Finite Group Databasebeta

← C37×#28480 #22649733

Subgroups — C37×#28480 #22649733

Order 9472.

1272 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#496C211yesmaximal, characteristic, complemented
2C2×C37×#496C211yesmaximal, characteristic, complemented
3C2×C37×#492C211yesmaximal, characteristic, complemented
4C2×C37×#460C211yesmaximal, characteristic, complemented
5C2×C37×#463C211yesmaximal, characteristic, complemented
6C2×C37×#440C211yesmaximal, characteristic, complemented
7C37×#2545C211yesmaximal, characteristic, complemented
8C37×#2541C211yesmaximal, characteristic, complemented
9C37×#2014C211yesmaximal, characteristic, complemented
10C37×#2013C211yesmaximal, characteristic, complemented
11C37×#2012C211yesmaximal, characteristic, complemented
12C37×#2011C211yesmaximal, characteristic, complemented
13C37×#1973C211yesmaximal, characteristic, complemented
14C37×#1970C211yesmaximal, characteristic, complemented
15C37×#1771C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C22×SD16×C37C2211yescharacteristic
22C22×D8×C37C2211yescharacteristic
23C22×D8×C37C2211yescharacteristic
24C22×D8×C37C2211yescharacteristic
25C2×C4⋊Q8×C37C2211yescharacteristic
26C2×#127×C37C2211yescharacteristic
27C2×#127×C37C2211yescharacteristic
28C2×#127×C37C2211yescharacteristic
29C2×#124×C37C2211yescharacteristic
30C2×#124×C37C2211yescharacteristic
31C2×#121×C37—22no—
32C2×C4×Q8×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C37×#496—24no—
35C37×#496—24no—
36C37×#492—24no—
37C37×#463—24no—
38C37×#460—24no—
39C37×#440—24no—
40C2×#107×C37C2211yescharacteristic
41C2×C4⋊C8×C37C2211yescharacteristic
42C2×#103×C37C2211yescharacteristic
43C2×#103×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#97×C37C2211yescharacteristic
49C2×#97×C37C2211yescharacteristic
50C2×C4×C8×C37C2211yescharacteristic
51C37×#396—22no—
52C37×#392—22no—
53C37×#391C2211yescharacteristic
54C37×#390C2211yescharacteristic
55C37×#390C2211yescharacteristic
56C37×#390C2211yescharacteristic
57C37×#388—22no—
58C4×C4⋊C4×C37C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×Q8×C37C2311yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37—22no—
65C22×D4×C37—22no—
66C22×D4×C37—21no—
67C22×D4×C37C2311yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C22×D4×C37C2311yescharacteristic
71C23×C4×C37—21no—
72C2×SD16×C37—22no—
73C2×SD16×C37—22no—
74C2×SD16×C37—22no—
75C2×SD16×C37—22no—
76C2×SD16×C37—22no—
77C2×SD16×C37—22no—
78C2×SD16×C37—22no—
79C2×SD16×C37—22no—
80C2×SD16×C37—22no—
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—22no—
84C2×SD16×C37—41no—
85C2×SD16×C37—41no—
86C2×SD16×C37—41no—
87C2×SD16×C37—41no—
88C2×SD16×C37—41no—
89C2×SD16×C37D414yescomplemented
90C2×D8×C37—22no—
91C2×D8×C37—22no—
92C2×D8×C37—22no—
93C2×D8×C37—22no—
94C2×D8×C37—22no—
95C2×D8×C37—22no—
96C2×D8×C37—41no—
97C2×D8×C37—41no—
98C2×D8×C37—41no—
99C22×C8×C37C2311yescharacteristic
100C22×C8×C37C2311yescharacteristic
101C22×C8×C37C2311yescharacteristic
102C22×C8×C37C2311yescharacteristic
103C4⋊Q8×C37—22no—
104C4⋊Q8×C37—41no—
105#127×C37—22no—
106#127×C37—22no—
107#127×C37—22no—
108#127×C37—22no—
109#127×C37—41no—
110#127×C37—41no—
111#124×C37—22no—
112#124×C37—22no—
113#124×C37—22no—
114#124×C37—41no—
115#121×C37—48no—
116C4×Q8×C37—22no—
117C4×Q8×C37—22no—
118C4×D4×C37—22no—
119C4×D4×C37—22no—
120C2×C4⋊C4×C37—22no—
121C2×C4⋊C4×C37—21no—
122C2×C4⋊C4×C37D412yes—
123C2×C4⋊C4×C37C2311yescharacteristic
124C2×C4⋊C4×C37C2311yescharacteristic
125C2×C22⋊C4×C37—22no—
126C2×C22⋊C4×C37—22no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—22no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—22no—
131C2×C22⋊C4×C37—21no—
132C2×C42×C37—21no—
133C2×C42×C37C2311yescharacteristic
134C2×C42×C37C2311yescharacteristic
135C2×C42×C37C2311yescharacteristic
136#107×C37—22no—
137C4⋊C8×C37D414yescomplemented
138#103×C37—22no—
139#103×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—22no—
144#97×C37—22no—
145#97×C37D414yescomplemented
146C4×C8×C37—22no—
147#95×C37—22no—
148#95×C37D412yes—
149C24×C37—21no—
150C24×C37—21no—
151C24×C37—21no—
152C24×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—21no—
159C2×Q8×C37—21no—
160C2×Q8×C37—21no—
161C2×Q8×C37—21no—
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37C2×D412yes—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—21no—
181C2×D4×C37—21no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—44no—
189C2×D4×C37—44no—
190C2×D4×C37—44no—
191C2×D4×C37—44no—
192C2×D4×C37—42no—
193C2×D4×C37—42no—
194C2×D4×C37—44no—
195C2×D4×C37—82no—
196C2×D4×C37—82no—
197C2×D4×C37—82no—
198C2×D4×C37C2×D412yes—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—44no—
204C22×C4×C37—42no—
205C22×C4×C37C2×D412yes—
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D412yes—
209C22×C4×C37C2411yescharacteristic
210SD16×C37—28no—
211SD16×C37—44no—
212SD16×C37—44no—
213SD16×C37—44no—
214SD16×C37—44no—
215SD16×C37—44no—
216D8×C37—44no—
217D8×C37—44no—
218D8×C37—44no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37C2×D412yes—
226C2×C8×C37C2×D412yes—
227C2×C8×C37C2×D412yes—
228C2×C8×C37C2×D412yes—
229C2×C8×C37C2×D412yes—
230C2×C8×C37#4112yes—
231C4⋊C4×C37—24no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—44no—
237C4⋊C4×C37—42no—
238C22⋊C4×C37—44no—
239C22⋊C4×C37—44no—
240C22⋊C4×C37—42no—
241C22⋊C4×C37—42no—
242C22⋊C4×C37—42no—
243C22⋊C4×C37—44no—
244C22⋊C4×C37—44no—
245C42×C37—21no—
246C42×C37—21no—
247C42×C37—21no—
248C42×C37—21no—
249C42×C37—42no—
250C42×C37C2×D412yes—
251C42×C37C2×D412yes—
252C23×C37—22no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37—42no—
256C23×C37—42no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—42no—
267C23×C37—42no—
268C23×C37—42no—
269C23×C37—42no—
270C23×C37—42no—
271C23×C37—42no—
272C23×C37C22×D411yescharacteristic
273Q8×C37—22no—
274Q8×C37—22no—
275Q8×C37—41no—
276Q8×C37—41no—
277Q8×C37—41no—
278Q8×C37—41no—
279Q8×C37—41no—
280Q8×C37—41no—
281D4×C37—22no—
282D4×C37—22no—
283D4×C37—41no—
284D4×C37—41no—
285D4×C37—41no—
286D4×C37—41no—
287D4×C37—41no—
288D4×C37—41no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—88no—
298D4×C37—84no—
299D4×C37—84no—
300D4×C37—88no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—42no—
317C2×C4×C37—42no—
318C2×C4×C37—84no—
319C2×C4×C37#12712yes—
320C2×C4×C37#12712yes—
321C2×C4×C37AGL(1,ℤ/8)14yes—
322C2×C4×C37C22×D411yescharacteristic
323C2×C4×C37C22×D411yescharacteristic
324C2×C4×C37C22×D411yescharacteristic
325C2×C4×C37C2×#4111yescharacteristic
326C2×C4×C37H(5,𝔽2)11yescharacteristic
327C2×C4×C37H(5,𝔽2)11yescharacteristic
328C8×C37—22no—
329C8×C37—22no—
330C8×C37—22no—
331C8×C37#12114yescomplemented
332#28480C3711yesmaximal, characteristic, direct product factor, Sylow
333C22×C37—44no—
334C22×C37—42no—
335C22×C37—82no—
336C22×C37—81no—
337C22×C37—81no—
338C22×C37—82no—
339C22×C37—82no—
340C22×C37—82no—
341C22×C37—81no—
342C22×C37—81no—
343C22×C37—81no—
344C22×C37—81no—
345C22×C37—81no—
346C22×C37—81no—
347C22×C37—82no—
348C22×C37—82no—
349C22×C37—82no—
350C22×C37—81no—
351C22×C37—81no—
352C22×C37—81no—
353C22×C37C2×#12711yescharacteristic
354C22×C37D4211yescharacteristic
355C22×C37#55011yescharacteristic
356C22×C37C2×AGL(1,ℤ/8)12yes—
357C22×C37#57712yes—
358C4×C37—22no—
359C4×C37—22no—
360C4×C37—24no—
361C4×C37—42no—
362C4×C37—42no—
363C4×C37—81no—
364C4×C37—81no—
365C4×C37—81no—
366C4×C37C2×#12111yescharacteristic
367C4×C37#53511yescharacteristic
368C4×C37D4211yescharacteristic
369C4×C37#55011yescharacteristic
370C2×#496C2×C3711yescharacteristic, complemented
371C2×#496C2×C3711yescharacteristic, complemented
372C2×#492C2×C3711yescharacteristic, complemented
373C2×#460C2×C3711yescharacteristic, complemented
374C2×#463C2×C3711yescharacteristic, complemented
375C2×#440C2×C3711yescharacteristic, complemented
376#2545C2×C3711yescharacteristic, complemented
377#2541C2×C3711yescharacteristic, complemented
378#2014C2×C3711yescharacteristic, complemented
379#2013C2×C3711yescharacteristic, complemented
380#2012C2×C3711yescharacteristic, complemented
381#2011C2×C3711yescharacteristic, complemented
382#1973C2×C3711yescharacteristic, complemented
383#1970C2×C3711yescharacteristic, complemented
384#1771C2×C3711yescharacteristic, complemented
385C2×C37—82no—
386C2×C37—161no—
387C2×C37—161no—
388C2×C37—161no—
389C2×C37#254111yescharacteristic
390C2×C37#315111yescharacteristic
391C2×C37#315411yescharacteristic
392C2×C37#326512yes—
393C2×C37#339712yes—
394C22×SD16C22×C3711yescharacteristic
395C22×SD16C22×C3711yescharacteristic
396C22×SD16C22×C3711yescharacteristic
397C22×SD16C22×C3711yescharacteristic
398C22×SD16C22×C3711yescharacteristic
399C22×SD16C22×C3711yescharacteristic
400C22×D8C22×C3711yescharacteristic
401C22×D8C22×C3711yescharacteristic
402C22×D8C22×C3711yescharacteristic
403C2×C4⋊Q8C22×C3711yescharacteristic
404C2×#127C22×C3711yescharacteristic
405C2×#127C22×C3711yescharacteristic
406C2×#127C22×C3711yescharacteristic
407C2×#124C22×C3711yescharacteristic
408C2×#124C22×C3711yescharacteristic
409C2×#121—22no—
410C2×C4×Q8C22×C3711yescharacteristic
411C2×C4×D4C22×C3711yescharacteristic
412#496—24no—
413#496—24no—
414#492—24no—
415#463—24no—
416#460—24no—
417#440—24no—
418C2×#107C22×C3711yescharacteristic
419C2×C4⋊C8C22×C3711yescharacteristic
420C2×#103C22×C3711yescharacteristic
421C2×#103C22×C3711yescharacteristic
422C2×#102C22×C3711yescharacteristic
423C2×#102C22×C3711yescharacteristic
424C2×#102C22×C3711yescharacteristic
425C2×#102C22×C3711yescharacteristic
426C2×#97C22×C3711yescharacteristic
427C2×#97C22×C3711yescharacteristic
428C2×C4×C8C22×C3711yescharacteristic
429#396—22no—
430#392—22no—
431#391C22×C3711yescharacteristic
432#390C22×C3711yescharacteristic
433#390C22×C3711yescharacteristic
434#390C22×C3711yescharacteristic
435#388—22no—
436C4×C4⋊C4C22×C3711yescharacteristic
437#336C22×C3711yescharacteristic
438#336C22×C3711yescharacteristic
439C37#2848011yescharacteristic, direct product factor, Sylow
440C22×Q8C23×C3711yescharacteristic
441C22×Q8C23×C3711yescharacteristic
442C22×D4—21no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—21no—
446C22×D4C23×C3711yescharacteristic
447C22×D4C23×C3711yescharacteristic
448C22×D4C23×C3711yescharacteristic
449C22×D4C23×C3711yescharacteristic
450C23×C4—21no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16—41no—
464C2×SD16—41no—
465C2×SD16—41no—
466C2×SD16—41no—
467C2×SD16—41no—
468C2×SD16D4×C3714yescomplemented
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×D8—41no—
477C2×D8—41no—
478C22×C8C23×C3711yescharacteristic
479C22×C8C23×C3711yescharacteristic
480C22×C8C23×C3711yescharacteristic
481C22×C8C23×C3711yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—41no—
484#127—22no—
485#127—22no—
486#127—22no—
487#127—22no—
488#127—41no—
489#127—41no—
490#124—22no—
491#124—22no—
492#124—22no—
493#124—41no—
494#121—48no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×D4—22no—
498C4×D4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4D4×C3712yes—
502C2×C4⋊C4C23×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—22no—
511C2×C42—21no—
512C2×C42C23×C3711yescharacteristic
513C2×C42C23×C3711yescharacteristic
514C2×C42C23×C3711yescharacteristic
515#107—22no—
516C4⋊C8D4×C3714yescomplemented
517#103—22no—
518#103—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#97—22no—
524#97D4×C3714yescomplemented
525C4×C8—22no—
526#95—22no—
527#95D4×C3712yes—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C3712yes—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4C2×D4×C3712yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4C2×D4×C3712yes—
585C22×C4C2×D4×C3711yescharacteristic
586C22×C4C2×D4×C3711yescharacteristic
587C22×C4C2×D4×C3712yes—
588C22×C4C24×C3711yescharacteristic
589SD16—28no—
590SD16—44no—
591SD16—44no—
592SD16—44no—
593SD16—44no—
594SD16—44no—
595D8—44no—
596D8—44no—
597D8—44no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×D4×C3712yes—
605C2×C8C2×D4×C3712yes—
606C2×C8C2×D4×C3712yes—
607C2×C8C2×D4×C3712yes—
608C2×C8C2×D4×C3712yes—
609C2×C8#41×C3712yes—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—42no—
629C42C2×D4×C3712yes—
630C42C2×D4×C3712yes—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23C22×D4×C3711yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—88no—
677D4—84no—
678D4—84no—
679D4—88no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—84no—
698C2×C4#127×C3712yes—
699C2×C4#127×C3712yes—
700C2×C4AGL(1,ℤ/8)×C3714yes—
701C2×C4C22×D4×C3711yescharacteristic
702C2×C4C22×D4×C3711yescharacteristic
703C2×C4C22×D4×C3711yescharacteristic
704C2×C4C2×#41×C3711yescharacteristic
705C2×C4H(5,𝔽2)×C3711yescharacteristic
706C2×C4H(5,𝔽2)×C3711yescharacteristic
707C8—22no—
708C8—22no—
709C8—22no—
710C8#121×C3714yescomplemented
711C22—44no—
712C22—42no—
713C22—82no—
714C22—81no—
715C22—81no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#127×C3711yescharacteristic
732C22D42×C3711yescharacteristic
733C22C37×#55011yescharacteristic
734C22C2×AGL(1,ℤ/8)×C3712yes—
735C22C37×#57712yes—
736C4—22no—
737C4—22no—
738C4—24no—
739C4—42no—
740C4—42no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4C2×#121×C3711yescharacteristic
745C4C37×#53511yescharacteristic
746C4D42×C3711yescharacteristic
747C4C37×#55011yescharacteristic
748C2—82no—
749C2—161no—
750C2—161no—
751C2—161no—
752C2C37×#254111yescharacteristic
753C2C37×#315111yescharacteristic
754C2C37×#315411yescharacteristic
755C2C37×#326512yes—
756C2C37×#339712yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C4⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#496C2semidirect
2. C2×C37×#496C2semidirect
3. C2×C37×#492C2semidirect
4. C2×C37×#460C2semidirect
5. C2×C37×#463C2semidirect
6. C2×C37×#440C2semidirect
7. C37×#2545C2semidirect
8. C37×#2541C2semidirect
9. C37×#2014C2semidirect
10. C37×#2013C2semidirect
11. C37×#2012C2semidirect
12. C37×#2011C2semidirect
13. C37×#1973C2semidirect
14. C37×#1970C2semidirect
15. C37×#1771C2semidirect
89. C2×SD16×C37D4semidirect
137. C4⋊C8×C37D4semidirect
145. #97×C37D4semidirect
331. C8×C37#121semidirect
332. #28480C37direct (N × H)
370. C2×#496C2×C37semidirect
371. C2×#496C2×C37semidirect
372. C2×#492C2×C37semidirect
373. C2×#460C2×C37semidirect
374. C2×#463C2×C37semidirect
375. C2×#440C2×C37semidirect
376. #2545C2×C37semidirect
377. #2541C2×C37semidirect
378. #2014C2×C37semidirect
379. #2013C2×C37semidirect
380. #2012C2×C37semidirect
381. #2011C2×C37semidirect
382. #1973C2×C37semidirect
383. #1970C2×C37semidirect
384. #1771C2×C37semidirect
439. C37#28480direct (N × H)
468. C2×SD16D4×C37semidirect
516. C4⋊C8D4×C37semidirect
524. #97D4×C37semidirect
710. C8#121×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4962
C2×C37×#4922
C2×C37×#4602
C2×C37×#4632
C2×C37×#4402
C37×#25452
C37×#25412
C37×#20142
C37×#20132
C37×#20122
C37×#20112
C37×#19732
C37×#19702
C37×#17712
#2848037