Finite Group Databasebeta

← C37×#25107 #22646360

Subgroups — C37×#25107 #22646360

Order 9472.

1074 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#468C211yesmaximal, characteristic
2C2×C37×#464C211yesmaximal, characteristic, complemented
3C2×C37×#451C211yesmaximal, characteristic, complemented
4C2×C37×#419C211yesmaximal, characteristic, complemented
5C37×#2436C211yesmaximal, characteristic
6C37×#2362C211yesmaximal, characteristic, complemented
7C37×#2068C211yesmaximal, characteristic, complemented
8C37×#2056C211yesmaximal, characteristic, complemented
9C37×#2042C211yesmaximal, characteristic, complemented
10C37×#2015C211yesmaximal, characteristic, complemented
11C37×#1983C211yesmaximal, characteristic, complemented
12C37×#1928C211yesmaximal, characteristic, complemented
13C37×#1878C211yesmaximal, characteristic, complemented
14C37×#1875C211yesmaximal, characteristic
15C37×#1851C211yesmaximal, characteristic, complemented
16C23×Q8×C37C2211yescharacteristic
17C22×Q16×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic
21C2×#124×C37C2211yescharacteristic
22C2×#124×C37C2211yescharacteristic
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×C4×Q8×C37C2211yescharacteristic
26C2×#117×C37C2211yescharacteristic
27C37×#468—24no—
28C37×#464—24no—
29C37×#451—24no—
30C2×#107×C37C2211yescharacteristic
31C2×C4⋊C8×C37C2211yescharacteristic
32C2×C4⋊C8×C37C2211yescharacteristic
33C37×#419—24no—
34C2×#103×C37C2211yescharacteristic
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#103×C37C2211yescharacteristic
38C2×#103×C37C2211yescharacteristic
39C2×#103×C37C2211yescharacteristic
40C2×#103×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×C22⋊C8×C37C2211yescharacteristic
45C37×#393—21no—
46C37×#393—21no—
47C37×#391C2211yescharacteristic
48C37×#391C2211yescharacteristic
49C37×#391C2211yescharacteristic
50C37×#389C2211yescharacteristic
51C37×#388—21no—
52C37×#388—21no—
53C37×#387—21no—
54C37×#386—21no—
55C37×#386—21no—
56C4×C4⋊C4×C37—21no—
57C4×C4⋊C4×C37C2211yescharacteristic
58C4×C22⋊C4×C37C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×Q8×C37—21no—
64C22×Q8×C37—22no—
65C22×Q8×C37—22no—
66C22×Q8×C37—22no—
67C22×Q8×C37—22no—
68C22×Q8×C37—41no—
69C22×Q8×C37—41no—
70C22×Q8×C37C2311yescharacteristic
71C22×Q8×C37C2311yescharacteristic
72C22×Q8×C37C2311yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37C2311yescharacteristic
75C23×C4×C37—21no—
76C23×C4×C37C2311yescharacteristic
77C2×Q16×C37—22no—
78C2×Q16×C37—22no—
79C2×Q16×C37—22no—
80C2×Q16×C37—22no—
81C2×Q16×C37—41no—
82C2×Q16×C37—41no—
83C2×SD16×C37—22no—
84C2×SD16×C37—22no—
85C2×SD16×C37—41no—
86C2×M16×C37—22no—
87C2×M16×C37—22no—
88C2×M16×C37—41no—
89C22×C8×C37C2311yescharacteristic
90C22×C8×C37C2311yescharacteristic
91C22×C8×C37C2311yescharacteristic
92C22×C8×C37C2311yescharacteristic
93#124×C37—22no—
94#124×C37—22no—
95#124×C37—41no—
96#124×C37—41no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37D414yes—
99#121×C37—22no—
100#121×C37—22no—
101C4×Q8×C37—22no—
102C4×Q8×C37—41no—
103#117×C37—22no—
104#117×C37—41no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C4⋊C4×C37C2311yescharacteristic
110C2×C4⋊C4×C37C2311yescharacteristic
111C2×C4⋊C4×C37C2311yescharacteristic
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37D411yescharacteristic
120C2×C22⋊C4×C37D411yescharacteristic
121C2×C42×C37—21no—
122C2×C42×C37—21no—
123C2×C42×C37—21no—
124C2×C42×C37C2311yescharacteristic
125C2×C42×C37C2311yescharacteristic
126#107×C37—22no—
127C4⋊C8×C37—22no—
128C4⋊C8×C37—41no—
129#103×C37—22no—
130#103×C37—22no—
131#103×C37—22no—
132#103×C37—22no—
133#103×C37—22no—
134#103×C37—22no—
135#103×C37D414yescomplemented
136#102×C37—22no—
137#102×C37—22no—
138#102×C37—41no—
139C22⋊C8×C37—22no—
140#95×C37—21no—
141#95×C37—21no—
142#95×C37—21no—
143#95×C37—21no—
144#95×C37—21no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37D411yescharacteristic
149#95×C37D411yescharacteristic
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—28no—
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×C37—21no—
165C2×Q8×C37—21no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×Q8×C37—42no—
169C2×Q8×C37—42no—
170C2×Q8×C37—44no—
171C2×Q8×C37—44no—
172C2×Q8×C37—44no—
173C2×Q8×C37—42no—
174C2×Q8×C37C2×D412yes—
175C2×Q8×C37C2×D412yes—
176C2×Q8×C37#4112yes—
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—42no—
184C2×D4×C37—42no—
185C2×D4×C37—42no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—42no—
198C22×C4×C37—42no—
199C22×C4×C37—42no—
200C22×C4×C37C2×D411yescharacteristic
201C22×C4×C37C2×D411yescharacteristic
202C22×C4×C37C2×D411yescharacteristic
203C22×C4×C37C2×D411yescharacteristic
204C22×C4×C37C2×D411yescharacteristic
205C22×C4×C37C2×D412yes—
206C22×C4×C37#4112yes—
207C22×C4×C37C2411yescharacteristic
208Q16×C37—44no—
209Q16×C37—44no—
210SD16×C37—44no—
211M16×C37—44no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37C2×D412yes—
224C4⋊C4×C37—24no—
225C4⋊C4×C37—21no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—42no—
232C4⋊C4×C37—42no—
233C4⋊C4×C37C2×D412yes—
234C4⋊C4×C37C2×D412yes—
235C22⋊C4×C37—24no—
236C22⋊C4×C37—41no—
237C22⋊C4×C37—41no—
238C22⋊C4×C37—42no—
239C22⋊C4×C37—42no—
240C22⋊C4×C37—42no—
241C22⋊C4×C37—42no—
242C22⋊C4×C37—42no—
243C22⋊C4×C37—42no—
244C42×C37—21no—
245C42×C37—21no—
246C42×C37—21no—
247C42×C37—21no—
248C42×C37—42no—
249C42×C37—42no—
250C42×C37—42no—
251C23×C37—21no—
252C23×C37—21no—
253C23×C37—21no—
254C23×C37—21no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37#12112yes—
265C23×C37C22×D411yescharacteristic
266Q8×C37—22no—
267Q8×C37—22no—
268Q8×C37—22no—
269Q8×C37—22no—
270Q8×C37—22no—
271Q8×C37—22no—
272Q8×C37—48no—
273Q8×C37—41no—
274Q8×C37—41no—
275Q8×C37—41no—
276Q8×C37—41no—
277Q8×C37—41no—
278Q8×C37—41no—
279D4×C37—41no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—84no—
284C2×C4×C37—21no—
285C2×C4×C37—21no—
286C2×C4×C37—22no—
287C2×C4×C37—22no—
288C2×C4×C37—22no—
289C2×C4×C37—22no—
290C2×C4×C37—22no—
291C2×C4×C37—22no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—22no—
295C2×C4×C37—22no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—22no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—48no—
308C2×C4×C37—41no—
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—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37#12112yes—
325C2×C4×C37C22×D411yescharacteristic
326C2×C4×C37C22×D411yescharacteristic
327C2×C4×C37C2×#4111yescharacteristic
328C2×C4×C37C2×#4111yescharacteristic
329C2×C4×C37H(5,𝔽2)11yescharacteristic
330C2×C4×C37H(5,𝔽2)11yescharacteristic
331C8×C37—22no—
332C8×C37—41no—
333C8×C37—41no—
334C8×C37—41no—
335#25107C3711yesmaximal, characteristic, direct product factor, Sylow
336C22×C37—22no—
337C22×C37—22no—
338C22×C37—22no—
339C22×C37—41no—
340C22×C37—41no—
341C22×C37—41no—
342C22×C37—41no—
343C22×C37—81no—
344C22×C37—81no—
345C22×C37—81no—
346C22×C37—81no—
347C22×C37—81no—
348C22×C37—81no—
349C22×C37—81no—
350C22×C37C2×#12111yescharacteristic
351C22×C37D4211yescharacteristic
352C22×C37#54611yescharacteristic
353C22×C37#57511yescharacteristic
354C22×C37#57511yescharacteristic
355C22×C37#57811yescharacteristic
356C22×C37#57811yescharacteristic
357C4×C37—22no—
358C4×C37—42no—
359C4×C37—42no—
360C4×C37—42no—
361C4×C37—41no—
362C4×C37—42no—
363C4×C37—41no—
364C4×C37—42no—
365C4×C37—41no—
366C4×C37—41no—
367C4×C37—81no—
368C4×C37—81no—
369C4×C37#52511yescharacteristic
370C4×C37#53811yescharacteristic
371C4×C37D4211yescharacteristic
372C4×C37#54611yescharacteristic
373C2×#468C2×C3711yescharacteristic
374C2×#464C2×C3711yescharacteristic, complemented
375C2×#451C2×C3711yescharacteristic, complemented
376C2×#419C2×C3711yescharacteristic, complemented
377#2436C2×C3711yescharacteristic
378#2362C2×C3711yescharacteristic, complemented
379#2068C2×C3711yescharacteristic, complemented
380#2056C2×C3711yescharacteristic, complemented
381#2042C2×C3711yescharacteristic, complemented
382#2015C2×C3711yescharacteristic, complemented
383#1983C2×C3711yescharacteristic, complemented
384#1928C2×C3711yescharacteristic, complemented
385#1878C2×C3711yescharacteristic, complemented
386#1875C2×C3711yescharacteristic
387#1851C2×C3711yescharacteristic, complemented
388C2×C37—42no—
389C2×C37—161no—
390C2×C37#242411yescharacteristic
391C2×C37#304011yescharacteristic
392C2×C37#304411yescharacteristic
393C2×C37#326911yescharacteristic
394C2×C37#327711yescharacteristic
395C2×C37#331311yescharacteristic
396C2×C37#332711yescharacteristic
397C23×Q8C22×C3711yescharacteristic
398C22×Q16C22×C3711yescharacteristic
399C22×Q16C22×C3711yescharacteristic
400C22×SD16C22×C3711yescharacteristic
401C22×M16C22×C3711yescharacteristic
402C2×#124C22×C3711yescharacteristic
403C2×#124C22×C3711yescharacteristic
404C2×C22⋊Q8C22×C3711yescharacteristic
405C2×#121C22×C3711yescharacteristic
406C2×C4×Q8C22×C3711yescharacteristic
407C2×#117C22×C3711yescharacteristic
408#468—24no—
409#464—24no—
410#451—24no—
411C2×#107C22×C3711yescharacteristic
412C2×C4⋊C8C22×C3711yescharacteristic
413C2×C4⋊C8C22×C3711yescharacteristic
414#419—24no—
415C2×#103C22×C3711yescharacteristic
416C2×#103C22×C3711yescharacteristic
417C2×#103C22×C3711yescharacteristic
418C2×#103C22×C3711yescharacteristic
419C2×#103C22×C3711yescharacteristic
420C2×#103C22×C3711yescharacteristic
421C2×#103C22×C3711yescharacteristic
422C2×#102C22×C3711yescharacteristic
423C2×#102C22×C3711yescharacteristic
424C2×#102C22×C3711yescharacteristic
425C2×C22⋊C8C22×C3711yescharacteristic
426#393—21no—
427#393—21no—
428#391C22×C3711yescharacteristic
429#391C22×C3711yescharacteristic
430#391C22×C3711yescharacteristic
431#389C22×C3711yescharacteristic
432#388—21no—
433#388—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C22×C3711yescharacteristic
439C4×C22⋊C4C22×C3711yescharacteristic
440#340C22×C3711yescharacteristic
441#340C22×C3711yescharacteristic
442#336C22×C3711yescharacteristic
443#336C22×C3711yescharacteristic
444C37#2510711yescharacteristic, direct product factor, Sylow
445C22×Q8—21no—
446C22×Q8—22no—
447C22×Q8—22no—
448C22×Q8—22no—
449C22×Q8—22no—
450C22×Q8—41no—
451C22×Q8—41no—
452C22×Q8C23×C3711yescharacteristic
453C22×Q8C23×C3711yescharacteristic
454C22×Q8C23×C3711yescharacteristic
455C22×D4—21no—
456C22×D4C23×C3711yescharacteristic
457C23×C4—21no—
458C23×C4C23×C3711yescharacteristic
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×Q16—41no—
464C2×Q16—41no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—41no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—41no—
471C22×C8C23×C3711yescharacteristic
472C22×C8C23×C3711yescharacteristic
473C22×C8C23×C3711yescharacteristic
474C22×C8C23×C3711yescharacteristic
475#124—22no—
476#124—22no—
477#124—41no—
478#124—41no—
479C22⋊Q8—22no—
480C22⋊Q8D4×C3714yes—
481#121—22no—
482#121—22no—
483C4×Q8—22no—
484C4×Q8—41no—
485#117—22no—
486#117—41no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C23×C3711yescharacteristic
491C2×C4⋊C4C23×C3711yescharacteristic
492C2×C4⋊C4C23×C3711yescharacteristic
493C2×C4⋊C4C23×C3711yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4D4×C3711yescharacteristic
502C2×C22⋊C4D4×C3711yescharacteristic
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C23×C3711yescharacteristic
507C2×C42C23×C3711yescharacteristic
508#107—22no—
509C4⋊C8—22no—
510C4⋊C8—41no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103D4×C3714yescomplemented
518#102—22no—
519#102—22no—
520#102—41no—
521C22⋊C8—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95D4×C3711yescharacteristic
531#95D4×C3711yescharacteristic
532C24—21no—
533C24C2×D4×C3711yescharacteristic
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—28no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—42no—
556C2×Q8C2×D4×C3712yes—
557C2×Q8C2×D4×C3712yes—
558C2×Q8#41×C3712yes—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4C2×D4×C3711yescharacteristic
583C22×C4C2×D4×C3711yescharacteristic
584C22×C4C2×D4×C3711yescharacteristic
585C22×C4C2×D4×C3711yescharacteristic
586C22×C4C2×D4×C3711yescharacteristic
587C22×C4C2×D4×C3712yes—
588C22×C4#41×C3712yes—
589C22×C4C24×C3711yescharacteristic
590Q16—44no—
591Q16—44no—
592SD16—44no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8C2×D4×C3712yes—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4C2×D4×C3712yes—
616C4⋊C4C2×D4×C3712yes—
617C22⋊C4—24no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—42no—
631C42—42no—
632C42—42no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23#121×C3712yes—
647C23C22×D4×C3711yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—48no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—84no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—48no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4#121×C3712yes—
707C2×C4C22×D4×C3711yescharacteristic
708C2×C4C22×D4×C3711yescharacteristic
709C2×C4C2×#41×C3711yescharacteristic
710C2×C4C2×#41×C3711yescharacteristic
711C2×C4H(5,𝔽2)×C3711yescharacteristic
712C2×C4H(5,𝔽2)×C3711yescharacteristic
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#121×C3711yescharacteristic
732C22D42×C3711yescharacteristic
733C22C37×#54611yescharacteristic
734C22C37×#57511yescharacteristic
735C22C37×#57511yescharacteristic
736C22C37×#57811yescharacteristic
737C22C37×#57811yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—41no—
743C4—42no—
744C4—41no—
745C4—42no—
746C4—41no—
747C4—41no—
748C4—81no—
749C4—81no—
750C4C37×#52511yescharacteristic
751C4C37×#53811yescharacteristic
752C4D42×C3711yescharacteristic
753C4C37×#54611yescharacteristic
754C2—42no—
755C2—161no—
756C2C37×#242411yescharacteristic
757C2C37×#304011yescharacteristic
758C2C37×#304411yescharacteristic
759C2C37×#326911yescharacteristic
760C2C37×#327711yescharacteristic
761C2C37×#331311yescharacteristic
762C2C37×#332711yescharacteristic
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
2. C2×C37×#464C2semidirect
3. C2×C37×#451C2semidirect
4. C2×C37×#419C2semidirect
6. C37×#2362C2semidirect
7. C37×#2068C2semidirect
8. C37×#2056C2semidirect
9. C37×#2042C2semidirect
10. C37×#2015C2semidirect
11. C37×#1983C2semidirect
12. C37×#1928C2semidirect
13. C37×#1878C2semidirect
15. C37×#1851C2semidirect
135. #103×C37D4semidirect
335. #25107C37direct (N × H)
374. C2×#464C2×C37semidirect
375. C2×#451C2×C37semidirect
376. C2×#419C2×C37semidirect
378. #2362C2×C37semidirect
379. #2068C2×C37semidirect
380. #2056C2×C37semidirect
381. #2042C2×C37semidirect
382. #2015C2×C37semidirect
383. #1983C2×C37semidirect
384. #1928C2×C37semidirect
385. #1878C2×C37semidirect
387. #1851C2×C37semidirect
444. C37#25107direct (N × H)
517. #103D4×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×#4642
C2×C37×#4512
C2×C37×#4192
C37×#24362
C37×#23622
C37×#20682
C37×#20562
C37×#20422
C37×#20152
C37×#19832
C37×#19282
C37×#18782
C37×#18752
C37×#18512
#2510737