Finite Group Databasebeta

← C37×#26245 #22647498

Subgroups — C37×#26245 #22647498

Order 9472.

898 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#485C211yesmaximal, characteristic, complemented
2C2×C37×#482C211yesmaximal, characteristic, complemented
3C37×#2540C211yesmaximal, characteristic
4C37×#2354C211yesmaximal, characteristic, complemented
5C37×#2035C211yesmaximal, characteristic, complemented
6C37×#2035C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#1983C211yesmaximal, characteristic, complemented
10C37×#1959C211yesmaximal, characteristic, complemented
11C37×#1955C211yesmaximal, characteristic, complemented
12C37×#1948C211yesmaximal, characteristic, complemented
13C37×#1875C211yesmaximal, characteristic, complemented
14C37×#1873C211yesmaximal, characteristic, complemented
15C37×#1776C211yesmaximal, characteristic, complemented
16C2×#124×C37C2211yescharacteristic
17C2×C22⋊Q8×C37C2211yescharacteristic
18C2×C22⋊Q8×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×#121×C37C2211yescharacteristic
21C2×C4×D4×C37C2211yescharacteristic
22C2×#117×C37C2211yescharacteristic
23C2×#117×C37C2211yescharacteristic
24C37×#485—24no—
25C37×#482—24no—
26C2×#107×C37C2211yescharacteristic
27C2×#106×C37C2211yescharacteristic
28C2×#106×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C2×C22⋊C8×C37C2211yescharacteristic
41C2×C22⋊C8×C37C2211yescharacteristic
42C2×C22⋊C8×C37C2211yescharacteristic
43C2×#97×C37C2211yescharacteristic
44C37×#399—21no—
45C37×#392—21no—
46C37×#390—21no—
47C37×#390—21no—
48C37×#390—21no—
49C37×#388—21no—
50C37×#388—21no—
51C37×#384C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C37×#380C2211yescharacteristic
54C4×C4⋊C4×C37—21no—
55C4×C4⋊C4×C37C2211yescharacteristic
56C4×C4⋊C4×C37C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37D411yescharacteristic
65C22×D4×C37C2311yescharacteristic
66C23×C4×C37C2311yescharacteristic
67C23×C4×C37C2311yescharacteristic
68C22×C8×C37C2311yescharacteristic
69C22×C8×C37C2311yescharacteristic
70C22×C8×C37C2311yescharacteristic
71C22×C8×C37C2311yescharacteristic
72#124×C37—22no—
73#124×C37—22no—
74C22⋊Q8×C37—22no—
75C22⋊Q8×C37—22no—
76C22⋊Q8×C37—41no—
77C22⋊Q8×C37—41no—
78#121×C37—22no—
79#121×C37—22no—
80#121×C37—41no—
81#121×C37—41no—
82C4×D4×C37—22no—
83C4×D4×C37—22no—
84#117×C37—22no—
85#117×C37—22no—
86#117×C37—41no—
87#117×C37—41no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37D411yescharacteristic
93C2×C4⋊C4×C37C2311yescharacteristic
94C2×C4⋊C4×C37C2311yescharacteristic
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
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×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×C37—21no—
113C2×C42×C37—21no—
114C2×C42×C37—21no—
115C2×C42×C37C2311yescharacteristic
116#107×C37D414yescomplemented
117#106×C37—22no—
118#106×C37—22no—
119#106×C37—22no—
120C4⋊C8×C37—22no—
121#103×C37—22no—
122#103×C37—22no—
123#103×C37—41no—
124#103×C37—41no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—41no—
128#102×C37—41no—
129C22⋊C8×C37—22no—
130C22⋊C8×C37—22no—
131C22⋊C8×C37—41no—
132C22⋊C8×C37—41no—
133#97×C37—22no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138C24×C37—21no—
139C24×C37C2×D411yescharacteristic
140C24×C37C2×D411yescharacteristic
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×D4×C37—22no—
148C2×D4×C37—21no—
149C2×D4×C37—21no—
150C2×D4×C37—21no—
151C2×D4×C37—21no—
152C2×D4×C37—21no—
153C2×D4×C37—21no—
154C2×D4×C37—41no—
155C2×D4×C37—41no—
156C2×D4×C37—42no—
157C2×D4×C37—42no—
158C2×D4×C37—42no—
159C2×D4×C37—42no—
160C2×D4×C37—81no—
161C2×D4×C37—81no—
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—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183C22×C4×C37C2×D411yescharacteristic
184C22×C4×C37C2×D411yescharacteristic
185C22×C4×C37C2411yescharacteristic
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×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37C2×D412yes—
198C4⋊C4×C37—22no—
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—21no—
208C4⋊C4×C37—42no—
209C4⋊C4×C37—42no—
210C4⋊C4×C37—42no—
211C4⋊C4×C37—81no—
212C4⋊C4×C37C2×D412yes—
213C4⋊C4×C37C2×D412yes—
214C4⋊C4×C37#4112yes—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—42no—
218C22⋊C4×C37—42no—
219C22⋊C4×C37—42no—
220C22⋊C4×C37—42no—
221C22⋊C4×C37—42no—
222C22⋊C4×C37—42no—
223C22⋊C4×C37—42no—
224C22⋊C4×C37—42no—
225C22⋊C4×C37—81no—
226C22⋊C4×C37—81no—
227C42×C37—42no—
228C42×C37—42no—
229C42×C37—42no—
230C42×C37—81no—
231C42×C37#4112yes—
232C42×C37#4112yes—
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—21no—
241C23×C37—21no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—21no—
247C23×C37—41no—
248C23×C37—41no—
249C23×C37—41no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37C22×D411yescharacteristic
255Q8×C37—41no—
256Q8×C37—41no—
257Q8×C37—41no—
258Q8×C37—41no—
259D4×C37—44no—
260D4×C37—41no—
261D4×C37—41no—
262D4×C37—41no—
263D4×C37—41no—
264D4×C37—84no—
265D4×C37—84no—
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—22no—
273C2×C4×C37—21no—
274C2×C4×C37—21no—
275C2×C4×C37—22no—
276C2×C4×C37—22no—
277C2×C4×C37—21no—
278C2×C4×C37—21no—
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—41no—
296C2×C4×C37—41no—
297C2×C4×C37—41no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37—41no—
301C2×C4×C37—41no—
302C2×C4×C37—41no—
303C2×C4×C37—41no—
304C2×C4×C37—41no—
305C2×C4×C37#12312yes—
306C2×C4×C37#12312yes—
307C2×C4×C37C22×D411yescharacteristic
308C2×C4×C37C2×#4111yescharacteristic
309C2×C4×C37C2×#4111yescharacteristic
310C2×C4×C37C2×#4111yescharacteristic
311C2×C4×C37H(5,𝔽2)11yescharacteristic
312C2×C4×C37H(5,𝔽2)11yescharacteristic
313C8×C37—22no—
314C8×C37—41no—
315C8×C37—41no—
316C8×C37—41no—
317#26245C3711yesmaximal, characteristic, direct product factor, Sylow
318C22×C37—41no—
319C22×C37—41no—
320C22×C37—41no—
321C22×C37—41no—
322C22×C37—41no—
323C22×C37—41no—
324C22×C37—41no—
325C22×C37—41no—
326C22×C37—41no—
327C22×C37—41no—
328C22×C37—41no—
329C22×C37—41no—
330C22×C37—41no—
331C22×C37—41no—
332C22×C37—81no—
333C22×C37—81no—
334C22×C37—81no—
335C22×C37—81no—
336C22×C37—81no—
337C22×C37—81no—
338C22×C37—81no—
339C22×C37C2×#12311yescharacteristic
340C22×C37D4211yescharacteristic
341C22×C37#54611yescharacteristic
342C22×C37#57511yescharacteristic
343C22×C37#57511yescharacteristic
344C22×C37#57711yescharacteristic
345C22×C37#57711yescharacteristic
346C4×C37—22no—
347C4×C37—22no—
348C4×C37—41no—
349C4×C37—41no—
350C4×C37—42no—
351C4×C37—42no—
352C4×C37—42no—
353C4×C37—81no—
354C4×C37—81no—
355C4×C37—81no—
356C4×C37—81no—
357C4×C37#53211yescharacteristic
358C4×C37#54011yescharacteristic
359C4×C37#55011yescharacteristic
360C4×C37#55911yescharacteristic
361C2×#485C2×C3711yescharacteristic, complemented
362C2×#482C2×C3711yescharacteristic, complemented
363#2540C2×C3711yescharacteristic
364#2354C2×C3711yescharacteristic, complemented
365#2035C2×C3711yescharacteristic, complemented
366#2035C2×C3711yescharacteristic, complemented
367#2034C2×C3711yescharacteristic, complemented
368#2034C2×C3711yescharacteristic, complemented
369#1983C2×C3711yescharacteristic, complemented
370#1959C2×C3711yescharacteristic, complemented
371#1955C2×C3711yescharacteristic, complemented
372#1948C2×C3711yescharacteristic, complemented
373#1875C2×C3711yescharacteristic, complemented
374#1873C2×C3711yescharacteristic, complemented
375#1776C2×C3711yescharacteristic, complemented
376C2×C37—81no—
377C2×C37—81no—
378C2×C37—161no—
379C2×C37#244511yescharacteristic
380C2×C37#309311yescharacteristic
381C2×C37#309911yescharacteristic
382C2×C37#326711yescharacteristic
383C2×C37#327111yescharacteristic
384C2×C37#331111yescharacteristic
385C2×C37#332111yescharacteristic
386C2×#124C22×C3711yescharacteristic
387C2×C22⋊Q8C22×C3711yescharacteristic
388C2×C22⋊Q8C22×C3711yescharacteristic
389C2×#121C22×C3711yescharacteristic
390C2×#121C22×C3711yescharacteristic
391C2×C4×D4C22×C3711yescharacteristic
392C2×#117C22×C3711yescharacteristic
393C2×#117C22×C3711yescharacteristic
394#485—24no—
395#482—24no—
396C2×#107C22×C3711yescharacteristic
397C2×#106C22×C3711yescharacteristic
398C2×#106C22×C3711yescharacteristic
399C2×#106C22×C3711yescharacteristic
400C2×C4⋊C8C22×C3711yescharacteristic
401C2×#103C22×C3711yescharacteristic
402C2×#103C22×C3711yescharacteristic
403C2×#103C22×C3711yescharacteristic
404C2×#103C22×C3711yescharacteristic
405C2×#102C22×C3711yescharacteristic
406C2×#102C22×C3711yescharacteristic
407C2×#102C22×C3711yescharacteristic
408C2×#102C22×C3711yescharacteristic
409C2×C22⋊C8C22×C3711yescharacteristic
410C2×C22⋊C8C22×C3711yescharacteristic
411C2×C22⋊C8C22×C3711yescharacteristic
412C2×C22⋊C8C22×C3711yescharacteristic
413C2×#97C22×C3711yescharacteristic
414#399—21no—
415#392—21no—
416#390—21no—
417#390—21no—
418#390—21no—
419#388—21no—
420#388—21no—
421#384C22×C3711yescharacteristic
422#380C22×C3711yescharacteristic
423#380C22×C3711yescharacteristic
424C4×C4⋊C4—21no—
425C4×C4⋊C4C22×C3711yescharacteristic
426C4×C4⋊C4C22×C3711yescharacteristic
427#340C22×C3711yescharacteristic
428#340C22×C3711yescharacteristic
429#340C22×C3711yescharacteristic
430#340C22×C3711yescharacteristic
431C37#2624511yescharacteristic, direct product factor, Sylow
432C22×Q8C23×C3711yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4D4×C3711yescharacteristic
436C22×D4C23×C3711yescharacteristic
437C23×C4C23×C3711yescharacteristic
438C23×C4C23×C3711yescharacteristic
439C22×C8C23×C3711yescharacteristic
440C22×C8C23×C3711yescharacteristic
441C22×C8C23×C3711yescharacteristic
442C22×C8C23×C3711yescharacteristic
443#124—22no—
444#124—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—41no—
448C22⋊Q8—41no—
449#121—22no—
450#121—22no—
451#121—41no—
452#121—41no—
453C4×D4—22no—
454C4×D4—22no—
455#117—22no—
456#117—22no—
457#117—41no—
458#117—41no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C3711yescharacteristic
464C2×C4⋊C4C23×C3711yescharacteristic
465C2×C4⋊C4C23×C3711yescharacteristic
466C2×C4⋊C4C23×C3711yescharacteristic
467C2×C4⋊C4C23×C3711yescharacteristic
468C2×C4⋊C4C23×C3711yescharacteristic
469C2×C4⋊C4C23×C3711yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C3711yescharacteristic
481C2×C22⋊C4D4×C3711yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42C23×C3711yescharacteristic
487#107D4×C3714yescomplemented
488#106—22no—
489#106—22no—
490#106—22no—
491C4⋊C8—22no—
492#103—22no—
493#103—22no—
494#103—41no—
495#103—41no—
496#102—22no—
497#102—22no—
498#102—41no—
499#102—41no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—41no—
503C22⋊C8—41no—
504#97—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C24—21no—
510C24C2×D4×C3711yescharacteristic
511C24C2×D4×C3711yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4C2×D4×C3711yescharacteristic
553C22×C4C2×D4×C3711yescharacteristic
554C22×C4C2×D4×C3711yescharacteristic
555C22×C4C2×D4×C3711yescharacteristic
556C22×C4C24×C3711yescharacteristic
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8C2×D4×C3712yes—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4C2×D4×C3712yes—
584C4⋊C4C2×D4×C3712yes—
585C4⋊C4#41×C3712yes—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C42—42no—
599C42—42no—
600C42—42no—
601C42—81no—
602C42#41×C3712yes—
603C42#41×C3712yes—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C22×D4×C3711yescharacteristic
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630D4—44no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—84no—
636D4—84no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4#123×C3712yes—
677C2×C4#123×C3712yes—
678C2×C4C22×D4×C3711yescharacteristic
679C2×C4C2×#41×C3711yescharacteristic
680C2×C4C2×#41×C3711yescharacteristic
681C2×C4C2×#41×C3711yescharacteristic
682C2×C4H(5,𝔽2)×C3711yescharacteristic
683C2×C4H(5,𝔽2)×C3711yescharacteristic
684C8—22no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×#123×C3711yescharacteristic
710C22D42×C3711yescharacteristic
711C22C37×#54611yescharacteristic
712C22C37×#57511yescharacteristic
713C22C37×#57511yescharacteristic
714C22C37×#57711yescharacteristic
715C22C37×#57711yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4C37×#53211yescharacteristic
728C4C37×#54011yescharacteristic
729C4C37×#55011yescharacteristic
730C4C37×#55911yescharacteristic
731C2—81no—
732C2—81no—
733C2—161no—
734C2C37×#244511yescharacteristic
735C2C37×#309311yescharacteristic
736C2C37×#309911yescharacteristic
737C2C37×#326711yescharacteristic
738C2C37×#327111yescharacteristic
739C2C37×#331111yescharacteristic
740C2C37×#332111yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2540C2
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×#485C2semidirect
2. C2×C37×#482C2semidirect
4. C37×#2354C2semidirect
5. C37×#2035C2semidirect
6. C37×#2035C2semidirect
7. C37×#2034C2semidirect
8. C37×#2034C2semidirect
9. C37×#1983C2semidirect
10. C37×#1959C2semidirect
11. C37×#1955C2semidirect
12. C37×#1948C2semidirect
13. C37×#1875C2semidirect
14. C37×#1873C2semidirect
15. C37×#1776C2semidirect
116. #107×C37D4semidirect
317. #26245C37direct (N × H)
361. C2×#485C2×C37semidirect
362. C2×#482C2×C37semidirect
364. #2354C2×C37semidirect
365. #2035C2×C37semidirect
366. #2035C2×C37semidirect
367. #2034C2×C37semidirect
368. #2034C2×C37semidirect
369. #1983C2×C37semidirect
370. #1959C2×C37semidirect
371. #1955C2×C37semidirect
372. #1948C2×C37semidirect
373. #1875C2×C37semidirect
374. #1873C2×C37semidirect
375. #1776C2×C37semidirect
431. C37#26245direct (N × H)
487. #107D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4852
C2×C37×#4822
C37×#25402
C37×#23542
C37×#20352
C37×#20342
C37×#19832
C37×#19592
C37×#19552
C37×#19482
C37×#18752
C37×#18732
C37×#17762
#2624537