Finite Group Databasebeta

← C37×#22464 #22643717

Subgroups — C37×#22464 #22643717

Order 9472.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#577C211yesmaximal, characteristic
2C2×C37×#444C211yesmaximal, characteristic, complemented
3C37×#2951C211yesmaximal, characteristic, complemented
4C37×#2898C211yesmaximal, characteristic, complemented
5C37×#2897C211yesmaximal, characteristic, complemented
6C37×#1977C211yesmaximal, characteristic, complemented
7C37×#1973C211yesmaximal, characteristic, complemented
8C37×#1908C211yesmaximal, characteristic, complemented
9C37×#1907C211yesmaximal, characteristic, complemented
10C37×#1883C211yesmaximal, characteristic, complemented
11C37×#1882C211yesmaximal, characteristic, complemented
12C37×#1816C211yesmaximal, characteristic, complemented
13C37×#1793C211yesmaximal, characteristic, complemented
14C37×#1792C211yesmaximal, characteristic, complemented
15C37×#1765C211yesmaximal, characteristic, complemented
16C2×2−1+4×C37C2211yescharacteristic
17C2×H(5,𝔽2)×C37C2211yescharacteristic
18C37×#577—24no—
19C37×#577C418yescomplemented
20C2×#137×C37—21no—
21C2×#137×C37C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C37—21no—
23C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
24C2×#135×C37—21no—
25C2×#135×C37C2211yescharacteristic
26C22×SD16×C37—21no—
27C22×SD16×C37C2211yescharacteristic
28C2×#131×C37C2211yescharacteristic
29C2×#131×C37C2211yescharacteristic
30C2×#131×C37C2211yescharacteristic, complemented
31C37×#520C2211yescharacteristic
32C37×#520C2211yescharacteristic, complemented
33C37×#444—24no—
34C37×#440—21no—
35C37×#440—21no—
36C4×Q16×C37—21no—
37C4×D8×C37—21no—
38C2×#108×C37C2211yescharacteristic, complemented
39C2×#107×C37C2211yescharacteristic, complemented
40C2×#104×C37C2211yescharacteristic
41C2×#104×C37C2211yescharacteristic
42C2×#104×C37C2211yescharacteristic, complemented
43C37×#419—21no—
44C37×#419C2211yescharacteristic, complemented
45C37×#418—21no—
46C37×#418C2211yescharacteristic
47C37×#417—21no—
48C37×#417—21no—
49C37×#417C2211yescharacteristic
50C37×#417C2211yescharacteristic
51C37×#417C2211yescharacteristic
52C37×#417C2211yescharacteristic, complemented
53C37×#416—21no—
54C37×#416—21no—
55C37×#416C2211yescharacteristic
56C2×#103×C37—21no—
57C2×#103×C37C2211yescharacteristic, complemented
58C2×#102×C37—21no—
59C2×#102×C37C2211yescharacteristic
60C2×#101×C37C2211yescharacteristic, complemented
61C2×#100×C37C2211yescharacteristic
62C37×#405C2211yescharacteristic, complemented
63C2×#97×C37C2211yescharacteristic, complemented
64C37×#391C2211yescharacteristic, complemented
65C37×#390C2211yescharacteristic
66C37×#343C2211yescharacteristic, complemented
67C37×#343C2211yescharacteristic, complemented
68C37×#341C2211yescharacteristic, complemented
69C37×#339C2211yescharacteristic, complemented
702−1+4×C37—22no—
712−1+4×C37—22no—
722−1+4×C37—41no—
732−1+4×C37C2×C414yescomplemented
74H(5,𝔽2)×C37—22no—
75H(5,𝔽2)×C37—22no—
76H(5,𝔽2)×C37—41no—
77H(5,𝔽2)×C37C2×C414yescomplemented
78C2×#41×C37—21no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—21no—
82C2×#41×C37—41no—
83C2×#41×C37C2311yescharacteristic
84C2×#41×C37C2311yescharacteristic
85C2×#41×C37C2311yescharacteristic
86C22×Q8×C37—21no—
87C22×Q8×C37—21no—
88C22×Q8×C37C2311yescharacteristic
89C22×D4×C37—21no—
90C22×D4×C37—21no—
91C22×D4×C37—41no—
92C22×D4×C37C2311yescharacteristic
93#137×C37—22no—
94#137×C37—28no—
95#137×C37C2×C414yescomplemented
96AGL(1,ℤ/8)×C37—22no—
97AGL(1,ℤ/8)×C37—28no—
98AGL(1,ℤ/8)×C37C2×C414yescomplemented
99#135×C37—28no—
100#135×C37C2×C414yes—
101#135×C37D414yes—
102C2×Q16×C37—21no—
103C2×Q16×C37D411yescharacteristic
104C2×SD16×C37—21no—
105C2×SD16×C37—21no—
106C2×SD16×C37—28no—
107C2×SD16×C37—21no—
108C2×SD16×C37—21no—
109C2×SD16×C37—22no—
110C2×SD16×C37C2×C414yescomplemented
111C2×SD16×C37D411yescharacteristic
112C2×SD16×C37D411yescharacteristic
113C2×D8×C37—21no—
114C2×D8×C37D411yescharacteristic
115#131×C37—22no—
116#131×C37—22no—
117#131×C37—22no—
118#131×C37—41no—
119#131×C37—41no—
120#131×C37C2×C414yescomplemented
121C2×M16×C37—21no—
122C2×M16×C37—21no—
123C2×M16×C37—21no—
124C2×M16×C37C2311yescharacteristic
125C2×M16×C37C2311yescharacteristic
126C2×M16×C37C2311yescharacteristic
127C2×M16×C37C2311yescharacteristic
128C22×C8×C37—21no—
129C22×C8×C37—21no—
130C22×C8×C37—21no—
131C22×C8×C37C2311yescharacteristic
132C22×C8×C37C2311yescharacteristic
133C4×Q8×C37—21no—
134C4×Q8×C37—21no—
135C4×D4×C37—21no—
136C4×D4×C37—21no—
137C4×D4×C37—41no—
138C4×D4×C37—41no—
139#117×C37—21no—
140#117×C37—21no—
141#117×C37C2311yescharacteristic
142C2×C4⋊C4×C37—21no—
143C2×C4⋊C4×C37—21no—
144C2×C4⋊C4×C37C2311yescharacteristic
145C2×C4⋊C4×C37C2311yescharacteristic
146C2×C22⋊C4×C37—41no—
147C2×C42×C37C2311yescharacteristic
148#108×C37—22no—
149#107×C37—21no—
150#107×C37—21no—
151#104×C37—22no—
152#104×C37—22no—
153#104×C37—22no—
154#103×C37—21no—
155#103×C37—21no—
156#103×C37—21no—
157#103×C37—21no—
158#103×C37—21no—
159#103×C37—21no—
160#103×C37—21no—
161#103×C37—21no—
162#103×C37D411yescharacteristic
163#103×C37D411yescharacteristic
164#102×C37—21no—
165#102×C37—21no—
166#102×C37—21no—
167#102×C37—21no—
168#102×C37—21no—
169#102×C37—21no—
170#102×C37—21no—
171#102×C37—21no—
172#102×C37D411yescharacteristic
173#102×C37D411yescharacteristic
174#101×C37—41no—
175#100×C37—41no—
176#97×C37—22no—
177#97×C37—21no—
178C4×C8×C37—21no—
179#95×C37—41no—
180C24×C37—21no—
181C24×C37—41no—
182#41×C37—21no—
183#41×C37—21no—
184#41×C37—21no—
185#41×C37—21no—
186#41×C37—21no—
187#41×C37—21no—
188#41×C37—24no—
189#41×C37—24no—
190#41×C37—24no—
191#41×C37—24no—
192#41×C37—44no—
193#41×C37—42no—
194#41×C37—42no—
195#41×C37—42no—
196#41×C37—42no—
197#41×C37—44no—
198#41×C37C22×C412yes—
199#41×C37C22×C412yes—
200#41×C37C22×C412yes—
201#41×C37C2×D412yes—
202#41×C37C2×D412yes—
203#41×C37#4112yes—
204C2×Q8×C37—21no—
205C2×Q8×C37—24no—
206C2×Q8×C37—24no—
207C2×Q8×C37—21no—
208C2×Q8×C37—21no—
209C2×Q8×C37—21no—
210C2×Q8×C37—21no—
211C2×Q8×C37—41no—
212C2×Q8×C37—42no—
213C2×Q8×C37—42no—
214C2×Q8×C37C22×C412yes—
215C2×Q8×C37C2×D411yescharacteristic
216C2×Q8×C37C2×D411yescharacteristic
217C2×Q8×C37C2×D411yescharacteristic
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—24no—
222C2×D4×C37—24no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—21no—
228C2×D4×C37—42no—
229C2×D4×C37—42no—
230C2×D4×C37—41no—
231C2×D4×C37—41no—
232C2×D4×C37—44no—
233C2×D4×C37—44no—
234C2×D4×C37—41no—
235C2×D4×C37C22×C412yes—
236C2×D4×C37C2×D411yescharacteristic
237C2×D4×C37C2×D411yescharacteristic
238C2×D4×C37C2×D411yescharacteristic
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—41no—
247C22×C4×C37—41no—
248C22×C4×C37—41no—
249C22×C4×C37—41no—
250C22×C4×C37—41no—
251C22×C4×C37C2411yescharacteristic
252Q16×C37—24no—
253Q16×C37C22⋊C414yescomplemented
254SD16×C37—24no—
255SD16×C37—24no—
256SD16×C37—24no—
257SD16×C37—24no—
258SD16×C37C22⋊C414yescomplemented
259SD16×C37C22⋊C414yescomplemented
260D8×C37—24no—
261D8×C37C22⋊C414yescomplemented
262M16×C37—21no—
263M16×C37—24no—
264M16×C37—21no—
265M16×C37—21no—
266M16×C37—21no—
267M16×C37—21no—
268M16×C37—21no—
269M16×C37—21no—
270M16×C37—42no—
271M16×C37—42no—
272M16×C37C22×C412yes—
273C2×C8×C37—21no—
274C2×C8×C37—21no—
275C2×C8×C37—21no—
276C2×C8×C37—24no—
277C2×C8×C37—21no—
278C2×C8×C37—21no—
279C2×C8×C37—21no—
280C2×C8×C37—42no—
281C2×C8×C37—42no—
282C2×C8×C37C22×C412yes—
283C2×C8×C37C2×D411yescharacteristic
284C2×C8×C37C2×D411yescharacteristic
285C2×C8×C37C2×D411yescharacteristic
286C2×C8×C37C2×D411yescharacteristic
287C2×C8×C37C2×D412yes—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—21no—
291C4⋊C4×C37—21no—
292C4⋊C4×C37—41no—
293C4⋊C4×C37—41no—
294C4⋊C4×C37C2×D411yescharacteristic
295C4⋊C4×C37C2×D411yescharacteristic
296C22⋊C4×C37—21no—
297C22⋊C4×C37—41no—
298C22⋊C4×C37—41no—
299C22⋊C4×C37—82no—
300C42×C37—21no—
301C42×C37—21no—
302C42×C37—21no—
303C42×C37—41no—
304C42×C37—41no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—22no—
309C23×C37—44no—
310C23×C37—41no—
311C23×C37—41no—
312C23×C37—81no—
313C23×C37—81no—
314C23×C37—161no—
315C23×C37—161no—
316C23×C37H(5,𝔽2)11yescharacteristic
317Q8×C37—21no—
318Q8×C37—21no—
319Q8×C37—21no—
320Q8×C37—22no—
321Q8×C37—22no—
322Q8×C37—44no—
323Q8×C37—41no—
324Q8×C37—41no—
325Q8×C37C2×C22⋊C412yes—
326Q8×C37C2×C22⋊C412yes—
327Q8×C37C4×D412yes—
328D4×C37—22no—
329D4×C37—22no—
330D4×C37—22no—
331D4×C37—22no—
332D4×C37—22no—
333D4×C37—22no—
334D4×C37—22no—
335D4×C37—22no—
336D4×C37—21no—
337D4×C37—21no—
338D4×C37—21no—
339D4×C37—44no—
340D4×C37—44no—
341D4×C37—44no—
342D4×C37—41no—
343D4×C37—41no—
344D4×C37C2×C22⋊C412yes—
345D4×C37C2×C22⋊C412yes—
346D4×C37C4×D412yes—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—22no—
351C2×C4×C37—22no—
352C2×C4×C37—22no—
353C2×C4×C37—22no—
354C2×C4×C37—22no—
355C2×C4×C37—22no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—44no—
360C2×C4×C37—44no—
361C2×C4×C37—44no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
368C2×C4×C37—41no—
369C2×C4×C37—81no—
370C2×C4×C37—81no—
371C2×C4×C37—161no—
372C2×C4×C37—161no—
373C2×C4×C37C23×C411yescharacteristic
374C2×C4×C37C22×D411yescharacteristic
375C2×C4×C37C22×D411yescharacteristic
376C2×C4×C37C22×D411yescharacteristic
377C2×C4×C37C2×#4111yescharacteristic
378C2×C4×C37H(5,𝔽2)11yescharacteristic
379C8×C37—22no—
380C8×C37—21no—
381C8×C37—21no—
382C8×C37—41no—
383C8×C37—41no—
384C8×C37—41no—
385C8×C37C2×C22⋊C412yes—
386C8×C37C2×C22⋊C412yes—
387#22464C3711yesmaximal, characteristic, direct product factor, Sylow
388C22×C37—21no—
389C22×C37—21no—
390C22×C37—22no—
391C22×C37—22no—
392C22×C37—22no—
393C22×C37—41no—
394C22×C37—41no—
395C22×C37—41no—
396C22×C37—41no—
397C22×C37—41no—
398C22×C37—41no—
399C22×C37—42no—
400C22×C37—82no—
401C22×C37—81no—
402C22×C37—81no—
403C22×C37—161no—
404C22×C37—164no—
405C22×C37#51811yescharacteristic
406C22×C37D4211yescharacteristic
407C22×C37#54611yescharacteristic
408C4×C37—22no—
409C4×C37—22no—
410C4×C37—22no—
411C4×C37—42no—
412C4×C37—41no—
413C4×C37—41no—
414C4×C37—81no—
415C4×C37—81no—
416C4×C37—81no—
417C4×C37C22×C22⋊C411yescharacteristic
418C4×C37C2×C4×D411yescharacteristic
419C4×C37D4211yescharacteristic
420C4×C37#54611yescharacteristic
421C2×#577C2×C3711yescharacteristic
422C2×#444C2×C3711yescharacteristic, complemented
423#2951C2×C3711yescharacteristic, complemented
424#2898C2×C3711yescharacteristic, complemented
425#2897C2×C3711yescharacteristic, complemented
426#1977C2×C3711yescharacteristic, complemented
427#1973C2×C3711yescharacteristic, complemented
428#1908C2×C3711yescharacteristic, complemented
429#1907C2×C3711yescharacteristic, complemented
430#1883C2×C3711yescharacteristic, complemented
431#1882C2×C3711yescharacteristic, complemented
432#1816C2×C3711yescharacteristic, complemented
433#1793C2×C3711yescharacteristic, complemented
434#1792C2×C3711yescharacteristic, complemented
435#1765C2×C3711yescharacteristic, complemented
436C2×C37—21no—
437C2×C37—21no—
438C2×C37—42no—
439C2×C37—42no—
440C2×C37—42no—
441C2×C37—82no—
442C2×C37D4×C22⋊C411yescharacteristic
443C2×C37#328811yescharacteristic
444C2×C37#328911yescharacteristic
445C2×2−1+4C22×C3711yescharacteristic
446C2×H(5,𝔽2)C22×C3711yescharacteristic
447#577—24no—
448#577C4×C3718yescomplemented
449C2×#137—21no—
450C2×#137C22×C3711yescharacteristic
451C2×AGL(1,ℤ/8)—21no—
452C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
453C2×#135—21no—
454C2×#135C22×C3711yescharacteristic
455C22×SD16—21no—
456C22×SD16C22×C3711yescharacteristic
457C2×#131C22×C3711yescharacteristic
458C2×#131C22×C3711yescharacteristic
459C2×#131C22×C3711yescharacteristic, complemented
460#520C22×C3711yescharacteristic
461#520C22×C3711yescharacteristic, complemented
462#444—24no—
463#440—21no—
464#440—21no—
465C4×Q16—21no—
466C4×D8—21no—
467C2×#108C22×C3711yescharacteristic, complemented
468C2×#107C22×C3711yescharacteristic, complemented
469C2×#104C22×C3711yescharacteristic
470C2×#104C22×C3711yescharacteristic
471C2×#104C22×C3711yescharacteristic, complemented
472#419—21no—
473#419C22×C3711yescharacteristic, complemented
474#418—21no—
475#418C22×C3711yescharacteristic
476#417—21no—
477#417—21no—
478#417C22×C3711yescharacteristic
479#417C22×C3711yescharacteristic
480#417C22×C3711yescharacteristic
481#417C22×C3711yescharacteristic, complemented
482#416—21no—
483#416—21no—
484#416C22×C3711yescharacteristic
485C2×#103—21no—
486C2×#103C22×C3711yescharacteristic, complemented
487C2×#102—21no—
488C2×#102C22×C3711yescharacteristic
489C2×#101C22×C3711yescharacteristic, complemented
490C2×#100C22×C3711yescharacteristic
491#405C22×C3711yescharacteristic, complemented
492C2×#97C22×C3711yescharacteristic, complemented
493#391C22×C3711yescharacteristic, complemented
494#390C22×C3711yescharacteristic
495#343C22×C3711yescharacteristic, complemented
496#343C22×C3711yescharacteristic, complemented
497#341C22×C3711yescharacteristic, complemented
498#339C22×C3711yescharacteristic, complemented
499C37#2246411yescharacteristic, direct product factor, Sylow
5002−1+4—22no—
5012−1+4—22no—
5022−1+4—41no—
5032−1+4C2×C4×C3714yescomplemented
504H(5,𝔽2)—22no—
505H(5,𝔽2)—22no—
506H(5,𝔽2)—41no—
507H(5,𝔽2)C2×C4×C3714yescomplemented
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—41no—
513C2×#41C23×C3711yescharacteristic
514C2×#41C23×C3711yescharacteristic
515C2×#41C23×C3711yescharacteristic
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C23×C3711yescharacteristic
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4C23×C3711yescharacteristic
523#137—22no—
524#137—28no—
525#137C2×C4×C3714yescomplemented
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—28no—
528AGL(1,ℤ/8)C2×C4×C3714yescomplemented
529#135—28no—
530#135C2×C4×C3714yes—
531#135D4×C3714yes—
532C2×Q16—21no—
533C2×Q16D4×C3711yescharacteristic
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—28no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—22no—
540C2×SD16C2×C4×C3714yescomplemented
541C2×SD16D4×C3711yescharacteristic
542C2×SD16D4×C3711yescharacteristic
543C2×D8—21no—
544C2×D8D4×C3711yescharacteristic
545#131—22no—
546#131—22no—
547#131—22no—
548#131—41no—
549#131—41no—
550#131C2×C4×C3714yescomplemented
551C2×M16—21no—
552C2×M16—21no—
553C2×M16—21no—
554C2×M16C23×C3711yescharacteristic
555C2×M16C23×C3711yescharacteristic
556C2×M16C23×C3711yescharacteristic
557C2×M16C23×C3711yescharacteristic
558C22×C8—21no—
559C22×C8—21no—
560C22×C8—21no—
561C22×C8C23×C3711yescharacteristic
562C22×C8C23×C3711yescharacteristic
563C4×Q8—21no—
564C4×Q8—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—41no—
568C4×D4—41no—
569#117—21no—
570#117—21no—
571#117C23×C3711yescharacteristic
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4C23×C3711yescharacteristic
575C2×C4⋊C4C23×C3711yescharacteristic
576C2×C22⋊C4—41no—
577C2×C42C23×C3711yescharacteristic
578#108—22no—
579#107—21no—
580#107—21no—
581#104—22no—
582#104—22no—
583#104—22no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—21no—
590#103—21no—
591#103—21no—
592#103D4×C3711yescharacteristic
593#103D4×C3711yescharacteristic
594#102—21no—
595#102—21no—
596#102—21no—
597#102—21no—
598#102—21no—
599#102—21no—
600#102—21no—
601#102—21no—
602#102D4×C3711yescharacteristic
603#102D4×C3711yescharacteristic
604#101—41no—
605#100—41no—
606#97—22no—
607#97—21no—
608C4×C8—21no—
609#95—41no—
610C24—21no—
611C24—41no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—24no—
622#41—44no—
623#41—42no—
624#41—42no—
625#41—42no—
626#41—42no—
627#41—44no—
628#41C22×C4×C3712yes—
629#41C22×C4×C3712yes—
630#41C22×C4×C3712yes—
631#41C2×D4×C3712yes—
632#41C2×D4×C3712yes—
633#41#41×C3712yes—
634C2×Q8—21no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—41no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8C22×C4×C3712yes—
645C2×Q8C2×D4×C3711yescharacteristic
646C2×Q8C2×D4×C3711yescharacteristic
647C2×Q8C2×D4×C3711yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—41no—
661C2×D4—41no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—41no—
665C2×D4C22×C4×C3712yes—
666C2×D4C2×D4×C3711yescharacteristic
667C2×D4C2×D4×C3711yescharacteristic
668C2×D4C2×D4×C3711yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4C24×C3711yescharacteristic
682Q16—24no—
683Q16C22⋊C4×C3714yescomplemented
684SD16—24no—
685SD16—24no—
686SD16—24no—
687SD16—24no—
688SD16C22⋊C4×C3714yescomplemented
689SD16C22⋊C4×C3714yescomplemented
690D8—24no—
691D8C22⋊C4×C3714yescomplemented
692M16—21no—
693M16—24no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—21no—
698M16—21no—
699M16—21no—
700M16—42no—
701M16—42no—
702M16C22×C4×C3712yes—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—24no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—42no—
711C2×C8—42no—
712C2×C8C22×C4×C3712yes—
713C2×C8C2×D4×C3711yescharacteristic
714C2×C8C2×D4×C3711yescharacteristic
715C2×C8C2×D4×C3711yescharacteristic
716C2×C8C2×D4×C3711yescharacteristic
717C2×C8C2×D4×C3712yes—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—41no—
723C4⋊C4—41no—
724C4⋊C4C2×D4×C3711yescharacteristic
725C4⋊C4C2×D4×C3711yescharacteristic
726C22⋊C4—21no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—82no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—41no—
734C42—41no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—44no—
740C23—41no—
741C23—41no—
742C23—81no—
743C23—81no—
744C23—161no—
745C23—161no—
746C23H(5,𝔽2)×C3711yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—22no—
751Q8—22no—
752Q8—44no—
753Q8—41no—
754Q8—41no—
755Q8C2×C22⋊C4×C3712yes—
756Q8C2×C22⋊C4×C3712yes—
757Q8C4×D4×C3712yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—21no—
765D4—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—44no—
770D4—44no—
771D4—44no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊C4×C3712yes—
775D4C2×C22⋊C4×C3712yes—
776D4C4×D4×C3712yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—161no—
802C2×C4—161no—
803C2×C4C23×C4×C3711yescharacteristic
804C2×C4C22×D4×C3711yescharacteristic
805C2×C4C22×D4×C3711yescharacteristic
806C2×C4C22×D4×C3711yescharacteristic
807C2×C4C2×#41×C3711yescharacteristic
808C2×C4H(5,𝔽2)×C3711yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—41no—
813C8—41no—
814C8—41no—
815C8C2×C22⋊C4×C3712yes—
816C8C2×C22⋊C4×C3712yes—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—82no—
830C22—81no—
831C22—81no—
832C22—161no—
833C22—164no—
834C22C37×#51811yescharacteristic
835C22D42×C3711yescharacteristic
836C22C37×#54611yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—41no—
841C4—41no—
842C4—42no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4C22×C22⋊C4×C3711yescharacteristic
847C4C2×C4×D4×C3711yescharacteristic
848C4D42×C3711yescharacteristic
849C4C37×#54611yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—42no—
855C2—82no—
856C2D4×C22⋊C4×C3711yescharacteristic
857C2C37×#328811yescharacteristic
858C2C37×#328911yescharacteristic
subgroupG/H
center, socleC22×C37D42
commutatorC2×C4C23×C4×C37
Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#577C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#444C2semidirect
3. C37×#2951C2semidirect
4. C37×#2898C2semidirect
5. C37×#2897C2semidirect
6. C37×#1977C2semidirect
7. C37×#1973C2semidirect
8. C37×#1908C2semidirect
9. C37×#1907C2semidirect
10. C37×#1883C2semidirect
11. C37×#1882C2semidirect
12. C37×#1816C2semidirect
13. C37×#1793C2semidirect
14. C37×#1792C2semidirect
15. C37×#1765C2semidirect
19. C37×#577C4semidirect
30. C2×#131×C37C22semidirect
32. C37×#520C22semidirect
38. C2×#108×C37C22semidirect
39. C2×#107×C37C22semidirect
42. C2×#104×C37C22semidirect
44. C37×#419C22semidirect
52. C37×#417C22semidirect
57. C2×#103×C37C22semidirect
60. C2×#101×C37C22semidirect
62. C37×#405C22semidirect
63. C2×#97×C37C22semidirect
64. C37×#391C22semidirect
66. C37×#343C22semidirect
67. C37×#343C22semidirect
68. C37×#341C22semidirect
69. C37×#339C22semidirect
73. 2−1+4×C37C2×C4semidirect
77. H(5,𝔽2)×C37C2×C4semidirect
95. #137×C37C2×C4semidirect
98. AGL(1,ℤ/8)×C37C2×C4semidirect
110. C2×SD16×C37C2×C4semidirect
120. #131×C37C2×C4semidirect
253. Q16×C37C22⋊C4semidirect
258. SD16×C37C22⋊C4semidirect
259. SD16×C37C22⋊C4semidirect
261. D8×C37C22⋊C4semidirect
387. #22464C37direct (N × H)
422. C2×#444C2×C37semidirect
423. #2951C2×C37semidirect
424. #2898C2×C37semidirect
425. #2897C2×C37semidirect
426. #1977C2×C37semidirect
427. #1973C2×C37semidirect
428. #1908C2×C37semidirect
429. #1907C2×C37semidirect
430. #1883C2×C37semidirect
431. #1882C2×C37semidirect
432. #1816C2×C37semidirect
433. #1793C2×C37semidirect
434. #1792C2×C37semidirect
435. #1765C2×C37semidirect
448. #577C4×C37semidirect
459. C2×#131C22×C37semidirect
461. #520C22×C37semidirect
467. C2×#108C22×C37semidirect
468. C2×#107C22×C37semidirect
471. C2×#104C22×C37semidirect
473. #419C22×C37semidirect
481. #417C22×C37semidirect
486. C2×#103C22×C37semidirect
489. C2×#101C22×C37semidirect
491. #405C22×C37semidirect
492. C2×#97C22×C37semidirect
493. #391C22×C37semidirect
495. #343C22×C37semidirect
496. #343C22×C37semidirect
497. #341C22×C37semidirect
498. #339C22×C37semidirect
499. C37#22464direct (N × H)
503. 2−1+4C2×C4×C37semidirect
507. H(5,𝔽2)C2×C4×C37semidirect
525. #137C2×C4×C37semidirect
528. AGL(1,ℤ/8)C2×C4×C37semidirect
540. C2×SD16C2×C4×C37semidirect
550. #131C2×C4×C37semidirect
683. Q16C22⋊C4×C37semidirect
688. SD16C22⋊C4×C37semidirect
689. SD16C22⋊C4×C37semidirect
691. D8C22⋊C4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5772
C2×C37×#4442
C37×#29512
C37×#28982
C37×#28972
C37×#19772
C37×#19732
C37×#19082
C37×#19072
C37×#18832
C37×#18822
C37×#18162
C37×#17932
C37×#17922
C37×#17652
#2246437