Finite Group Databasebeta

← C37×#24890 #22646143

Subgroups — C37×#24890 #22646143

Order 9472.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#482C211yesmaximal, characteristic, complemented
2C2×C37×#418C211yesmaximal, characteristic, complemented
3C37×#2408C211yesmaximal, characteristic
4C37×#2354C211yesmaximal, characteristic, complemented
5C37×#2093C211yesmaximal, characteristic, complemented
6C37×#2071C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#1926C211yesmaximal, characteristic, complemented
10C37×#1926C211yesmaximal, characteristic, complemented
11C37×#1875C211yesmaximal, characteristic, complemented
12C37×#1870C211yesmaximal, characteristic, complemented
13C37×#1854C211yesmaximal, characteristic, complemented
14C37×#1809C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C2×#121×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×#120×C37—21no—
21C2×C4×D4×C37C2211yescharacteristic
22C2×#117×C37C2211yescharacteristic
23C2×#117×C37C2211yescharacteristic, complemented
24C37×#482—24no—
25C2×#107×C37C2211yescharacteristic, complemented
26C2×#107×C37C2211yescharacteristic, complemented
27C2×#106×C37C2211yescharacteristic, complemented
28C2×#106×C37C2211yescharacteristic, complemented
29C37×#418—24no—
30C2×#102×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic, complemented
40C2×C22⋊C8×C37C2211yescharacteristic, complemented
41C37×#394—21no—
42C37×#392—21no—
43C37×#390—21no—
44C37×#390C2211yescharacteristic
45C37×#390C2211yescharacteristic
46C37×#388—21no—
47C37×#388—21no—
48C37×#384C2211yescharacteristic, complemented
49C37×#380C2211yescharacteristic
50C37×#380C2211yescharacteristic
51C37×#380C2211yescharacteristic, complemented
52C37×#379—21no—
53C4×C4⋊C4×C37—21no—
54C4×C4⋊C4×C37C2211yescharacteristic, complemented
55C37×#340C2211yescharacteristic, complemented
56C37×#340C2211yescharacteristic, complemented
57C37×#340C2211yescharacteristic, complemented
58C37×#340C2211yescharacteristic, complemented
59C37×#336C2211yescharacteristic, complemented
60C37×#336C2211yescharacteristic, complemented
61C25×C37—21no—
62C22×D4×C37—22no—
63C22×D4×C37—22no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37—22no—
68C22×D4×C37—22no—
69C22×D4×C37—41no—
70C22×D4×C37—41no—
71C22×D4×C37D411yescharacteristic
72C22×D4×C37C2311yescharacteristic
73C22×D4×C37C2311yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C23×C4×C37C2311yescharacteristic
76C2×M16×C37—22no—
77C2×M16×C37—22no—
78C2×M16×C37—41no—
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83#121×C37—22no—
84#121×C37—22no—
85#121×C37—41no—
86#121×C37—41no—
87#120×C37—44no—
88C4×D4×C37—22no—
89C4×D4×C37—22no—
90#117×C37—22no—
91#117×C37—22no—
92#117×C37—41no—
93#117×C37—41no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37D411yescharacteristic
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×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37D411yescharacteristic
115C2×C22⋊C4×C37D411yescharacteristic
116C2×C42×C37—21no—
117C2×C42×C37—21no—
118C2×C42×C37—21no—
119C2×C42×C37C2311yescharacteristic
120#107×C37—22no—
121#107×C37—41no—
122#106×C37—22no—
123#106×C37—41no—
124#102×C37—22no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—22no—
129#102×C37—41no—
130#102×C37—41no—
131#102×C37D414yescomplemented
132C22⋊C8×C37—22no—
133C22⋊C8×C37—22no—
134C22⋊C8×C37—41no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37—21no—
139C24×C37—21no—
140C24×C37—21no—
141C24×C37—42no—
142C24×C37—42no—
143C24×C37—42no—
144C24×C37—42no—
145C24×C37—42no—
146C24×C37—81no—
147C24×C37—81no—
148C24×C37C2×D411yescharacteristic
149C24×C37C2×D411yescharacteristic
150C2×D4×C37—28no—
151C2×D4×C37—22no—
152C2×D4×C37—22no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—44no—
164C2×D4×C37—44no—
165C2×D4×C37—41no—
166C2×D4×C37—42no—
167C2×D4×C37—42no—
168C2×D4×C37—44no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
172C2×D4×C37—42no—
173C2×D4×C37—42no—
174C2×D4×C37—81no—
175C2×D4×C37—81no—
176C2×D4×C37C2×D412yes—
177C2×D4×C37#4112yes—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
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×C37C2×D411yescharacteristic
195C22×C4×C37C2×D411yescharacteristic
196C22×C4×C37C2×D411yescharacteristic
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37#4112yes—
199C22×C4×C37#4112yes—
200C22×C4×C37C2411yescharacteristic
201M16×C37—44no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—21no—
209C2×C8×C37—21no—
210C2×C8×C37—21no—
211C2×C8×C37—21no—
212C2×C8×C37—21no—
213C2×C8×C37C2×D412yes—
214C4⋊C4×C37—22no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—21no—
225C4⋊C4×C37—21no—
226C4⋊C4×C37—42no—
227C4⋊C4×C37—81no—
228C4⋊C4×C37C2×D412yes—
229C22⋊C4×C37—22no—
230C22⋊C4×C37—22no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—42no—
235C22⋊C4×C37—42no—
236C22⋊C4×C37—42no—
237C22⋊C4×C37—42no—
238C22⋊C4×C37—81no—
239C22⋊C4×C37—81no—
240C22⋊C4×C37—81no—
241C22⋊C4×C37—81no—
242C42×C37—21no—
243C42×C37—21no—
244C42×C37—42no—
245C42×C37—42no—
246C42×C37—42no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—21no—
253C23×C37—21no—
254C23×C37—21no—
255C23×C37—22no—
256C23×C37—22no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—48no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—84no—
276C23×C37—84no—
277C23×C37—84no—
278C23×C37—84no—
279C23×C37—84no—
280C23×C37—84no—
281C23×C37#12312yes—
282C23×C37C22×D411yescharacteristic
283D4×C37—22no—
284D4×C37—22no—
285D4×C37—22no—
286D4×C37—22no—
287D4×C37—44no—
288D4×C37—48no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—84no—
294D4×C37—84no—
295C2×C4×C37—21no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—22no—
300C2×C4×C37—22no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—22no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
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—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37#12312yes—
332C2×C4×C37AGL(1,ℤ/8)12yes—
333C2×C4×C37C22×D411yescharacteristic
334C2×C4×C37C2×#4111yescharacteristic
335C2×C4×C37C2×#4111yescharacteristic
336C2×C4×C37C2×#4111yescharacteristic
337C2×C4×C37H(5,𝔽2)11yescharacteristic
338C2×C4×C37H(5,𝔽2)11yescharacteristic
339C8×C37—22no—
340C8×C37—41no—
341C8×C37—41no—
342C8×C37—41no—
343#24890C3711yesmaximal, characteristic, direct product factor, Sylow
344C22×C37—22no—
345C22×C37—22no—
346C22×C37—22no—
347C22×C37—41no—
348C22×C37—41no—
349C22×C37—41no—
350C22×C37—41no—
351C22×C37—41no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—42no—
355C22×C37—42no—
356C22×C37—41no—
357C22×C37—42no—
358C22×C37—41no—
359C22×C37—42no—
360C22×C37—41no—
361C22×C37—42no—
362C22×C37—41no—
363C22×C37—42no—
364C22×C37—816no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37—81no—
369C22×C37—81no—
370C22×C37—81no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37C2×#12311yescharacteristic
374C22×C37D4211yescharacteristic
375C22×C37#54611yescharacteristic
376C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C37#57511yescharacteristic
378C22×C37#57611yescharacteristic
379C22×C37#57711yescharacteristic
380C4×C37—22no—
381C4×C37—22no—
382C4×C37—41no—
383C4×C37—41no—
384C4×C37—42no—
385C4×C37—81no—
386C4×C37—81no—
387C4×C37—81no—
388C4×C37—81no—
389C4×C37—81no—
390C4×C37#52511yescharacteristic
391C4×C37#53811yescharacteristic
392C4×C37#54611yescharacteristic
393C4×C37#55111yescharacteristic
394C2×#482C2×C3711yescharacteristic, complemented
395C2×#418C2×C3711yescharacteristic, complemented
396#2408C2×C3711yescharacteristic
397#2354C2×C3711yescharacteristic, complemented
398#2093C2×C3711yescharacteristic, complemented
399#2071C2×C3711yescharacteristic, complemented
400#2034C2×C3711yescharacteristic, complemented
401#2033C2×C3711yescharacteristic, complemented
402#1926C2×C3711yescharacteristic, complemented
403#1926C2×C3711yescharacteristic, complemented
404#1875C2×C3711yescharacteristic, complemented
405#1870C2×C3711yescharacteristic, complemented
406#1854C2×C3711yescharacteristic, complemented
407#1809C2×C3711yescharacteristic, complemented
408#1786C2×C3711yescharacteristic, complemented
409C2×C37—42no—
410C2×C37—81no—
411C2×C37—82no—
412C2×C37—82no—
413C2×C37#241811yescharacteristic
414C2×C37#309411yescharacteristic
415C2×C37#309611yescharacteristic
416C2×C37#326711yescharacteristic
417C2×C37#327411yescharacteristic
418C2×C37#331911yescharacteristic
419C2×C37#332411yescharacteristic
420C23×D4C22×C3711yescharacteristic
421C22×M16C22×C3711yescharacteristic
422C2×#121C22×C3711yescharacteristic
423C2×#121C22×C3711yescharacteristic
424C2×#120—21no—
425C2×C4×D4C22×C3711yescharacteristic
426C2×#117C22×C3711yescharacteristic
427C2×#117C22×C3711yescharacteristic, complemented
428#482—24no—
429C2×#107C22×C3711yescharacteristic, complemented
430C2×#107C22×C3711yescharacteristic, complemented
431C2×#106C22×C3711yescharacteristic, complemented
432C2×#106C22×C3711yescharacteristic, complemented
433#418—24no—
434C2×#102C22×C3711yescharacteristic
435C2×#102C22×C3711yescharacteristic
436C2×#102C22×C3711yescharacteristic
437C2×#102C22×C3711yescharacteristic
438C2×#102C22×C3711yescharacteristic
439C2×#102C22×C3711yescharacteristic
440C2×#102C22×C3711yescharacteristic
441C2×#102C22×C3711yescharacteristic
442C2×C22⋊C8C22×C3711yescharacteristic
443C2×C22⋊C8C22×C3711yescharacteristic, complemented
444C2×C22⋊C8C22×C3711yescharacteristic, complemented
445#394—21no—
446#392—21no—
447#390—21no—
448#390C22×C3711yescharacteristic
449#390C22×C3711yescharacteristic
450#388—21no—
451#388—21no—
452#384C22×C3711yescharacteristic, complemented
453#380C22×C3711yescharacteristic
454#380C22×C3711yescharacteristic
455#380C22×C3711yescharacteristic, complemented
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C22×C3711yescharacteristic, complemented
459#340C22×C3711yescharacteristic, complemented
460#340C22×C3711yescharacteristic, complemented
461#340C22×C3711yescharacteristic, complemented
462#340C22×C3711yescharacteristic, complemented
463#336C22×C3711yescharacteristic, complemented
464#336C22×C3711yescharacteristic, complemented
465C37#2489011yescharacteristic, direct product factor, Sylow
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C3711yescharacteristic
477C22×D4C23×C3711yescharacteristic
478C22×D4C23×C3711yescharacteristic
479C23×C4C23×C3711yescharacteristic
480C23×C4C23×C3711yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C3711yescharacteristic
485C22×C8C23×C3711yescharacteristic
486C22×C8C23×C3711yescharacteristic
487C22×C8C23×C3711yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C3711yescharacteristic
502C2×C4⋊C4C23×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C4⋊C4C23×C3711yescharacteristic
505C2×C4⋊C4C23×C3711yescharacteristic
506C2×C4⋊C4C23×C3711yescharacteristic
507C2×C4⋊C4C23×C3711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C3711yescharacteristic
520C2×C22⋊C4D4×C3711yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C3711yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C3714yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C3711yescharacteristic
554C24C2×D4×C3711yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C3712yes—
582C2×D4#41×C3712yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4C2×D4×C3711yescharacteristic
600C22×C4C2×D4×C3711yescharacteristic
601C22×C4C2×D4×C3711yescharacteristic
602C22×C4C2×D4×C3711yescharacteristic
603C22×C4#41×C3712yes—
604C22×C4#41×C3712yes—
605C22×C4C24×C3711yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C3712yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C3712yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C3712yes—
687C23C22×D4×C3711yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4#123×C3712yes—
737C2×C4AGL(1,ℤ/8)×C3712yes—
738C2×C4C22×D4×C3711yescharacteristic
739C2×C4C2×#41×C3711yescharacteristic
740C2×C4C2×#41×C3711yescharacteristic
741C2×C4C2×#41×C3711yescharacteristic
742C2×C4H(5,𝔽2)×C3711yescharacteristic
743C2×C4H(5,𝔽2)×C3711yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C3711yescharacteristic
778C22D42×C3711yescharacteristic
779C22C37×#54611yescharacteristic
780C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
781C22C37×#57511yescharacteristic
782C22C37×#57611yescharacteristic
783C22C37×#57711yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C37×#52511yescharacteristic
795C4C37×#53811yescharacteristic
796C4C37×#54611yescharacteristic
797C4C37×#55111yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2C37×#241811yescharacteristic
803C2C37×#309411yescharacteristic
804C2C37×#309611yescharacteristic
805C2C37×#326711yescharacteristic
806C2C37×#327411yescharacteristic
807C2C37×#331911yescharacteristic
808C2C37×#332411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2408C2
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×#482C2semidirect
2. C2×C37×#418C2semidirect
4. C37×#2354C2semidirect
5. C37×#2093C2semidirect
6. C37×#2071C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#1926C2semidirect
10. C37×#1926C2semidirect
11. C37×#1875C2semidirect
12. C37×#1870C2semidirect
13. C37×#1854C2semidirect
14. C37×#1809C2semidirect
15. C37×#1786C2semidirect
23. C2×#117×C37C22semidirect
25. C2×#107×C37C22semidirect
26. C2×#107×C37C22semidirect
27. C2×#106×C37C22semidirect
28. C2×#106×C37C22semidirect
39. C2×C22⋊C8×C37C22semidirect
40. C2×C22⋊C8×C37C22semidirect
48. C37×#384C22semidirect
51. C37×#380C22semidirect
54. C4×C4⋊C4×C37C22semidirect
55. C37×#340C22semidirect
56. C37×#340C22semidirect
57. C37×#340C22semidirect
58. C37×#340C22semidirect
59. C37×#336C22semidirect
60. C37×#336C22semidirect
131. #102×C37D4semidirect
343. #24890C37direct (N × H)
394. C2×#482C2×C37semidirect
395. C2×#418C2×C37semidirect
397. #2354C2×C37semidirect
398. #2093C2×C37semidirect
399. #2071C2×C37semidirect
400. #2034C2×C37semidirect
401. #2033C2×C37semidirect
402. #1926C2×C37semidirect
403. #1926C2×C37semidirect
404. #1875C2×C37semidirect
405. #1870C2×C37semidirect
406. #1854C2×C37semidirect
407. #1809C2×C37semidirect
408. #1786C2×C37semidirect
427. C2×#117C22×C37semidirect
429. C2×#107C22×C37semidirect
430. C2×#107C22×C37semidirect
431. C2×#106C22×C37semidirect
432. C2×#106C22×C37semidirect
443. C2×C22⋊C8C22×C37semidirect
444. C2×C22⋊C8C22×C37semidirect
452. #384C22×C37semidirect
455. #380C22×C37semidirect
458. C4×C4⋊C4C22×C37semidirect
459. #340C22×C37semidirect
460. #340C22×C37semidirect
461. #340C22×C37semidirect
462. #340C22×C37semidirect
463. #336C22×C37semidirect
464. #336C22×C37semidirect
465. C37#24890direct (N × H)
536. #102D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4822
C2×C37×#4182
C37×#24082
C37×#23542
C37×#20932
C37×#20712
C37×#20342
C37×#20332
C37×#19262
C37×#18752
C37×#18702
C37×#18542
C37×#18092
C37×#17862
#2489037