Finite Group Databasebeta

← C37×#23878 #22645131

Subgroups — C37×#23878 #22645131

Order 9472.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#575C211yesmaximal, characteristic, complemented
2C37×#3488C211yesmaximal, characteristic, complemented
3C2×C37×#455C211yesmaximal, characteristic, complemented
4C2×C37×#453C211yesmaximal, characteristic, complemented
5C37×#3005C211yesmaximal, characteristic, complemented
6C37×#2431C211yesmaximal, characteristic, complemented
7C37×#2007C211yesmaximal, characteristic, complemented
8C37×#2006C211yesmaximal, characteristic, complemented
9C37×#2004C211yesmaximal, characteristic, complemented
10C37×#2002C211yesmaximal, characteristic, complemented
11C37×#1900C211yesmaximal, characteristic, complemented
12C37×#1883C211yesmaximal, characteristic, complemented
13C37×#1882C211yesmaximal, characteristic, complemented
14C37×#1871C211yesmaximal, characteristic, complemented
15C37×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C22×#41×C37C2211yescharacteristic, complemented
19C37×#575—24no—
20C37×#575—24no—
21C2×#137×C37—21no—
22C2×#137×C37C2211yescharacteristic
23C2×#137×C37C2211yescharacteristic, complemented
24C2×#137×C37C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C37—21no—
26C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
29C2×#135×C37—21no—
30C2×#135×C37—21no—
31C22×M16×C37C2211yescharacteristic, complemented
32C37×#550—21no—
33C37×#548—21no—
34C37×#546—21no—
35C37×#546—22no—
36D42×C37—22no—
37D42×C37—21no—
38C37×#537—21no—
39C37×#537C2211yescharacteristic
40C37×#535—21no—
41C37×#535C2211yescharacteristic
42C2×#127×C37C2211yescharacteristic, complemented
43C2×#124×C37C2211yescharacteristic, complemented
44C37×#525—21no—
45C37×#525C2211yescharacteristic
46C2×#121×C37—21no—
47C2×#121×C37C2211yescharacteristic
48C37×#520C2211yescharacteristic
49C37×#455—24no—
50C37×#453—24no—
51C37×#452—21no—
52C37×#452—21no—
53C37×#449—21no—
54C37×#449—21no—
55C2×#104×C37C2211yescharacteristic
56C2×#104×C37C2211yescharacteristic
57C2×#104×C37C2211yescharacteristic, complemented
58C2×#104×C37C2211yescharacteristic, complemented
59C2×#104×C37C2211yescharacteristic, complemented
60C2×#104×C37C2211yescharacteristic, complemented
61C37×#419C2211yescharacteristic, complemented
62C37×#418C2211yescharacteristic, complemented
63C2×#100×C37C2211yescharacteristic, complemented
64C2×#100×C37C2211yescharacteristic, complemented
65C37×#407C2211yescharacteristic, complemented
66C37×#392—22no—
67C37×#391C2211yescharacteristic, complemented
68C37×#390C2211yescharacteristic, complemented
69C37×#386—22no—
70C4×C22⋊C4×C37C2211yescharacteristic, complemented
71C37×#343C2211yescharacteristic, complemented
72C37×#343C2211yescharacteristic, complemented
73C37×#339C2211yescharacteristic, complemented
74C37×#339C2211yescharacteristic, complemented
75H(5,𝔽2)×C37—22no—
76H(5,𝔽2)×C37—22no—
77H(5,𝔽2)×C37—41no—
78H(5,𝔽2)×C37—41no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—21no—
82C2×#41×C37—21no—
83C2×#41×C37—22no—
84C2×#41×C37—22no—
85C2×#41×C37—22no—
86C2×#41×C37—22no—
87C2×#41×C37—21no—
88C2×#41×C37—21no—
89C2×#41×C37—21no—
90C2×#41×C37—21no—
91C2×#41×C37—41no—
92C2×#41×C37—41no—
93C2×#41×C37—41no—
94C2×#41×C37—41no—
95C2×#41×C37D411yescharacteristic, complemented
96C2×#41×C37D411yescharacteristic, complemented
97C2×#41×C37C2311yescharacteristic
98C2×#41×C37C2311yescharacteristic
99C2×#41×C37C2311yescharacteristic
100C22×Q8×C37D411yescharacteristic, complemented
101C22×Q8×C37C2311yescharacteristic
102C22×D4×C37—21no—
103C22×D4×C37—22no—
104C22×D4×C37—22no—
105C22×D4×C37—21no—
106C22×D4×C37—21no—
107C22×D4×C37—21no—
108C22×D4×C37—22no—
109C22×D4×C37D412yes—
110C22×D4×C37D411yescharacteristic, complemented
111C22×D4×C37C2311yescharacteristic
112C22×D4×C37C2311yescharacteristic
113C23×C4×C37—21no—
114C23×C4×C37—21no—
115C23×C4×C37C2311yescharacteristic
116#137×C37—28no—
117#137×C37—22no—
118#137×C37—22no—
119#137×C37—22no—
120#137×C37—22no—
121#137×C37—41no—
122#137×C37D414yescomplemented
123AGL(1,ℤ/8)×C37—28no—
124AGL(1,ℤ/8)×C37—22no—
125AGL(1,ℤ/8)×C37—22no—
126AGL(1,ℤ/8)×C37—22no—
127AGL(1,ℤ/8)×C37—22no—
128AGL(1,ℤ/8)×C37—41no—
129AGL(1,ℤ/8)×C37D414yescomplemented
130#135×C37—28no—
131#135×C37—28no—
132C2×Q16×C37—21no—
133C2×Q16×C37—21no—
134C2×Q16×C37—21no—
135C2×SD16×C37—21no—
136C2×SD16×C37—21no—
137C2×SD16×C37—21no—
138C2×SD16×C37—21no—
139C2×SD16×C37—21no—
140C2×SD16×C37—21no—
141C2×D8×C37—21no—
142C2×D8×C37—21no—
143C2×D8×C37—21no—
144C2×M16×C37—21no—
145C2×M16×C37—22no—
146C2×M16×C37—22no—
147C2×M16×C37C2311yescharacteristic
148C2×M16×C37C2311yescharacteristic
149C2×M16×C37C2311yescharacteristic
150C2×M16×C37C2311yescharacteristic
151C22×C8×C37—21no—
152#127×C37—22no—
153#127×C37—21no—
154#127×C37—22no—
155#127×C37—41no—
156#124×C37—22no—
157#124×C37—21no—
158#124×C37—22no—
159#124×C37—41no—
160#123×C37—22no—
161#123×C37—21no—
162C22⋊Q8×C37—22no—
163C22⋊Q8×C37—21no—
164C22⋊Q8×C37—21no—
165C22⋊Q8×C37D411yescharacteristic, complemented
166C22⋊Q8×C37D411yescharacteristic, complemented
167#121×C37—22no—
168#121×C37—22no—
169#121×C37—22no—
170#121×C37—22no—
171#121×C37—22no—
172#121×C37—21no—
173#121×C37—21no—
174#121×C37—21no—
175#121×C37—21no—
176#121×C37—21no—
177#121×C37—21no—
178#121×C37—22no—
179#121×C37—21no—
180#121×C37—21no—
181#121×C37D411yescharacteristic, complemented
182#121×C37D411yescharacteristic, complemented
183#120×C37—22no—
184#120×C37—22no—
185#120×C37—22no—
186#120×C37—21no—
187#120×C37—22no—
188C4×Q8×C37—21no—
189C4×D4×C37—22no—
190C4×D4×C37—22no—
191C4×D4×C37—21no—
192C4×D4×C37—22no—
193C4×D4×C37—21no—
194C4×D4×C37—21no—
195#117×C37—21no—
196#117×C37C2311yescharacteristic
197C2×C4⋊C4×C37—21no—
198C2×C4⋊C4×C37C2311yescharacteristic
199C2×C22⋊C4×C37—22no—
200C2×C22⋊C4×C37—22no—
201C2×C22⋊C4×C37—21no—
202C2×C22⋊C4×C37—22no—
203C2×C22⋊C4×C37D412yes—
204C2×C42×C37C2311yescharacteristic
205C2×C42×C37C2311yescharacteristic
206#104×C37—22no—
207#104×C37—22no—
208#104×C37—22no—
209#104×C37—22no—
210#104×C37—41no—
211#104×C37—41no—
212#103×C37—21no—
213#103×C37—21no—
214#102×C37—21no—
215#102×C37—21no—
216#100×C37—22no—
217#100×C37—22no—
218C22⋊C8×C37—21no—
219C22⋊C8×C37—21no—
220#95×C37—21no—
221#95×C37—22no—
222C24×C37—22no—
223C24×C37—21no—
224C24×C37—21no—
225C24×C37C2×D412yes—
226C24×C37C2×D411yescharacteristic
227#41×C37—21no—
228#41×C37—21no—
229#41×C37—24no—
230#41×C37—24no—
231#41×C37—22no—
232#41×C37—22no—
233#41×C37—21no—
234#41×C37—21no—
235#41×C37—21no—
236#41×C37—21no—
237#41×C37—21no—
238#41×C37—21no—
239#41×C37—21no—
240#41×C37—21no—
241#41×C37—42no—
242#41×C37—42no—
243#41×C37—41no—
244#41×C37—41no—
245#41×C37—42no—
246#41×C37—42no—
247#41×C37—42no—
248#41×C37—42no—
249#41×C37—42no—
250#41×C37—42no—
251#41×C37—42no—
252#41×C37—42no—
253#41×C37—42no—
254#41×C37—42no—
255#41×C37—42no—
256#41×C37—42no—
257#41×C37C2×D412yes—
258#41×C37C2×D412yes—
259C2×Q8×C37—21no—
260C2×Q8×C37—21no—
261C2×Q8×C37—22no—
262C2×Q8×C37—21no—
263C2×Q8×C37—21no—
264C2×Q8×C37—21no—
265C2×Q8×C37—21no—
266C2×Q8×C37—41no—
267C2×Q8×C37C2×D411yescharacteristic
268C2×Q8×C37C2×D411yescharacteristic
269C2×Q8×C37C2×D411yescharacteristic
270C2×Q8×C37C2×D412yescomplemented
271C2×D4×C37—21no—
272C2×D4×C37—22no—
273C2×D4×C37—22no—
274C2×D4×C37—22no—
275C2×D4×C37—22no—
276C2×D4×C37—21no—
277C2×D4×C37—21no—
278C2×D4×C37—21no—
279C2×D4×C37—21no—
280C2×D4×C37—21no—
281C2×D4×C37—22no—
282C2×D4×C37—22no—
283C2×D4×C37—22no—
284C2×D4×C37—21no—
285C2×D4×C37—22no—
286C2×D4×C37—21no—
287C2×D4×C37—21no—
288C2×D4×C37—21no—
289C2×D4×C37—21no—
290C2×D4×C37—21no—
291C2×D4×C37—21no—
292C2×D4×C37—21no—
293C2×D4×C37—21no—
294C2×D4×C37—21no—
295C2×D4×C37—21no—
296C2×D4×C37—21no—
297C2×D4×C37—21no—
298C2×D4×C37—41no—
299C2×D4×C37—42no—
300C2×D4×C37—42no—
301C2×D4×C37—42no—
302C2×D4×C37—44no—
303C2×D4×C37—42no—
304C2×D4×C37—42no—
305C2×D4×C37—44no—
306C2×D4×C37—44no—
307C2×D4×C37—42no—
308C2×D4×C37—42no—
309C2×D4×C37—41no—
310C2×D4×C37—41no—
311C2×D4×C37—42no—
312C2×D4×C37—44no—
313C2×D4×C37—82no—
314C2×D4×C37—82no—
315C2×D4×C37—84no—
316C2×D4×C37C2×D411yescharacteristic
317C2×D4×C37C2×D411yescharacteristic
318C2×D4×C37C2×D411yescharacteristic
319C2×D4×C37C2×D412yescomplemented
320C22×C4×C37—21no—
321C22×C4×C37—21no—
322C22×C4×C37—21no—
323C22×C4×C37—21no—
324C22×C4×C37—21no—
325C22×C4×C37—22no—
326C22×C4×C37—21no—
327C22×C4×C37—21no—
328C22×C4×C37—21no—
329C22×C4×C37—22no—
330C22×C4×C37—21no—
331C22×C4×C37—21no—
332C22×C4×C37—21no—
333C22×C4×C37—21no—
334C22×C4×C37—21no—
335C22×C4×C37—42no—
336C22×C4×C37—42no—
337C22×C4×C37—42no—
338C22×C4×C37—42no—
339C22×C4×C37—41no—
340C22×C4×C37—41no—
341C22×C4×C37C2×D411yescharacteristic
342C22×C4×C37C2×D411yescharacteristic
343C22×C4×C37C2×D411yescharacteristic
344C22×C4×C37C2×D411yescharacteristic
345C22×C4×C37C2×D411yescharacteristic
346C22×C4×C37C2×D412yes—
347C22×C4×C37C2411yescharacteristic
348Q16×C37—24no—
349Q16×C37—24no—
350Q16×C37—42no—
351SD16×C37—24no—
352SD16×C37—24no—
353SD16×C37—24no—
354SD16×C37—24no—
355SD16×C37—42no—
356SD16×C37—42no—
357D8×C37—24no—
358D8×C37—24no—
359D8×C37—42no—
360M16×C37—24no—
361M16×C37—21no—
362M16×C37—21no—
363M16×C37—21no—
364M16×C37—21no—
365M16×C37—21no—
366M16×C37—21no—
367M16×C37C2×D412yescomplemented
368M16×C37C2×D412yescomplemented
369C2×C8×C37—24no—
370C2×C8×C37—21no—
371C2×C8×C37—21no—
372C2×C8×C37—21no—
373C2×C8×C37—21no—
374C4⋊C4×C37—22no—
375C4⋊C4×C37—22no—
376C4⋊C4×C37—21no—
377C4⋊C4×C37—21no—
378C4⋊C4×C37—21no—
379C4⋊C4×C37—21no—
380C4⋊C4×C37C2×D411yescharacteristic
381C4⋊C4×C37C2×D411yescharacteristic
382C22⋊C4×C37—22no—
383C22⋊C4×C37—22no—
384C22⋊C4×C37—22no—
385C22⋊C4×C37—22no—
386C22⋊C4×C37—22no—
387C22⋊C4×C37—21no—
388C22⋊C4×C37—21no—
389C22⋊C4×C37—21no—
390C22⋊C4×C37—21no—
391C22⋊C4×C37—22no—
392C22⋊C4×C37—22no—
393C22⋊C4×C37—21no—
394C22⋊C4×C37—44no—
395C22⋊C4×C37—42no—
396C22⋊C4×C37—82no—
397C42×C37—22no—
398C42×C37—21no—
399C42×C37—21no—
400C42×C37—21no—
401C42×C37—21no—
402C42×C37—21no—
403C23×C37—21no—
404C23×C37—21no—
405C23×C37—21no—
406C23×C37—22no—
407C23×C37—21no—
408C23×C37—21no—
409C23×C37—22no—
410C23×C37—22no—
411C23×C37—22no—
412C23×C37—41no—
413C23×C37—41no—
414C23×C37—42no—
415C23×C37—42no—
416C23×C37—42no—
417C23×C37—42no—
418C23×C37—44no—
419C23×C37—42no—
420C23×C37—42no—
421C23×C37—41no—
422C23×C37—41no—
423C23×C37—81no—
424C23×C37—82no—
425C23×C37—82no—
426C23×C37#12011yescharacteristic
427C23×C37#12011yescharacteristic
428C23×C37C22×D411yescharacteristic
429Q8×C37—21no—
430Q8×C37—21no—
431Q8×C37—22no—
432Q8×C37—21no—
433Q8×C37—21no—
434Q8×C37—22no—
435Q8×C37—21no—
436Q8×C37—42no—
437Q8×C37—41no—
438Q8×C37—41no—
439Q8×C37#12012yes—
440D4×C37—22no—
441D4×C37—22no—
442D4×C37—21no—
443D4×C37—22no—
444D4×C37—21no—
445D4×C37—21no—
446D4×C37—21no—
447D4×C37—22no—
448D4×C37—21no—
449D4×C37—42no—
450D4×C37—42no—
451D4×C37—44no—
452D4×C37—42no—
453D4×C37—44no—
454D4×C37—44no—
455D4×C37—42no—
456D4×C37—44no—
457D4×C37—44no—
458D4×C37—41no—
459D4×C37—41no—
460D4×C37—41no—
461D4×C37—41no—
462D4×C37—41no—
463D4×C37—41no—
464D4×C37—41no—
465D4×C37—41no—
466D4×C37—41no—
467D4×C37—41no—
468D4×C37—81no—
469D4×C37—82no—
470D4×C37—82no—
471D4×C37—82no—
472D4×C37—82no—
473D4×C37—88no—
474D4×C37#12012yes—
475C2×C4×C37—21no—
476C2×C4×C37—21no—
477C2×C4×C37—21no—
478C2×C4×C37—21no—
479C2×C4×C37—21no—
480C2×C4×C37—21no—
481C2×C4×C37—21no—
482C2×C4×C37—21no—
483C2×C4×C37—21no—
484C2×C4×C37—21no—
485C2×C4×C37—21no—
486C2×C4×C37—22no—
487C2×C4×C37—22no—
488C2×C4×C37—22no—
489C2×C4×C37—21no—
490C2×C4×C37—22no—
491C2×C4×C37—21no—
492C2×C4×C37—21no—
493C2×C4×C37—21no—
494C2×C4×C37—22no—
495C2×C4×C37—42no—
496C2×C4×C37—42no—
497C2×C4×C37—42no—
498C2×C4×C37—44no—
499C2×C4×C37—44no—
500C2×C4×C37—44no—
501C2×C4×C37—41no—
502C2×C4×C37—41no—
503C2×C4×C37—41no—
504C2×C4×C37—41no—
505C2×C4×C37—41no—
506C2×C4×C37—41no—
507C2×C4×C37—41no—
508C2×C4×C37—41no—
509C2×C4×C37—42no—
510C2×C4×C37—41no—
511C2×C4×C37—41no—
512C2×C4×C37—41no—
513C2×C4×C37—82no—
514C2×C4×C37#12011yescharacteristic
515C2×C4×C37#12011yescharacteristic
516C2×C4×C37C22×D411yescharacteristic
517C2×C4×C37C22×D411yescharacteristic
518C2×C4×C37C22×D411yescharacteristic
519C2×C4×C37C22×D411yescharacteristic
520C2×C4×C37H(5,𝔽2)11yescharacteristic
521C2×C4×C37H(5,𝔽2)11yescharacteristic
522C8×C37—22no—
523C8×C37—22no—
524C8×C37—41no—
525C8×C37—41no—
526#23878C3711yesmaximal, characteristic, direct product factor, Sylow
527C22×C37—21no—
528C22×C37—21no—
529C22×C37—21no—
530C22×C37—21no—
531C22×C37—22no—
532C22×C37—21no—
533C22×C37—21no—
534C22×C37—21no—
535C22×C37—21no—
536C22×C37—44no—
537C22×C37—41no—
538C22×C37—41no—
539C22×C37—41no—
540C22×C37—42no—
541C22×C37—41no—
542C22×C37—42no—
543C22×C37—41no—
544C22×C37—42no—
545C22×C37—41no—
546C22×C37—42no—
547C22×C37—41no—
548C22×C37—41no—
549C22×C37—81no—
550C22×C37—81no—
551C22×C37—82no—
552C22×C37—82no—
553C22×C37—82no—
554C22×C37—84no—
555C22×C37—81no—
556C22×C37—81no—
557C22×C37—164no—
558C22×C37C2×#12011yescharacteristic
559C22×C37D4211yescharacteristic
560C22×C37D4211yescharacteristic
561C4×C37—21no—
562C4×C37—21no—
563C4×C37—22no—
564C4×C37—42no—
565C4×C37—41no—
566C4×C37—41no—
567C4×C37—42no—
568C4×C37—41no—
569C4×C37—42no—
570C4×C37—41no—
571C4×C37—81no—
572C4×C37C2×#12011yescharacteristic
573C4×C37#53411yescharacteristic
574C4×C37D4211yescharacteristic
575C4×C37D4211yescharacteristic
576C2×#575C2×C3711yescharacteristic, complemented
577#3488C2×C3711yescharacteristic, complemented
578C2×#455C2×C3711yescharacteristic, complemented
579C2×#453C2×C3711yescharacteristic, complemented
580#3005C2×C3711yescharacteristic, complemented
581#2431C2×C3711yescharacteristic, complemented
582#2007C2×C3711yescharacteristic, complemented
583#2006C2×C3711yescharacteristic, complemented
584#2004C2×C3711yescharacteristic, complemented
585#2002C2×C3711yescharacteristic, complemented
586#1900C2×C3711yescharacteristic, complemented
587#1883C2×C3711yescharacteristic, complemented
588#1882C2×C3711yescharacteristic, complemented
589#1871C2×C3711yescharacteristic, complemented
590#1789C2×C3711yescharacteristic, complemented
591C2×C37—21no—
592C2×C37—21no—
593C2×C37—41no—
594C2×C37—41no—
595C2×C37—42no—
596C2×C37—82no—
597C2×C37—81no—
598C2×C37—82no—
599C2×C37—81no—
600C2×C37#240311yescharacteristic
601C2×C37#301811yescharacteristic
602C2×C37#301911yescharacteristic
603C2×H(5,𝔽2)C22×C3711yescharacteristic
604C22×#41C22×C3711yescharacteristic
605C22×#41C22×C3711yescharacteristic, complemented
606#575—24no—
607#575—24no—
608C2×#137—21no—
609C2×#137C22×C3711yescharacteristic
610C2×#137C22×C3711yescharacteristic, complemented
611C2×#137C22×C3711yescharacteristic, complemented
612C2×AGL(1,ℤ/8)—21no—
613C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
614C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
615C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
616C2×#135—21no—
617C2×#135—21no—
618C22×M16C22×C3711yescharacteristic, complemented
619#550—21no—
620#548—21no—
621#546—21no—
622#546—22no—
623D42—22no—
624D42—21no—
625#537—21no—
626#537C22×C3711yescharacteristic
627#535—21no—
628#535C22×C3711yescharacteristic
629C2×#127C22×C3711yescharacteristic, complemented
630C2×#124C22×C3711yescharacteristic, complemented
631#525—21no—
632#525C22×C3711yescharacteristic
633C2×#121—21no—
634C2×#121C22×C3711yescharacteristic
635#520C22×C3711yescharacteristic
636#455—24no—
637#453—24no—
638#452—21no—
639#452—21no—
640#449—21no—
641#449—21no—
642C2×#104C22×C3711yescharacteristic
643C2×#104C22×C3711yescharacteristic
644C2×#104C22×C3711yescharacteristic, complemented
645C2×#104C22×C3711yescharacteristic, complemented
646C2×#104C22×C3711yescharacteristic, complemented
647C2×#104C22×C3711yescharacteristic, complemented
648#419C22×C3711yescharacteristic, complemented
649#418C22×C3711yescharacteristic, complemented
650C2×#100C22×C3711yescharacteristic, complemented
651C2×#100C22×C3711yescharacteristic, complemented
652#407C22×C3711yescharacteristic, complemented
653#392—22no—
654#391C22×C3711yescharacteristic, complemented
655#390C22×C3711yescharacteristic, complemented
656#386—22no—
657C4×C22⋊C4C22×C3711yescharacteristic, complemented
658#343C22×C3711yescharacteristic, complemented
659#343C22×C3711yescharacteristic, complemented
660#339C22×C3711yescharacteristic, complemented
661#339C22×C3711yescharacteristic, complemented
662C37#2387811yescharacteristic, direct product factor, Sylow
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C3711yescharacteristic, complemented
684C2×#41D4×C3711yescharacteristic, complemented
685C2×#41C23×C3711yescharacteristic
686C2×#41C23×C3711yescharacteristic
687C2×#41C23×C3711yescharacteristic
688C22×Q8D4×C3711yescharacteristic, complemented
689C22×Q8C23×C3711yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C3712yes—
698C22×D4D4×C3711yescharacteristic, complemented
699C22×D4C23×C3711yescharacteristic
700C22×D4C23×C3711yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C3711yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C3714yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C3714yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C3711yescharacteristic
736C2×M16C23×C3711yescharacteristic
737C2×M16C23×C3711yescharacteristic
738C2×M16C23×C3711yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C3711yescharacteristic, complemented
754C22⋊Q8D4×C3711yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C3711yescharacteristic, complemented
770#121D4×C3711yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C3711yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C3711yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C3712yes—
792C2×C42C23×C3711yescharacteristic
793C2×C42C23×C3711yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C3712yes—
814C24C2×D4×C3711yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C3712yes—
846#41C2×D4×C3712yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C3711yescharacteristic
856C2×Q8C2×D4×C3711yescharacteristic
857C2×Q8C2×D4×C3711yescharacteristic
858C2×Q8C2×D4×C3712yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C3711yescharacteristic
905C2×D4C2×D4×C3711yescharacteristic
906C2×D4C2×D4×C3711yescharacteristic
907C2×D4C2×D4×C3712yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C3711yescharacteristic
930C22×C4C2×D4×C3711yescharacteristic
931C22×C4C2×D4×C3711yescharacteristic
932C22×C4C2×D4×C3711yescharacteristic
933C22×C4C2×D4×C3711yescharacteristic
934C22×C4C2×D4×C3712yes—
935C22×C4C24×C3711yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C3712yescomplemented
956M16C2×D4×C3712yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C3711yescharacteristic
969C4⋊C4C2×D4×C3711yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C3711yescharacteristic
1015C23#120×C3711yescharacteristic
1016C23C22×D4×C3711yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C3712yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C3712yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C3711yescharacteristic
1103C2×C4#120×C3711yescharacteristic
1104C2×C4C22×D4×C3711yescharacteristic
1105C2×C4C22×D4×C3711yescharacteristic
1106C2×C4C22×D4×C3711yescharacteristic
1107C2×C4C22×D4×C3711yescharacteristic
1108C2×C4H(5,𝔽2)×C3711yescharacteristic
1109C2×C4H(5,𝔽2)×C3711yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C3711yescharacteristic
1146C22D42×C3711yescharacteristic
1147C22D42×C3711yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×#120×C3711yescharacteristic
1160C4C37×#53411yescharacteristic
1161C4D42×C3711yescharacteristic
1162C4D42×C3711yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C37×#240311yescharacteristic
1173C2C37×#301811yescharacteristic
1174C2C37×#301911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
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. C2×C37×#575C2semidirect
2. C37×#3488C2semidirect
3. C2×C37×#455C2semidirect
4. C2×C37×#453C2semidirect
5. C37×#3005C2semidirect
6. C37×#2431C2semidirect
7. C37×#2007C2semidirect
8. C37×#2006C2semidirect
9. C37×#2004C2semidirect
10. C37×#2002C2semidirect
11. C37×#1900C2semidirect
12. C37×#1883C2semidirect
13. C37×#1882C2semidirect
14. C37×#1871C2semidirect
15. C37×#1789C2semidirect
18. C22×#41×C37C22semidirect
23. C2×#137×C37C22semidirect
24. C2×#137×C37C22semidirect
27. C2×AGL(1,ℤ/8)×C37C22semidirect
28. C2×AGL(1,ℤ/8)×C37C22semidirect
31. C22×M16×C37C22semidirect
42. C2×#127×C37C22semidirect
43. C2×#124×C37C22semidirect
57. C2×#104×C37C22semidirect
58. C2×#104×C37C22semidirect
59. C2×#104×C37C22semidirect
60. C2×#104×C37C22semidirect
61. C37×#419C22semidirect
62. C37×#418C22semidirect
63. C2×#100×C37C22semidirect
64. C2×#100×C37C22semidirect
65. C37×#407C22semidirect
67. C37×#391C22semidirect
68. C37×#390C22semidirect
70. C4×C22⋊C4×C37C22semidirect
71. C37×#343C22semidirect
72. C37×#343C22semidirect
73. C37×#339C22semidirect
74. C37×#339C22semidirect
95. C2×#41×C37D4semidirect
96. C2×#41×C37D4semidirect
100. C22×Q8×C37D4semidirect
110. C22×D4×C37D4semidirect
122. #137×C37D4semidirect
129. AGL(1,ℤ/8)×C37D4semidirect
165. C22⋊Q8×C37D4semidirect
166. C22⋊Q8×C37D4semidirect
181. #121×C37D4semidirect
182. #121×C37D4semidirect
270. C2×Q8×C37C2×D4semidirect
319. C2×D4×C37C2×D4semidirect
367. M16×C37C2×D4semidirect
368. M16×C37C2×D4semidirect
526. #23878C37direct (N × H)
576. C2×#575C2×C37semidirect
577. #3488C2×C37semidirect
578. C2×#455C2×C37semidirect
579. C2×#453C2×C37semidirect
580. #3005C2×C37semidirect
581. #2431C2×C37semidirect
582. #2007C2×C37semidirect
583. #2006C2×C37semidirect
584. #2004C2×C37semidirect
585. #2002C2×C37semidirect
586. #1900C2×C37semidirect
587. #1883C2×C37semidirect
588. #1882C2×C37semidirect
589. #1871C2×C37semidirect
590. #1789C2×C37semidirect
605. C22×#41C22×C37semidirect
610. C2×#137C22×C37semidirect
611. C2×#137C22×C37semidirect
614. C2×AGL(1,ℤ/8)C22×C37semidirect
615. C2×AGL(1,ℤ/8)C22×C37semidirect
618. C22×M16C22×C37semidirect
629. C2×#127C22×C37semidirect
630. C2×#124C22×C37semidirect
644. C2×#104C22×C37semidirect
645. C2×#104C22×C37semidirect
646. C2×#104C22×C37semidirect
647. C2×#104C22×C37semidirect
648. #419C22×C37semidirect
649. #418C22×C37semidirect
650. C2×#100C22×C37semidirect
651. C2×#100C22×C37semidirect
652. #407C22×C37semidirect
654. #391C22×C37semidirect
655. #390C22×C37semidirect
657. C4×C22⋊C4C22×C37semidirect
658. #343C22×C37semidirect
659. #343C22×C37semidirect
660. #339C22×C37semidirect
661. #339C22×C37semidirect
662. C37#23878direct (N × H)
683. C2×#41D4×C37semidirect
684. C2×#41D4×C37semidirect
688. C22×Q8D4×C37semidirect
698. C22×D4D4×C37semidirect
710. #137D4×C37semidirect
717. AGL(1,ℤ/8)D4×C37semidirect
753. C22⋊Q8D4×C37semidirect
754. C22⋊Q8D4×C37semidirect
769. #121D4×C37semidirect
770. #121D4×C37semidirect
858. C2×Q8C2×D4×C37semidirect
907. C2×D4C2×D4×C37semidirect
955. M16C2×D4×C37semidirect
956. M16C2×D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5752
C37×#34882
C2×C37×#4552
C2×C37×#4532
C37×#30052
C37×#24312
C37×#20072
C37×#20062
C37×#20042
C37×#20022
C37×#19002
C37×#18832
C37×#18822
C37×#18712
C37×#17892
#2387837