Finite Group Databasebeta

← C37×#15493 #22636746

Subgroups — C37×#15493 #22636746

Order 9472.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#399C211yesmaximal, characteristic, complemented
2C2×C37×#397C211yesmaximal, characteristic, complemented
3C2×C37×#394C211yesmaximal, characteristic, complemented
4C2×C37×#392C211yesmaximal, characteristic
5C2×C37×#390C211yesmaximal, characteristic, complemented
6C2×C37×#386C211yesmaximal, characteristic, complemented
7C2×C37×#386C211yesmaximal, characteristic, complemented
8C2×C37×#380C211yesmaximal, characteristic, complemented
9C37×#1445C211yesmaximal, characteristic, complemented
10C37×#1439C211yesmaximal, characteristic, complemented
11C37×#1439C211yesmaximal, characteristic, complemented
12C37×#1438C211yesmaximal, characteristic, complemented
13C37×#1438C211yesmaximal, characteristic, complemented
14C37×#1437C211yesmaximal, characteristic, complemented
15C37×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C24×C4×C37C2211yescharacteristic
20C22×C4⋊C4×C37C2211yescharacteristic
21C22×C4⋊C4×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic
24C22×C22⋊C4×C37C2211yescharacteristic
25C22×C22⋊C4×C37C2211yescharacteristic
26C22×C22⋊C4×C37C2211yescharacteristic
27C22×C22⋊C4×C37C2211yescharacteristic
28C22×C22⋊C4×C37C2211yescharacteristic
29C22×C22⋊C4×C37C2211yescharacteristic
30C22×C22⋊C4×C37C2211yescharacteristic
31C22×C22⋊C4×C37C2211yescharacteristic
32C22×C22⋊C4×C37C2211yescharacteristic
33C22×C22⋊C4×C37C2211yescharacteristic
34C22×C22⋊C4×C37C2211yescharacteristic
35C22×C22⋊C4×C37C2211yescharacteristic
36C22×C22⋊C4×C37C2211yescharacteristic
37C22×C22⋊C4×C37C2211yescharacteristic
38C22×C42×C37C2211yescharacteristic
39C37×#399—24no—
40C37×#397—24no—
41C37×#394—24no—
42C37×#392—24no—
43C37×#390—24no—
44C37×#386—24no—
45C37×#386—24no—
46C37×#380—24no—
47C2×#95×C37C2211yescharacteristic
48C2×#95×C37C2211yescharacteristic
49C2×#95×C37C2211yescharacteristic
50C2×#95×C37C2211yescharacteristic
51C2×#95×C37C2211yescharacteristic
52C2×#95×C37C2211yescharacteristic
53C2×#95×C37C2211yescharacteristic
54C2×#95×C37C2211yescharacteristic
55C2×#95×C37C2211yescharacteristic
56C2×#95×C37C2211yescharacteristic
57C2×#95×C37C2211yescharacteristic
58C2×#95×C37C2211yescharacteristic
59C25×C37C2311yescharacteristic
60C25×C37C2311yescharacteristic
61C25×C37C2311yescharacteristic
62C22×D4×C37—22no—
63C22×D4×C37—22no—
64C22×D4×C37—22no—
65C22×D4×C37—22no—
66C22×D4×C37—22no—
67C22×D4×C37—22no—
68C22×D4×C37—22no—
69C22×D4×C37—22no—
70C22×D4×C37—22no—
71C22×D4×C37—22no—
72C22×D4×C37—22no—
73C22×D4×C37—22no—
74C22×D4×C37—41no—
75C22×D4×C37—41no—
76C22×D4×C37—41no—
77C22×D4×C37—41no—
78C22×D4×C37—41no—
79C22×D4×C37—41no—
80C22×D4×C37—41no—
81C22×D4×C37—41no—
82C22×D4×C37D414yes—
83C23×C4×C37—22no—
84C23×C4×C37—22no—
85C23×C4×C37—22no—
86C23×C4×C37—22no—
87C23×C4×C37—22no—
88C23×C4×C37—41no—
89C23×C4×C37—41no—
90C23×C4×C37C2311yescharacteristic
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C23×C4×C37C2311yescharacteristic
94C23×C4×C37C2311yescharacteristic
95C23×C4×C37C2311yescharacteristic
96C23×C4×C37C2311yescharacteristic
97C23×C4×C37C2311yescharacteristic
98C23×C4×C37C2311yescharacteristic
99C23×C4×C37C2311yescharacteristic
100C23×C4×C37C2311yescharacteristic
101C23×C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37—22no—
103C2×C4⋊C4×C37—22no—
104C2×C4⋊C4×C37—22no—
105C2×C4⋊C4×C37—22no—
106C2×C4⋊C4×C37—22no—
107C2×C4⋊C4×C37—22no—
108C2×C4⋊C4×C37—22no—
109C2×C4⋊C4×C37—41no—
110C2×C4⋊C4×C37—41no—
111C2×C4⋊C4×C37—41no—
112C2×C4⋊C4×C37—41no—
113C2×C4⋊C4×C37D414yescomplemented
114C2×C22⋊C4×C37—22no—
115C2×C22⋊C4×C37—22no—
116C2×C22⋊C4×C37—22no—
117C2×C22⋊C4×C37—22no—
118C2×C22⋊C4×C37—22no—
119C2×C22⋊C4×C37—22no—
120C2×C22⋊C4×C37—22no—
121C2×C22⋊C4×C37—22no—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—22no—
124C2×C22⋊C4×C37—22no—
125C2×C22⋊C4×C37—22no—
126C2×C22⋊C4×C37—22no—
127C2×C22⋊C4×C37—22no—
128C2×C22⋊C4×C37—22no—
129C2×C22⋊C4×C37—22no—
130C2×C22⋊C4×C37—22no—
131C2×C22⋊C4×C37—22no—
132C2×C22⋊C4×C37—22no—
133C2×C22⋊C4×C37—22no—
134C2×C22⋊C4×C37—22no—
135C2×C22⋊C4×C37—22no—
136C2×C22⋊C4×C37—22no—
137C2×C22⋊C4×C37—22no—
138C2×C22⋊C4×C37—22no—
139C2×C22⋊C4×C37—22no—
140C2×C22⋊C4×C37—22no—
141C2×C22⋊C4×C37—22no—
142C2×C22⋊C4×C37—22no—
143C2×C22⋊C4×C37—22no—
144C2×C22⋊C4×C37—41no—
145C2×C22⋊C4×C37—41no—
146C2×C22⋊C4×C37—41no—
147C2×C22⋊C4×C37—41no—
148C2×C22⋊C4×C37—41no—
149C2×C22⋊C4×C37—41no—
150C2×C22⋊C4×C37—41no—
151C2×C22⋊C4×C37—41no—
152C2×C22⋊C4×C37—41no—
153C2×C22⋊C4×C37—41no—
154C2×C22⋊C4×C37—41no—
155C2×C22⋊C4×C37—41no—
156C2×C42×C37—22no—
157C2×C42×C37—41no—
158C2×C42×C37—41no—
159#95×C37—22no—
160#95×C37—22no—
161#95×C37—22no—
162#95×C37—22no—
163#95×C37—22no—
164#95×C37—22no—
165#95×C37—22no—
166#95×C37—22no—
167#95×C37—41no—
168#95×C37—41no—
169#95×C37D414yescomplemented
170#95×C37D414yescomplemented
171C24×C37—21no—
172C24×C37—21no—
173C24×C37—21no—
174C24×C37—21no—
175C24×C37—21no—
176C24×C37—21no—
177C24×C37—21no—
178C24×C37—21no—
179C24×C37—21no—
180C24×C37—21no—
181C24×C37—21no—
182C24×C37—21no—
183C24×C37—21no—
184C24×C37—21no—
185C24×C37—21no—
186C24×C37—21no—
187C24×C37—21no—
188C24×C37—21no—
189C24×C37—21no—
190C24×C37—21no—
191C24×C37—21no—
192C24×C37—21no—
193C24×C37—21no—
194C24×C37—21no—
195C24×C37—21no—
196C24×C37—21no—
197C24×C37—21no—
198C24×C37—21no—
199C24×C37—21no—
200C24×C37—21no—
201C24×C37—21no—
202C24×C37—21no—
203C24×C37—21no—
204C24×C37—21no—
205C24×C37—21no—
206C24×C37—21no—
207C24×C37—21no—
208C24×C37—21no—
209C24×C37—21no—
210C24×C37—21no—
211C24×C37C2×D412yes—
212C24×C37C2×D412yes—
213C24×C37#4112yes—
214C24×C37#4112yes—
215C24×C37#4112yes—
216C24×C37C2411yescharacteristic
217C2×D4×C37—28no—
218C2×D4×C37—28no—
219C2×D4×C37—28no—
220C2×D4×C37—44no—
221C2×D4×C37—44no—
222C2×D4×C37—44no—
223C2×D4×C37—44no—
224C2×D4×C37—44no—
225C2×D4×C37—44no—
226C2×D4×C37—44no—
227C2×D4×C37—44no—
228C2×D4×C37—44no—
229C2×D4×C37—44no—
230C2×D4×C37—44no—
231C2×D4×C37—44no—
232C2×D4×C37—44no—
233C2×D4×C37—44no—
234C2×D4×C37—44no—
235C2×D4×C37—44no—
236C2×D4×C37—44no—
237C2×D4×C37—44no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—28no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—21no—
259C22×C4×C37—21no—
260C22×C4×C37—21no—
261C22×C4×C37—21no—
262C22×C4×C37—21no—
263C22×C4×C37—21no—
264C22×C4×C37—21no—
265C22×C4×C37—21no—
266C22×C4×C37—21no—
267C22×C4×C37—21no—
268C22×C4×C37—21no—
269C22×C4×C37—21no—
270C22×C4×C37—21no—
271C22×C4×C37—21no—
272C22×C4×C37—21no—
273C22×C4×C37—21no—
274C22×C4×C37—21no—
275C22×C4×C37—21no—
276C22×C4×C37—21no—
277C22×C4×C37—21no—
278C22×C4×C37—21no—
279C22×C4×C37—21no—
280C22×C4×C37—21no—
281C22×C4×C37—21no—
282C22×C4×C37—21no—
283C22×C4×C37—21no—
284C22×C4×C37—21no—
285C22×C4×C37—21no—
286C22×C4×C37—21no—
287C22×C4×C37—21no—
288C22×C4×C37—21no—
289C22×C4×C37—21no—
290C22×C4×C37—21no—
291C22×C4×C37—21no—
292C22×C4×C37—21no—
293C22×C4×C37—21no—
294C22×C4×C37—21no—
295C22×C4×C37—21no—
296C22×C4×C37—21no—
297C22×C4×C37—21no—
298C22×C4×C37—21no—
299C22×C4×C37—21no—
300C22×C4×C37—21no—
301C22×C4×C37—21no—
302C22×C4×C37—21no—
303C22×C4×C37—21no—
304C22×C4×C37—21no—
305C22×C4×C37—21no—
306C22×C4×C37—21no—
307C22×C4×C37—21no—
308C22×C4×C37—21no—
309C22×C4×C37—21no—
310C22×C4×C37—21no—
311C22×C4×C37—44no—
312C22×C4×C37—44no—
313C22×C4×C37—44no—
314C22×C4×C37—44no—
315C22×C4×C37—44no—
316C22×C4×C37—44no—
317C22×C4×C37C2×D412yes—
318C22×C4×C37C2×D412yes—
319C22×C4×C37C2×D412yes—
320C22×C4×C37C2×D412yes—
321C22×C4×C37C2×D412yes—
322C22×C4×C37C2×D412yes—
323C22×C4×C37C2×D412yes—
324C22×C4×C37C2×D412yes—
325C22×C4×C37C2×D412yes—
326C22×C4×C37C2×D412yes—
327C22×C4×C37#4112yes—
328C22×C4×C37#4112yes—
329C4⋊C4×C37—44no—
330C4⋊C4×C37—44no—
331C4⋊C4×C37—44no—
332C4⋊C4×C37—44no—
333C22⋊C4×C37—44no—
334C22⋊C4×C37—44no—
335C22⋊C4×C37—44no—
336C22⋊C4×C37—44no—
337C22⋊C4×C37—44no—
338C22⋊C4×C37—44no—
339C22⋊C4×C37—44no—
340C22⋊C4×C37—44no—
341C22⋊C4×C37—44no—
342C22⋊C4×C37—44no—
343C22⋊C4×C37—44no—
344C22⋊C4×C37—44no—
345C22⋊C4×C37—44no—
346C22⋊C4×C37—44no—
347C42×C37—44no—
348C23×C37—22no—
349C23×C37—22no—
350C23×C37—22no—
351C23×C37—22no—
352C23×C37—22no—
353C23×C37—22no—
354C23×C37—22no—
355C23×C37—22no—
356C23×C37—22no—
357C23×C37—22no—
358C23×C37—22no—
359C23×C37—22no—
360C23×C37—22no—
361C23×C37—22no—
362C23×C37—22no—
363C23×C37—22no—
364C23×C37—22no—
365C23×C37—22no—
366C23×C37—22no—
367C23×C37—22no—
368C23×C37—22no—
369C23×C37—22no—
370C23×C37—22no—
371C23×C37—22no—
372C23×C37—22no—
373C23×C37—22no—
374C23×C37—22no—
375C23×C37—22no—
376C23×C37—22no—
377C23×C37—22no—
378C23×C37—22no—
379C23×C37—22no—
380C23×C37—41no—
381C23×C37—41no—
382C23×C37—41no—
383C23×C37—41no—
384C23×C37—41no—
385C23×C37—41no—
386C23×C37—41no—
387C23×C37—41no—
388C23×C37—41no—
389C23×C37—41no—
390C23×C37—41no—
391C23×C37—41no—
392C23×C37—41no—
393C23×C37—41no—
394C23×C37—41no—
395C23×C37—41no—
396C23×C37—41no—
397C23×C37—41no—
398C23×C37—41no—
399C23×C37—41no—
400C23×C37—41no—
401C23×C37—41no—
402C23×C37—41no—
403C23×C37—41no—
404C23×C37—41no—
405C23×C37—41no—
406C23×C37—41no—
407C23×C37—41no—
408C23×C37—41no—
409C23×C37—41no—
410C23×C37—41no—
411C23×C37—41no—
412C23×C37—41no—
413C23×C37—41no—
414C23×C37—41no—
415C23×C37—41no—
416C23×C37—41no—
417C23×C37—41no—
418C23×C37—41no—
419C23×C37—41no—
420C23×C37—41no—
421C23×C37—41no—
422C23×C37—41no—
423C23×C37—41no—
424C23×C37—41no—
425C23×C37—41no—
426C23×C37—41no—
427C23×C37—41no—
428C23×C37—41no—
429C23×C37—41no—
430C23×C37—41no—
431C23×C37—41no—
432C23×C37—41no—
433C23×C37—41no—
434C23×C37—41no—
435C23×C37—41no—
436C23×C37—41no—
437C23×C37—41no—
438C23×C37—41no—
439C23×C37—41no—
440C23×C37—41no—
441C23×C37—41no—
442C23×C37—41no—
443C23×C37—41no—
444C23×C37—41no—
445C23×C37—41no—
446C23×C37—41no—
447C23×C37—41no—
448C23×C37—41no—
449C23×C37—41no—
450C23×C37—41no—
451C23×C37—41no—
452C23×C37#12314yes—
453C23×C37C22×D411yescharacteristic
454C23×C37C22×D411yescharacteristic
455C23×C37C22×D411yescharacteristic
456C23×C37C22×D411yescharacteristic
457C23×C37C2×#4111yescharacteristic
458C23×C37C2×#4111yescharacteristic
459C23×C37C2×#4111yescharacteristic
460C23×C37C2×#4111yescharacteristic
461C23×C37C2×#4111yescharacteristic
462C23×C37H(5,𝔽2)11yescharacteristic
463C23×C37H(5,𝔽2)11yescharacteristic
464C23×C37H(5,𝔽2)11yescharacteristic
465C23×C37H(5,𝔽2)11yescharacteristic
466C23×C37H(5,𝔽2)11yescharacteristic
467C23×C372−1+411yescharacteristic
468D4×C37—416no—
469D4×C37—416no—
470D4×C37—416no—
471C2×C4×C37—22no—
472C2×C4×C37—22no—
473C2×C4×C37—22no—
474C2×C4×C37—22no—
475C2×C4×C37—22no—
476C2×C4×C37—22no—
477C2×C4×C37—22no—
478C2×C4×C37—22no—
479C2×C4×C37—22no—
480C2×C4×C37—22no—
481C2×C4×C37—22no—
482C2×C4×C37—22no—
483C2×C4×C37—22no—
484C2×C4×C37—22no—
485C2×C4×C37—22no—
486C2×C4×C37—22no—
487C2×C4×C37—22no—
488C2×C4×C37—22no—
489C2×C4×C37—22no—
490C2×C4×C37—22no—
491C2×C4×C37—22no—
492C2×C4×C37—22no—
493C2×C4×C37—22no—
494C2×C4×C37—22no—
495C2×C4×C37—22no—
496C2×C4×C37—22no—
497C2×C4×C37—22no—
498C2×C4×C37—22no—
499C2×C4×C37—22no—
500C2×C4×C37—22no—
501C2×C4×C37—416no—
502C2×C4×C37—41no—
503C2×C4×C37—41no—
504C2×C4×C37—41no—
505C2×C4×C37—41no—
506C2×C4×C37—41no—
507C2×C4×C37—41no—
508C2×C4×C37—41no—
509C2×C4×C37—41no—
510C2×C4×C37—41no—
511C2×C4×C37—41no—
512C2×C4×C37—41no—
513C2×C4×C37—41no—
514C2×C4×C37—41no—
515C2×C4×C37—41no—
516C2×C4×C37—41no—
517C2×C4×C37—41no—
518C2×C4×C37—41no—
519C2×C4×C37—41no—
520C2×C4×C37—41no—
521C2×C4×C37—41no—
522C2×C4×C37—41no—
523C2×C4×C37—41no—
524C2×C4×C37—41no—
525C2×C4×C37—41no—
526C2×C4×C37—41no—
527C2×C4×C37—41no—
528C2×C4×C37—41no—
529C2×C4×C37—41no—
530C2×C4×C37—41no—
531C2×C4×C37—41no—
532C2×C4×C37—41no—
533C2×C4×C37—41no—
534C2×C4×C37—41no—
535C2×C4×C37—41no—
536C2×C4×C37—41no—
537C2×C4×C37—41no—
538C2×C4×C37—41no—
539C2×C4×C37—41no—
540C2×C4×C37—41no—
541C2×C4×C37—41no—
542C2×C4×C37—41no—
543C2×C4×C37—41no—
544C2×C4×C37—41no—
545C2×C4×C37—41no—
546C2×C4×C37—41no—
547C2×C4×C37—41no—
548C2×C4×C37—41no—
549C2×C4×C37—41no—
550C2×C4×C37—41no—
551C2×C4×C37—41no—
552C2×C4×C37—41no—
553C2×C4×C37—41no—
554C2×C4×C37#12114yes—
555C2×C4×C37#12714yes—
556#15493C3711yesmaximal, characteristic, direct product factor, Sylow
557C22×C37—24no—
558C22×C37—24no—
559C22×C37—24no—
560C22×C37—42no—
561C22×C37—42no—
562C22×C37—42no—
563C22×C37—42no—
564C22×C37—42no—
565C22×C37—42no—
566C22×C37—42no—
567C22×C37—42no—
568C22×C37—42no—
569C22×C37—42no—
570C22×C37—42no—
571C22×C37—42no—
572C22×C37—42no—
573C22×C37—42no—
574C22×C37—42no—
575C22×C37—42no—
576C22×C37—42no—
577C22×C37—42no—
578C22×C37—42no—
579C22×C37—42no—
580C22×C37—42no—
581C22×C37—42no—
582C22×C37—42no—
583C22×C37—42no—
584C22×C37—42no—
585C22×C37—42no—
586C22×C37—81no—
587C22×C37—81no—
588C22×C37—81no—
589C22×C37—81no—
590C22×C37—81no—
591C22×C37—81no—
592C22×C37—81no—
593C22×C37—81no—
594C22×C37—81no—
595C22×C37—81no—
596C22×C37—81no—
597C22×C37—81no—
598C22×C37—81no—
599C22×C37—81no—
600C22×C37—81no—
601C22×C37—81no—
602C22×C37C2×#12111yescharacteristic
603C22×C37C2×#12311yescharacteristic
604C22×C37#52511yescharacteristic
605C22×C37#52511yescharacteristic
606C22×C37#52911yescharacteristic
607C22×C37C2×#12711yescharacteristic
608C22×C37#53411yescharacteristic
609C22×C37#53411yescharacteristic
610C22×C37#53511yescharacteristic
611C22×C37#53711yescharacteristic
612C22×C37#53811yescharacteristic
613C22×C37#53811yescharacteristic
614C22×C37#53911yescharacteristic
615C22×C37#54011yescharacteristic
616C22×C37#54211yescharacteristic
617C22×C37D4211yescharacteristic
618C22×C37D4211yescharacteristic
619C22×C37#54611yescharacteristic
620C22×C37#54611yescharacteristic
621C22×C37#54611yescharacteristic
622C22×C37#54611yescharacteristic
623C22×C37#54611yescharacteristic
624C22×C37#54611yescharacteristic
625C22×C37#54611yescharacteristic
626C22×C37#54711yescharacteristic
627C22×C37#54811yescharacteristic
628C22×C37#54811yescharacteristic
629C22×C37#55011yescharacteristic
630C22×C37#55011yescharacteristic
631C22×C37#55111yescharacteristic
632C22×C37#55111yescharacteristic
633C22×C37#55111yescharacteristic
634C22×C37#55311yescharacteristic
635C22×C37#56011yescharacteristic
636C22×C37#56211yescharacteristic
637C4×C37—24no—
638C4×C37—24no—
639C4×C37—42no—
640C4×C37—42no—
641C4×C37—42no—
642C4×C37—42no—
643C4×C37—42no—
644C4×C37—42no—
645C4×C37—81no—
646C4×C37—81no—
647C4×C37—81no—
648C4×C37—81no—
649C2×#399C2×C3711yescharacteristic, complemented
650C2×#397C2×C3711yescharacteristic, complemented
651C2×#394C2×C3711yescharacteristic, complemented
652C2×#392C2×C3711yescharacteristic
653C2×#390C2×C3711yescharacteristic, complemented
654C2×#386C2×C3711yescharacteristic, complemented
655C2×#386C2×C3711yescharacteristic, complemented
656C2×#380C2×C3711yescharacteristic, complemented
657#1445C2×C3711yescharacteristic, complemented
658#1439C2×C3711yescharacteristic, complemented
659#1439C2×C3711yescharacteristic, complemented
660#1438C2×C3711yescharacteristic, complemented
661#1438C2×C3711yescharacteristic, complemented
662#1437C2×C3711yescharacteristic, complemented
663#1436C2×C3711yescharacteristic, complemented
664C2×C37—44no—
665C2×C37—82no—
666C2×C37—82no—
667C2×C37#241211yescharacteristic
668C2×C37#241811yescharacteristic
669C2×C37#242711yescharacteristic
670C2×C37#244311yescharacteristic
671C2×C37#246711yescharacteristic
672C2×C37#247111yescharacteristic
673C2×C37#253911yescharacteristic
674C2×C37#254011yescharacteristic
675C2×C37#254111yescharacteristic
676C2×C37#266811yescharacteristic
677C2×C37#267111yescharacteristic
678C2×C37#269611yescharacteristic
679C2×C37#270311yescharacteristic
680C2×C37#270511yescharacteristic
681C2×C37#273011yescharacteristic
682C23×D4C22×C3711yescharacteristic
683C23×D4C22×C3711yescharacteristic
684C23×D4C22×C3711yescharacteristic
685C24×C4C22×C3711yescharacteristic
686C22×C4⋊C4C22×C3711yescharacteristic
687C22×C4⋊C4C22×C3711yescharacteristic
688C22×C4⋊C4C22×C3711yescharacteristic
689C22×C4⋊C4C22×C3711yescharacteristic
690C22×C22⋊C4C22×C3711yescharacteristic
691C22×C22⋊C4C22×C3711yescharacteristic
692C22×C22⋊C4C22×C3711yescharacteristic
693C22×C22⋊C4C22×C3711yescharacteristic
694C22×C22⋊C4C22×C3711yescharacteristic
695C22×C22⋊C4C22×C3711yescharacteristic
696C22×C22⋊C4C22×C3711yescharacteristic
697C22×C22⋊C4C22×C3711yescharacteristic
698C22×C22⋊C4C22×C3711yescharacteristic
699C22×C22⋊C4C22×C3711yescharacteristic
700C22×C22⋊C4C22×C3711yescharacteristic
701C22×C22⋊C4C22×C3711yescharacteristic
702C22×C22⋊C4C22×C3711yescharacteristic
703C22×C22⋊C4C22×C3711yescharacteristic
704C22×C42C22×C3711yescharacteristic
705#399—24no—
706#397—24no—
707#394—24no—
708#392—24no—
709#390—24no—
710#386—24no—
711#386—24no—
712#380—24no—
713C2×#95C22×C3711yescharacteristic
714C2×#95C22×C3711yescharacteristic
715C2×#95C22×C3711yescharacteristic
716C2×#95C22×C3711yescharacteristic
717C2×#95C22×C3711yescharacteristic
718C2×#95C22×C3711yescharacteristic
719C2×#95C22×C3711yescharacteristic
720C2×#95C22×C3711yescharacteristic
721C2×#95C22×C3711yescharacteristic
722C2×#95C22×C3711yescharacteristic
723C2×#95C22×C3711yescharacteristic
724C2×#95C22×C3711yescharacteristic
725C37#1549311yescharacteristic, direct product factor, Sylow
726C25C23×C3711yescharacteristic
727C25C23×C3711yescharacteristic
728C25C23×C3711yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4D4×C3714yes—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4C23×C3711yescharacteristic
758C23×C4C23×C3711yescharacteristic
759C23×C4C23×C3711yescharacteristic
760C23×C4C23×C3711yescharacteristic
761C23×C4C23×C3711yescharacteristic
762C23×C4C23×C3711yescharacteristic
763C23×C4C23×C3711yescharacteristic
764C23×C4C23×C3711yescharacteristic
765C23×C4C23×C3711yescharacteristic
766C23×C4C23×C3711yescharacteristic
767C23×C4C23×C3711yescharacteristic
768C23×C4C23×C3711yescharacteristic
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4—41no—
780C2×C4⋊C4D4×C3714yescomplemented
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C42—22no—
824C2×C42—41no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—41no—
835#95—41no—
836#95D4×C3714yescomplemented
837#95D4×C3714yescomplemented
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24C2×D4×C3712yes—
879C24C2×D4×C3712yes—
880C24#41×C3712yes—
881C24#41×C3712yes—
882C24#41×C3712yes—
883C24C24×C3711yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—28no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C2×D4×C3712yes—
985C22×C4C2×D4×C3712yes—
986C22×C4C2×D4×C3712yes—
987C22×C4C2×D4×C3712yes—
988C22×C4C2×D4×C3712yes—
989C22×C4C2×D4×C3712yes—
990C22×C4C2×D4×C3712yes—
991C22×C4C2×D4×C3712yes—
992C22×C4C2×D4×C3712yes—
993C22×C4C2×D4×C3712yes—
994C22×C4#41×C3712yes—
995C22×C4#41×C3712yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C42—44no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23#123×C3714yes—
1120C23C22×D4×C3711yescharacteristic
1121C23C22×D4×C3711yescharacteristic
1122C23C22×D4×C3711yescharacteristic
1123C23C22×D4×C3711yescharacteristic
1124C23C2×#41×C3711yescharacteristic
1125C23C2×#41×C3711yescharacteristic
1126C23C2×#41×C3711yescharacteristic
1127C23C2×#41×C3711yescharacteristic
1128C23C2×#41×C3711yescharacteristic
1129C23H(5,𝔽2)×C3711yescharacteristic
1130C23H(5,𝔽2)×C3711yescharacteristic
1131C23H(5,𝔽2)×C3711yescharacteristic
1132C23H(5,𝔽2)×C3711yescharacteristic
1133C23H(5,𝔽2)×C3711yescharacteristic
1134C232−1+4×C3711yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—416no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4#121×C3714yes—
1222C2×C4#127×C3714yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×#121×C3711yescharacteristic
1269C22C2×#123×C3711yescharacteristic
1270C22C37×#52511yescharacteristic
1271C22C37×#52511yescharacteristic
1272C22C37×#52911yescharacteristic
1273C22C2×#127×C3711yescharacteristic
1274C22C37×#53411yescharacteristic
1275C22C37×#53411yescharacteristic
1276C22C37×#53511yescharacteristic
1277C22C37×#53711yescharacteristic
1278C22C37×#53811yescharacteristic
1279C22C37×#53811yescharacteristic
1280C22C37×#53911yescharacteristic
1281C22C37×#54011yescharacteristic
1282C22C37×#54211yescharacteristic
1283C22D42×C3711yescharacteristic
1284C22D42×C3711yescharacteristic
1285C22C37×#54611yescharacteristic
1286C22C37×#54611yescharacteristic
1287C22C37×#54611yescharacteristic
1288C22C37×#54611yescharacteristic
1289C22C37×#54611yescharacteristic
1290C22C37×#54611yescharacteristic
1291C22C37×#54611yescharacteristic
1292C22C37×#54711yescharacteristic
1293C22C37×#54811yescharacteristic
1294C22C37×#54811yescharacteristic
1295C22C37×#55011yescharacteristic
1296C22C37×#55011yescharacteristic
1297C22C37×#55111yescharacteristic
1298C22C37×#55111yescharacteristic
1299C22C37×#55111yescharacteristic
1300C22C37×#55311yescharacteristic
1301C22C37×#56011yescharacteristic
1302C22C37×#56211yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C37×#241211yescharacteristic
1319C2C37×#241811yescharacteristic
1320C2C37×#242711yescharacteristic
1321C2C37×#244311yescharacteristic
1322C2C37×#246711yescharacteristic
1323C2C37×#247111yescharacteristic
1324C2C37×#253911yescharacteristic
1325C2C37×#254011yescharacteristic
1326C2C37×#254111yescharacteristic
1327C2C37×#266811yescharacteristic
1328C2C37×#267111yescharacteristic
1329C2C37×#269611yescharacteristic
1330C2C37×#270311yescharacteristic
1331C2C37×#270511yescharacteristic
1332C2C37×#273011yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutator, Frattini, cosocleC24C24×C37
prime radicalC2×C37×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C37×#399C2semidirect
2. C2×C37×#397C2semidirect
3. C2×C37×#394C2semidirect
5. C2×C37×#390C2semidirect
6. C2×C37×#386C2semidirect
7. C2×C37×#386C2semidirect
8. C2×C37×#380C2semidirect
9. C37×#1445C2semidirect
10. C37×#1439C2semidirect
11. C37×#1439C2semidirect
12. C37×#1438C2semidirect
13. C37×#1438C2semidirect
14. C37×#1437C2semidirect
15. C37×#1436C2semidirect
113. C2×C4⋊C4×C37D4semidirect
169. #95×C37D4semidirect
170. #95×C37D4semidirect
556. #15493C37direct (N × H)
649. C2×#399C2×C37semidirect
650. C2×#397C2×C37semidirect
651. C2×#394C2×C37semidirect
653. C2×#390C2×C37semidirect
654. C2×#386C2×C37semidirect
655. C2×#386C2×C37semidirect
656. C2×#380C2×C37semidirect
657. #1445C2×C37semidirect
658. #1439C2×C37semidirect
659. #1439C2×C37semidirect
660. #1438C2×C37semidirect
661. #1438C2×C37semidirect
662. #1437C2×C37semidirect
663. #1436C2×C37semidirect
725. C37#15493direct (N × H)
780. C2×C4⋊C4D4×C37semidirect
836. #95D4×C37semidirect
837. #95D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#3992
C2×C37×#3972
C2×C37×#3942
C2×C37×#3922
C2×C37×#3902
C2×C37×#3862
C2×C37×#3802
C37×#14452
C37×#14392
C37×#14382
C37×#14372
C37×#14362
#1549337