Finite Group Databasebeta

← C37×#18823 #22640076

Subgroups — C37×#18823 #22640076

Order 9472.

912 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3520C211yesmaximal, characteristic
2C37×#3252C211yesmaximal, characteristic, complemented
3C37×#3231C211yesmaximal, characteristic, complemented
4C37×#3077C211yesmaximal, characteristic, complemented
5C37×#1654C211yesmaximal, characteristic, complemented
6C37×#1652C211yesmaximal, characteristic, complemented
7C37×#1649C211yesmaximal, characteristic, complemented
8C37×#1647C211yesmaximal, characteristic, complemented
9C37×#1638C211yesmaximal, characteristic, complemented
10C37×#1637C211yesmaximal, characteristic, complemented
11C37×#1635C211yesmaximal, characteristic, complemented
12C37×#1635C211yesmaximal, characteristic, complemented
13C37×#1561C211yesmaximal, characteristic, complemented
14C37×#1495C211yesmaximal, characteristic, complemented
15C37×#1486C211yesmaximal, characteristic, complemented
16C37×#556C2211yescharacteristic
17C37×#554—21no—
18C37×#552—21no—
19C37×#551—22no—
20D4×Q8×C37C2211yescharacteristic
21C37×#548—21no—
22C37×#547C2211yescharacteristic
23C37×#547C2211yescharacteristic
24C37×#546—21no—
25C37×#542—21no—
26C37×#539—22no—
27C37×#533C2211yescharacteristic
28C37×#533C2211yescharacteristic
29C37×#529C2211yescharacteristic
30C37×#525—21no—
31C2×C22⋊Q8×C37—21no—
32C37×#520—21no—
33C2×C4×D4×C37C2211yescharacteristic
34C37×#500C2211yescharacteristic, complemented
35C37×#498C2211yescharacteristic, complemented
36C37×#487C2211yescharacteristic, complemented
37C37×#487C2211yescharacteristic, complemented
38C37×#485—22no—
39C37×#479—22no—
40C37×#479—21no—
41C37×#478—21no—
42C37×#478—21no—
43C37×#477C2211yescharacteristic, complemented
44C37×#476C2211yescharacteristic
45C37×#476C2211yescharacteristic
46C37×#476C2211yescharacteristic, complemented
47C37×#474C2211yescharacteristic
48C37×#474C2211yescharacteristic
49C37×#470—21no—
50C37×#468—21no—
51C37×#464—21no—
52C37×#462C2211yescharacteristic, complemented
53C37×#461C2211yescharacteristic, complemented
54C37×#431C2211yescharacteristic
55C37×#428—21no—
56C37×#423C2211yescharacteristic
57C37×#423C2211yescharacteristic
58C37×#418—21no—
59C37×#332C2211yescharacteristic, complemented
60C37×#332C2211yescharacteristic, complemented
61C37×#332C2211yescharacteristic, complemented
62C37×#332C2211yescharacteristic, complemented
63C37×Q8⋊C8C2211yescharacteristic, complemented
64C37×Q8⋊C8C2211yescharacteristic, complemented
65C37×D4⋊C8C2211yescharacteristic
66C37×D4⋊C8C2211yescharacteristic
67C37×D4⋊C8C2211yescharacteristic
68C37×D4⋊C8C2211yescharacteristic
69C37×D4⋊C8C2211yescharacteristic, complemented
70C37×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C37—21no—
72C2×#41×C37—21no—
73C22×Q8×C37—21no—
74C22×D4×C37D411yescharacteristic
75C23×C4×C37—21no—
76C2×Q16×C37—21no—
77C2×SD16×C37—21no—
78C2×M16×C37—21no—
79C2×M16×C37—21no—
80C4⋊Q8×C37—21no—
81C4⋊Q8×C37C2311yescharacteristic
82C4⋊Q8×C37C2311yescharacteristic
83C4⋊Q8×C37C2311yescharacteristic
84C4⋊Q8×C37C2311yescharacteristic
85#126×C37—22no—
86#126×C37—22no—
87#126×C37—21no—
88#125×C37—22no—
89#125×C37—21no—
90#125×C37D411yescharacteristic
91#125×C37D412yes—
92#124×C37—22no—
93#124×C37—21no—
94#124×C37D411yescharacteristic
95#123×C37—22no—
96#123×C37—22no—
97#123×C37—21no—
98#123×C37—22no—
99#123×C37—22no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—22no—
102C22⋊Q8×C37—22no—
103C22⋊Q8×C37—21no—
104C22⋊Q8×C37—21no—
105C22⋊Q8×C37—21no—
106C22⋊Q8×C37—21no—
107C22⋊Q8×C37—21no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37D411yescharacteristic
113#121×C37—22no—
114#121×C37—21no—
115#121×C37—21no—
116#121×C37D411yescharacteristic
117#120×C37—22no—
118C4×Q8×C37—21no—
119C4×Q8×C37—21no—
120C4×Q8×C37—21no—
121C4×Q8×C37—21no—
122C4×Q8×C37—21no—
123C4×Q8×C37C2311yescharacteristic
124C4×D4×C37—22no—
125C4×D4×C37—22no—
126C4×D4×C37—22no—
127C4×D4×C37—21no—
128C4×D4×C37—21no—
129C4×D4×C37—21no—
130C4×D4×C37—21no—
131C4×D4×C37D411yescharacteristic
132C4×D4×C37D411yescharacteristic
133C4×D4×C37C2311yescharacteristic
134C4×D4×C37C2311yescharacteristic
135C4×D4×C37C2311yescharacteristic
136#117×C37—22no—
137#117×C37—21no—
138#117×C37—21no—
139#117×C37—21no—
140#117×C37D412yes—
141C2×C4⋊C4×C37—22no—
142C2×C4⋊C4×C37—21no—
143C2×C4⋊C4×C37—21no—
144C2×C4⋊C4×C37D411yescharacteristic
145C2×C22⋊C4×C37—22no—
146C2×C22⋊C4×C37—21no—
147C2×C42×C37C2311yescharacteristic
148#107×C37—21no—
149#107×C37—21no—
150#107×C37—21no—
151#107×C37—22no—
152#106×C37—21no—
153#106×C37—21no—
154#106×C37—21no—
155#106×C37—22no—
156C4⋊C8×C37—21no—
157C4⋊C8×C37—21no—
158C4⋊C8×C37—21no—
159C4⋊C8×C37C2311yescharacteristic
160C4⋊C8×C37C2311yescharacteristic
161C4⋊C8×C37C2311yescharacteristic
162C4⋊C8×C37C2311yescharacteristic
163#103×C37—21no—
164#103×C37—21no—
165#103×C37—21no—
166#103×C37—22no—
167#103×C37—22no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171#102×C37—21no—
172#102×C37—21no—
173C22⋊C8×C37—21no—
174C4×C8×C37C2311yescharacteristic
175C4×C8×C37C2311yescharacteristic
176C24×C37—21no—
177#41×C37—42no—
178#41×C37—42no—
179#41×C37—81no—
180#41×C37—81no—
181C2×Q8×C37—22no—
182C2×Q8×C37—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—81no—
187C2×Q8×C37—81no—
188C2×Q8×C37C2×D411yescharacteristic
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—21no—
192C2×D4×C37—22no—
193C2×D4×C37—21no—
194C2×D4×C37—41no—
195C2×D4×C37C2×D411yescharacteristic
196C2×D4×C37C2×D411yescharacteristic
197C2×D4×C37C2×D411yescharacteristic
198C22×C4×C37—22no—
199C22×C4×C37—22no—
200C22×C4×C37—22no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—81no—
208C22×C4×C37—81no—
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2×D411yescharacteristic
212Q16×C37—81no—
213SD16×C37—81no—
214M16×C37—42no—
215M16×C37—81no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C4⋊C4×C37—22no—
223C4⋊C4×C37—22no—
224C4⋊C4×C37—22no—
225C4⋊C4×C37—22no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—22no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—41no—
240C4⋊C4×C37—41no—
241C4⋊C4×C37C2×D411yescharacteristic
242C4⋊C4×C37C2×D412yes—
243C4⋊C4×C37C2×D411yescharacteristic
244C4⋊C4×C37C2×D412yes—
245C4⋊C4×C37C2×D411yescharacteristic
246C4⋊C4×C37C2×D411yescharacteristic
247C22⋊C4×C37—22no—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—22no—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—21no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—21no—
255C22⋊C4×C37—21no—
256C22⋊C4×C37—21no—
257C22⋊C4×C37—21no—
258C22⋊C4×C37—21no—
259C22⋊C4×C37—21no—
260C22⋊C4×C37—21no—
261C22⋊C4×C37—21no—
262C22⋊C4×C37—41no—
263C42×C37—22no—
264C42×C37—22no—
265C42×C37—21no—
266C42×C37—41no—
267C42×C37C2×D411yescharacteristic
268C42×C37C2×D411yescharacteristic
269C42×C37C2×D411yescharacteristic
270C42×C37C2411yescharacteristic
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—21no—
274C23×C37—42no—
275C23×C37—42no—
276C23×C37—81no—
277C23×C37#12011yescharacteristic
278Q8×C37—21no—
279Q8×C37—21no—
280Q8×C37—42no—
281Q8×C37—41no—
282Q8×C37—41no—
283Q8×C37—41no—
284Q8×C37—41no—
285Q8×C37—41no—
286Q8×C37—41no—
287Q8×C37—82no—
288D4×C37—21no—
289D4×C37—21no—
290D4×C37—21no—
291D4×C37—21no—
292D4×C37—21no—
293D4×C37—42no—
294D4×C37—42no—
295D4×C37—44no—
296D4×C37—82no—
297D4×C37#13712yes—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—22no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—22no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—41no—
310C2×C4×C37—44no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—81no—
320C2×C4×C37—81no—
321C2×C4×C37—81no—
322C2×C4×C37—82no—
323C2×C4×C37—82no—
324C2×C4×C37#12011yescharacteristic
325C2×C4×C37#12011yescharacteristic
326C2×C4×C37#12011yescharacteristic
327C2×C4×C37C22×D411yescharacteristic
328C2×C4×C37C22×D411yescharacteristic
329C2×C4×C37C22×D411yescharacteristic
330C8×C37—41no—
331C8×C37—41no—
332C8×C37—41no—
333C8×C37—41no—
334C8×C37—41no—
335C8×C37—41no—
336#18823C3711yesmaximal, characteristic, direct product factor, Sylow
337C22×C37—21no—
338C22×C37—22no—
339C22×C37—21no—
340C22×C37—21no—
341C22×C37—41no—
342C22×C37—41no—
343C22×C37—41no—
344C22×C37—41no—
345C22×C37—41no—
346C22×C37—41no—
347C22×C37—41no—
348C22×C37—41no—
349C22×C37—84no—
350C22×C37C2×#12011yescharacteristic
351C4×C37—21no—
352C4×C37—21no—
353C4×C37—21no—
354C4×C37—21no—
355C4×C37—41no—
356C4×C37—42no—
357C4×C37—41no—
358C4×C37—41no—
359C4×C37—42no—
360C4×C37—41no—
361C4×C37—41no—
362C4×C37—81no—
363C4×C37—81no—
364C4×C37C2×#13711yescharacteristic
365C4×C37#57511yescharacteristic
366C4×C37#57611yescharacteristic
367C4×C37#57711yescharacteristic
368#3520C2×C3711yescharacteristic
369#3252C2×C3711yescharacteristic, complemented
370#3231C2×C3711yescharacteristic, complemented
371#3077C2×C3711yescharacteristic, complemented
372#1654C2×C3711yescharacteristic, complemented
373#1652C2×C3711yescharacteristic, complemented
374#1649C2×C3711yescharacteristic, complemented
375#1647C2×C3711yescharacteristic, complemented
376#1638C2×C3711yescharacteristic, complemented
377#1637C2×C3711yescharacteristic, complemented
378#1635C2×C3711yescharacteristic, complemented
379#1635C2×C3711yescharacteristic, complemented
380#1561C2×C3711yescharacteristic, complemented
381#1495C2×C3711yescharacteristic, complemented
382#1486C2×C3711yescharacteristic, complemented
383C2×C37—41no—
384C2×C37—42no—
385C2×C37—81no—
386C2×C37—81no—
387C2×C37#300711yescharacteristic
388C2×C37#301211yescharacteristic
389C2×C37#302011yescharacteristic
390#556C22×C3711yescharacteristic
391#554—21no—
392#552—21no—
393#551—22no—
394D4×Q8C22×C3711yescharacteristic
395#548—21no—
396#547C22×C3711yescharacteristic
397#547C22×C3711yescharacteristic
398#546—21no—
399#542—21no—
400#539—22no—
401#533C22×C3711yescharacteristic
402#533C22×C3711yescharacteristic
403#529C22×C3711yescharacteristic
404#525—21no—
405C2×C22⋊Q8—21no—
406#520—21no—
407C2×C4×D4C22×C3711yescharacteristic
408#500C22×C3711yescharacteristic, complemented
409#498C22×C3711yescharacteristic, complemented
410#487C22×C3711yescharacteristic, complemented
411#487C22×C3711yescharacteristic, complemented
412#485—22no—
413#479—22no—
414#479—21no—
415#478—21no—
416#478—21no—
417#477C22×C3711yescharacteristic, complemented
418#476C22×C3711yescharacteristic
419#476C22×C3711yescharacteristic
420#476C22×C3711yescharacteristic, complemented
421#474C22×C3711yescharacteristic
422#474C22×C3711yescharacteristic
423#470—21no—
424#468—21no—
425#464—21no—
426#462C22×C3711yescharacteristic, complemented
427#461C22×C3711yescharacteristic, complemented
428#431C22×C3711yescharacteristic
429#428—21no—
430#423C22×C3711yescharacteristic
431#423C22×C3711yescharacteristic
432#418—21no—
433#332C22×C3711yescharacteristic, complemented
434#332C22×C3711yescharacteristic, complemented
435#332C22×C3711yescharacteristic, complemented
436#332C22×C3711yescharacteristic, complemented
437Q8⋊C8C22×C3711yescharacteristic, complemented
438Q8⋊C8C22×C3711yescharacteristic, complemented
439D4⋊C8C22×C3711yescharacteristic
440D4⋊C8C22×C3711yescharacteristic
441D4⋊C8C22×C3711yescharacteristic
442D4⋊C8C22×C3711yescharacteristic
443D4⋊C8C22×C3711yescharacteristic, complemented
444D4⋊C8C22×C3711yescharacteristic, complemented
445C37#1882311yescharacteristic, direct product factor, Sylow
446C2×#41—21no—
447C2×#41—21no—
448C22×Q8—21no—
449C22×D4D4×C3711yescharacteristic
450C23×C4—21no—
451C2×Q16—21no—
452C2×SD16—21no—
453C2×M16—21no—
454C2×M16—21no—
455C4⋊Q8—21no—
456C4⋊Q8C23×C3711yescharacteristic
457C4⋊Q8C23×C3711yescharacteristic
458C4⋊Q8C23×C3711yescharacteristic
459C4⋊Q8C23×C3711yescharacteristic
460#126—22no—
461#126—22no—
462#126—21no—
463#125—22no—
464#125—21no—
465#125D4×C3711yescharacteristic
466#125D4×C3712yes—
467#124—22no—
468#124—21no—
469#124D4×C3711yescharacteristic
470#123—22no—
471#123—22no—
472#123—21no—
473#123—22no—
474#123—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8D4×C3711yescharacteristic
488#121—22no—
489#121—21no—
490#121—21no—
491#121D4×C3711yescharacteristic
492#120—22no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8C23×C3711yescharacteristic
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4D4×C3711yescharacteristic
507C4×D4D4×C3711yescharacteristic
508C4×D4C23×C3711yescharacteristic
509C4×D4C23×C3711yescharacteristic
510C4×D4C23×C3711yescharacteristic
511#117—22no—
512#117—21no—
513#117—21no—
514#117—21no—
515#117D4×C3712yes—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C3711yescharacteristic
520C2×C22⋊C4—22no—
521C2×C22⋊C4—21no—
522C2×C42C23×C3711yescharacteristic
523#107—21no—
524#107—21no—
525#107—21no—
526#107—22no—
527#106—21no—
528#106—21no—
529#106—21no—
530#106—22no—
531C4⋊C8—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C3711yescharacteristic
535C4⋊C8C23×C3711yescharacteristic
536C4⋊C8C23×C3711yescharacteristic
537C4⋊C8C23×C3711yescharacteristic
538#103—21no—
539#103—21no—
540#103—21no—
541#103—22no—
542#103—22no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548C22⋊C8—21no—
549C4×C8C23×C3711yescharacteristic
550C4×C8C23×C3711yescharacteristic
551C24—21no—
552#41—42no—
553#41—42no—
554#41—81no—
555#41—81no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8C2×D4×C3711yescharacteristic
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—41no—
570C2×D4C2×D4×C3711yescharacteristic
571C2×D4C2×D4×C3711yescharacteristic
572C2×D4C2×D4×C3711yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C3711yescharacteristic
585C22×C4C2×D4×C3711yescharacteristic
586C22×C4C2×D4×C3711yescharacteristic
587Q16—81no—
588SD16—81no—
589M16—42no—
590M16—81no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4C2×D4×C3711yescharacteristic
617C4⋊C4C2×D4×C3712yes—
618C4⋊C4C2×D4×C3711yescharacteristic
619C4⋊C4C2×D4×C3712yes—
620C4⋊C4C2×D4×C3711yescharacteristic
621C4⋊C4C2×D4×C3711yescharacteristic
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—41no—
638C42—22no—
639C42—22no—
640C42—21no—
641C42—41no—
642C42C2×D4×C3711yescharacteristic
643C42C2×D4×C3711yescharacteristic
644C42C2×D4×C3711yescharacteristic
645C42C24×C3711yescharacteristic
646C23—21no—
647C23—21no—
648C23—21no—
649C23—42no—
650C23—42no—
651C23—81no—
652C23#120×C3711yescharacteristic
653Q8—21no—
654Q8—21no—
655Q8—42no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—82no—
663D4—21no—
664D4—21no—
665D4—21no—
666D4—21no—
667D4—21no—
668D4—42no—
669D4—44no—
670D4—42no—
671D4—82no—
672D4#137×C3712yes—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—44no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4#120×C3711yescharacteristic
700C2×C4#120×C3711yescharacteristic
701C2×C4#120×C3711yescharacteristic
702C2×C4C22×D4×C3711yescharacteristic
703C2×C4C22×D4×C3711yescharacteristic
704C2×C4C22×D4×C3711yescharacteristic
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C22—21no—
712C22—22no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—84no—
724C22C2×#120×C3711yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4C2×#137×C3711yescharacteristic
739C4C37×#57511yescharacteristic
740C4C37×#57611yescharacteristic
741C4C37×#57711yescharacteristic
742C2—41no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2C37×#300711yescharacteristic
747C2C37×#301211yescharacteristic
748C2C37×#302011yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3520C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3252C2semidirect
3. C37×#3231C2semidirect
4. C37×#3077C2semidirect
5. C37×#1654C2semidirect
6. C37×#1652C2semidirect
7. C37×#1649C2semidirect
8. C37×#1647C2semidirect
9. C37×#1638C2semidirect
10. C37×#1637C2semidirect
11. C37×#1635C2semidirect
12. C37×#1635C2semidirect
13. C37×#1561C2semidirect
14. C37×#1495C2semidirect
15. C37×#1486C2semidirect
34. C37×#500C22semidirect
35. C37×#498C22semidirect
36. C37×#487C22semidirect
37. C37×#487C22semidirect
43. C37×#477C22semidirect
46. C37×#476C22semidirect
52. C37×#462C22semidirect
53. C37×#461C22semidirect
59. C37×#332C22semidirect
60. C37×#332C22semidirect
61. C37×#332C22semidirect
62. C37×#332C22semidirect
63. C37×Q8⋊C8C22semidirect
64. C37×Q8⋊C8C22semidirect
69. C37×D4⋊C8C22semidirect
70. C37×D4⋊C8C22semidirect
336. #18823C37direct (N × H)
369. #3252C2×C37semidirect
370. #3231C2×C37semidirect
371. #3077C2×C37semidirect
372. #1654C2×C37semidirect
373. #1652C2×C37semidirect
374. #1649C2×C37semidirect
375. #1647C2×C37semidirect
376. #1638C2×C37semidirect
377. #1637C2×C37semidirect
378. #1635C2×C37semidirect
379. #1635C2×C37semidirect
380. #1561C2×C37semidirect
381. #1495C2×C37semidirect
382. #1486C2×C37semidirect
408. #500C22×C37semidirect
409. #498C22×C37semidirect
410. #487C22×C37semidirect
411. #487C22×C37semidirect
417. #477C22×C37semidirect
420. #476C22×C37semidirect
426. #462C22×C37semidirect
427. #461C22×C37semidirect
433. #332C22×C37semidirect
434. #332C22×C37semidirect
435. #332C22×C37semidirect
436. #332C22×C37semidirect
437. Q8⋊C8C22×C37semidirect
438. Q8⋊C8C22×C37semidirect
443. D4⋊C8C22×C37semidirect
444. D4⋊C8C22×C37semidirect
445. C37#18823direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35202
C37×#32522
C37×#32312
C37×#30772
C37×#16542
C37×#16522
C37×#16492
C37×#16472
C37×#16382
C37×#16372
C37×#16352
C37×#15612
C37×#14952
C37×#14862
#1882337