Finite Group Databasebeta

← C37×#25179 #22646432

Subgroups — C37×#25179 #22646432

Order 9472.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#460C211yesmaximal, characteristic, complemented
2C2×C37×#449C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C2×C37×#440C211yesmaximal, characteristic, complemented
5C37×#2428C211yesmaximal, characteristic, complemented
6C37×#2341C211yesmaximal, characteristic, complemented
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#2033C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1972C211yesmaximal, characteristic, complemented
12C37×#1924C211yesmaximal, characteristic, complemented
13C37×#1880C211yesmaximal, characteristic, complemented
14C37×#1879C211yesmaximal, characteristic, complemented
15C37×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#121×C37—21no—
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×C4×Q8×C37C2211yescharacteristic
26C2×C4×Q8×C37C2211yescharacteristic
27C2×C4×D4×C37C2211yescharacteristic
28C37×#460—24no—
29C37×#449—24no—
30C37×#449—24no—
31C37×#440—24no—
32C2×#107×C37C2211yescharacteristic
33C2×#106×C37C2211yescharacteristic
34C2×C4⋊C8×C37C2211yescharacteristic
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×C22⋊C8×C37C2211yescharacteristic
44C2×C22⋊C8×C37C2211yescharacteristic
45C2×#97×C37C2211yescharacteristic
46C37×#394—21no—
47C37×#392—21no—
48C37×#390—21no—
49C37×#390—21no—
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic
53C37×#389C2211yescharacteristic
54C37×#386—21no—
55C37×#380—21no—
56C37×#380C2211yescharacteristic
57C4×C22⋊C4×C37—21no—
58C4×C22⋊C4×C37C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C2×#41×C37—22no—
64C2×#41×C37—22no—
65C2×#41×C37—22no—
66C2×#41×C37—22no—
67C2×#41×C37—41no—
68C2×#41×C37—41no—
69C22×Q8×C37C2311yescharacteristic
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37C2311yescharacteristic
76C22×D4×C37C2311yescharacteristic
77C22×D4×C37C2311yescharacteristic
78C23×C4×C37—21no—
79C23×C4×C37—21no—
80C23×C4×C37C2311yescharacteristic
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—22no—
84C2×SD16×C37—22no—
85C2×SD16×C37—22no—
86C2×SD16×C37D414yescomplemented
87C2×D8×C37—22no—
88C2×D8×C37—22no—
89C2×D8×C37—22no—
90C2×D8×C37—22no—
91C2×D8×C37—41no—
92C2×D8×C37—41no—
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97#127×C37—22no—
98#127×C37—41no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—44no—
102#121×C37—41no—
103#121×C37—41no—
104C4×Q8×C37—22no—
105C4×Q8×C37—22no—
106C4×Q8×C37—41no—
107C4×Q8×C37—41no—
108C4×D4×C37—22no—
109C4×D4×C37—41no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37D411yescharacteristic
128C2×C22⋊C4×C37D411yescharacteristic
129C2×C42×C37—21no—
130C2×C42×C37—21no—
131C2×C42×C37C2311yescharacteristic
132C2×C42×C37C2311yescharacteristic
133#107×C37—22no—
134#106×C37—41no—
135C4⋊C8×C37—22no—
136#103×C37—22no—
137#103×C37D414yescomplemented
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—41no—
144C22⋊C8×C37—22no—
145C22⋊C8×C37—22no—
146#97×C37—22no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37D411yescharacteristic
150#95×C37D411yescharacteristic
151C24×C37—21no—
152C24×C37—21no—
153C24×C37—21no—
154C24×C37C2×D411yescharacteristic
155#41×C37—44no—
156#41×C37—44no—
157#41×C37—44no—
158#41×C37—44no—
159C2×Q8×C37—21no—
160C2×Q8×C37—21no—
161C2×Q8×C37—21no—
162C2×Q8×C37C2×D412yes—
163C2×Q8×C37C2×D412yes—
164C2×Q8×C37#4112yes—
165C2×D4×C37—24no—
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—42no—
183C2×D4×C37—42no—
184C2×D4×C37—42no—
185C2×D4×C37—42no—
186C2×D4×C37—42no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
191C2×D4×C37—42no—
192C2×D4×C37—81no—
193C2×D4×C37—81no—
194C2×D4×C37—81no—
195C2×D4×C37—81no—
196C2×D4×C37C2×D412yes—
197C2×D4×C37#4112yes—
198C22×C4×C37—21no—
199C22×C4×C37—24no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—21no—
208C22×C4×C37—21no—
209C22×C4×C37—21no—
210C22×C4×C37—42no—
211C22×C4×C37—42no—
212C22×C4×C37—42no—
213C22×C4×C37—42no—
214C22×C4×C37—81no—
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2×D411yescharacteristic
220C22×C4×C37C2411yescharacteristic
221SD16×C37—28no—
222SD16×C37—44no—
223D8×C37—44no—
224D8×C37—44no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37—21no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—21no—
235C2×C8×C37C2×D412yes—
236C2×C8×C37C2×D412yes—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—21no—
243C4⋊C4×C37—21no—
244C4⋊C4×C37—42no—
245C4⋊C4×C37—42no—
246C4⋊C4×C37—42no—
247C4⋊C4×C37C2×D412yes—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—41no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—81no—
257C22⋊C4×C37—81no—
258C22⋊C4×C37—81no—
259C22⋊C4×C37—81no—
260C42×C37—21no—
261C42×C37—21no—
262C42×C37—21no—
263C42×C37—21no—
264C42×C37—42no—
265C42×C37—42no—
266C23×C37—21no—
267C23×C37—22no—
268C23×C37—22no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—21no—
274C23×C37—21no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37—41no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—41no—
289C23×C37—41no—
290C23×C37—41no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37—41no—
294C23×C37C22×D411yescharacteristic
295Q8×C37—22no—
296Q8×C37—22no—
297Q8×C37—22no—
298Q8×C37#12114yescomplemented
299D4×C37—22no—
300D4×C37—22no—
301D4×C37—22no—
302D4×C37—22no—
303D4×C37—48no—
304D4×C37—41no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—41no—
309D4×C37—41no—
310D4×C37—41no—
311D4×C37—41no—
312D4×C37—84no—
313D4×C37—84no—
314D4×C37—84no—
315D4×C37—84no—
316C2×C4×C37—22no—
317C2×C4×C37—21no—
318C2×C4×C37—22no—
319C2×C4×C37—22no—
320C2×C4×C37—21no—
321C2×C4×C37—21no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
324C2×C4×C37—21no—
325C2×C4×C37—22no—
326C2×C4×C37—21no—
327C2×C4×C37—21no—
328C2×C4×C37—21no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—48no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
346C2×C4×C37—41no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—84no—
351C2×C4×C37AGL(1,ℤ/8)12yes—
352C2×C4×C37C22×D411yescharacteristic
353C2×C4×C37C22×D411yescharacteristic
354C2×C4×C37C2×#4111yescharacteristic
355C2×C4×C37C2×#4111yescharacteristic
356C2×C4×C37H(5,𝔽2)11yescharacteristic
357C2×C4×C37H(5,𝔽2)11yescharacteristic
358C8×C37—22no—
359C8×C37—22no—
360C8×C37—41no—
361C8×C37—41no—
362#25179C3711yesmaximal, characteristic, direct product factor, Sylow
363C22×C37—41no—
364C22×C37—42no—
365C22×C37—41no—
366C22×C37—42no—
367C22×C37—42no—
368C22×C37—41no—
369C22×C37—42no—
370C22×C37—41no—
371C22×C37—42no—
372C22×C37—42no—
373C22×C37—41no—
374C22×C37—41no—
375C22×C37—41no—
376C22×C37—81no—
377C22×C37—81no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37—81no—
382C22×C37—81no—
383C22×C37—81no—
384C22×C37—81no—
385C22×C37—81no—
386C22×C37—81no—
387C22×C37—81no—
388C22×C37—81no—
389C22×C37—81no—
390C22×C37—81no—
391C22×C37#52511yescharacteristic
392C22×C37D4211yescharacteristic
393C22×C37D4211yescharacteristic
394C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C37#57511yescharacteristic
396C22×C37#57611yescharacteristic
397C22×C37#57711yescharacteristic
398C4×C37—24no—
399C4×C37—22no—
400C4×C37—41no—
401C4×C37—41no—
402C4×C37—41no—
403C4×C37—41no—
404C4×C37—42no—
405C4×C37—81no—
406C4×C37—81no—
407C4×C37—81no—
408C4×C37C2×#12111yescharacteristic
409C4×C37#53811yescharacteristic
410C4×C37#54611yescharacteristic
411C4×C37#54611yescharacteristic
412C2×#460C2×C3711yescharacteristic, complemented
413C2×#449C2×C3711yescharacteristic, complemented
414C2×#449C2×C3711yescharacteristic, complemented
415C2×#440C2×C3711yescharacteristic, complemented
416#2428C2×C3711yescharacteristic, complemented
417#2341C2×C3711yescharacteristic, complemented
418#2067C2×C3711yescharacteristic, complemented
419#2034C2×C3711yescharacteristic, complemented
420#2033C2×C3711yescharacteristic, complemented
421#2011C2×C3711yescharacteristic, complemented
422#1972C2×C3711yescharacteristic, complemented
423#1924C2×C3711yescharacteristic, complemented
424#1880C2×C3711yescharacteristic, complemented
425#1879C2×C3711yescharacteristic, complemented
426#1865C2×C3711yescharacteristic, complemented
427C2×C37—81no—
428C2×C37—82no—
429C2×C37—82no—
430C2×C37—161no—
431C2×C37#242411yescharacteristic
432C2×C37#311511yescharacteristic
433C2×C37#311911yescharacteristic
434C2×C37#326511yescharacteristic
435C2×C37#326811yescharacteristic
436C2×C37#327111yescharacteristic
437C2×C37#327411yescharacteristic
438C22×#41C22×C3711yescharacteristic
439C22×SD16C22×C3711yescharacteristic
440C22×SD16C22×C3711yescharacteristic
441C22×D8C22×C3711yescharacteristic
442C22×D8C22×C3711yescharacteristic
443C2×#127C22×C3711yescharacteristic
444C2×#121—21no—
445C2×#121C22×C3711yescharacteristic
446C2×#121C22×C3711yescharacteristic
447C2×C4×Q8C22×C3711yescharacteristic
448C2×C4×Q8C22×C3711yescharacteristic
449C2×C4×D4C22×C3711yescharacteristic
450#460—24no—
451#449—24no—
452#449—24no—
453#440—24no—
454C2×#107C22×C3711yescharacteristic
455C2×#106C22×C3711yescharacteristic
456C2×C4⋊C8C22×C3711yescharacteristic
457C2×#103C22×C3711yescharacteristic
458C2×#103C22×C3711yescharacteristic
459C2×#102C22×C3711yescharacteristic
460C2×#102C22×C3711yescharacteristic
461C2×#102C22×C3711yescharacteristic
462C2×#102C22×C3711yescharacteristic
463C2×#102C22×C3711yescharacteristic
464C2×#102C22×C3711yescharacteristic
465C2×C22⋊C8C22×C3711yescharacteristic
466C2×C22⋊C8C22×C3711yescharacteristic
467C2×#97C22×C3711yescharacteristic
468#394—21no—
469#392—21no—
470#390—21no—
471#390—21no—
472#390C22×C3711yescharacteristic
473#390C22×C3711yescharacteristic
474#390C22×C3711yescharacteristic
475#389C22×C3711yescharacteristic
476#386—21no—
477#380—21no—
478#380C22×C3711yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4C22×C3711yescharacteristic
481#340C22×C3711yescharacteristic
482#340C22×C3711yescharacteristic
483#336C22×C3711yescharacteristic
484#336C22×C3711yescharacteristic
485C37#2517911yescharacteristic, direct product factor, Sylow
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C3711yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C3711yescharacteristic
499C22×D4C23×C3711yescharacteristic
500C22×D4C23×C3711yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C3711yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C3714yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C3711yescharacteristic
517C22×C8C23×C3711yescharacteristic
518C22×C8C23×C3711yescharacteristic
519C22×C8C23×C3711yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C3711yescharacteristic
537C2×C4⋊C4C23×C3711yescharacteristic
538C2×C4⋊C4C23×C3711yescharacteristic
539C2×C4⋊C4C23×C3711yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C3711yescharacteristic
551C2×C22⋊C4D4×C3711yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C3711yescharacteristic
555C2×C42C23×C3711yescharacteristic
556#107—22no—
557#106—41no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C3714yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#95—21no—
571#95—21no—
572#95D4×C3711yescharacteristic
573#95D4×C3711yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C3711yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C3712yes—
586C2×Q8C2×D4×C3712yes—
587C2×Q8#41×C3712yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C3712yes—
620C2×D4#41×C3712yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C3711yescharacteristic
639C22×C4C2×D4×C3711yescharacteristic
640C22×C4C2×D4×C3711yescharacteristic
641C22×C4C2×D4×C3711yescharacteristic
642C22×C4C2×D4×C3711yescharacteristic
643C22×C4C24×C3711yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C3712yes—
659C2×C8C2×D4×C3712yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C3712yes—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C3711yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C3714yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4AGL(1,ℤ/8)×C3712yes—
775C2×C4C22×D4×C3711yescharacteristic
776C2×C4C22×D4×C3711yescharacteristic
777C2×C4C2×#41×C3711yescharacteristic
778C2×C4C2×#41×C3711yescharacteristic
779C2×C4H(5,𝔽2)×C3711yescharacteristic
780C2×C4H(5,𝔽2)×C3711yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—41no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C37×#52511yescharacteristic
814C22D42×C3711yescharacteristic
815C22D42×C3711yescharacteristic
816C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
817C22C37×#57511yescharacteristic
818C22C37×#57611yescharacteristic
819C22C37×#57711yescharacteristic
820C4—24no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C3711yescharacteristic
831C4C37×#53811yescharacteristic
832C4C37×#54611yescharacteristic
833C4C37×#54611yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C37×#242411yescharacteristic
839C2C37×#311511yescharacteristic
840C2C37×#311911yescharacteristic
841C2C37×#326511yescharacteristic
842C2C37×#326811yescharacteristic
843C2C37×#327111yescharacteristic
844C2C37×#327411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#460C2semidirect
2. C2×C37×#449C2semidirect
3. C2×C37×#449C2semidirect
4. C2×C37×#440C2semidirect
5. C37×#2428C2semidirect
6. C37×#2341C2semidirect
7. C37×#2067C2semidirect
8. C37×#2034C2semidirect
9. C37×#2033C2semidirect
10. C37×#2011C2semidirect
11. C37×#1972C2semidirect
12. C37×#1924C2semidirect
13. C37×#1880C2semidirect
14. C37×#1879C2semidirect
15. C37×#1865C2semidirect
86. C2×SD16×C37D4semidirect
137. #103×C37D4semidirect
298. Q8×C37#121semidirect
362. #25179C37direct (N × H)
412. C2×#460C2×C37semidirect
413. C2×#449C2×C37semidirect
414. C2×#449C2×C37semidirect
415. C2×#440C2×C37semidirect
416. #2428C2×C37semidirect
417. #2341C2×C37semidirect
418. #2067C2×C37semidirect
419. #2034C2×C37semidirect
420. #2033C2×C37semidirect
421. #2011C2×C37semidirect
422. #1972C2×C37semidirect
423. #1924C2×C37semidirect
424. #1880C2×C37semidirect
425. #1879C2×C37semidirect
426. #1865C2×C37semidirect
485. C37#25179direct (N × H)
509. C2×SD16D4×C37semidirect
560. #103D4×C37semidirect
721. Q8#121×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4602
C2×C37×#4492
C2×C37×#4402
C37×#24282
C37×#23412
C37×#20672
C37×#20342
C37×#20332
C37×#20112
C37×#19722
C37×#19242
C37×#18802
C37×#18792
C37×#18652
#2517937