Finite Group Databasebeta

← C37×#25138 #22646391

Subgroups — C37×#25138 #22646391

Order 9472.

1118 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#468C211yesmaximal, characteristic, complemented
2C2×C37×#448C211yesmaximal, characteristic, complemented
3C2×C37×#436C211yesmaximal, characteristic, complemented
4C2×C37×#419C211yesmaximal, characteristic, complemented
5C37×#2414C211yesmaximal, characteristic
6C37×#2409C211yesmaximal, characteristic, complemented
7C37×#2068C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2035C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1968C211yesmaximal, characteristic, complemented
12C37×#1933C211yesmaximal, characteristic, complemented
13C37×#1895C211yesmaximal, characteristic, complemented
14C37×#1894C211yesmaximal, characteristic, complemented
15C37×#1854C211yesmaximal, characteristic, complemented
16C23×Q8×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C2×#117×C37C2211yescharacteristic
27C37×#468—24no—
28C37×#448—24no—
29C37×#436—24no—
30C2×#107×C37C2211yescharacteristic
31C2×#106×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×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×C22⋊C8×C37C2211yescharacteristic
43C2×C22⋊C8×C37C2211yescharacteristic
44C2×C4×C8×C37C2211yescharacteristic
45C37×#395—21no—
46C37×#394—21no—
47C37×#393—21no—
48C37×#392—21no—
49C37×#391C2211yescharacteristic
50C37×#391C2211yescharacteristic
51C37×#390—21no—
52C37×#390C2211yescharacteristic
53C37×#389C2211yescharacteristic
54C37×#388—21no—
55C37×#386—21no—
56C37×#385—21no—
57C37×#380C2211yescharacteristic
58C37×#380C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#340C2211yescharacteristic
62C37×#340C2211yescharacteristic
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×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37D411yescharacteristic
75C22×D4×C37C2311yescharacteristic
76C23×C4×C37—21no—
77C23×C4×C37C2311yescharacteristic
78C23×C4×C37C2311yescharacteristic
79C2×SD16×C37—22no—
80C2×SD16×C37—22no—
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—41no—
84C2×SD16×C37—41no—
85C2×M16×C37—22no—
86C2×M16×C37—22no—
87C2×M16×C37—22no—
88C2×M16×C37—22no—
89C2×M16×C37—41no—
90C2×M16×C37—41no—
91C22×C8×C37C2311yescharacteristic
92C22×C8×C37C2311yescharacteristic
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—41no—
98C22⋊Q8×C37—41no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37—41no—
103C4×D4×C37—22no—
104C4×D4×C37—22no—
105#117×C37—22no—
106#117×C37—41no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37D411yescharacteristic
111C2×C4⋊C4×C37C2311yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37D411yescharacteristic
126C2×C22⋊C4×C37D411yescharacteristic
127C2×C42×C37—21no—
128C2×C42×C37C2311yescharacteristic
129#107×C37—22no—
130#106×C37—41no—
131C4⋊C8×C37—22no—
132#103×C37—22no—
133#103×C37—22no—
134#103×C37—22no—
135#103×C37—22no—
136#103×C37—22no—
137#103×C37D414yescomplemented
138#102×C37—22no—
139#102×C37—41no—
140C22⋊C8×C37—22no—
141C22⋊C8×C37D414yescomplemented
142C4×C8×C37—22no—
143#95×C37—21no—
144#95×C37—21no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37—21no—
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152C24×C37C2×D411yescharacteristic
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—42no—
165C2×Q8×C37—42no—
166C2×Q8×C37—44no—
167C2×Q8×C37—44no—
168C2×Q8×C37—44no—
169C2×Q8×C37—42no—
170C2×Q8×C37C2×D412yes—
171C2×Q8×C37#4112yes—
172C2×D4×C37—22no—
173C2×D4×C37—22no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—41no—
181C2×D4×C37—42no—
182C2×D4×C37—42no—
183C2×D4×C37—42no—
184C2×D4×C37—81no—
185C2×D4×C37—81no—
186C2×D4×C37—81no—
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—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—42no—
205C22×C4×C37—42no—
206C22×C4×C37—42no—
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D411yescharacteristic
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D412yes—
211C22×C4×C37C2×D411yescharacteristic
212C22×C4×C37#4112yes—
213C22×C4×C37C2411yescharacteristic
214SD16×C37—44no—
215SD16×C37—44no—
216M16×C37—44no—
217M16×C37—44no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37C2×D412yes—
228C2×C8×C37C2×D412yes—
229C2×C8×C37C2×D412yes—
230C4⋊C4×C37—22no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—42no—
241C4⋊C4×C37—42no—
242C4⋊C4×C37—81no—
243C4⋊C4×C37C2×D412yes—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—42no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37—81no—
254C22⋊C4×C37—81no—
255C42×C37—21no—
256C42×C37—21no—
257C42×C37—42no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37#12112yes—
279C23×C37C22×D411yescharacteristic
280Q8×C37—22no—
281Q8×C37—22no—
282Q8×C37—22no—
283Q8×C37—22no—
284Q8×C37—48no—
285Q8×C37—41no—
286Q8×C37—41no—
287Q8×C37—41no—
288Q8×C37—41no—
289D4×C37—44no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—84no—
295D4×C37—84no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
300C2×C4×C37—22no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—22no—
307C2×C4×C37—21no—
308C2×C4×C37—22no—
309C2×C4×C37—22no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
312C2×C4×C37—21no—
313C2×C4×C37—48no—
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—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37#12112yes—
337C2×C4×C37#13712yes—
338C2×C4×C37C22×D411yescharacteristic
339C2×C4×C37C22×D411yescharacteristic
340C2×C4×C37C2×#4111yescharacteristic
341C2×C4×C37C2×#4111yescharacteristic
342C2×C4×C37H(5,𝔽2)11yescharacteristic
343C2×C4×C37H(5,𝔽2)11yescharacteristic
344C8×C37—22no—
345C8×C37—22no—
346C8×C37—22no—
347C8×C37—41no—
348#25138C3711yesmaximal, characteristic, direct product factor, Sylow
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—22no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—41no—
362C22×C37—41no—
363C22×C37—81no—
364C22×C37—81no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37—81no—
369C22×C37—81no—
370C22×C37C2×#12111yescharacteristic
371C22×C37D4211yescharacteristic
372C22×C37#54611yescharacteristic
373C22×C37C2×#13711yescharacteristic
374C22×C37#57511yescharacteristic
375C22×C37#57711yescharacteristic
376C22×C37#57711yescharacteristic
377C4×C37—22no—
378C4×C37—22no—
379C4×C37—41no—
380C4×C37—42no—
381C4×C37—42no—
382C4×C37—42no—
383C4×C37—41no—
384C4×C37—81no—
385C4×C37—81no—
386C4×C37—81no—
387C4×C37—81no—
388C4×C37#52511yescharacteristic
389C4×C37#53811yescharacteristic
390C4×C37D4211yescharacteristic
391C4×C37#54611yescharacteristic
392C2×#468C2×C3711yescharacteristic, complemented
393C2×#448C2×C3711yescharacteristic, complemented
394C2×#436C2×C3711yescharacteristic, complemented
395C2×#419C2×C3711yescharacteristic, complemented
396#2414C2×C3711yescharacteristic
397#2409C2×C3711yescharacteristic, complemented
398#2068C2×C3711yescharacteristic, complemented
399#2055C2×C3711yescharacteristic, complemented
400#2035C2×C3711yescharacteristic, complemented
401#2000C2×C3711yescharacteristic, complemented
402#1968C2×C3711yescharacteristic, complemented
403#1933C2×C3711yescharacteristic, complemented
404#1895C2×C3711yescharacteristic, complemented
405#1894C2×C3711yescharacteristic, complemented
406#1854C2×C3711yescharacteristic, complemented
407C2×C37—42no—
408C2×C37—81no—
409C2×C37—161no—
410C2×C37#242411yescharacteristic
411C2×C37#305611yescharacteristic
412C2×C37#305711yescharacteristic
413C2×C37#327511yescharacteristic
414C2×C37#327811yescharacteristic
415C2×C37#332611yescharacteristic
416C2×C37#332911yescharacteristic
417C23×Q8C22×C3711yescharacteristic
418C22×SD16C22×C3711yescharacteristic
419C22×SD16C22×C3711yescharacteristic
420C22×M16C22×C3711yescharacteristic
421C22×M16C22×C3711yescharacteristic
422C2×C22⋊Q8C22×C3711yescharacteristic
423C2×C22⋊Q8C22×C3711yescharacteristic
424C2×#121C22×C3711yescharacteristic
425C2×#121C22×C3711yescharacteristic
426C2×C4×D4C22×C3711yescharacteristic
427C2×#117C22×C3711yescharacteristic
428#468—24no—
429#448—24no—
430#436—24no—
431C2×#107C22×C3711yescharacteristic
432C2×#106C22×C3711yescharacteristic
433C2×C4⋊C8C22×C3711yescharacteristic
434#419—24no—
435C2×#103C22×C3711yescharacteristic
436C2×#103C22×C3711yescharacteristic
437C2×#103C22×C3711yescharacteristic
438C2×#103C22×C3711yescharacteristic
439C2×#103C22×C3711yescharacteristic
440C2×#103C22×C3711yescharacteristic
441C2×#102C22×C3711yescharacteristic
442C2×#102C22×C3711yescharacteristic
443C2×C22⋊C8C22×C3711yescharacteristic
444C2×C22⋊C8C22×C3711yescharacteristic
445C2×C4×C8C22×C3711yescharacteristic
446#395—21no—
447#394—21no—
448#393—21no—
449#392—21no—
450#391C22×C3711yescharacteristic
451#391C22×C3711yescharacteristic
452#390—21no—
453#390C22×C3711yescharacteristic
454#389C22×C3711yescharacteristic
455#388—21no—
456#386—21no—
457#385—21no—
458#380C22×C3711yescharacteristic
459#380C22×C3711yescharacteristic
460#340C22×C3711yescharacteristic
461#340C22×C3711yescharacteristic
462#340C22×C3711yescharacteristic
463#340C22×C3711yescharacteristic
464C37#2513811yescharacteristic, direct product factor, Sylow
465C22×Q8—21no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—41no—
471C22×Q8—41no—
472C22×Q8C23×C3711yescharacteristic
473C22×Q8C23×C3711yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4D4×C3711yescharacteristic
477C22×D4C23×C3711yescharacteristic
478C23×C4—21no—
479C23×C4C23×C3711yescharacteristic
480C23×C4C23×C3711yescharacteristic
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—41no—
486C2×SD16—41no—
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C2×M16—41no—
493C22×C8C23×C3711yescharacteristic
494C22×C8C23×C3711yescharacteristic
495C22×C8C23×C3711yescharacteristic
496C22×C8C23×C3711yescharacteristic
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500C22⋊Q8—41no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505C4×D4—22no—
506C4×D4—22no—
507#117—22no—
508#117—41no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4D4×C3711yescharacteristic
513C2×C4⋊C4C23×C3711yescharacteristic
514C2×C4⋊C4C23×C3711yescharacteristic
515C2×C4⋊C4C23×C3711yescharacteristic
516C2×C4⋊C4C23×C3711yescharacteristic
517C2×C4⋊C4C23×C3711yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4D4×C3711yescharacteristic
528C2×C22⋊C4D4×C3711yescharacteristic
529C2×C42—21no—
530C2×C42C23×C3711yescharacteristic
531#107—22no—
532#106—41no—
533C4⋊C8—22no—
534#103—22no—
535#103—22no—
536#103—22no—
537#103—22no—
538#103—22no—
539#103D4×C3714yescomplemented
540#102—22no—
541#102—41no—
542C22⋊C8—22no—
543C22⋊C8D4×C3714yescomplemented
544C4×C8—22no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24—21no—
553C24C2×D4×C3711yescharacteristic
554C24C2×D4×C3711yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—28no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8C2×D4×C3712yes—
573C2×Q8#41×C3712yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—41no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
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×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4C2×D4×C3711yescharacteristic
610C22×C4C2×D4×C3711yescharacteristic
611C22×C4C2×D4×C3711yescharacteristic
612C22×C4C2×D4×C3712yes—
613C22×C4C2×D4×C3711yescharacteristic
614C22×C4#41×C3712yes—
615C22×C4C24×C3711yescharacteristic
616SD16—44no—
617SD16—44no—
618M16—44no—
619M16—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8C2×D4×C3712yes—
630C2×C8C2×D4×C3712yes—
631C2×C8C2×D4×C3712yes—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—81no—
645C4⋊C4C2×D4×C3712yes—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—81no—
656C22⋊C4—81no—
657C42—21no—
658C42—21no—
659C42—42no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23#121×C3712yes—
681C23C22×D4×C3711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691D4—44no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697D4—84no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—48no—
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—41no—
737C2×C4—41no—
738C2×C4#121×C3712yes—
739C2×C4#137×C3712yes—
740C2×C4C22×D4×C3711yescharacteristic
741C2×C4C22×D4×C3711yescharacteristic
742C2×C4C2×#41×C3711yescharacteristic
743C2×C4C2×#41×C3711yescharacteristic
744C2×C4H(5,𝔽2)×C3711yescharacteristic
745C2×C4H(5,𝔽2)×C3711yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×#121×C3711yescharacteristic
772C22D42×C3711yescharacteristic
773C22C37×#54611yescharacteristic
774C22C2×#137×C3711yescharacteristic
775C22C37×#57511yescharacteristic
776C22C37×#57711yescharacteristic
777C22C37×#57711yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4—81no—
789C4C37×#52511yescharacteristic
790C4C37×#53811yescharacteristic
791C4D42×C3711yescharacteristic
792C4C37×#54611yescharacteristic
793C2—42no—
794C2—81no—
795C2—161no—
796C2C37×#242411yescharacteristic
797C2C37×#305611yescharacteristic
798C2C37×#305711yescharacteristic
799C2C37×#327511yescharacteristic
800C2C37×#327811yescharacteristic
801C2C37×#332611yescharacteristic
802C2C37×#332911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2414C2
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×#468C2semidirect
2. C2×C37×#448C2semidirect
3. C2×C37×#436C2semidirect
4. C2×C37×#419C2semidirect
6. C37×#2409C2semidirect
7. C37×#2068C2semidirect
8. C37×#2055C2semidirect
9. C37×#2035C2semidirect
10. C37×#2000C2semidirect
11. C37×#1968C2semidirect
12. C37×#1933C2semidirect
13. C37×#1895C2semidirect
14. C37×#1894C2semidirect
15. C37×#1854C2semidirect
137. #103×C37D4semidirect
141. C22⋊C8×C37D4semidirect
348. #25138C37direct (N × H)
392. C2×#468C2×C37semidirect
393. C2×#448C2×C37semidirect
394. C2×#436C2×C37semidirect
395. C2×#419C2×C37semidirect
397. #2409C2×C37semidirect
398. #2068C2×C37semidirect
399. #2055C2×C37semidirect
400. #2035C2×C37semidirect
401. #2000C2×C37semidirect
402. #1968C2×C37semidirect
403. #1933C2×C37semidirect
404. #1895C2×C37semidirect
405. #1894C2×C37semidirect
406. #1854C2×C37semidirect
464. C37#25138direct (N × H)
539. #103D4×C37semidirect
543. C22⋊C8D4×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×#4482
C2×C37×#4362
C2×C37×#4192
C37×#24142
C37×#24092
C37×#20682
C37×#20552
C37×#20352
C37×#20002
C37×#19682
C37×#19332
C37×#18952
C37×#18942
C37×#18542
#2513837