711yescharacteristic
604#103—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608C22⋊C8—21no—
609C22⋊C8—21no—
610C22⋊C8C23×C3712yes—
611C22⋊C8C23×C3712yes—
612#95—22no—
613#95—22no—
614#95—21no—
615#95C23×C3712yes—
616C24—21no—
617C24—21no—
618C24C2×D4×C3711yescharacteristic
619C24C2×D4×C3711yescharacteristic
620#41—42no—
621#41—82no—
622C2×Q8—21no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—42no—
629C2×Q8—42no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—41no—
634C2×Q8—41no—
635C2×Q8C2×D4×C3711yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—82no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4C2×D4×C3711yescharacteristic
659C2×D4C2×D4×C3711yescharacteristic
660C2×D4C2×D4×C3711yescharacteristic
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4C2×D4×C3711yescharacteristic
676C22×C4C2×D4×C3711yescharacteristic
677C22×C4C2×D4×C3711yescharacteristic
678C22×C4C2×D4×C3711yescharacteristic
679C22×C4C2×D4×C3711yescharacteristic
680C22×C4C2×D4×C3711yescharacteristic
681C22×C4C2×D4×C3711yescharacteristic
682C22×C4C2×D4×C3711yescharacteristic
683C22×C4C24×C3711yescharacteristic
684Q16—44no—
685SD16—44no—
686SD16—44no—
687SD16—44no—
688M16—42no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—42no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—44no—
706C4⋊C4C2×D4×C3711yescharacteristic
707C4⋊C4C2×D4×C3711yescharacteristic
708C4⋊C4C2×D4×C3711yescharacteristic
709C4⋊C4C2×D4×C3711yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
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—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—44no—
736C22⋊C4—42no—
737C42—21no—
738C42—21no—
739C42—21no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23#120×C3711yescharacteristic
757C23#120×C3711yescharacteristic
758C23C22×D4×C3711yescharacteristic
759Q8—24no—
760Q8—24no—
761Q8—41no—
762Q8—42no—
763Q8—42no—
764Q8—44no—
765Q8—44no—
766Q8—81no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784D4—81no—
785D4—81no—
786D4—81no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4#120×C3711yescharacteristic
820C2×C4#120×C3711yescharacteristic
821C2×C4C22×D4×C3711yescharacteristic
822C2×C4C22×D4×C3711yescharacteristic
823C8—42no—
824C8—42no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—44no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—82no—
846C22—162no—
847C22—162no—
848C22C37×B(4,𝔽2)12yes—
849C22C2×#120×C3711yescharacteristic
850C22C37×#57712yes—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—44no—
862C4—41no—
863C4—41no—
864C4—82no—
865C2—22no—
866C2—22no—
867C2—41no—
868C2—81no—
869C2—81no—
870C2—81no—
871C2—81no—
872C2C37×#300911yescharacteristic
873C2C37×#302211yescharacteristic
874C2C2×C37×B(4,𝔽2)11yescharacteristic
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×#3004C2semidirect
3. C2×C37×#448C2semidirect
4. C37×#2614C2semidirect
5. C37×#1606C2semidirect
6. C37×#1604C2semidirect
7. C37×#1603C2semidirect
8. C37×#1601C2semidirect
9. C37×#1516C2semidirect
10. C37×#1510C2semidirect
11. C37×#1468C2semidirect
12. C23×Q8×C37C22semidirect
36. C37×#451C22semidirect
41. C37×#448C22semidirect
42. C37×#448C22semidirect
45. C37×#407C22semidirect
46. C2×C22⋊C8×C37C22semidirect
48. C37×#395C22semidirect
50. C37×#393C22semidirect
52. C37×#381C22semidirect
53. C37×#328C22semidirect
55. C37×#327C22semidirect
56. C37×#327C22semidirect
57. C37×#324C22semidirect
58. C37×#323C22semidirect
387. #18225C37direct (N × H)
429. #3004C2×C37semidirect
430. C2×#448C2×C37semidirect
431. #2614C2×C37semidirect
432. #1606C2×C37semidirect
433. #1604C2×C37semidirect
434. #1603C2×C37semidirect
435. #1601C2×C37semidirect
436. #1516C2×C37semidirect
437. #1510C2×C37semidirect
438. #1468C2×C37semidirect
449. C23×Q8C22×C37semidirect
473. #451C22×C37semidirect
478. #448C22×C37semidirect
479. #448C22×C37semidirect
482. #407C22×C37semidirect
483. C2×C22⋊C8C22×C37semidirect
485. #395C22×C37semidirect
487. #393C22×C37semidirect
489. #381C22×C37semidirect
490. #328C22×C37semidirect
492. #327C22×C37semidirect
493. #327C22×C37semidirect
494. #324C22×C37semidirect
495. #323C22×C37semidirect
496. C37#18225direct (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×#30042
C2×C37×#4482
C37×#26142
C37×#16062
C37×#16042
C37×#16032
C37×#16012
C37×#15162
C37×#15102
C37×#14682
#1822537