Finite Group Databasebeta

← C37×#25202 #22646455

Subgroups — C37×#25202 #22646455

Order 9472.

942 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#481C211yesmaximal, characteristic
2C2×C37×#465C211yesmaximal, characteristic
3C37×#2502C211yesmaximal, characteristic, complemented
4C37×#2361C211yesmaximal, characteristic
5C37×#2084C211yesmaximal, characteristic, complemented
6C37×#2071C211yesmaximal, characteristic, complemented
7C37×#2066C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#1948C211yesmaximal, characteristic, complemented
10C37×#1927C211yesmaximal, characteristic, complemented
11C37×#1877C211yesmaximal, characteristic, complemented
12C37×#1872C211yesmaximal, characteristic, complemented
13C37×#1850C211yesmaximal, characteristic, complemented
14C37×#1802C211yesmaximal, characteristic, complemented
15C2×C37×#340C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C23×C8×C37C2211yescharacteristic
18C2×C22⋊Q8×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×C4×D4×C37—21no—
21C2×C4×D4×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic
24C37×#481—24no—
25C37×#465—24no—
26C2×#106×C37C2211yescharacteristic
27C2×#106×C37C2211yescharacteristic
28C2×#106×C37C2211yescharacteristic
29C2×C4⋊C8×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C37×#398—21no—
39C37×#398—21no—
40C37×#391C2211yescharacteristic
41C37×#391C2211yescharacteristic
42C37×#390C2211yescharacteristic
43C37×#389C2211yescharacteristic
44C37×#388—21no—
45C37×#386—21no—
46C37×#385—21no—
47C37×#385—21no—
48C37×#385—21no—
49C37×#384C2211yescharacteristic
50C37×#384C2211yescharacteristic
51C4×C4⋊C4×C37C2211yescharacteristic
52C4×C22⋊C4×C37C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—21no—
63C22×D4×C37C2311yescharacteristic
64C23×C4×C37—21no—
65C23×C4×C37—21no—
66C23×C4×C37—21no—
67C23×C4×C37C2311yescharacteristic
68C2×SD16×C37—22no—
69C2×SD16×C37—22no—
70C2×SD16×C37—41no—
71C22×C8×C37—22no—
72C22×C8×C37—22no—
73C22×C8×C37—41no—
74C22×C8×C37C2311yescharacteristic
75C22×C8×C37C2311yescharacteristic
76C22×C8×C37C2311yescharacteristic
77C22×C8×C37C2311yescharacteristic
78C22⋊Q8×C37—22no—
79C22⋊Q8×C37—22no—
80#121×C37—22no—
81#121×C37D414yes—
82C4×D4×C37—22no—
83C4×D4×C37—41no—
84C4×D4×C37—44no—
85C2×C4⋊C4×C37—22no—
86C2×C4⋊C4×C37—22no—
87C2×C4⋊C4×C37—22no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37—41no—
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37D411yescharacteristic
109C2×C22⋊C4×C37D411yescharacteristic
110C2×C42×C37—21no—
111C2×C42×C37C2311yescharacteristic
112C2×C42×C37C2311yescharacteristic
113#106×C37—22no—
114#106×C37—22no—
115#106×C37—22no—
116C4⋊C8×C37—22no—
117C4⋊C8×C37—41no—
118#103×C37—22no—
119#103×C37—22no—
120#103×C37—41no—
121#102×C37—22no—
122#102×C37—22no—
123#102×C37—22no—
124C22⋊C8×C37—22no—
125#95×C37—21no—
126#95×C37—21no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37D411yescharacteristic
132#95×C37D411yescharacteristic
133C24×C37—21no—
134C24×C37C2×D411yescharacteristic
135C2×Q8×C37—21no—
136C2×Q8×C37—21no—
137C2×Q8×C37—21no—
138C2×Q8×C37—21no—
139C2×Q8×C37—21no—
140C2×Q8×C37—21no—
141C2×D4×C37—24no—
142C2×D4×C37—21no—
143C2×D4×C37—21no—
144C2×D4×C37—21no—
145C2×D4×C37—21no—
146C2×D4×C37—21no—
147C2×D4×C37—42no—
148C2×D4×C37—42no—
149C2×D4×C37C2×D412yes—
150C22×C4×C37—21no—
151C22×C4×C37—21no—
152C22×C4×C37—21no—
153C22×C4×C37—21no—
154C22×C4×C37—21no—
155C22×C4×C37—21no—
156C22×C4×C37—21no—
157C22×C4×C37—21no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—42no—
162C22×C4×C37—42no—
163C22×C4×C37—42no—
164C22×C4×C37—42no—
165C22×C4×C37—42no—
166C22×C4×C37—81no—
167C22×C4×C37—81no—
168C22×C4×C37—81no—
169C22×C4×C37—81no—
170C22×C4×C37C2×D411yescharacteristic
171C22×C4×C37C2×D411yescharacteristic
172C22×C4×C37C2×D411yescharacteristic
173C22×C4×C37C2×D412yes—
174C22×C4×C37C2×D411yescharacteristic
175C22×C4×C37C2×D411yescharacteristic
176C22×C4×C37#4112yes—
177C22×C4×C37C2411yescharacteristic
178SD16×C37—44no—
179C2×C8×C37—21no—
180C2×C8×C37—21no—
181C2×C8×C37—21no—
182C2×C8×C37—21no—
183C2×C8×C37—21no—
184C2×C8×C37—21no—
185C2×C8×C37—21no—
186C2×C8×C37—21no—
187C2×C8×C37—21no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—44no—
191C2×C8×C37#4112yes—
192C4⋊C4×C37—21no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—42no—
203C4⋊C4×C37—42no—
204C4⋊C4×C37—42no—
205C4⋊C4×C37—42no—
206C4⋊C4×C37—81no—
207C4⋊C4×C37—81no—
208C4⋊C4×C37—81no—
209C4⋊C4×C37—81no—
210C4⋊C4×C37C2×D412yes—
211C4⋊C4×C37#4112yes—
212C22⋊C4×C37—22no—
213C22⋊C4×C37—24no—
214C22⋊C4×C37—42no—
215C22⋊C4×C37—42no—
216C22⋊C4×C37—42no—
217C22⋊C4×C37—81no—
218C22⋊C4×C37SD1614yescomplemented
219C42×C37—21no—
220C42×C37—21no—
221C42×C37—21no—
222C42×C37—21no—
223C42×C37—42no—
224C23×C37—21no—
225C23×C37—21no—
226C23×C37—21no—
227C23×C37—21no—
228C23×C37—22no—
229C23×C37—41no—
230C23×C37—41no—
231C23×C37—41no—
232C23×C37—41no—
233C23×C37—41no—
234C23×C37—41no—
235C23×C37#12112yes—
236C23×C37C2×SD1612yes—
237C23×C37#13712yes—
238C23×C37C22×D411yescharacteristic
239Q8×C37—41no—
240Q8×C37—41no—
241Q8×C37—41no—
242Q8×C37—41no—
243D4×C37—22no—
244D4×C37—22no—
245D4×C37—48no—
246D4×C37—41no—
247D4×C37—41no—
248C2×C4×C37—21no—
249C2×C4×C37—21no—
250C2×C4×C37—21no—
251C2×C4×C37—21no—
252C2×C4×C37—21no—
253C2×C4×C37—21no—
254C2×C4×C37—22no—
255C2×C4×C37—22no—
256C2×C4×C37—22no—
257C2×C4×C37—22no—
258C2×C4×C37—22no—
259C2×C4×C37—21no—
260C2×C4×C37—22no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—21no—
264C2×C4×C37—21no—
265C2×C4×C37—21no—
266C2×C4×C37—41no—
267C2×C4×C37—41no—
268C2×C4×C37—41no—
269C2×C4×C37—41no—
270C2×C4×C37—41no—
271C2×C4×C37—41no—
272C2×C4×C37—41no—
273C2×C4×C37—41no—
274C2×C4×C37—41no—
275C2×C4×C37—41no—
276C2×C4×C37—41no—
277C2×C4×C37—41no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—41no—
281C2×C4×C37—41no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—41no—
285C2×C4×C37—84no—
286C2×C4×C37—84no—
287C2×C4×C37—84no—
288C2×C4×C37#12112yes—
289C2×C4×C37C2×SD1612yes—
290C2×C4×C37C2×SD1612yes—
291C2×C4×C37C22×D411yescharacteristic
292C2×C4×C37C2×#4111yescharacteristic
293C2×C4×C37C2×#4111yescharacteristic
294C2×C4×C37C2×#4111yescharacteristic
295C2×C4×C37H(5,𝔽2)11yescharacteristic
296C2×C4×C372−1+411yescharacteristic
297C8×C37—22no—
298C8×C37—41no—
299C8×C37—41no—
300C8×C37—41no—
301#25202C3711yesmaximal, characteristic, direct product factor, Sylow
302C22×C37—22no—
303C22×C37—22no—
304C22×C37—22no—
305C22×C37—22no—
306C22×C37—22no—
307C22×C37—22no—
308C22×C37—42no—
309C22×C37—42no—
310C22×C37—42no—
311C22×C37—81no—
312C22×C37—81no—
313C22×C37—81no—
314C22×C37—81no—
315C22×C37#46114yes—
316C22×C37C2×#12111yescharacteristic
317C22×C37#54611yescharacteristic
318C22×C37#54711yescharacteristic
319C22×C37C22×SD1611yescharacteristic
320C22×C37C2×#13711yescharacteristic
321C22×C37#57611yescharacteristic
322C22×C37#57711yescharacteristic
323C4×C37—22no—
324C4×C37—22no—
325C4×C37—22no—
326C4×C37—41no—
327C4×C37—42no—
328C4×C37—42no—
329C4×C37—41no—
330C4×C37—81no—
331C4×C37—81no—
332C4×C37—81no—
333C4×C37—81no—
334C4×C37—81no—
335C4×C37#52911yescharacteristic
336C4×C37#53911yescharacteristic
337C4×C37#54611yescharacteristic
338C4×C37#54711yescharacteristic
339C2×#481C2×C3711yescharacteristic
340C2×#465C2×C3711yescharacteristic
341#2502C2×C3711yescharacteristic, complemented
342#2361C2×C3711yescharacteristic
343#2084C2×C3711yescharacteristic, complemented
344#2071C2×C3711yescharacteristic, complemented
345#2066C2×C3711yescharacteristic, complemented
346#2055C2×C3711yescharacteristic, complemented
347#1948C2×C3711yescharacteristic, complemented
348#1927C2×C3711yescharacteristic, complemented
349#1877C2×C3711yescharacteristic, complemented
350#1872C2×C3711yescharacteristic, complemented
351#1850C2×C3711yescharacteristic, complemented
352#1802C2×C3711yescharacteristic, complemented
353C2×#340C2×C3711yescharacteristic, complemented
354C2×C37—24no—
355C2×C37—82no—
356C2×C37#242511yescharacteristic
357C2×C37C2×#46111yescharacteristic
358C2×C37#304511yescharacteristic
359C2×C37#329511yescharacteristic
360C2×C37#331611yescharacteristic
361C2×C37#333511yescharacteristic
362C2×C37#334611yescharacteristic
363C22×SD16C22×C3711yescharacteristic
364C23×C8C22×C3711yescharacteristic
365C2×C22⋊Q8C22×C3711yescharacteristic
366C2×#121C22×C3711yescharacteristic
367C2×C4×D4—21no—
368C2×C4×D4C22×C3711yescharacteristic
369C22×C4⋊C4C22×C3711yescharacteristic
370C22×C4⋊C4C22×C3711yescharacteristic
371#481—24no—
372#465—24no—
373C2×#106C22×C3711yescharacteristic
374C2×#106C22×C3711yescharacteristic
375C2×#106C22×C3711yescharacteristic
376C2×C4⋊C8C22×C3711yescharacteristic
377C2×C4⋊C8C22×C3711yescharacteristic
378C2×#103C22×C3711yescharacteristic
379C2×#103C22×C3711yescharacteristic
380C2×#103C22×C3711yescharacteristic
381C2×#102C22×C3711yescharacteristic
382C2×#102C22×C3711yescharacteristic
383C2×#102C22×C3711yescharacteristic
384C2×C22⋊C8C22×C3711yescharacteristic
385#398—21no—
386#398—21no—
387#391C22×C3711yescharacteristic
388#391C22×C3711yescharacteristic
389#390C22×C3711yescharacteristic
390#389C22×C3711yescharacteristic
391#388—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#384C22×C3711yescharacteristic
397#384C22×C3711yescharacteristic
398C4×C4⋊C4C22×C3711yescharacteristic
399C4×C22⋊C4C22×C3711yescharacteristic
400#340C22×C3711yescharacteristic
401#340C22×C3711yescharacteristic
402#340C22×C3711yescharacteristic
403#340C22×C3711yescharacteristic
404#340C22×C3711yescharacteristic
405#340C22×C3711yescharacteristic
406#336C22×C3711yescharacteristic
407#336C22×C3711yescharacteristic
408C37#2520211yescharacteristic, direct product factor, Sylow
409C22×Q8C23×C3711yescharacteristic
410C22×D4—21no—
411C22×D4C23×C3711yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4C23×C3711yescharacteristic
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—41no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—41no—
422C22×C8C23×C3711yescharacteristic
423C22×C8C23×C3711yescharacteristic
424C22×C8C23×C3711yescharacteristic
425C22×C8C23×C3711yescharacteristic
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428#121—22no—
429#121D4×C3714yes—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—44no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4C23×C3711yescharacteristic
446C2×C4⋊C4C23×C3711yescharacteristic
447C2×C4⋊C4C23×C3711yescharacteristic
448C2×C4⋊C4C23×C3711yescharacteristic
449C2×C4⋊C4C23×C3711yescharacteristic
450C2×C4⋊C4C23×C3711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C3711yescharacteristic
457C2×C22⋊C4D4×C3711yescharacteristic
458C2×C42—21no—
459C2×C42C23×C3711yescharacteristic
460C2×C42C23×C3711yescharacteristic
461#106—22no—
462#106—22no—
463#106—22no—
464C4⋊C8—22no—
465C4⋊C8—41no—
466#103—22no—
467#103—22no—
468#103—41no—
469#102—22no—
470#102—22no—
471#102—22no—
472C22⋊C8—22no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C3711yescharacteristic
480#95D4×C3711yescharacteristic
481C24—21no—
482C24C2×D4×C3711yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C2×D4×C3712yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4C2×D4×C3711yescharacteristic
519C22×C4C2×D4×C3711yescharacteristic
520C22×C4C2×D4×C3711yescharacteristic
521C22×C4C2×D4×C3712yes—
522C22×C4C2×D4×C3711yescharacteristic
523C22×C4C2×D4×C3711yescharacteristic
524C22×C4#41×C3712yes—
525C22×C4C24×C3711yescharacteristic
526SD16—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—44no—
539C2×C8#41×C3712yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4C2×D4×C3712yes—
559C4⋊C4#41×C3712yes—
560C22⋊C4—22no—
561C22⋊C4—24no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4SD16×C3714yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23#121×C3712yes—
584C23C2×SD16×C3712yes—
585C23#137×C3712yes—
586C23C22×D4×C3711yescharacteristic
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4—41no—
595D4—41no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4#121×C3712yes—
637C2×C4C2×SD16×C3712yes—
638C2×C4C2×SD16×C3712yes—
639C2×C4C22×D4×C3711yescharacteristic
640C2×C4C2×#41×C3711yescharacteristic
641C2×C4C2×#41×C3711yescharacteristic
642C2×C4C2×#41×C3711yescharacteristic
643C2×C4H(5,𝔽2)×C3711yescharacteristic
644C2×C42−1+4×C3711yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22C37×#46114yes—
663C22C2×#121×C3711yescharacteristic
664C22C37×#54611yescharacteristic
665C22C37×#54711yescharacteristic
666C22C22×SD16×C3711yescharacteristic
667C22C2×#137×C3711yescharacteristic
668C22C37×#57611yescharacteristic
669C22C37×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C37×#52911yescharacteristic
683C4C37×#53911yescharacteristic
684C4C37×#54611yescharacteristic
685C4C37×#54711yescharacteristic
686C2—24no—
687C2—82no—
688C2C37×#242511yescharacteristic
689C2C2×C37×#46111yescharacteristic
690C2C37×#304511yescharacteristic
691C2C37×#329511yescharacteristic
692C2C37×#331611yescharacteristic
693C2C37×#333511yescharacteristic
694C2C37×#334611yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
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
3. C37×#2502C2semidirect
5. C37×#2084C2semidirect
6. C37×#2071C2semidirect
7. C37×#2066C2semidirect
8. C37×#2055C2semidirect
9. C37×#1948C2semidirect
10. C37×#1927C2semidirect
11. C37×#1877C2semidirect
12. C37×#1872C2semidirect
13. C37×#1850C2semidirect
14. C37×#1802C2semidirect
15. C2×C37×#340C2semidirect
218. C22⋊C4×C37SD16semidirect
301. #25202C37direct (N × H)
341. #2502C2×C37semidirect
343. #2084C2×C37semidirect
344. #2071C2×C37semidirect
345. #2066C2×C37semidirect
346. #2055C2×C37semidirect
347. #1948C2×C37semidirect
348. #1927C2×C37semidirect
349. #1877C2×C37semidirect
350. #1872C2×C37semidirect
351. #1850C2×C37semidirect
352. #1802C2×C37semidirect
353. C2×#340C2×C37semidirect
408. C37#25202direct (N × H)
566. C22⋊C4SD16×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4812
C2×C37×#4652
C37×#25022
C37×#23612
C37×#20842
C37×#20712
C37×#20662
C37×#20552
C37×#19482
C37×#19272
C37×#18772
C37×#18722
C37×#18502
C37×#18022
C2×C37×#3402
#2520237