Finite Group Databasebeta

← C37×#61848 #22683101

Subgroups — C37×#61848 #22683101

Order 9472.

1660 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3556C211yesmaximal, characteristic, complemented
2C37×#3501C211yesmaximal, characteristic
3C37×#3388C214yesmaximal, complemented
4C37×#3386C212yesmaximal, complemented
5C37×#3381C212yesmaximal, complemented
6C37×#3372C212yesmaximal, complemented
7C37×#3372C214yesmaximal, complemented
8C37×#3359C212yesmaximal, complemented
9C37×#3242C214yesmaximal, complemented
10C37×#3237C211yesmaximal, characteristic, complemented
11C37×#3231C211yesmaximal, characteristic, complemented
12C37×#3123C214yesmaximal
13C37×#3110C211yesmaximal, characteristic
14C37×#3101C211yesmaximal, characteristic
15C37×#2985C211yesmaximal, characteristic, complemented
16C37×#564—22no—
17C37×#557—21no—
18C37×#557—21no—
19C37×#557C2212yescomplemented
20C37×#557C2212yescomplemented
21C37×#557C2212yescomplemented
22C37×#557C2212yescomplemented
23C37×#554—21no—
24C37×#554—22no—
25C37×#554C2212yes—
26C37×#554C2214yes—
27D4×Q8×C37—21no—
28D4×Q8×C37C2212yes—
29C37×#544C2212yes—
30C37×#543—22no—
31C37×#541—22no—
32C37×#541—22no—
33C37×#541C2214yes—
34C37×#533C2211yescharacteristic
35C37×#533C2211yescharacteristic
36C37×#533C2211yescharacteristic
37C37×#533C2211yescharacteristic
38C2×C22⋊Q8×C37—22no—
39C37×#518C2212yes—
40C2×C4×D4×C37C2211yescharacteristic
41C37×#501C2214yescomplemented
42C37×#501C2212yescomplemented
43C37×#500C2211yescharacteristic, complemented
44C37×#499C2214yescomplemented
45C37×#498C2211yescharacteristic, complemented
46C37×#491C2212yescomplemented
47C37×#491C2214yescomplemented
48C37×#487C2211yescharacteristic, complemented
49C37×#487C2211yescharacteristic, complemented
50C37×#487C2214yescomplemented
51C37×#485C2214yes—
52C37×#485C2214yes—
53C37×#484C2212yes—
54C37×#483C2212yes—
55C37×#479C2214yescomplemented
56C37×#479C2214yescomplemented
57C37×#479C2214yescomplemented
58C37×#478C2214yes—
59C37×#478C2214yes—
60C37×#477C2212yescomplemented
61C37×#477C2214yescomplemented
62C37×#476C2212yes—
63C37×#475C2212yescomplemented
64C37×#475C2214yescomplemented
65C37×#474C2212yes—
66C37×#461C2214yes—
67C37×#461C2214yes—
68C37×#461C2212yes—
69C37×#461C2212yes—
70C37×#450C2212yes—
71C37×#450C2212yes—
72C37×#446C2212yescomplemented
73C37×#446C2214yescomplemented
74C8×Q8×C37C2212yescomplemented
75C37×#440C2214yes—
76C37×#440C2214yes—
77C37×#440C2214yes—
78C4×SD16×C37C2214yes—
79C4×SD16×C37C2214yes—
80C4×SD16×C37C2212yes—
81C4×SD16×C37C2212yes—
82C37×#433C2214yes—
83C37×#432C2211yescharacteristic
84C37×#431C2211yescharacteristic
85C22×Q8×C37—22no—
86C22×D4×C37C2311yescharacteristic
87C23×C4×C37—21no—
88C2×SD16×C37C2312yes—
89C2×SD16×C37C2314yes—
90C2×SD16×C37C2312yes—
91C4⋊Q8×C37—22no—
92C4⋊Q8×C37—22no—
93C4⋊Q8×C37—22no—
94C4⋊Q8×C37D411yescharacteristic
95C4⋊Q8×C37D411yescharacteristic
96C4⋊Q8×C37C2311yescharacteristic
97C4⋊Q8×C37C2311yescharacteristic
98C4⋊Q8×C37C2314yes—
99C4⋊Q8×C37C2311yescharacteristic
100C4⋊Q8×C37C2311yescharacteristic
101C4⋊Q8×C37C2311yescharacteristic
102C4⋊Q8×C37C2311yescharacteristic
103C4⋊Q8×C37C2314yes—
104#126×C37—24no—
105#126×C37—24no—
106#125×C37—22no—
107#125×C37—22no—
108#125×C37—24no—
109#125×C37—24no—
110#125×C37—24no—
111#125×C37—24no—
112#125×C37—24no—
113#125×C37—24no—
114#125×C37—22no—
115#125×C37—21no—
116#125×C37—21no—
117#125×C37D412yes—
118#125×C37C2312yes—
119#125×C37C2314yes—
120#125×C37C2314yes—
121C22⋊Q8×C37—22no—
122C22⋊Q8×C37—24no—
123C22⋊Q8×C37—21no—
124C22⋊Q8×C37—21no—
125C22⋊Q8×C37—21no—
126C22⋊Q8×C37—21no—
127C22⋊Q8×C37—22no—
128C22⋊Q8×C37—24no—
129C22⋊Q8×C37—24no—
130C22⋊Q8×C37—24no—
131C22⋊Q8×C37—24no—
132C22⋊Q8×C37—24no—
133C22⋊Q8×C37D412yes—
134C22⋊Q8×C37D412yes—
135C22⋊Q8×C37C2312yes—
136C22⋊Q8×C37C2312yes—
137C4×Q8×C37—22no—
138C4×Q8×C37—22no—
139C4×Q8×C37—22no—
140C4×Q8×C37—22no—
141C4×Q8×C37—21no—
142C4×Q8×C37—21no—
143C4×Q8×C37—21no—
144C4×Q8×C37—21no—
145C4×Q8×C37C2312yes—
146C4×Q8×C37C2312yes—
147C4×Q8×C37C2314yes—
148C4×Q8×C37C2314yes—
149C4×Q8×C37C2312yes—
150C4×Q8×C37C2312yes—
151C4×D4×C37—22no—
152C4×D4×C37—22no—
153C4×D4×C37—21no—
154C4×D4×C37—21no—
155C4×D4×C37C2312yes—
156C4×D4×C37C2314yes—
157C4×D4×C37C2314yes—
158C4×D4×C37C2312yes—
159#117×C37—21no—
160#117×C37—21no—
161#117×C37C2312yes—
162#117×C37C2312yes—
163C2×C4⋊C4×C37—24no—
164C2×C4⋊C4×C37—22no—
165C2×C4⋊C4×C37C2311yescharacteristic
166C2×C22⋊C4×C37—21no—
167C2×C22⋊C4×C37—24no—
168C2×C42×C37C2311yescharacteristic
169#107×C37C2314yes—
170#107×C37C2314yes—
171#107×C37C2314yes—
172#106×C37C2312yes—
173#106×C37C2314yes—
174#106×C37C2312yes—
175#106×C37C2314yes—
176C4⋊C8×C37C2312yes—
177C4⋊C8×C37C2312yes—
178C4⋊C8×C37C2314yes—
179C4⋊C8×C37C2314yes—
180#103×C37C2314yes—
181#103×C37C2312yes—
182#103×C37C2314yes—
183#103×C37C2312yes—
184#103×C37C2314yes—
185#103×C37C2314yes—
186#103×C37C2314yes—
187#102×C37C2312yes—
188#102×C37C2314yes—
189#102×C37C2312yes—
190C22⋊C8×C37C2312yes—
191C22⋊C8×C37C2312yes—
192#97×C37C2312yes—
193#97×C37C2314yes—
194C4×C8×C37C2311yescharacteristic
195C4×C8×C37C2311yescharacteristic
196C4×C8×C37C2314yes—
197C24×C37—21no—
198C2×Q8×C37—21no—
199C2×Q8×C37—21no—
200C2×Q8×C37—21no—
201C2×Q8×C37—21no—
202C2×Q8×C37—24no—
203C2×Q8×C37—84no—
204C2×Q8×C37C2×D412yes—
205C2×Q8×C37C2×D412yes—
206C2×Q8×C37C2412yes—
207C2×Q8×C37C2412yes—
208C2×D4×C37—24no—
209C2×D4×C37—21no—
210C2×D4×C37C2412yes—
211C22×C4×C37—21no—
212C22×C4×C37—22no—
213C22×C4×C37—24no—
214C22×C4×C37—24no—
215C22×C4×C37—22no—
216C22×C4×C37—82no—
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2411yescharacteristic
220SD16×C37—24no—
221SD16×C37—28no—
222SD16×C37—24no—
223C2×C8×C37C2412yes—
224C2×C8×C37C2412yes—
225C2×C8×C37C2414yes—
226C4⋊C4×C37—22no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—24no—
229C4⋊C4×C37—24no—
230C4⋊C4×C37—24no—
231C4⋊C4×C37—21no—
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—22no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—22no—
241C4⋊C4×C37—22no—
242C4⋊C4×C37—24no—
243C4⋊C4×C37—24no—
244C4⋊C4×C37—24no—
245C4⋊C4×C37—24no—
246C4⋊C4×C37—22no—
247C4⋊C4×C37—22no—
248C4⋊C4×C37—24no—
249C4⋊C4×C37—24no—
250C4⋊C4×C37C2×D412yes—
251C4⋊C4×C37C2×D414yes—
252C4⋊C4×C37C2×D412yes—
253C4⋊C4×C37C2×D412yes—
254C4⋊C4×C37C2×D412yes—
255C4⋊C4×C37C2×D414yes—
256C4⋊C4×C37C2412yes—
257C4⋊C4×C37C2412yes—
258C4⋊C4×C37C2412yes—
259C4⋊C4×C37C2412yes—
260C4⋊C4×C37C2412yes—
261C22⋊C4×C37—22no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—22no—
264C22⋊C4×C37—24no—
265C22⋊C4×C37—24no—
266C22⋊C4×C37—22no—
267C22⋊C4×C37—22no—
268C22⋊C4×C37C2×D414yes—
269C42×C37—22no—
270C42×C37—22no—
271C42×C37—22no—
272C42×C37—24no—
273C42×C37—24no—
274C42×C37C2×D411yescharacteristic
275C42×C37C2×D411yescharacteristic
276C42×C37C2411yescharacteristic
277C42×C37C2414yes—
278C42×C37C2411yescharacteristic
279C23×C37—24no—
280C23×C37—22no—
281C23×C37—81no—
282C23×C37—81no—
283C23×C37C22×D411yescharacteristic
284Q8×C37—24no—
285Q8×C37—22no—
286Q8×C37—24no—
287Q8×C37—22no—
288Q8×C37—42no—
289Q8×C37—42no—
290Q8×C37—42no—
291Q8×C37—42no—
292Q8×C37—81no—
293Q8×C37—84no—
294D4×C37—24no—
295D4×C37—22no—
296D4×C372−1+414yes—
297C2×C4×C37—22no—
298C2×C4×C37—22no—
299C2×C4×C37—22no—
300C2×C4×C37—22no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—41no—
307C2×C4×C37—44no—
308C2×C4×C37—84no—
309C2×C4×C37—82no—
310C2×C4×C37—84no—
311C2×C4×C37—81no—
312C2×C4×C37C22×D411yescharacteristic
313C2×C4×C37C22×D411yescharacteristic
314C2×C4×C37C22×D414yes—
315C2×C4×C37C22×D414yes—
316C2×C4×C37C22×D411yescharacteristic
317C2×C4×C37C22×D411yescharacteristic
318C2×C4×C37C22×D411yescharacteristic
319C2×C4×C37C2511yescharacteristic
320C8×C37—22no—
321C8×C37—22no—
322C8×C37—24no—
323#61848C3711yesmaximal, characteristic, direct product factor, Sylow
324C22×C37—21no—
325C22×C37—21no—
326C22×C37—24no—
327C22×C37—21no—
328C22×C37—42no—
329C22×C37—42no—
330C22×C37—84no—
331C22×C37C23×D411yescharacteristic
332C4×C37—21no—
333C4×C37—21no—
334C4×C37—24no—
335C4×C37—21no—
336C4×C37—21no—
337C4×C37—24no—
338C4×C37—42no—
339C4×C37—42no—
340C4×C37—42no—
341C4×C37—42no—
342C4×C37—42no—
343C4×C37—42no—
344C4×C37—42no—
345C4×C37#57712yes—
346C4×C37C2×2−1+412yes—
347#3556C2×C3711yescharacteristic, complemented
348#3501C2×C3711yescharacteristic
349#3388C2×C3714yescomplemented
350#3386C2×C3712yescomplemented
351#3381C2×C3712yescomplemented
352#3372C2×C3712yescomplemented
353#3372C2×C3714yescomplemented
354#3359C2×C3712yescomplemented
355#3242C2×C3714yescomplemented
356#3237C2×C3711yescharacteristic, complemented
357#3231C2×C3711yescharacteristic, complemented
358#3123C2×C3714yes—
359#3110C2×C3711yescharacteristic
360#3101C2×C3711yescharacteristic
361#2985C2×C3711yescharacteristic, complemented
362C2×C37—41no—
363C2×C37—44no—
364C2×C37#348611yescharacteristic
365C2×C37C2×#57711yescharacteristic
366C2×C37#358611yescharacteristic
367#564—22no—
368#557—21no—
369#557—21no—
370#557C22×C3712yescomplemented
371#557C22×C3712yescomplemented
372#557C22×C3712yescomplemented
373#557C22×C3712yescomplemented
374#554—21no—
375#554—22no—
376#554C22×C3712yes—
377#554C22×C3714yes—
378D4×Q8—21no—
379D4×Q8C22×C3712yes—
380#544C22×C3712yes—
381#543—22no—
382#541—22no—
383#541—22no—
384#541C22×C3714yes—
385#533C22×C3711yescharacteristic
386#533C22×C3711yescharacteristic
387#533C22×C3711yescharacteristic
388#533C22×C3711yescharacteristic
389C2×C22⋊Q8—22no—
390#518C22×C3712yes—
391C2×C4×D4C22×C3711yescharacteristic
392#501C22×C3714yescomplemented
393#501C22×C3712yescomplemented
394#500C22×C3711yescharacteristic, complemented
395#499C22×C3714yescomplemented
396#498C22×C3711yescharacteristic, complemented
397#491C22×C3712yescomplemented
398#491C22×C3714yescomplemented
399#487C22×C3711yescharacteristic, complemented
400#487C22×C3714yescomplemented
401#487C22×C3711yescharacteristic, complemented
402#485C22×C3714yes—
403#485C22×C3714yes—
404#484C22×C3712yes—
405#483C22×C3712yes—
406#479C22×C3714yescomplemented
407#479C22×C3714yescomplemented
408#479C22×C3714yescomplemented
409#478C22×C3714yes—
410#478C22×C3714yes—
411#477C22×C3712yescomplemented
412#477C22×C3714yescomplemented
413#476C22×C3712yes—
414#475C22×C3712yescomplemented
415#475C22×C3714yescomplemented
416#474C22×C3712yes—
417#461C22×C3712yes—
418#461C22×C3712yes—
419#461C22×C3714yes—
420#461C22×C3714yes—
421#450C22×C3712yes—
422#450C22×C3712yes—
423#446C22×C3712yescomplemented
424#446C22×C3714yescomplemented
425C8×Q8C22×C3712yescomplemented
426#440C22×C3714yes—
427#440C22×C3714yes—
428#440C22×C3714yes—
429C4×SD16C22×C3712yes—
430C4×SD16C22×C3712yes—
431C4×SD16C22×C3714yes—
432C4×SD16C22×C3714yes—
433#433C22×C3714yes—
434#432C22×C3711yescharacteristic
435#431C22×C3711yescharacteristic
436C37#6184811yescharacteristic, direct product factor, Sylow
437C22×Q8—22no—
438C22×D4C23×C3711yescharacteristic
439C23×C4—21no—
440C2×SD16C23×C3712yes—
441C2×SD16C23×C3712yes—
442C2×SD16C23×C3714yes—
443C4⋊Q8—22no—
444C4⋊Q8—22no—
445C4⋊Q8—22no—
446C4⋊Q8D4×C3711yescharacteristic
447C4⋊Q8D4×C3711yescharacteristic
448C4⋊Q8C23×C3711yescharacteristic
449C4⋊Q8C23×C3711yescharacteristic
450C4⋊Q8C23×C3714yes—
451C4⋊Q8C23×C3711yescharacteristic
452C4⋊Q8C23×C3711yescharacteristic
453C4⋊Q8C23×C3711yescharacteristic
454C4⋊Q8C23×C3711yescharacteristic
455C4⋊Q8C23×C3714yes—
456#126—24no—
457#126—24no—
458#125—22no—
459#125—22no—
460#125—24no—
461#125—24no—
462#125—24no—
463#125—24no—
464#125—24no—
465#125—24no—
466#125—22no—
467#125—21no—
468#125—21no—
469#125D4×C3712yes—
470#125C23×C3712yes—
471#125C23×C3714yes—
472#125C23×C3714yes—
473C22⋊Q8—22no—
474C22⋊Q8—24no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—22no—
480C22⋊Q8—24no—
481C22⋊Q8—24no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8—24no—
485C22⋊Q8D4×C3712yes—
486C22⋊Q8D4×C3712yes—
487C22⋊Q8C23×C3712yes—
488C22⋊Q8C23×C3712yes—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8C23×C3712yes—
498C4×Q8C23×C3712yes—
499C4×Q8C23×C3714yes—
500C4×Q8C23×C3714yes—
501C4×Q8C23×C3712yes—
502C4×Q8C23×C3712yes—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4C23×C3712yes—
508C4×D4C23×C3712yes—
509C4×D4C23×C3714yes—
510C4×D4C23×C3714yes—
511#117—21no—
512#117—21no—
513#117C23×C3712yes—
514#117C23×C3712yes—
515C2×C4⋊C4—24no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4C23×C3711yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—24no—
520C2×C42C23×C3711yescharacteristic
521#107C23×C3714yes—
522#107C23×C3714yes—
523#107C23×C3714yes—
524#106C23×C3712yes—
525#106C23×C3714yes—
526#106C23×C3712yes—
527#106C23×C3714yes—
528C4⋊C8C23×C3712yes—
529C4⋊C8C23×C3712yes—
530C4⋊C8C23×C3714yes—
531C4⋊C8C23×C3714yes—
532#103C23×C3714yes—
533#103C23×C3712yes—
534#103C23×C3714yes—
535#103C23×C3712yes—
536#103C23×C3714yes—
537#103C23×C3714yes—
538#103C23×C3714yes—
539#102C23×C3712yes—
540#102C23×C3714yes—
541#102C23×C3712yes—
542C22⋊C8C23×C3712yes—
543C22⋊C8C23×C3712yes—
544#97C23×C3712yes—
545#97C23×C3714yes—
546C4×C8C23×C3711yescharacteristic
547C4×C8C23×C3711yescharacteristic
548C4×C8C23×C3714yes—
549C24—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—24no—
555C2×Q8—84no—
556C2×Q8C2×D4×C3712yes—
557C2×Q8C2×D4×C3712yes—
558C2×Q8C24×C3712yes—
559C2×Q8C24×C3712yes—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4C24×C3712yes—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—82no—
569C22×C4C2×D4×C3711yescharacteristic
570C22×C4C2×D4×C3711yescharacteristic
571C22×C4C24×C3711yescharacteristic
572SD16—24no—
573SD16—24no—
574SD16—28no—
575C2×C8C24×C3712yes—
576C2×C8C24×C3712yes—
577C2×C8C24×C3714yes—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4C2×D4×C3712yes—
603C4⋊C4C2×D4×C3714yes—
604C4⋊C4C2×D4×C3712yes—
605C4⋊C4C2×D4×C3712yes—
606C4⋊C4C2×D4×C3712yes—
607C4⋊C4C2×D4×C3714yes—
608C4⋊C4C24×C3712yes—
609C4⋊C4C24×C3712yes—
610C4⋊C4C24×C3712yes—
611C4⋊C4C24×C3712yes—
612C4⋊C4C24×C3712yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4C2×D4×C3714yes—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—24no—
625C42—24no—
626C42C2×D4×C3711yescharacteristic
627C42C2×D4×C3711yescharacteristic
628C42C24×C3711yescharacteristic
629C42C24×C3714yes—
630C42C24×C3711yescharacteristic
631C23—24no—
632C23—22no—
633C23—81no—
634C23—81no—
635C23C22×D4×C3711yescharacteristic
636Q8—24no—
637Q8—22no—
638Q8—24no—
639Q8—22no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—84no—
645Q8—81no—
646D4—24no—
647D4—22no—
648D42−1+4×C3714yes—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—44no—
660C2×C4—82no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4—81no—
664C2×C4C22×D4×C3711yescharacteristic
665C2×C4C22×D4×C3711yescharacteristic
666C2×C4C22×D4×C3714yes—
667C2×C4C22×D4×C3714yes—
668C2×C4C22×D4×C3711yescharacteristic
669C2×C4C22×D4×C3711yescharacteristic
670C2×C4C22×D4×C3711yescharacteristic
671C2×C4C25×C3711yescharacteristic
672C8—22no—
673C8—22no—
674C8—24no—
675C22—21no—
676C22—24no—
677C22—21no—
678C22—21no—
679C22—42no—
680C22—42no—
681C22—84no—
682C22C23×D4×C3711yescharacteristic
683C4—21no—
684C4—21no—
685C4—24no—
686C4—21no—
687C4—21no—
688C4—24no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4C37×#57712yes—
697C4C2×2−1+4×C3712yes—
698C2—41no—
699C2—44no—
700C2C37×#348611yescharacteristic
701C2C2×C37×#57711yescharacteristic
702C2C37×#358611yescharacteristic
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
prime radicalC22×D4×C37C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C37×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3556C2semidirect
3. C37×#3388C2semidirect
4. C37×#3386C2semidirect
5. C37×#3381C2semidirect
6. C37×#3372C2semidirect
7. C37×#3372C2semidirect
8. C37×#3359C2semidirect
9. C37×#3242C2semidirect
10. C37×#3237C2semidirect
11. C37×#3231C2semidirect
15. C37×#2985C2semidirect
19. C37×#557C22semidirect
20. C37×#557C22semidirect
21. C37×#557C22semidirect
22. C37×#557C22semidirect
41. C37×#501C22semidirect
42. C37×#501C22semidirect
43. C37×#500C22semidirect
44. C37×#499C22semidirect
45. C37×#498C22semidirect
46. C37×#491C22semidirect
47. C37×#491C22semidirect
48. C37×#487C22semidirect
49. C37×#487C22semidirect
50. C37×#487C22semidirect
55. C37×#479C22semidirect
56. C37×#479C22semidirect
57. C37×#479C22semidirect
60. C37×#477C22semidirect
61. C37×#477C22semidirect
63. C37×#475C22semidirect
64. C37×#475C22semidirect
72. C37×#446C22semidirect
73. C37×#446C22semidirect
74. C8×Q8×C37C22semidirect
323. #61848C37direct (N × H)
347. #3556C2×C37semidirect
349. #3388C2×C37semidirect
350. #3386C2×C37semidirect
351. #3381C2×C37semidirect
352. #3372C2×C37semidirect
353. #3372C2×C37semidirect
354. #3359C2×C37semidirect
355. #3242C2×C37semidirect
356. #3237C2×C37semidirect
357. #3231C2×C37semidirect
361. #2985C2×C37semidirect
370. #557C22×C37semidirect
371. #557C22×C37semidirect
372. #557C22×C37semidirect
373. #557C22×C37semidirect
392. #501C22×C37semidirect
393. #501C22×C37semidirect
394. #500C22×C37semidirect
395. #499C22×C37semidirect
396. #498C22×C37semidirect
397. #491C22×C37semidirect
398. #491C22×C37semidirect
399. #487C22×C37semidirect
400. #487C22×C37semidirect
401. #487C22×C37semidirect
406. #479C22×C37semidirect
407. #479C22×C37semidirect
408. #479C22×C37semidirect
411. #477C22×C37semidirect
412. #477C22×C37semidirect
414. #475C22×C37semidirect
415. #475C22×C37semidirect
423. #446C22×C37semidirect
424. #446C22×C37semidirect
425. C8×Q8C22×C37semidirect
436. C37#61848direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35562
C37×#35012
C37×#33882
C37×#33862
C37×#33812
C37×#33722
C37×#33592
C37×#32422
C37×#32372
C37×#32312
C37×#31232
C37×#31102
C37×#31012
C37×#29852
#6184837