Finite Group Databasebeta

← C37×#29702 #22650955

Subgroups — C37×#29702 #22650955

Order 9472.

1004 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#542C211yesmaximal, characteristic
2C2×C37×#479C211yesmaximal, characteristic, complemented
3C2×C37×#478C211yesmaximal, characteristic, complemented
4C37×#2629C211yesmaximal, characteristic, complemented
5C37×#2058C211yesmaximal, characteristic, complemented
6C37×#2057C211yesmaximal, characteristic, complemented
7C37×#2042C211yesmaximal, characteristic, complemented
8C37×#2042C211yesmaximal, characteristic, complemented
9C37×#2036C211yesmaximal, characteristic, complemented
10C37×#2035C211yesmaximal, characteristic, complemented
11C37×#2034C211yesmaximal, characteristic
12C37×#2033C211yesmaximal, characteristic
13C37×#1803C211yesmaximal, characteristic, complemented
14C37×#1802C211yesmaximal, characteristic, complemented
15C37×#1798C211yesmaximal, characteristic, complemented
16C37×#542—24no—
17C37×#542—24no—
18C2×C4⋊Q8×C37C2211yescharacteristic
19C2×#126×C37—21no—
20C2×#125×C37C2211yescharacteristic
21C2×#124×C37—21no—
22C2×#124×C37C2211yescharacteristic
23C2×#123×C37—21no—
24C2×C22⋊Q8×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×C4×Q8×C37C2211yescharacteristic
28C2×C4×D4×C37C2211yescharacteristic
29C2×#117×C37C2211yescharacteristic
30C37×#479—24no—
31C37×#478—24no—
32C2×#107×C37C2211yescharacteristic
33C2×#107×C37C2211yescharacteristic
34C2×#106×C37C2211yescharacteristic
35C2×#106×C37C2211yescharacteristic
36C2×C4⋊C8×C37C2211yescharacteristic
37C2×C4⋊C8×C37C2211yescharacteristic
38C2×#103×C37C2211yescharacteristic
39C2×#103×C37C2211yescharacteristic
40C2×#103×C37C2211yescharacteristic
41C2×#103×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C37×#398—21no—
49C37×#398—21no—
50C37×#396—21no—
51C37×#396—21no—
52C37×#389C2211yescharacteristic
53C37×#389C2211yescharacteristic
54C37×#384C2211yescharacteristic
55C37×#380C2211yescharacteristic
56C37×#380C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×Q8×C37—21no—
64C22×Q8×C37C2311yescharacteristic
65C22×D4×C37—21no—
66C22×D4×C37C2311yescharacteristic
67C23×C4×C37—21no—
68C23×C4×C37C2311yescharacteristic
69C22×C8×C37C2311yescharacteristic
70C22×C8×C37C2311yescharacteristic
71C22×C8×C37C2311yescharacteristic
72C22×C8×C37C2311yescharacteristic
73C4⋊Q8×C37—22no—
74C4⋊Q8×C37—22no—
75#126×C37—28no—
76#125×C37—22no—
77#125×C37—22no—
78#124×C37—28no—
79#124×C37—22no—
80#124×C37—22no—
81#123×C37—28no—
82C22⋊Q8×C37—28no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—22no—
85#121×C37—22no—
86#121×C37—22no—
87C4×Q8×C37—22no—
88C4×Q8×C37D414yes—
89C4×D4×C37—22no—
90C4×D4×C37D414yes—
91#117×C37—22no—
92#117×C37—22no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37—21no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37—21no—
101C2×C4⋊C4×C37—21no—
102C2×C4⋊C4×C37D411yescharacteristic
103C2×C4⋊C4×C37D411yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C4⋊C4×C37C2311yescharacteristic
107C2×C4⋊C4×C37C2311yescharacteristic
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C4⋊C4×C37C2311yescharacteristic
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37D411yescharacteristic
118C2×C22⋊C4×C37D411yescharacteristic
119C2×C42×C37—21no—
120C2×C42×C37C2311yescharacteristic
121C2×C42×C37C2311yescharacteristic
122#107×C37—22no—
123#107×C37—22no—
124#106×C37—22no—
125#106×C37—22no—
126C4⋊C8×C37—22no—
127C4⋊C8×C37—22no—
128#103×C37—22no—
129#103×C37—22no—
130#103×C37—41no—
131#103×C37—41no—
132#102×C37—22no—
133#102×C37—22no—
134#102×C37—41no—
135#102×C37—41no—
136C22⋊C8×C37—41no—
137C22⋊C8×C37—41no—
138#95×C37—21no—
139#95×C37—21no—
140#95×C37—21no—
141#95×C37—21no—
142C24×C37—21no—
143C24×C37C2×D411yescharacteristic
144C2×Q8×C37—24no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37—81no—
151C2×Q8×C37—81no—
152C2×Q8×C37C2×D412yes—
153C2×D4×C37—24no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—81no—
160C2×D4×C37—81no—
161C2×D4×C37C2×D412yes—
162C22×C4×C37—21no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—24no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—81no—
177C22×C4×C37—81no—
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2×D411yescharacteristic
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183C22×C4×C37C2411yescharacteristic
184C2×C8×C37—21no—
185C2×C8×C37—21no—
186C2×C8×C37—21no—
187C2×C8×C37—21no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C4⋊C4×C37—24no—
197C4⋊C4×C37—24no—
198C4⋊C4×C37—24no—
199C4⋊C4×C37—22no—
200C4⋊C4×C37—22no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—42no—
212C4⋊C4×C37—42no—
213C4⋊C4×C37—81no—
214C4⋊C4×C37—81no—
215C4⋊C4×C37—81no—
216C4⋊C4×C37—81no—
217C4⋊C4×C37C2×D412yes—
218C4⋊C4×C37C2×D412yes—
219C22⋊C4×C37—24no—
220C22⋊C4×C37—24no—
221C22⋊C4×C37—24no—
222C22⋊C4×C37—24no—
223C22⋊C4×C37—24no—
224C22⋊C4×C37—22no—
225C22⋊C4×C37—22no—
226C22⋊C4×C37—81no—
227C22⋊C4×C37—81no—
228C42×C37—24no—
229C42×C37—21no—
230C42×C37—21no—
231C42×C37C2×D412yes—
232C42×C37C2×D412yes—
233C23×C37—21no—
234C23×C37—22no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—21no—
241C23×C37—41no—
242C23×C37—41no—
243C23×C37—41no—
244C23×C37—41no—
245C23×C37—41no—
246C23×C37—41no—
247C23×C37C22×D411yescharacteristic
248Q8×C37—22no—
249Q8×C37—22no—
250Q8×C37—41no—
251Q8×C37—41no—
252Q8×C37—84no—
253D4×C37—22no—
254D4×C37—22no—
255D4×C37—41no—
256D4×C37—41no—
257D4×C37—84no—
258C2×C4×C37—21no—
259C2×C4×C37—21no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—22no—
264C2×C4×C37—21no—
265C2×C4×C37—22no—
266C2×C4×C37—21no—
267C2×C4×C37—22no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
272C2×C4×C37—21no—
273C2×C4×C37—21no—
274C2×C4×C37—41no—
275C2×C4×C37—41no—
276C2×C4×C37—41no—
277C2×C4×C37—41no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—41no—
281C2×C4×C37—41no—
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—84no—
297C2×C4×C37#12012yes—
298C2×C4×C37#12012yes—
299C2×C4×C37C22×D411yescharacteristic
300C2×C4×C37C22×D411yescharacteristic
301C2×C4×C37H(5,𝔽2)11yescharacteristic
302C2×C4×C372−1+411yescharacteristic
303C2×C4×C372−1+411yescharacteristic
304C2×C4×C372−1+411yescharacteristic
305C8×C37—41no—
306C8×C37—41no—
307C8×C37—41no—
308C8×C37—41no—
309#29702C3711yesmaximal, characteristic, direct product factor, Sylow
310C22×C37—41no—
311C22×C37—42no—
312C22×C37—41no—
313C22×C37—41no—
314C22×C37—41no—
315C22×C37—41no—
316C22×C37—42no—
317C22×C37—41no—
318C22×C37—41no—
319C22×C37—42no—
320C22×C37—81no—
321C22×C37—81no—
322C22×C37—81no—
323C22×C37—81no—
324C22×C37C2×#12011yescharacteristic
325C22×C37#53611yescharacteristic
326C22×C37#53711yescharacteristic
327C22×C37#57611yescharacteristic
328C22×C37#57711yescharacteristic
329C22×C37#57711yescharacteristic
330C22×C37#57811yescharacteristic
331C4×C37—22no—
332C4×C37—22no—
333C4×C37—41no—
334C4×C37—42no—
335C4×C37—41no—
336C4×C37—42no—
337C4×C37—42no—
338C4×C37—41no—
339C4×C37—81no—
340C4×C37—81no—
341C4×C37—81no—
342C4×C37—81no—
343C4×C37#53611yescharacteristic
344C4×C37#53611yescharacteristic
345C4×C37#53711yescharacteristic
346C4×C37#53711yescharacteristic
347C2×#542C2×C3711yescharacteristic
348C2×#479C2×C3711yescharacteristic, complemented
349C2×#478C2×C3711yescharacteristic, complemented
350#2629C2×C3711yescharacteristic, complemented
351#2058C2×C3711yescharacteristic, complemented
352#2057C2×C3711yescharacteristic, complemented
353#2042C2×C3711yescharacteristic, complemented
354#2042C2×C3711yescharacteristic, complemented
355#2036C2×C3711yescharacteristic, complemented
356#2035C2×C3711yescharacteristic, complemented
357#2034C2×C3711yescharacteristic
358#2033C2×C3711yescharacteristic
359#1803C2×C3711yescharacteristic, complemented
360#1802C2×C3711yescharacteristic, complemented
361#1798C2×C3711yescharacteristic, complemented
362C2×C37—81no—
363C2×C37—82no—
364C2×C37#261611yescharacteristic
365C2×C37#301211yescharacteristic
366C2×C37#301311yescharacteristic
367C2×C37#324311yescharacteristic
368C2×C37#324411yescharacteristic
369C2×C37#325711yescharacteristic
370C2×C37#325811yescharacteristic
371#542—24no—
372#542—24no—
373C2×C4⋊Q8C22×C3711yescharacteristic
374C2×#126—21no—
375C2×#125C22×C3711yescharacteristic
376C2×#124—21no—
377C2×#124C22×C3711yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8—21no—
380C2×C22⋊Q8C22×C3711yescharacteristic
381C2×#121C22×C3711yescharacteristic
382C2×C4×Q8C22×C3711yescharacteristic
383C2×C4×D4C22×C3711yescharacteristic
384C2×#117C22×C3711yescharacteristic
385#479—24no—
386#478—24no—
387C2×#107C22×C3711yescharacteristic
388C2×#107C22×C3711yescharacteristic
389C2×#106C22×C3711yescharacteristic
390C2×#106C22×C3711yescharacteristic
391C2×C4⋊C8C22×C3711yescharacteristic
392C2×C4⋊C8C22×C3711yescharacteristic
393C2×#103C22×C3711yescharacteristic
394C2×#103C22×C3711yescharacteristic
395C2×#103C22×C3711yescharacteristic
396C2×#103C22×C3711yescharacteristic
397C2×#102C22×C3711yescharacteristic
398C2×#102C22×C3711yescharacteristic
399C2×#102C22×C3711yescharacteristic
400C2×#102C22×C3711yescharacteristic
401C2×C22⋊C8C22×C3711yescharacteristic
402C2×C22⋊C8C22×C3711yescharacteristic
403#398—21no—
404#398—21no—
405#396—21no—
406#396—21no—
407#389C22×C3711yescharacteristic
408#389C22×C3711yescharacteristic
409#384C22×C3711yescharacteristic
410#380C22×C3711yescharacteristic
411#380C22×C3711yescharacteristic
412#340C22×C3711yescharacteristic
413#340C22×C3711yescharacteristic
414#340C22×C3711yescharacteristic
415#340C22×C3711yescharacteristic
416#336C22×C3711yescharacteristic
417#336C22×C3711yescharacteristic
418C37#2970211yescharacteristic, direct product factor, Sylow
419C22×Q8—21no—
420C22×Q8C23×C3711yescharacteristic
421C22×D4—21no—
422C22×D4C23×C3711yescharacteristic
423C23×C4—21no—
424C23×C4C23×C3711yescharacteristic
425C22×C8C23×C3711yescharacteristic
426C22×C8C23×C3711yescharacteristic
427C22×C8C23×C3711yescharacteristic
428C22×C8C23×C3711yescharacteristic
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431#126—28no—
432#125—22no—
433#125—22no—
434#124—28no—
435#124—22no—
436#124—22no—
437#123—28no—
438C22⋊Q8—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441#121—22no—
442#121—22no—
443C4×Q8—22no—
444C4×Q8D4×C3714yes—
445C4×D4—22no—
446C4×D4D4×C3714yes—
447#117—22no—
448#117—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4D4×C3711yescharacteristic
459C2×C4⋊C4D4×C3711yescharacteristic
460C2×C4⋊C4C23×C3711yescharacteristic
461C2×C4⋊C4C23×C3711yescharacteristic
462C2×C4⋊C4C23×C3711yescharacteristic
463C2×C4⋊C4C23×C3711yescharacteristic
464C2×C4⋊C4C23×C3711yescharacteristic
465C2×C4⋊C4C23×C3711yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4D4×C3711yescharacteristic
474C2×C22⋊C4D4×C3711yescharacteristic
475C2×C42—21no—
476C2×C42C23×C3711yescharacteristic
477C2×C42C23×C3711yescharacteristic
478#107—22no—
479#107—22no—
480#106—22no—
481#106—22no—
482C4⋊C8—22no—
483C4⋊C8—22no—
484#103—22no—
485#103—22no—
486#103—41no—
487#103—41no—
488#102—22no—
489#102—22no—
490#102—41no—
491#102—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498C24—21no—
499C24C2×D4×C3711yescharacteristic
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×Q8C2×D4×C3712yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—81no—
516C2×D4—81no—
517C2×D4C2×D4×C3712yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C3711yescharacteristic
535C22×C4C2×D4×C3711yescharacteristic
536C22×C4C2×D4×C3711yescharacteristic
537C22×C4C2×D4×C3711yescharacteristic
538C22×C4C2×D4×C3711yescharacteristic
539C22×C4C24×C3711yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—81no—
570C4⋊C4—81no—
571C4⋊C4—81no—
572C4⋊C4—81no—
573C4⋊C4C2×D4×C3712yes—
574C4⋊C4C2×D4×C3712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—24no—
585C42—21no—
586C42—21no—
587C42C2×D4×C3712yes—
588C42C2×D4×C3712yes—
589C23—21no—
590C23—22no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×D4×C3711yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608Q8—84no—
609D4—22no—
610D4—22no—
611D4—41no—
612D4—41no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
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—84no—
653C2×C4#120×C3712yes—
654C2×C4#120×C3712yes—
655C2×C4C22×D4×C3711yescharacteristic
656C2×C4C22×D4×C3711yescharacteristic
657C2×C4H(5,𝔽2)×C3711yescharacteristic
658C2×C42−1+4×C3711yescharacteristic
659C2×C42−1+4×C3711yescharacteristic
660C2×C42−1+4×C3711yescharacteristic
661C8—41no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×#120×C3711yescharacteristic
680C22C37×#53611yescharacteristic
681C22C37×#53711yescharacteristic
682C22C37×#57611yescharacteristic
683C22C37×#57711yescharacteristic
684C22C37×#57711yescharacteristic
685C22C37×#57811yescharacteristic
686C4—22no—
687C4—22no—
688C4—41no—
689C4—42no—
690C4—41no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C37×#53611yescharacteristic
699C4C37×#53611yescharacteristic
700C4C37×#53711yescharacteristic
701C4C37×#53711yescharacteristic
702C2—81no—
703C2—82no—
704C2C37×#261611yescharacteristic
705C2C37×#301211yescharacteristic
706C2C37×#301311yescharacteristic
707C2C37×#324311yescharacteristic
708C2C37×#324411yescharacteristic
709C2C37×#325711yescharacteristic
710C2C37×#325811yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#479C2semidirect
3. C2×C37×#478C2semidirect
4. C37×#2629C2semidirect
5. C37×#2058C2semidirect
6. C37×#2057C2semidirect
7. C37×#2042C2semidirect
8. C37×#2042C2semidirect
9. C37×#2036C2semidirect
10. C37×#2035C2semidirect
13. C37×#1803C2semidirect
14. C37×#1802C2semidirect
15. C37×#1798C2semidirect
309. #29702C37direct (N × H)
348. C2×#479C2×C37semidirect
349. C2×#478C2×C37semidirect
350. #2629C2×C37semidirect
351. #2058C2×C37semidirect
352. #2057C2×C37semidirect
353. #2042C2×C37semidirect
354. #2042C2×C37semidirect
355. #2036C2×C37semidirect
356. #2035C2×C37semidirect
359. #1803C2×C37semidirect
360. #1802C2×C37semidirect
361. #1798C2×C37semidirect
418. C37#29702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5422
C2×C37×#4792
C2×C37×#4782
C37×#26292
C37×#20582
C37×#20572
C37×#20422
C37×#20362
C37×#20352
C37×#20342
C37×#20332
C37×#18032
C37×#18022
C37×#17982
#2970237