Finite Group Databasebeta

← C37×#28992 #22650245

Subgroups — C37×#28992 #22650245

Order 9472.

842 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
1C37×#2491C211yesmaximal, characteristic, complemented
2C37×#2420C211yesmaximal, characteristic, complemented
3C37×#2077C211yesmaximal, characteristic, complemented
4C37×#2073C211yesmaximal, characteristic, complemented
5C37×#2023C211yesmaximal, characteristic, complemented
6C37×#1999C211yesmaximal, characteristic
7C37×#1993C211yesmaximal, characteristic, complemented
8C37×#1972C211yesmaximal, characteristic, complemented
9C37×#1934C211yesmaximal, characteristic, complemented
10C37×#1920C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1895C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C4×#102×C37C211yesmaximal, characteristic, complemented
15C37×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C2×C4⋊Q8×C37C2211yescharacteristic
19C2×#124×C37—21no—
20C2×#121×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×C4×D4×C37C2211yescharacteristic
23C2×#106×C37C2211yescharacteristic
24C2×#102×C37C2211yescharacteristic
25C2×#102×C37C2211yescharacteristic
26C2×#102×C37C2211yescharacteristic
27C2×#102×C37C2211yescharacteristic
28C2×#102×C37C2211yescharacteristic
29C2×#102×C37C2211yescharacteristic
30C2×C22⋊C8×C37C2211yescharacteristic
31C2×#97×C37C2211yescharacteristic
32C2×C4×C8×C37C2211yescharacteristic
33C37×#397—21no—
34C37×#394—21no—
35C37×#394—21no—
36C37×#393—21no—
37C37×#390C2211yescharacteristic
38C37×#390C2211yescharacteristic
39C37×#390C2211yescharacteristic
40C37×#389C2211yescharacteristic
41C37×#388—21no—
42C37×#386—21no—
43C37×#382C2211yescharacteristic
44C37×#381—21no—
45C37×#380C2211yescharacteristic
46C37×#380C2211yescharacteristic
47C4×C4⋊C4×C37C2211yescharacteristic
48C4×C22⋊C4×C37C2211yescharacteristic
49C37×#340C2211yescharacteristic
50C37×#340C2211yescharacteristic
51C37×#340C2211yescharacteristic
52C37×#340C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C22×Q8×C37—21no—
60C22×D4×C37—21no—
61C22×D4×C37—21no—
62C22×D4×C37C2311yescharacteristic
63C22×D4×C37C2311yescharacteristic
64C23×C4×C37—21no—
65C23×C4×C37C2311yescharacteristic
66C2×D8×C37—22no—
67C2×D8×C37—22no—
68C2×D8×C37—41no—
69C2×M16×C37—22no—
70C2×M16×C37—41no—
71C2×M16×C37—41no—
72C22×C8×C37C2311yescharacteristic
73C22×C8×C37C2311yescharacteristic
74C22×C8×C37C2311yescharacteristic
75C22×C8×C37C2311yescharacteristic
76C4⋊Q8×C37—22no—
77C4⋊Q8×C37—41no—
78#124×C37—44no—
79#121×C37—22no—
80#121×C37—22no—
81#121×C37—41no—
82#121×C37—41no—
83C4×D4×C37—22no—
84C4×D4×C37—41no—
85C2×C4⋊C4×C37—21no—
86C2×C4⋊C4×C37—21no—
87C2×C4⋊C4×C37C2311yescharacteristic
88C2×C4⋊C4×C37C2311yescharacteristic
89C2×C4⋊C4×C37C2311yescharacteristic
90C2×C4⋊C4×C37C2311yescharacteristic
91C2×C4⋊C4×C37C2311yescharacteristic
92C2×C4⋊C4×C37C2311yescharacteristic
93C2×C22⋊C4×C37—21no—
94C2×C22⋊C4×C37—21no—
95C2×C22⋊C4×C37—21no—
96C2×C22⋊C4×C37—21no—
97C2×C22⋊C4×C37—21no—
98C2×C22⋊C4×C37—21no—
99C2×C22⋊C4×C37—21no—
100C2×C22⋊C4×C37—21no—
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37D411yescharacteristic
105C2×C22⋊C4×C37D411yescharacteristic
106C2×C42×C37—21no—
107C2×C42×C37C2311yescharacteristic
108C2×C42×C37C2311yescharacteristic
109#106×C37—22no—
110#102×C37—22no—
111#102×C37—22no—
112#102×C37—22no—
113#102×C37—41no—
114#102×C37—41no—
115#102×C37—41no—
116C22⋊C8×C37—22no—
117#97×C37—41no—
118C4×C8×C37—41no—
119#95×C37—21no—
120#95×C37—21no—
121#95×C37—21no—
122#95×C37—21no—
123#95×C37—21no—
124#95×C37—21no—
125#95×C37D411yescharacteristic
126#95×C37D411yescharacteristic
127C24×C37—21no—
128C24×C37—21no—
129C24×C37C2×D411yescharacteristic
130C2×Q8×C37—42no—
131C2×Q8×C37—42no—
132C2×Q8×C37—81no—
133C2×D4×C37—21no—
134C2×D4×C37—21no—
135C2×D4×C37—21no—
136C2×D4×C37—21no—
137C2×D4×C37—21no—
138C2×D4×C37—21no—
139C2×D4×C37—21no—
140C2×D4×C37—21no—
141C2×D4×C37—21no—
142C2×D4×C37—21no—
143C2×D4×C37—21no—
144C2×D4×C37—42no—
145C2×D4×C37—42no—
146C2×D4×C37—42no—
147C2×D4×C37—42no—
148C2×D4×C37—81no—
149C2×D4×C37—81no—
150C2×D4×C37#4112yes—
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—21no—
162C22×C4×C37—21no—
163C22×C4×C37—42no—
164C22×C4×C37—42no—
165C22×C4×C37—81no—
166C22×C4×C37C2×D411yescharacteristic
167C22×C4×C37C2×D411yescharacteristic
168C22×C4×C37C2×D411yescharacteristic
169C22×C4×C37C2×D411yescharacteristic
170C22×C4×C37C2×D411yescharacteristic
171C22×C4×C37C2411yescharacteristic
172D8×C37—44no—
173M16×C37—44no—
174C2×C8×C37—21no—
175C2×C8×C37—21no—
176C2×C8×C37—21no—
177C2×C8×C37—21no—
178C2×C8×C37—21no—
179C2×C8×C37—21no—
180C2×C8×C37—21no—
181C2×C8×C37—21no—
182C2×C8×C37—21no—
183C2×C8×C37—21no—
184C2×C8×C37#4112yes—
185C2×C8×C37#4112yes—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—21no—
192C4⋊C4×C37—21no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—42no—
198C4⋊C4×C37—81no—
199C4⋊C4×C37#4112yes—
200C22⋊C4×C37—22no—
201C22⋊C4×C37—41no—
202C22⋊C4×C37—42no—
203C22⋊C4×C37—42no—
204C22⋊C4×C37—42no—
205C22⋊C4×C37—42no—
206C22⋊C4×C37—42no—
207C22⋊C4×C37—42no—
208C22⋊C4×C37—42no—
209C22⋊C4×C37—81no—
210C22⋊C4×C37—81no—
211C22⋊C4×C37—81no—
212C22⋊C4×C37—81no—
213C42×C37—21no—
214C42×C37—21no—
215C42×C37—21no—
216C42×C37—21no—
217C42×C37—42no—
218C23×C37—21no—
219C23×C37—22no—
220C23×C37—21no—
221C23×C37—21no—
222C23×C37—21no—
223C23×C37—21no—
224C23×C37—21no—
225C23×C37—21no—
226C23×C37—41no—
227C23×C37—41no—
228C23×C37—41no—
229C23×C37—41no—
230C23×C37—41no—
231C23×C37—41no—
232C23×C37—41no—
233C23×C37—41no—
234C23×C37—41no—
235C23×C37—41no—
236C23×C37—41no—
237C23×C37—41no—
238C23×C37—41no—
239C23×C37C22×D411yescharacteristic
240Q8×C37—84no—
241D4×C37—22no—
242D4×C37—22no—
243D4×C37—41no—
244D4×C37—41no—
245D4×C37—41no—
246D4×C37—41no—
247D4×C37—41no—
248D4×C37—41no—
249D4×C37—84no—
250D4×C37—84no—
251C2×C4×C37—21no—
252C2×C4×C37—21no—
253C2×C4×C37—21no—
254C2×C4×C37—21no—
255C2×C4×C37—21no—
256C2×C4×C37—21no—
257C2×C4×C37—21no—
258C2×C4×C37—21no—
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—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—41no—
286C2×C4×C37—41no—
287C2×C4×C37—84no—
288C2×C4×C37AGL(1,ℤ/8)12yes—
289C2×C4×C37C2×#4111yescharacteristic
290C2×C4×C37C2×#4111yescharacteristic
291C2×C4×C37C2×#4111yescharacteristic
292C2×C4×C37C2×#4111yescharacteristic
293C2×C4×C37H(5,𝔽2)11yescharacteristic
294C2×C4×C37H(5,𝔽2)11yescharacteristic
295C8×C37—22no—
296C8×C37—22no—
297C8×C37—41no—
298C8×C37—41no—
299#28992C3711yesmaximal, characteristic, direct product factor, Sylow
300C22×C37—41no—
301C22×C37—41no—
302C22×C37—42no—
303C22×C37—41no—
304C22×C37—41no—
305C22×C37—42no—
306C22×C37—41no—
307C22×C37—42no—
308C22×C37—41no—
309C22×C37—41no—
310C22×C37—81no—
311C22×C37—81no—
312C22×C37—81no—
313C22×C37—81no—
314C22×C37—81no—
315C22×C37—81no—
316C22×C37—81no—
317C22×C37—81no—
318C22×C37—81no—
319C22×C37—81no—
320C22×C37—81no—
321C22×C37#53211yescharacteristic
322C22×C37#54611yescharacteristic
323C22×C37#54611yescharacteristic
324C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C37#57511yescharacteristic
326C22×C37#57611yescharacteristic
327C22×C37#57711yescharacteristic
328C4×C37—22no—
329C4×C37—41no—
330C4×C37—41no—
331C4×C37—41no—
332C4×C37—42no—
333C4×C37—41no—
334C4×C37—81no—
335C4×C37—81no—
336C4×C37—81no—
337C4×C37—81no—
338C4×C37—81no—
339C4×C37#52911yescharacteristic
340C4×C37#53811yescharacteristic
341C4×C37#55111yescharacteristic
342C4×C37#55911yescharacteristic
343#2491C2×C3711yescharacteristic, complemented
344#2420C2×C3711yescharacteristic, complemented
345#2077C2×C3711yescharacteristic, complemented
346#2073C2×C3711yescharacteristic, complemented
347#2023C2×C3711yescharacteristic, complemented
348#1999C2×C3711yescharacteristic
349#1993C2×C3711yescharacteristic, complemented
350#1972C2×C3711yescharacteristic, complemented
351#1934C2×C3711yescharacteristic, complemented
352#1920C2×C3711yescharacteristic, complemented
353#1895C2×C3711yescharacteristic, complemented
354#1895C2×C3711yescharacteristic, complemented
355#1879C2×C3711yescharacteristic, complemented
356C4×#102C2×C3711yescharacteristic, complemented
357#1753C2×C3711yescharacteristic, complemented
358C2×C37—81no—
359C2×C37—82no—
360C2×C37—161no—
361C2×C37#255711yescharacteristic
362C2×C37#317111yescharacteristic
363C2×C37#317911yescharacteristic
364C2×C37#330611yescharacteristic
365C2×C37#331911yescharacteristic
366C2×C37#332511yescharacteristic
367C2×C37#332611yescharacteristic
368C22×D8C22×C3711yescharacteristic
369C22×M16C22×C3711yescharacteristic
370C2×C4⋊Q8C22×C3711yescharacteristic
371C2×#124—21no—
372C2×#121C22×C3711yescharacteristic
373C2×#121C22×C3711yescharacteristic
374C2×C4×D4C22×C3711yescharacteristic
375C2×#106C22×C3711yescharacteristic
376C2×#102C22×C3711yescharacteristic
377C2×#102C22×C3711yescharacteristic
378C2×#102C22×C3711yescharacteristic
379C2×#102C22×C3711yescharacteristic
380C2×#102C22×C3711yescharacteristic
381C2×#102C22×C3711yescharacteristic
382C2×C22⋊C8C22×C3711yescharacteristic
383C2×#97C22×C3711yescharacteristic
384C2×C4×C8C22×C3711yescharacteristic
385#397—21no—
386#394—21no—
387#394—21no—
388#393—21no—
389#390C22×C3711yescharacteristic
390#390C22×C3711yescharacteristic
391#390C22×C3711yescharacteristic
392#389C22×C3711yescharacteristic
393#388—21no—
394#386—21no—
395#382C22×C3711yescharacteristic
396#381—21no—
397#380C22×C3711yescharacteristic
398#380C22×C3711yescharacteristic
399C4×C4⋊C4C22×C3711yescharacteristic
400C4×C22⋊C4C22×C3711yescharacteristic
401#340C22×C3711yescharacteristic
402#340C22×C3711yescharacteristic
403#340C22×C3711yescharacteristic
404#340C22×C3711yescharacteristic
405#340C22×C3711yescharacteristic
406#340C22×C3711yescharacteristic
407#340C22×C3711yescharacteristic
408#340C22×C3711yescharacteristic
409#336C22×C3711yescharacteristic
410#336C22×C3711yescharacteristic
411C37#2899211yescharacteristic, direct product factor, Sylow
412C22×Q8—21no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C23×C3711yescharacteristic
416C22×D4C23×C3711yescharacteristic
417C23×C4—21no—
418C23×C4C23×C3711yescharacteristic
419C2×D8—22no—
420C2×D8—22no—
421C2×D8—41no—
422C2×M16—22no—
423C2×M16—41no—
424C2×M16—41no—
425C22×C8C23×C3711yescharacteristic
426C22×C8C23×C3711yescharacteristic
427C22×C8C23×C3711yescharacteristic
428C22×C8C23×C3711yescharacteristic
429C4⋊Q8—22no—
430C4⋊Q8—41no—
431#124—44no—
432#121—22no—
433#121—22no—
434#121—41no—
435#121—41no—
436C4×D4—22no—
437C4×D4—41no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4C23×C3711yescharacteristic
441C2×C4⋊C4C23×C3711yescharacteristic
442C2×C4⋊C4C23×C3711yescharacteristic
443C2×C4⋊C4C23×C3711yescharacteristic
444C2×C4⋊C4C23×C3711yescharacteristic
445C2×C4⋊C4C23×C3711yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C3711yescharacteristic
458C2×C22⋊C4D4×C3711yescharacteristic
459C2×C42—21no—
460C2×C42C23×C3711yescharacteristic
461C2×C42C23×C3711yescharacteristic
462#106—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102—41no—
467#102—41no—
468#102—41no—
469C22⋊C8—22no—
470#97—41no—
471C4×C8—41no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95D4×C3711yescharacteristic
479#95D4×C3711yescharacteristic
480C24—21no—
481C24—21no—
482C24C2×D4×C3711yescharacteristic
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—81no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4#41×C3712yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4C2×D4×C3711yescharacteristic
520C22×C4C2×D4×C3711yescharacteristic
521C22×C4C2×D4×C3711yescharacteristic
522C22×C4C2×D4×C3711yescharacteristic
523C22×C4C2×D4×C3711yescharacteristic
524C22×C4C24×C3711yescharacteristic
525D8—44no—
526M16—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#41×C3712yes—
538C2×C8#41×C3712yes—
539C4⋊C4—21no—
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—81no—
552C4⋊C4#41×C3712yes—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C23—21no—
572C23—22no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×D4×C3711yescharacteristic
593Q8—84no—
594D4—22no—
595D4—22no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—84no—
603D4—84no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
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—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4AGL(1,ℤ/8)×C3712yes—
642C2×C4C2×#41×C3711yescharacteristic
643C2×C4C2×#41×C3711yescharacteristic
644C2×C4C2×#41×C3711yescharacteristic
645C2×C4C2×#41×C3711yescharacteristic
646C2×C4H(5,𝔽2)×C3711yescharacteristic
647C2×C4H(5,𝔽2)×C3711yescharacteristic
648C8—22no—
649C8—22no—
650C8—41no—
651C8—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—41no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C37×#53211yescharacteristic
674C22C37×#54611yescharacteristic
675C22C37×#54611yescharacteristic
676C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
677C22C37×#57511yescharacteristic
678C22C37×#57611yescharacteristic
679C22C37×#57711yescharacteristic
680C4—22no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4C37×#52911yescharacteristic
692C4C37×#53811yescharacteristic
693C4C37×#55111yescharacteristic
694C4C37×#55911yescharacteristic
695C2—81no—
696C2—82no—
697C2—161no—
698C2C37×#255711yescharacteristic
699C2C37×#317111yescharacteristic
700C2C37×#317911yescharacteristic
701C2C37×#330611yescharacteristic
702C2C37×#331911yescharacteristic
703C2C37×#332511yescharacteristic
704C2C37×#332611yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#1999C2
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. C37×#2491C2semidirect
2. C37×#2420C2semidirect
3. C37×#2077C2semidirect
4. C37×#2073C2semidirect
5. C37×#2023C2semidirect
7. C37×#1993C2semidirect
8. C37×#1972C2semidirect
9. C37×#1934C2semidirect
10. C37×#1920C2semidirect
11. C37×#1895C2semidirect
12. C37×#1895C2semidirect
13. C37×#1879C2semidirect
14. C4×#102×C37C2semidirect
15. C37×#1753C2semidirect
299. #28992C37direct (N × H)
343. #2491C2×C37semidirect
344. #2420C2×C37semidirect
345. #2077C2×C37semidirect
346. #2073C2×C37semidirect
347. #2023C2×C37semidirect
349. #1993C2×C37semidirect
350. #1972C2×C37semidirect
351. #1934C2×C37semidirect
352. #1920C2×C37semidirect
353. #1895C2×C37semidirect
354. #1895C2×C37semidirect
355. #1879C2×C37semidirect
356. C4×#102C2×C37semidirect
357. #1753C2×C37semidirect
411. C37#28992direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#24912
C37×#24202
C37×#20772
C37×#20732
C37×#20232
C37×#19992
C37×#19932
C37×#19722
C37×#19342
C37×#19202
C37×#18952
C37×#18792
C4×#102×C372
C37×#17532
#2899237