Finite Group Databasebeta

← C37×#25139 #22646392

Subgroups — C37×#25139 #22646392

Order 9472.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#468C211yesmaximal, characteristic, complemented
2C2×C37×#449C211yesmaximal, characteristic, complemented
3C2×C37×#436C211yesmaximal, characteristic, complemented
4C2×C37×#417C211yesmaximal, characteristic, complemented
5C37×#2416C211yesmaximal, characteristic, complemented
6C37×#2407C211yesmaximal, characteristic, complemented
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2036C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1970C211yesmaximal, characteristic, complemented
12C37×#1933C211yesmaximal, characteristic, complemented
13C37×#1895C211yesmaximal, characteristic, complemented
14C37×#1895C211yesmaximal, characteristic, complemented
15C37×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×#121×C37—21no—
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic
26C2×C4×D4×C37C2211yescharacteristic
27C22×C4⋊C4×C37C2211yescharacteristic
28C37×#468—24no—
29C37×#449—24no—
30C37×#436—24no—
31C2×#107×C37C2211yescharacteristic
32C2×#107×C37C2211yescharacteristic
33C2×C4⋊C8×C37C2211yescharacteristic
34C37×#417—24no—
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#103×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×C4×C8×C37C2211yescharacteristic
46C37×#396—21no—
47C37×#394—21no—
48C37×#394—21no—
49C37×#392—21no—
50C37×#391C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic
53C37×#389C2211yescharacteristic
54C37×#386—21no—
55C37×#386—21no—
56C37×#385—21no—
57C37×#380C2211yescharacteristic
58C37×#380C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#340C2211yescharacteristic
62C37×#340C2211yescharacteristic
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×C37D411yescharacteristic
75C22×D4×C37C2311yescharacteristic
76C22×D4×C37C2311yescharacteristic
77C23×C4×C37—21no—
78C23×C4×C37—21no—
79C23×C4×C37C2311yescharacteristic
80C23×C4×C37C2311yescharacteristic
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—41no—
84C2×D8×C37—22no—
85C2×D8×C37—22no—
86C2×D8×C37—41no—
87C2×M16×C37—22no—
88C2×M16×C37—22no—
89C2×M16×C37—22no—
90C2×M16×C37—22no—
91C2×M16×C37—41no—
92C2×M16×C37—41no—
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—41no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—41no—
104#121×C37—41no—
105#121×C37—44no—
106C4×D4×C37—22no—
107C4×D4×C37—22no—
108C2×C4⋊C4×C37—22no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—41no—
113C2×C4⋊C4×C37D411yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37D411yescharacteristic
130C2×C22⋊C4×C37D411yescharacteristic
131C2×C42×C37C2311yescharacteristic
132#107×C37—22no—
133#107×C37—41no—
134C4⋊C8×C37—22no—
135#103×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—41no—
143C22⋊C8×C37—22no—
144C22⋊C8×C37D414yescomplemented
145C4×C8×C37—22no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37—21no—
150#95×C37—21no—
151C24×C37—21no—
152C24×C37—21no—
153C24×C37C2×D411yescharacteristic
154C24×C37C2×D411yescharacteristic
155#41×C37—28no—
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×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37C2×D412yes—
165C2×D4×C37—22no—
166C2×D4×C37—22no—
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—41no—
179C2×D4×C37—42no—
180C2×D4×C37—42no—
181C2×D4×C37—42no—
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—81no—
190C2×D4×C37—81no—
191C2×D4×C37#4112yes—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
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—42no—
209C22×C4×C37—42no—
210C22×C4×C37—42no—
211C22×C4×C37—42no—
212C22×C4×C37—42no—
213C22×C4×C37—81no—
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D412yes—
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37#4112yes—
220C22×C4×C37C2411yescharacteristic
221SD16×C37—44no—
222D8×C37—44no—
223M16×C37—44no—
224M16×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×C37C2×D412yes—
235C2×C8×C37C2×D412yes—
236C2×C8×C37C2×D412yes—
237C4⋊C4×C37—22no—
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—21no—
245C4⋊C4×C37—21no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—42no—
248C4⋊C4×C37—42no—
249C4⋊C4×C37—42no—
250C4⋊C4×C37C2×D412yes—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—42no—
257C22⋊C4×C37—42no—
258C22⋊C4×C37—42no—
259C22⋊C4×C37—42no—
260C22⋊C4×C37—81no—
261C22⋊C4×C37—81no—
262C22⋊C4×C37—81no—
263C42×C37—21no—
264C42×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—22no—
274C23×C37—21no—
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
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#12112yes—
293C23×C37C22×D411yescharacteristic
294Q8×C37—22no—
295Q8×C37—22no—
296Q8×C37—41no—
297Q8×C37—41no—
298D4×C37—22no—
299D4×C37—22no—
300D4×C37—44no—
301D4×C37—48no—
302D4×C37—41no—
303D4×C37—41no—
304D4×C37—41no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—84no—
309D4×C37—84no—
310D4×C37—84no—
311C2×C4×C37—21no—
312C2×C4×C37—21no—
313C2×C4×C37—21no—
314C2×C4×C37—21no—
315C2×C4×C37—22no—
316C2×C4×C37—22no—
317C2×C4×C37—22no—
318C2×C4×C37—22no—
319C2×C4×C37—21no—
320C2×C4×C37—21no—
321C2×C4×C37—21no—
322C2×C4×C37—22no—
323C2×C4×C37—22no—
324C2×C4×C37—21no—
325C2×C4×C37—21no—
326C2×C4×C37—21no—
327C2×C4×C37—48no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
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—84no—
349C2×C4×C37#12112yes—
350C2×C4×C37AGL(1,ℤ/8)12yes—
351C2×C4×C37C22×D411yescharacteristic
352C2×C4×C37C22×D411yescharacteristic
353C2×C4×C37C2×#4111yescharacteristic
354C2×C4×C37C2×#4111yescharacteristic
355C2×C4×C37H(5,𝔽2)11yescharacteristic
356C2×C4×C37H(5,𝔽2)11yescharacteristic
357C8×C37—22no—
358C8×C37—22no—
359C8×C37—22no—
360C8×C37—41no—
361#25139C3711yesmaximal, characteristic, direct product factor, Sylow
362C22×C37—22no—
363C22×C37—22no—
364C22×C37—22no—
365C22×C37—41no—
366C22×C37—41no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—42no—
371C22×C37—42no—
372C22×C37—41no—
373C22×C37—41no—
374C22×C37—41no—
375C22×C37—41no—
376C22×C37—41no—
377C22×C37—41no—
378C22×C37—42no—
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×C37C2×#12111yescharacteristic
391C22×C37D4211yescharacteristic
392C22×C37#54611yescharacteristic
393C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C37#57511yescharacteristic
395C22×C37#57611yescharacteristic
396C22×C37#57811yescharacteristic
397C4×C37—22no—
398C4×C37—22no—
399C4×C37—41no—
400C4×C37—42no—
401C4×C37—42no—
402C4×C37—41no—
403C4×C37—81no—
404C4×C37—81no—
405C4×C37—81no—
406C4×C37—81no—
407C4×C37#52511yescharacteristic
408C4×C37#53811yescharacteristic
409C4×C37D4211yescharacteristic
410C4×C37#54611yescharacteristic
411C2×#468C2×C3711yescharacteristic, complemented
412C2×#449C2×C3711yescharacteristic, complemented
413C2×#436C2×C3711yescharacteristic, complemented
414C2×#417C2×C3711yescharacteristic, complemented
415#2416C2×C3711yescharacteristic, complemented
416#2407C2×C3711yescharacteristic, complemented
417#2067C2×C3711yescharacteristic, complemented
418#2055C2×C3711yescharacteristic, complemented
419#2036C2×C3711yescharacteristic, complemented
420#1999C2×C3711yescharacteristic, complemented
421#1970C2×C3711yescharacteristic, complemented
422#1933C2×C3711yescharacteristic, complemented
423#1895C2×C3711yescharacteristic, complemented
424#1895C2×C3711yescharacteristic, complemented
425#1852C2×C3711yescharacteristic, complemented
426C2×C37—42no—
427C2×C37—81no—
428C2×C37—82no—
429C2×C37—161no—
430C2×C37#242411yescharacteristic
431C2×C37#305511yescharacteristic
432C2×C37#306111yescharacteristic
433C2×C37#327411yescharacteristic
434C2×C37#327711yescharacteristic
435C2×C37#332211yescharacteristic
436C2×C37#333011yescharacteristic
437C22×#41C22×C3711yescharacteristic
438C22×SD16C22×C3711yescharacteristic
439C22×D8C22×C3711yescharacteristic
440C22×M16C22×C3711yescharacteristic
441C22×M16C22×C3711yescharacteristic
442C2×C22⋊Q8C22×C3711yescharacteristic
443C2×#121—21no—
444C2×#121C22×C3711yescharacteristic
445C2×#121C22×C3711yescharacteristic
446C2×#121C22×C3711yescharacteristic
447C2×C4×D4C22×C3711yescharacteristic
448C22×C4⋊C4C22×C3711yescharacteristic
449#468—24no—
450#449—24no—
451#436—24no—
452C2×#107C22×C3711yescharacteristic
453C2×#107C22×C3711yescharacteristic
454C2×C4⋊C8C22×C3711yescharacteristic
455#417—24no—
456C2×#103C22×C3711yescharacteristic
457C2×#103C22×C3711yescharacteristic
458C2×#103C22×C3711yescharacteristic
459C2×#102C22×C3711yescharacteristic
460C2×#102C22×C3711yescharacteristic
461C2×#102C22×C3711yescharacteristic
462C2×#102C22×C3711yescharacteristic
463C2×#102C22×C3711yescharacteristic
464C2×C22⋊C8C22×C3711yescharacteristic
465C2×C22⋊C8C22×C3711yescharacteristic
466C2×C4×C8C22×C3711yescharacteristic
467#396—21no—
468#394—21no—
469#394—21no—
470#392—21no—
471#391C22×C3711yescharacteristic
472#390C22×C3711yescharacteristic
473#390C22×C3711yescharacteristic
474#389C22×C3711yescharacteristic
475#386—21no—
476#386—21no—
477#385—21no—
478#380C22×C3711yescharacteristic
479#380C22×C3711yescharacteristic
480#340C22×C3711yescharacteristic
481#340C22×C3711yescharacteristic
482#340C22×C3711yescharacteristic
483#340C22×C3711yescharacteristic
484C37#2513911yescharacteristic, direct product factor, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C3711yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C3711yescharacteristic
497C22×D4C23×C3711yescharacteristic
498C22×D4C23×C3711yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C3711yescharacteristic
502C23×C4C23×C3711yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C3711yescharacteristic
516C22×C8C23×C3711yescharacteristic
517C22×C8C23×C3711yescharacteristic
518C22×C8C23×C3711yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C3711yescharacteristic
536C2×C4⋊C4C23×C3711yescharacteristic
537C2×C4⋊C4C23×C3711yescharacteristic
538C2×C4⋊C4C23×C3711yescharacteristic
539C2×C4⋊C4C23×C3711yescharacteristic
540C2×C4⋊C4C23×C3711yescharacteristic
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⋊C4—21no—
551C2×C22⋊C4D4×C3711yescharacteristic
552C2×C22⋊C4D4×C3711yescharacteristic
553C2×C42C23×C3711yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C3714yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C3714yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C3711yescharacteristic
576C24C2×D4×C3711yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C3712yes—
587C2×D4—22no—
588C2×D4—22no—
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—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C3712yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C3711yescharacteristic
637C22×C4C2×D4×C3711yescharacteristic
638C22×C4C2×D4×C3711yescharacteristic
639C22×C4C2×D4×C3712yes—
640C22×C4C2×D4×C3711yescharacteristic
641C22×C4#41×C3712yes—
642C22×C4C24×C3711yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
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×C8C2×D4×C3712yes—
657C2×C8C2×D4×C3712yes—
658C2×C8C2×D4×C3712yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C3712yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
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#121×C3712yes—
715C23C22×D4×C3711yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
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—84no—
771C2×C4#121×C3712yes—
772C2×C4AGL(1,ℤ/8)×C3712yes—
773C2×C4C22×D4×C3711yescharacteristic
774C2×C4C22×D4×C3711yescharacteristic
775C2×C4C2×#41×C3711yescharacteristic
776C2×C4C2×#41×C3711yescharacteristic
777C2×C4H(5,𝔽2)×C3711yescharacteristic
778C2×C4H(5,𝔽2)×C3711yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C3711yescharacteristic
812C22D42×C3711yescharacteristic
813C22C37×#54611yescharacteristic
814C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
815C22C37×#57511yescharacteristic
816C22C37×#57611yescharacteristic
817C22C37×#57811yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4C37×#52511yescharacteristic
829C4C37×#53811yescharacteristic
830C4D42×C3711yescharacteristic
831C4C37×#54611yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C37×#242411yescharacteristic
837C2C37×#305511yescharacteristic
838C2C37×#306111yescharacteristic
839C2C37×#327411yescharacteristic
840C2C37×#327711yescharacteristic
841C2C37×#332211yescharacteristic
842C2C37×#333011yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#468C2semidirect
2. C2×C37×#449C2semidirect
3. C2×C37×#436C2semidirect
4. C2×C37×#417C2semidirect
5. C37×#2416C2semidirect
6. C37×#2407C2semidirect
7. C37×#2067C2semidirect
8. C37×#2055C2semidirect
9. C37×#2036C2semidirect
10. C37×#1999C2semidirect
11. C37×#1970C2semidirect
12. C37×#1933C2semidirect
13. C37×#1895C2semidirect
14. C37×#1895C2semidirect
15. C37×#1852C2semidirect
137. #103×C37D4semidirect
144. C22⋊C8×C37D4semidirect
361. #25139C37direct (N × H)
411. C2×#468C2×C37semidirect
412. C2×#449C2×C37semidirect
413. C2×#436C2×C37semidirect
414. C2×#417C2×C37semidirect
415. #2416C2×C37semidirect
416. #2407C2×C37semidirect
417. #2067C2×C37semidirect
418. #2055C2×C37semidirect
419. #2036C2×C37semidirect
420. #1999C2×C37semidirect
421. #1970C2×C37semidirect
422. #1933C2×C37semidirect
423. #1895C2×C37semidirect
424. #1895C2×C37semidirect
425. #1852C2×C37semidirect
484. C37#25139direct (N × H)
559. #103D4×C37semidirect
566. C22⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4682
C2×C37×#4492
C2×C37×#4362
C2×C37×#4172
C37×#24162
C37×#24072
C37×#20672
C37×#20552
C37×#20362
C37×#19992
C37×#19702
C37×#19332
C37×#18952
C37×#18522
#2513937