Finite Group Databasebeta

← C37×#26986 #22648239

Subgroups — C37×#26986 #22648239

Order 9472.

880 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#470C211yesmaximal, characteristic, complemented
2C2×C37×#440C211yesmaximal, characteristic, complemented
3C37×#2427C211yesmaximal, characteristic
4C37×#2421C211yesmaximal, characteristic, complemented
5C37×#2085C211yesmaximal, characteristic, complemented
6C37×#2036C211yesmaximal, characteristic, complemented
7C37×#2015C211yesmaximal, characteristic, complemented
8C37×#2000C211yesmaximal, characteristic
9C37×#1958C211yesmaximal, characteristic, complemented
10C37×#1935C211yesmaximal, characteristic, complemented
11C37×#1933C211yesmaximal, characteristic, complemented
12C37×#1895C211yesmaximal, characteristic
13C37×#1878C211yesmaximal, characteristic, complemented
14C37×#1864C211yesmaximal, characteristic, complemented
15C37×#1753C211yesmaximal, characteristic, complemented
16C22×Q16×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C2×#124×C37C2211yescharacteristic
20C2×C22⋊Q8×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×C4×Q8×C37C2211yescharacteristic
24C2×C4×D4×C37C2211yescharacteristic
25C37×#470—24no—
26C37×#440—24no—
27C2×#107×C37C2211yescharacteristic
28C2×#106×C37C2211yescharacteristic
29C2×#103×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×#97×C37C2211yescharacteristic
39C2×C4×C8×C37C2211yescharacteristic
40C37×#400—21no—
41C37×#397—21no—
42C37×#397—21no—
43C37×#394—21no—
44C37×#391C2211yescharacteristic
45C37×#391C2211yescharacteristic
46C37×#389C2211yescharacteristic
47C37×#389C2211yescharacteristic
48C37×#388—21no—
49C37×#387—21no—
50C37×#386—21no—
51C37×#382C2211yescharacteristic
52C37×#380—21no—
53C37×#380C2211yescharacteristic
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×Q8×C37C2311yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37C2311yescharacteristic
65C23×C4×C37—21no—
66C23×C4×C37C2311yescharacteristic
67C2×Q16×C37—22no—
68C2×Q16×C37—22no—
69C2×Q16×C37—41no—
70C2×SD16×C37—22no—
71C2×SD16×C37—22no—
72C2×SD16×C37—22no—
73C2×M16×C37—22no—
74C2×M16×C37—22no—
75C2×M16×C37—41no—
76C22×C8×C37C2311yescharacteristic
77C22×C8×C37C2311yescharacteristic
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80#124×C37—22no—
81#124×C37—41no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—41no—
85C22⋊Q8×C37—41no—
86#121×C37—22no—
87#121×C37—41no—
88C4×Q8×C37—22no—
89C4×Q8×C37—41no—
90C4×D4×C37—22no—
91C4×D4×C37—41no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37—21no—
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C22⋊C4×C37—21no—
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×C37—21no—
109C2×C22⋊C4×C37D411yescharacteristic
110C2×C22⋊C4×C37D411yescharacteristic
111C2×C42×C37—21no—
112C2×C42×C37C2311yescharacteristic
113C2×C42×C37C2311yescharacteristic
114#107×C37—22no—
115#106×C37—22no—
116#103×C37—22no—
117#103×C37—22no—
118#103×C37—41no—
119#103×C37—41no—
120#103×C37D414yescomplemented
121#102×C37—22no—
122#102×C37—22no—
123#102×C37—41no—
124C22⋊C8×C37—22no—
125#97×C37—22no—
126C4×C8×C37—41no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37D411yescharacteristic
137#95×C37D411yescharacteristic
138C24×C37—21no—
139C24×C37C2×D411yescharacteristic
140C2×Q8×C37—21no—
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37—21no—
151C2×Q8×C37C2×D412yes—
152C2×D4×C37—21no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—42no—
158C2×D4×C37—42no—
159C2×D4×C37—81no—
160C2×D4×C37#4112yes—
161C22×C4×C37—21no—
162C22×C4×C37—21no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—42no—
175C22×C4×C37—42no—
176C22×C4×C37—81no—
177C22×C4×C37C2×D411yescharacteristic
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2×D411yescharacteristic
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2411yescharacteristic
183Q16×C37—44no—
184SD16×C37—28no—
185M16×C37—44no—
186C2×C8×C37—21no—
187C2×C8×C37—21no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37C2×D412yes—
196C2×C8×C37#4112yes—
197C2×C8×C37#4112yes—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—42no—
208C4⋊C4×C37—42no—
209C4⋊C4×C37—42no—
210C4⋊C4×C37—42no—
211C4⋊C4×C37—81no—
212C4⋊C4×C37C2×D412yes—
213C22⋊C4×C37—41no—
214C22⋊C4×C37—41no—
215C22⋊C4×C37—42no—
216C22⋊C4×C37—42no—
217C22⋊C4×C37—42no—
218C22⋊C4×C37—42no—
219C22⋊C4×C37—42no—
220C22⋊C4×C37—42no—
221C22⋊C4×C37—42no—
222C42×C37—21no—
223C42×C37—21no—
224C42×C37—21no—
225C42×C37—21no—
226C42×C37—42no—
227C23×C37—21no—
228C23×C37—21no—
229C23×C37—22no—
230C23×C37—21no—
231C23×C37—21no—
232C23×C37—21no—
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—41no—
236C23×C37—41no—
237C23×C37—41no—
238C23×C37—41no—
239C23×C37—41no—
240C23×C37—41no—
241C23×C37C22×D411yescharacteristic
242Q8×C37—22no—
243Q8×C37—22no—
244Q8×C37—41no—
245Q8×C37—41no—
246Q8×C37—41no—
247Q8×C37—41no—
248Q8×C37—41no—
249Q8×C37—41no—
250D4×C37—22no—
251D4×C37—22no—
252D4×C37—41no—
253D4×C37—41no—
254D4×C37—84no—
255C2×C4×C37—21no—
256C2×C4×C37—21no—
257C2×C4×C37—21no—
258C2×C4×C37—22no—
259C2×C4×C37—22no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—21no—
264C2×C4×C37—21no—
265C2×C4×C37—21no—
266C2×C4×C37—21no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
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—41no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—41no—
295C2×C4×C37—84no—
296C2×C4×C37C22×D411yescharacteristic
297C2×C4×C37C2×#4111yescharacteristic
298C2×C4×C37C2×#4111yescharacteristic
299C2×C4×C37C2×#4111yescharacteristic
300C2×C4×C37H(5,𝔽2)11yescharacteristic
301C2×C4×C37H(5,𝔽2)11yescharacteristic
302C8×C37—22no—
303C8×C37—22no—
304C8×C37—22no—
305C8×C37—41no—
306#26986C3711yesmaximal, characteristic, direct product factor, Sylow
307C22×C37—41no—
308C22×C37—41no—
309C22×C37—41no—
310C22×C37—42no—
311C22×C37—41no—
312C22×C37—41no—
313C22×C37—41no—
314C22×C37—42no—
315C22×C37—41no—
316C22×C37—42no—
317C22×C37—81no—
318C22×C37—81no—
319C22×C37—81no—
320C22×C37—81no—
321C22×C37#53211yescharacteristic
322C22×C37D4211yescharacteristic
323C22×C37#54611yescharacteristic
324C22×C37#57511yescharacteristic
325C22×C37#57511yescharacteristic
326C22×C37#57711yescharacteristic
327C22×C37#57811yescharacteristic
328C4×C37—41no—
329C4×C37—42no—
330C4×C37—41no—
331C4×C37—42no—
332C4×C37—41no—
333C4×C37—41no—
334C4×C37—41no—
335C4×C37—81no—
336C4×C37—81no—
337C4×C37—81no—
338C4×C37—81no—
339C4×C37—81no—
340C4×C37#52511yescharacteristic
341C4×C37#54011yescharacteristic
342C4×C37#54611yescharacteristic
343C4×C37#55311yescharacteristic
344C2×#470C2×C3711yescharacteristic, complemented
345C2×#440C2×C3711yescharacteristic, complemented
346#2427C2×C3711yescharacteristic
347#2421C2×C3711yescharacteristic, complemented
348#2085C2×C3711yescharacteristic, complemented
349#2036C2×C3711yescharacteristic, complemented
350#2015C2×C3711yescharacteristic, complemented
351#2000C2×C3711yescharacteristic
352#1958C2×C3711yescharacteristic, complemented
353#1935C2×C3711yescharacteristic, complemented
354#1933C2×C3711yescharacteristic, complemented
355#1895C2×C3711yescharacteristic
356#1878C2×C3711yescharacteristic, complemented
357#1864C2×C3711yescharacteristic, complemented
358#1753C2×C3711yescharacteristic, complemented
359C2×C37—81no—
360C2×C37—82no—
361C2×C37#246411yescharacteristic
362C2×C37#317811yescharacteristic
363C2×C37#318311yescharacteristic
364C2×C37#327511yescharacteristic
365C2×C37#327711yescharacteristic
366C2×C37#331111yescharacteristic
367C2×C37#331511yescharacteristic
368C22×Q16C22×C3711yescharacteristic
369C22×SD16C22×C3711yescharacteristic
370C22×M16C22×C3711yescharacteristic
371C2×#124C22×C3711yescharacteristic
372C2×C22⋊Q8C22×C3711yescharacteristic
373C2×C22⋊Q8C22×C3711yescharacteristic
374C2×#121C22×C3711yescharacteristic
375C2×C4×Q8C22×C3711yescharacteristic
376C2×C4×D4C22×C3711yescharacteristic
377#470—24no—
378#440—24no—
379C2×#107C22×C3711yescharacteristic
380C2×#106C22×C3711yescharacteristic
381C2×#103C22×C3711yescharacteristic
382C2×#103C22×C3711yescharacteristic
383C2×#103C22×C3711yescharacteristic
384C2×#103C22×C3711yescharacteristic
385C2×#103C22×C3711yescharacteristic
386C2×#102C22×C3711yescharacteristic
387C2×#102C22×C3711yescharacteristic
388C2×#102C22×C3711yescharacteristic
389C2×C22⋊C8C22×C3711yescharacteristic
390C2×#97C22×C3711yescharacteristic
391C2×C4×C8C22×C3711yescharacteristic
392#400—21no—
393#397—21no—
394#397—21no—
395#394—21no—
396#391C22×C3711yescharacteristic
397#391C22×C3711yescharacteristic
398#389C22×C3711yescharacteristic
399#389C22×C3711yescharacteristic
400#388—21no—
401#387—21no—
402#386—21no—
403#382C22×C3711yescharacteristic
404#380—21no—
405#380C22×C3711yescharacteristic
406C4×C22⋊C4C22×C3711yescharacteristic
407#340C22×C3711yescharacteristic
408#340C22×C3711yescharacteristic
409#340C22×C3711yescharacteristic
410#340C22×C3711yescharacteristic
411#336C22×C3711yescharacteristic
412#336C22×C3711yescharacteristic
413C37#2698611yescharacteristic, direct product factor, Sylow
414C22×Q8C23×C3711yescharacteristic
415C22×Q8C23×C3711yescharacteristic
416C22×D4—21no—
417C22×D4C23×C3711yescharacteristic
418C23×C4—21no—
419C23×C4C23×C3711yescharacteristic
420C2×Q16—22no—
421C2×Q16—22no—
422C2×Q16—41no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—41no—
429C22×C8C23×C3711yescharacteristic
430C22×C8C23×C3711yescharacteristic
431C22×C8C23×C3711yescharacteristic
432C22×C8C23×C3711yescharacteristic
433#124—22no—
434#124—41no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—41no—
438C22⋊Q8—41no—
439#121—22no—
440#121—41no—
441C4×Q8—22no—
442C4×Q8—41no—
443C4×D4—22no—
444C4×D4—41no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C3711yescharacteristic
451C2×C4⋊C4C23×C3711yescharacteristic
452C2×C4⋊C4C23×C3711yescharacteristic
453C2×C4⋊C4C23×C3711yescharacteristic
454C2×C4⋊C4C23×C3711yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C3711yescharacteristic
463C2×C22⋊C4D4×C3711yescharacteristic
464C2×C42—21no—
465C2×C42C23×C3711yescharacteristic
466C2×C42C23×C3711yescharacteristic
467#107—22no—
468#106—22no—
469#103—22no—
470#103—22no—
471#103—41no—
472#103—41no—
473#103D4×C3714yescomplemented
474#102—22no—
475#102—22no—
476#102—41no—
477C22⋊C8—22no—
478#97—22no—
479C4×C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C3711yescharacteristic
490#95D4×C3711yescharacteristic
491C24—21no—
492C24C2×D4×C3711yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×D4×C3712yes—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4#41×C3712yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4C2×D4×C3711yescharacteristic
531C22×C4C2×D4×C3711yescharacteristic
532C22×C4C2×D4×C3711yescharacteristic
533C22×C4C2×D4×C3711yescharacteristic
534C22×C4C2×D4×C3711yescharacteristic
535C22×C4C24×C3711yescharacteristic
536Q16—44no—
537SD16—28no—
538M16—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C2×D4×C3712yes—
549C2×C8#41×C3712yes—
550C2×C8#41×C3712yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4C2×D4×C3712yes—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22×D4×C3711yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
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—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4C22×D4×C3711yescharacteristic
650C2×C4C2×#41×C3711yescharacteristic
651C2×C4C2×#41×C3711yescharacteristic
652C2×C4C2×#41×C3711yescharacteristic
653C2×C4H(5,𝔽2)×C3711yescharacteristic
654C2×C4H(5,𝔽2)×C3711yescharacteristic
655C8—22no—
656C8—22no—
657C8—22no—
658C8—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—42no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C37×#53211yescharacteristic
674C22D42×C3711yescharacteristic
675C22C37×#54611yescharacteristic
676C22C37×#57511yescharacteristic
677C22C37×#57511yescharacteristic
678C22C37×#57711yescharacteristic
679C22C37×#57811yescharacteristic
680C4—41no—
681C4—42no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C37×#52511yescharacteristic
693C4C37×#54011yescharacteristic
694C4C37×#54611yescharacteristic
695C4C37×#55311yescharacteristic
696C2—81no—
697C2—82no—
698C2C37×#246411yescharacteristic
699C2C37×#317811yescharacteristic
700C2C37×#318311yescharacteristic
701C2C37×#327511yescharacteristic
702C2C37×#327711yescharacteristic
703C2C37×#331111yescharacteristic
704C2C37×#331511yescharacteristic
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
1. C2×C37×#470C2semidirect
2. C2×C37×#440C2semidirect
4. C37×#2421C2semidirect
5. C37×#2085C2semidirect
6. C37×#2036C2semidirect
7. C37×#2015C2semidirect
9. C37×#1958C2semidirect
10. C37×#1935C2semidirect
11. C37×#1933C2semidirect
13. C37×#1878C2semidirect
14. C37×#1864C2semidirect
15. C37×#1753C2semidirect
120. #103×C37D4semidirect
306. #26986C37direct (N × H)
344. C2×#470C2×C37semidirect
345. C2×#440C2×C37semidirect
347. #2421C2×C37semidirect
348. #2085C2×C37semidirect
349. #2036C2×C37semidirect
350. #2015C2×C37semidirect
352. #1958C2×C37semidirect
353. #1935C2×C37semidirect
354. #1933C2×C37semidirect
356. #1878C2×C37semidirect
357. #1864C2×C37semidirect
358. #1753C2×C37semidirect
413. C37#26986direct (N × H)
473. #103D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4702
C2×C37×#4402
C37×#24272
C37×#24212
C37×#20852
C37×#20362
C37×#20152
C37×#20002
C37×#19582
C37×#19352
C37×#19332
C37×#18952
C37×#18782
C37×#18642
C37×#17532
#2698637