Finite Group Databasebeta

← C37×#25530 #22646783

Subgroups — C37×#25530 #22646783

Order 9472.

1056 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3495C211yesmaximal, characteristic, complemented
2C37×#3094C211yesmaximal, characteristic, complemented
3C37×#3055C211yesmaximal, characteristic
4C37×#2620C211yesmaximal, characteristic, complemented
5C37×#2060C211yesmaximal, characteristic, complemented
6C37×#2038C211yesmaximal, characteristic, complemented
7C37×#2027C211yesmaximal, characteristic, complemented
8C37×#2003C211yesmaximal, characteristic, complemented
9C37×#1901C211yesmaximal, characteristic, complemented
10C37×#1897C211yesmaximal, characteristic, complemented
11C37×#1888C211yesmaximal, characteristic, complemented
12C37×#1883C211yesmaximal, characteristic, complemented
13C37×#1859C211yesmaximal, characteristic, complemented
14C37×#1857C211yesmaximal, characteristic, complemented
15C37×#1733C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C37×#556—21no—
19C37×#554—21no—
20C37×#552—21no—
21C37×#552—22no—
22C37×#552—21no—
23C37×#551—22no—
24C37×#544C2211yescharacteristic
25C37×#542—21no—
26C37×#541—21no—
27C37×#536C2211yescharacteristic
28C37×#533—21no—
29C37×#529—21no—
30C2×#124×C37C2211yescharacteristic
31C37×#525C2211yescharacteristic
32C2×C22⋊Q8×C37C2211yescharacteristic
33C2×#121×C37C2211yescharacteristic
34C37×#520C2211yescharacteristic
35C37×#519C2211yescharacteristic
36C2×#117×C37C2211yescharacteristic
37C2×#117×C37C2211yescharacteristic
38C37×#482—21no—
39C37×#482—21no—
40C37×#481—21no—
41C37×#480—21no—
42C37×#469—21no—
43C37×#468—21no—
44C37×#466—21no—
45C37×#465—21no—
46C37×#428C2211yescharacteristic
47C37×#428C2211yescharacteristic
48C37×#428C2211yescharacteristic
49C2×#104×C37C2211yescharacteristic
50C2×#104×C37C2211yescharacteristic
51C37×#418C2211yescharacteristic
52C37×#418C2211yescharacteristic
53C37×#418C2211yescharacteristic
54C37×#417C2211yescharacteristic
55C2×#101×C37C2211yescharacteristic
56C2×#101×C37C2211yescharacteristic
57C37×#407C2211yescharacteristic
58C37×#396—22no—
59C37×#394—22no—
60C37×#391C2211yescharacteristic
61C37×#390C2211yescharacteristic
62C37×#384C2211yescharacteristic
63C37×#343C2211yescharacteristic
64C37×#343C2211yescharacteristic
65C37×#339C2211yescharacteristic
66C37×#339C2211yescharacteristic
67C37×#339C2211yescharacteristic
68C37×#339C2211yescharacteristic
69C37×#339C2211yescharacteristic
70C37×#339C2211yescharacteristic
71C2×#41×C37C2311yescharacteristic
72C22×Q8×C37C2311yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37C2311yescharacteristic
75C23×C4×C37C2311yescharacteristic
76AGL(1,ℤ/8)×C37—22no—
77AGL(1,ℤ/8)×C37—41no—
78C2×SD16×C37—21no—
79C2×D8×C37—21no—
80C2×M16×C37—21no—
81C2×M16×C37—22no—
82C2×M16×C37—41no—
83C2×M16×C37C2311yescharacteristic
84C2×M16×C37C2311yescharacteristic
85C2×M16×C37C2311yescharacteristic
86C2×M16×C37C2311yescharacteristic
87C22×C8×C37—21no—
88C4⋊Q8×C37—21no—
89C4⋊Q8×C37—21no—
90C4⋊Q8×C37—21no—
91#126×C37—22no—
92#126×C37—22no—
93#126×C37—22no—
94#126×C37—22no—
95#125×C37—22no—
96#125×C37—22no—
97#125×C37—22no—
98#125×C37—21no—
99#125×C37—21no—
100#124×C37—22no—
101#124×C37—21no—
102#124×C37—22no—
103#124×C37—41no—
104#123×C37—22no—
105#123×C37—22no—
106#123×C37—21no—
107#123×C37—22no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—22no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37—21no—
113C22⋊Q8×C37—21no—
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—21no—
116C22⋊Q8×C37—21no—
117C22⋊Q8×C37D411yescharacteristic
118C22⋊Q8×C37D411yescharacteristic
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37D411yescharacteristic
124#121×C37D411yescharacteristic
125#120×C37—21no—
126C4×Q8×C37—22no—
127C4×Q8×C37—21no—
128C4×Q8×C37—21no—
129C4×Q8×C37—21no—
130C4×Q8×C37—21no—
131C4×Q8×C37—21no—
132C4×D4×C37—22no—
133C4×D4×C37—21no—
134C4×D4×C37—22no—
135C4×D4×C37—21no—
136C4×D4×C37—21no—
137#117×C37—22no—
138#117×C37—22no—
139#117×C37—22no—
140#117×C37—21no—
141#117×C37—21no—
142#117×C37—21no—
143#117×C37—22no—
144#117×C37—41no—
145#117×C37D411yescharacteristic
146#117×C37D411yescharacteristic
147#117×C37C2311yescharacteristic
148#117×C37C2311yescharacteristic
149#117×C37C2311yescharacteristic
150C2×C4⋊C4×C37—21no—
151C2×C4⋊C4×C37—21no—
152C2×C4⋊C4×C37—22no—
153C2×C4⋊C4×C37D412yes—
154C2×C4⋊C4×C37D411yescharacteristic
155C2×C4⋊C4×C37D411yescharacteristic
156C2×C4⋊C4×C37C2311yescharacteristic
157C2×C4⋊C4×C37C2311yescharacteristic
158C2×C22⋊C4×C37—21no—
159C2×C22⋊C4×C37—21no—
160C2×C22⋊C4×C37—21no—
161C2×C22⋊C4×C37—22no—
162C2×C22⋊C4×C37—22no—
163C2×C22⋊C4×C37D412yes—
164C2×C42×C37—21no—
165C2×C42×C37C2311yescharacteristic
166C2×C42×C37C2311yescharacteristic
167#107×C37—21no—
168#107×C37—21no—
169#107×C37—21no—
170#106×C37—21no—
171#106×C37—21no—
172#106×C37—21no—
173#104×C37—22no—
174#104×C37—41no—
175#103×C37—21no—
176#102×C37—21no—
177#102×C37—21no—
178#102×C37—21no—
179#102×C37—21no—
180#102×C37—21no—
181#102×C37—21no—
182#102×C37—21no—
183#101×C37—22no—
184#101×C37—41no—
185C22⋊C8×C37—21no—
186C22⋊C8×C37—21no—
187#95×C37—22no—
188C24×C37—21no—
189C24×C37C2×D411yescharacteristic
190#41×C37—21no—
191#41×C37—21no—
192#41×C37—21no—
193#41×C37—21no—
194C2×Q8×C37—22no—
195C2×Q8×C37—21no—
196C2×Q8×C37—21no—
197C2×Q8×C37—21no—
198C2×Q8×C37—21no—
199C2×Q8×C37—21no—
200C2×Q8×C37—21no—
201C2×Q8×C37C2×D411yescharacteristic
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—41no—
212C2×D4×C37—41no—
213C2×D4×C37—82no—
214C2×D4×C37C2×D411yescharacteristic
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—22no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37C2×D412yes—
227C22×C4×C37C2×D411yescharacteristic
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D411yescharacteristic
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2×D411yescharacteristic
232C22×C4×C37C2×D412yes—
233C22×C4×C37C2411yescharacteristic
234SD16×C37—42no—
235D8×C37—42no—
236M16×C37—21no—
237M16×C37—21no—
238M16×C37—21no—
239M16×C37—21no—
240M16×C37—21no—
241M16×C37—21no—
242M16×C37—21no—
243M16×C37—42no—
244M16×C37#4112yes—
245C2×C8×C37—21no—
246C2×C8×C37—21no—
247C2×C8×C37—21no—
248C2×C8×C37—21no—
249C2×C8×C37—42no—
250C4⋊C4×C37—22no—
251C4⋊C4×C37—22no—
252C4⋊C4×C37—22no—
253C4⋊C4×C37—22no—
254C4⋊C4×C37—22no—
255C4⋊C4×C37—22no—
256C4⋊C4×C37—22no—
257C4⋊C4×C37—22no—
258C4⋊C4×C37—21no—
259C4⋊C4×C37—21no—
260C4⋊C4×C37—22no—
261C4⋊C4×C37—22no—
262C4⋊C4×C37—21no—
263C4⋊C4×C37—21no—
264C4⋊C4×C37—21no—
265C4⋊C4×C37—21no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—42no—
269C4⋊C4×C37—82no—
270C4⋊C4×C37C2×D411yescharacteristic
271C4⋊C4×C37C2×D411yescharacteristic
272C4⋊C4×C37C2×D411yescharacteristic
273C4⋊C4×C37C2×D411yescharacteristic
274C4⋊C4×C37C2×D411yescharacteristic
275C4⋊C4×C37C2×D411yescharacteristic
276C22⋊C4×C37—22no—
277C22⋊C4×C37—22no—
278C22⋊C4×C37—22no—
279C22⋊C4×C37—21no—
280C22⋊C4×C37—21no—
281C22⋊C4×C37—22no—
282C22⋊C4×C37—22no—
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—44no—
291C22⋊C4×C37—42no—
292C22⋊C4×C37—41no—
293C22⋊C4×C37—41no—
294C22⋊C4×C37—82no—
295C42×C37—22no—
296C42×C37—22no—
297C42×C37—22no—
298C42×C37—21no—
299C42×C37—21no—
300C42×C37—21no—
301C42×C37—21no—
302C42×C37—21no—
303C42×C37—21no—
304C42×C37—21no—
305C42×C37—21no—
306C42×C37#4112yes—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—41no—
311C23×C37—41no—
312C23×C37—42no—
313C23×C37—42no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37#12011yescharacteristic
318C23×C37#12011yescharacteristic
319C23×C37C22×D411yescharacteristic
320Q8×C37—21no—
321Q8×C37—21no—
322Q8×C37—41no—
323Q8×C37—41no—
324Q8×C37—41no—
325Q8×C37—41no—
326Q8×C37—82no—
327D4×C37—21no—
328D4×C37—21no—
329D4×C37—42no—
330D4×C37—41no—
331D4×C37—41no—
332D4×C37—41no—
333D4×C37—41no—
334D4×C37—41no—
335D4×C37—41no—
336D4×C37—81no—
337D4×C37—82no—
338D4×C37—82no—
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—22no—
355C2×C4×C37—21no—
356C2×C4×C37—21no—
357C2×C4×C37—22no—
358C2×C4×C37—22no—
359C2×C4×C37—22no—
360C2×C4×C37—22no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—42no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—42no—
367C2×C4×C37—41no—
368C2×C4×C37—42no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
371C2×C4×C37—41no—
372C2×C4×C37—81no—
373C2×C4×C37—82no—
374C2×C4×C37#12011yescharacteristic
375C2×C4×C37#12011yescharacteristic
376C2×C4×C37C22×D411yescharacteristic
377C2×C4×C37C22×D411yescharacteristic
378C2×C4×C37C2×#4111yescharacteristic
379C2×C4×C37C2×#4111yescharacteristic
380C2×C4×C37H(5,𝔽2)11yescharacteristic
381C2×C4×C372−1+411yescharacteristic
382C8×C37—22no—
383C8×C37—41no—
384C8×C37—41no—
385C8×C37—41no—
386#25530C3711yesmaximal, characteristic, direct product factor, Sylow
387C22×C37—21no—
388C22×C37—21no—
389C22×C37—21no—
390C22×C37—21no—
391C22×C37—21no—
392C22×C37—21no—
393C22×C37—21no—
394C22×C37—21no—
395C22×C37—41no—
396C22×C37—41no—
397C22×C37—41no—
398C22×C37—81no—
399C22×C37—81no—
400C22×C37—82no—
401C22×C37—82no—
402C22×C37—81no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37C2×#12011yescharacteristic
406C22×C37#54611yescharacteristic
407C22×C37#54711yescharacteristic
408C4×C37—21no—
409C4×C37—21no—
410C4×C37—42no—
411C4×C37—42no—
412C4×C37—41no—
413C4×C37—41no—
414C4×C37—41no—
415C4×C37—41no—
416C4×C37—42no—
417C4×C37—41no—
418C4×C37—41no—
419C4×C37—41no—
420C4×C37—81no—
421C4×C37—81no—
422C4×C37#53211yescharacteristic
423C4×C37#53711yescharacteristic
424C4×C37#54611yescharacteristic
425C4×C37#54711yescharacteristic
426#3495C2×C3711yescharacteristic, complemented
427#3094C2×C3711yescharacteristic, complemented
428#3055C2×C3711yescharacteristic
429#2620C2×C3711yescharacteristic, complemented
430#2060C2×C3711yescharacteristic, complemented
431#2038C2×C3711yescharacteristic, complemented
432#2027C2×C3711yescharacteristic, complemented
433#2003C2×C3711yescharacteristic, complemented
434#1901C2×C3711yescharacteristic, complemented
435#1897C2×C3711yescharacteristic, complemented
436#1888C2×C3711yescharacteristic, complemented
437#1883C2×C3711yescharacteristic, complemented
438#1859C2×C3711yescharacteristic, complemented
439#1857C2×C3711yescharacteristic, complemented
440#1733C2×C3711yescharacteristic, complemented
441C2×C37—21no—
442C2×C37—21no—
443C2×C37—41no—
444C2×C37—41no—
445C2×C37—81no—
446C2×C37—161no—
447C2×C37#243011yescharacteristic
448C2×C37#302011yescharacteristic
449C2×C37#302111yescharacteristic
450C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
451C22×M16C22×C3711yescharacteristic
452#556—21no—
453#554—21no—
454#552—21no—
455#552—22no—
456#552—21no—
457#551—22no—
458#544C22×C3711yescharacteristic
459#542—21no—
460#541—21no—
461#536C22×C3711yescharacteristic
462#533—21no—
463#529—21no—
464C2×#124C22×C3711yescharacteristic
465#525C22×C3711yescharacteristic
466C2×C22⋊Q8C22×C3711yescharacteristic
467C2×#121C22×C3711yescharacteristic
468#520C22×C3711yescharacteristic
469#519C22×C3711yescharacteristic
470C2×#117C22×C3711yescharacteristic
471C2×#117C22×C3711yescharacteristic
472#482—21no—
473#482—21no—
474#481—21no—
475#480—21no—
476#469—21no—
477#468—21no—
478#466—21no—
479#465—21no—
480#428C22×C3711yescharacteristic
481#428C22×C3711yescharacteristic
482#428C22×C3711yescharacteristic
483C2×#104C22×C3711yescharacteristic
484C2×#104C22×C3711yescharacteristic
485#418C22×C3711yescharacteristic
486#418C22×C3711yescharacteristic
487#418C22×C3711yescharacteristic
488#417C22×C3711yescharacteristic
489C2×#101C22×C3711yescharacteristic
490C2×#101C22×C3711yescharacteristic
491#407C22×C3711yescharacteristic
492#396—22no—
493#394—22no—
494#391C22×C3711yescharacteristic
495#390C22×C3711yescharacteristic
496#384C22×C3711yescharacteristic
497#343C22×C3711yescharacteristic
498#343C22×C3711yescharacteristic
499#339C22×C3711yescharacteristic
500#339C22×C3711yescharacteristic
501#339C22×C3711yescharacteristic
502#339C22×C3711yescharacteristic
503#339C22×C3711yescharacteristic
504#339C22×C3711yescharacteristic
505C37#2553011yescharacteristic, direct product factor, Sylow
506C2×#41C23×C3711yescharacteristic
507C22×Q8C23×C3711yescharacteristic
508C22×D4—21no—
509C22×D4C23×C3711yescharacteristic
510C23×C4C23×C3711yescharacteristic
511AGL(1,ℤ/8)—22no—
512AGL(1,ℤ/8)—41no—
513C2×SD16—21no—
514C2×D8—21no—
515C2×M16—21no—
516C2×M16—22no—
517C2×M16—41no—
518C2×M16C23×C3711yescharacteristic
519C2×M16C23×C3711yescharacteristic
520C2×M16C23×C3711yescharacteristic
521C2×M16C23×C3711yescharacteristic
522C22×C8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526#126—22no—
527#126—22no—
528#126—22no—
529#126—22no—
530#125—22no—
531#125—22no—
532#125—22no—
533#125—21no—
534#125—21no—
535#124—22no—
536#124—21no—
537#124—22no—
538#124—41no—
539#123—22no—
540#123—22no—
541#123—21no—
542#123—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—22no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8D4×C3711yescharacteristic
553C22⋊Q8D4×C3711yescharacteristic
554#121—21no—
555#121—21no—
556#121—21no—
557#121—21no—
558#121D4×C3711yescharacteristic
559#121D4×C3711yescharacteristic
560#120—21no—
561C4×Q8—22no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×D4—22no—
568C4×D4—21no—
569C4×D4—22no—
570C4×D4—21no—
571C4×D4—21no—
572#117—22no—
573#117—22no—
574#117—21no—
575#117—21no—
576#117—22no—
577#117—21no—
578#117—22no—
579#117—41no—
580#117D4×C3711yescharacteristic
581#117D4×C3711yescharacteristic
582#117C23×C3711yescharacteristic
583#117C23×C3711yescharacteristic
584#117C23×C3711yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4D4×C3712yes—
589C2×C4⋊C4D4×C3711yescharacteristic
590C2×C4⋊C4D4×C3711yescharacteristic
591C2×C4⋊C4C23×C3711yescharacteristic
592C2×C4⋊C4C23×C3711yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4D4×C3712yes—
599C2×C42—21no—
600C2×C42C23×C3711yescharacteristic
601C2×C42C23×C3711yescharacteristic
602#107—21no—
603#107—21no—
604#107—21no—
605#106—21no—
606#106—21no—
607#106—21no—
608#104—22no—
609#104—41no—
610#103—21no—
611#102—21no—
612#102—21no—
613#102—21no—
614#102—21no—
615#102—21no—
616#102—21no—
617#102—21no—
618#101—22no—
619#101—41no—
620C22⋊C8—21no—
621C22⋊C8—21no—
622#95—22no—
623C24—21no—
624C24C2×D4×C3711yescharacteristic
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629C2×Q8—22no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×D4×C3711yescharacteristic
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—41no—
647C2×D4—41no—
648C2×D4—82no—
649C2×D4C2×D4×C3711yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4C2×D4×C3712yes—
662C22×C4C2×D4×C3711yescharacteristic
663C22×C4C2×D4×C3711yescharacteristic
664C22×C4C2×D4×C3711yescharacteristic
665C22×C4C2×D4×C3711yescharacteristic
666C22×C4C2×D4×C3711yescharacteristic
667C22×C4C2×D4×C3712yes—
668C22×C4C24×C3711yescharacteristic
669SD16—42no—
670D8—42no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16#41×C3712yes—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—42no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—82no—
705C4⋊C4C2×D4×C3711yescharacteristic
706C4⋊C4C2×D4×C3711yescharacteristic
707C4⋊C4C2×D4×C3711yescharacteristic
708C4⋊C4C2×D4×C3711yescharacteristic
709C4⋊C4C2×D4×C3711yescharacteristic
710C4⋊C4C2×D4×C3711yescharacteristic
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—44no—
726C22⋊C4—42no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—82no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42#41×C3712yes—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—42no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23#120×C3711yescharacteristic
753C23#120×C3711yescharacteristic
754C23C22×D4×C3711yescharacteristic
755Q8—21no—
756Q8—21no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—82no—
762D4—21no—
763D4—21no—
764D4—42no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—81no—
772D4—82no—
773D4—82no—
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—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4#120×C3711yescharacteristic
810C2×C4#120×C3711yescharacteristic
811C2×C4C22×D4×C3711yescharacteristic
812C2×C4C22×D4×C3711yescharacteristic
813C2×C4C2×#41×C3711yescharacteristic
814C2×C4C2×#41×C3711yescharacteristic
815C2×C4H(5,𝔽2)×C3711yescharacteristic
816C2×C42−1+4×C3711yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—82no—
835C22—82no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C3711yescharacteristic
840C22C37×#54611yescharacteristic
841C22C37×#54711yescharacteristic
842C4—21no—
843C4—21no—
844C4—42no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C37×#53211yescharacteristic
857C4C37×#53711yescharacteristic
858C4C37×#54611yescharacteristic
859C4C37×#54711yescharacteristic
860C2—21no—
861C2—21no—
862C2—41no—
863C2—41no—
864C2—81no—
865C2—161no—
866C2C37×#243011yescharacteristic
867C2C37×#302011yescharacteristic
868C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3055C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3495C2semidirect
2. C37×#3094C2semidirect
4. C37×#2620C2semidirect
5. C37×#2060C2semidirect
6. C37×#2038C2semidirect
7. C37×#2027C2semidirect
8. C37×#2003C2semidirect
9. C37×#1901C2semidirect
10. C37×#1897C2semidirect
11. C37×#1888C2semidirect
12. C37×#1883C2semidirect
13. C37×#1859C2semidirect
14. C37×#1857C2semidirect
15. C37×#1733C2semidirect
386. #25530C37direct (N × H)
426. #3495C2×C37semidirect
427. #3094C2×C37semidirect
429. #2620C2×C37semidirect
430. #2060C2×C37semidirect
431. #2038C2×C37semidirect
432. #2027C2×C37semidirect
433. #2003C2×C37semidirect
434. #1901C2×C37semidirect
435. #1897C2×C37semidirect
436. #1888C2×C37semidirect
437. #1883C2×C37semidirect
438. #1859C2×C37semidirect
439. #1857C2×C37semidirect
440. #1733C2×C37semidirect
505. C37#25530direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34952
C37×#30942
C37×#30552
C37×#26202
C37×#20602
C37×#20382
C37×#20272
C37×#20032
C37×#19012
C37×#18972
C37×#18882
C37×#18832
C37×#18592
C37×#18572
C37×#17332
#2553037