Finite Group Databasebeta

← C37×#18434 #22639687

Subgroups — C37×#18434 #22639687

Order 9472.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3560C211yesmaximal, characteristic, complemented
2C37×#3213C211yesmaximal, characteristic, complemented
3C37×#3211C211yesmaximal, characteristic, complemented
4C37×#2662C211yesmaximal, characteristic, complemented
5C37×#1606C211yesmaximal, characteristic, complemented
6C37×#1604C211yesmaximal, characteristic, complemented
7C37×#1603C211yesmaximal, characteristic, complemented
8C37×#1601C211yesmaximal, characteristic, complemented
9C37×#1600C211yesmaximal, characteristic, complemented
10C37×#1598C211yesmaximal, characteristic, complemented
11C37×#1597C211yesmaximal, characteristic, complemented
12C37×#1595C211yesmaximal, characteristic, complemented
13C37×#1509C211yesmaximal, characteristic, complemented
14C37×#1502C211yesmaximal, characteristic, complemented
15C37×#1473C211yesmaximal, characteristic, complemented
16C37×#563—21no—
17C37×#560—21no—
18C37×#553—21no—
19C37×#553—21no—
20C37×#551—21no—
21C37×#547—21no—
22C37×#546—21no—
23C37×#546—21no—
24C37×#542—21no—
25C37×#539—21no—
26C37×#539C2211yescharacteristic
27C37×#538—21no—
28C37×#538—21no—
29C37×#538C2211yescharacteristic
30C37×#537C2211yescharacteristic
31C37×#534C2211yescharacteristic
32C37×#532C2211yescharacteristic
33C37×#529C2211yescharacteristic
34C2×#126×C37C2211yescharacteristic
35C2×#124×C37C2211yescharacteristic, complemented
36C37×#496—21no—
37C37×#495—21no—
38C37×#489—21no—
39C37×#488—21no—
40C37×#464—21no—
41C37×#463—21no—
42C37×#463—21no—
43C37×#463—21no—
44C37×#451C2211yescharacteristic, complemented
45C37×#450C2211yescharacteristic, complemented
46C37×#448C2211yescharacteristic
47C37×#448C2211yescharacteristic
48C37×#448C2211yescharacteristic, complemented
49C37×#447C2211yescharacteristic
50C37×#447C2211yescharacteristic
51C37×#447C2211yescharacteristic, complemented
52C37×#432C2211yescharacteristic, complemented
53C37×#431C2211yescharacteristic, complemented
54C37×#396—21no—
55C37×#395C2211yescharacteristic, complemented
56C37×#394—21no—
57C37×#394C2211yescharacteristic, complemented
58C37×#393C2211yescharacteristic
59C37×#392C2211yescharacteristic
60C37×#390—21no—
61C37×#388—21no—
62C4×C4⋊C4×C37C2211yescharacteristic, complemented
63C37×#328C2211yescharacteristic, complemented
64C37×#328C2211yescharacteristic, complemented
65C37×#327C2211yescharacteristic
66C37×#327C2211yescharacteristic
67C37×#327C2211yescharacteristic
68C37×#327C2211yescharacteristic
69C37×#327C2211yescharacteristic, complemented
70C37×#327C2211yescharacteristic, complemented
71C37×#324C2211yescharacteristic, complemented
72C37×#324C2211yescharacteristic, complemented
73C37×#323C2211yescharacteristic
74C37×#323C2211yescharacteristic
75C2×#41×C37—21no—
76C2×#41×C37—21no—
77C22×Q8×C37C2311yescharacteristic
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37C2311yescharacteristic
81C2×Q16×C37—21no—
82C2×SD16×C37—21no—
83C2×SD16×C37—21no—
84C2×SD16×C37—21no—
85C2×SD16×C37—21no—
86C2×D8×C37—21no—
87C2×D8×C37—21no—
88C2×D8×C37—21no—
89C4⋊Q8×C37—21no—
90C4⋊Q8×C37D411yescharacteristic, complemented
91#127×C37D411yescharacteristic, complemented
92#126×C37—21no—
93#126×C37—21no—
94#126×C37—21no—
95#126×C37—21no—
96#126×C37—21no—
97#126×C37—21no—
98#126×C37—21no—
99#126×C37—21no—
100#126×C37—21no—
101#125×C37—21no—
102#125×C37—21no—
103#125×C37D411yescharacteristic, complemented
104#124×C37—21no—
105#124×C37—21no—
106#124×C37—21no—
107#124×C37—21no—
108#124×C37—21no—
109#124×C37—21no—
110#124×C37—21no—
111#124×C37—21no—
112#124×C37D411yescharacteristic, complemented
113#123×C37—21no—
114#123×C37—21no—
115#123×C37—21no—
116#123×C37—21no—
117#123×C37—21no—
118#123×C37—21no—
119#123×C37—21no—
120#123×C37—21no—
121#123×C37—21no—
122#123×C37—21no—
123#123×C37—21no—
124#123×C37—21no—
125C22⋊Q8×C37—21no—
126C22⋊Q8×C37—21no—
127C22⋊Q8×C37—21no—
128C22⋊Q8×C37—21no—
129C22⋊Q8×C37—21no—
130C22⋊Q8×C37—21no—
131C22⋊Q8×C37—21no—
132C22⋊Q8×C37C2311yescharacteristic
133#121×C37—21no—
134#121×C37—21no—
135#121×C37—21no—
136#121×C37—21no—
137#121×C37—21no—
138#121×C37—21no—
139#121×C37—21no—
140#121×C37—21no—
141#121×C37—21no—
142#121×C37—21no—
143#121×C37—21no—
144#121×C37—21no—
145#121×C37C2311yescharacteristic
146#121×C37C2311yescharacteristic
147#121×C37C2311yescharacteristic
148#120×C37—21no—
149#120×C37—21no—
150#120×C37—21no—
151#120×C37—21no—
152#120×C37—21no—
153C4×Q8×C37D411yescharacteristic, complemented
154C4×D4×C37—21no—
155C4×D4×C37—21no—
156C4×D4×C37—21no—
157C4×D4×C37—21no—
158C4×D4×C37—21no—
159C4×D4×C37—21no—
160C4×D4×C37—21no—
161C4×D4×C37—21no—
162C4×D4×C37D411yescharacteristic, complemented
163C4×D4×C37D411yescharacteristic, complemented
164C4×D4×C37D411yescharacteristic, complemented
165#117×C37—21no—
166#117×C37—21no—
167C2×C4⋊C4×C37—21no—
168C2×C4⋊C4×C37—21no—
169C2×C4⋊C4×C37—21no—
170C2×C4⋊C4×C37D411yescharacteristic
171C2×C4⋊C4×C37D411yescharacteristic
172C2×C4⋊C4×C37C2311yescharacteristic
173C2×C22⋊C4×C37—21no—
174C2×C22⋊C4×C37—21no—
175C2×C22⋊C4×C37—21no—
176C2×C22⋊C4×C37—21no—
177C2×C22⋊C4×C37—21no—
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—21no—
180C2×C22⋊C4×C37—21no—
181C2×C22⋊C4×C37D411yescharacteristic
182C2×C22⋊C4×C37D411yescharacteristic
183C2×C22⋊C4×C37C2311yescharacteristic
184C2×C42×C37—21no—
185C2×C42×C37C2311yescharacteristic
186C4⋊C8×C37—21no—
187C4⋊C8×C37—21no—
188#103×C37—21no—
189#103×C37—21no—
190#103×C37—21no—
191#103×C37—21no—
192#102×C37—21no—
193#102×C37—21no—
194#102×C37—21no—
195#102×C37—21no—
196C22⋊C8×C37C2311yescharacteristic
197C22⋊C8×C37C2311yescharacteristic
198C22⋊C8×C37C2311yescharacteristic
199C22⋊C8×C37C2311yescharacteristic
200#97×C37—21no—
201C4×C8×C37—21no—
202#95×C37—21no—
203#95×C37—21no—
204#95×C37C2311yescharacteristic
205#95×C37C2311yescharacteristic
206C24×C37—21no—
207C24×C37—21no—
208C24×C37C2×D411yescharacteristic
209#41×C37—81no—
210#41×C37—81no—
211#41×C37—81no—
212#41×C37—81no—
213C2×Q8×C37—21no—
214C2×Q8×C37—21no—
215C2×Q8×C37—21no—
216C2×Q8×C37—21no—
217C2×Q8×C37—81no—
218C2×Q8×C37C2×D411yescharacteristic
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—21no—
228C2×D4×C37—21no—
229C2×D4×C37—21no—
230C2×D4×C37—21no—
231C2×D4×C37—21no—
232C2×D4×C37—21no—
233C2×D4×C37—42no—
234C2×D4×C37—81no—
235C2×D4×C37—81no—
236C2×D4×C37—81no—
237C2×D4×C37—81no—
238C2×D4×C37—81no—
239C2×D4×C37C2×D411yescharacteristic
240C2×D4×C37C2×D411yescharacteristic
241C2×D4×C37C2×D411yescharacteristic
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
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×C37C2×D411yescharacteristic
254C22×C4×C37C2×D411yescharacteristic
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2×D411yescharacteristic
257C22×C4×C37C2×D411yescharacteristic
258C22×C4×C37C2411yescharacteristic
259Q16×C37—81no—
260SD16×C37—81no—
261SD16×C37—81no—
262SD16×C37—81no—
263SD16×C37—81no—
264D8×C37—81no—
265D8×C37—81no—
266D8×C37—81no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—21no—
285C4⋊C4×C37—21no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—42no—
289C4⋊C4×C37—81no—
290C4⋊C4×C37C2×D411yescharacteristic
291C4⋊C4×C37C2×D411yescharacteristic
292C4⋊C4×C37C2×D411yescharacteristic
293C4⋊C4×C37C2×D411yescharacteristic
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—21no—
312C22⋊C4×C37—21no—
313C22⋊C4×C37—21no—
314C22⋊C4×C37—21no—
315C22⋊C4×C37—21no—
316C22⋊C4×C37—21no—
317C22⋊C4×C37—21no—
318C22⋊C4×C37—21no—
319C22⋊C4×C37—42no—
320C22⋊C4×C37—41no—
321C22⋊C4×C37—41no—
322C22⋊C4×C37—41no—
323C22⋊C4×C37—41no—
324C22⋊C4×C37—81no—
325C22⋊C4×C37—81no—
326C22⋊C4×C37—81no—
327C42×C37—21no—
328C42×C37—21no—
329C42×C37—21no—
330C42×C37—81no—
331C42×C37C2×D411yescharacteristic
332C42×C37C2×D411yescharacteristic
333C42×C37C2×D411yescharacteristic
334C42×C37C2×D411yescharacteristic
335C23×C37—21no—
336C23×C37—21no—
337C23×C37—21no—
338C23×C37—21no—
339C23×C37—21no—
340C23×C37—21no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—41no—
348C23×C37—41no—
349C23×C37—41no—
350C23×C37—81no—
351C23×C37—81no—
352C23×C37—81no—
353C23×C37C22×D411yescharacteristic
354Q8×C37—41no—
355Q8×C37—41no—
356Q8×C37—41no—
357Q8×C37—41no—
358Q8×C37—41no—
359Q8×C37—81no—
360Q8×C37—81no—
361D4×C37—41no—
362D4×C37—41no—
363D4×C37—41no—
364D4×C37—41no—
365D4×C37—41no—
366D4×C37—41no—
367D4×C37—41no—
368D4×C37—41no—
369D4×C37—41no—
370D4×C37—41no—
371D4×C37—41no—
372D4×C37—41no—
373D4×C37—41no—
374D4×C37—81no—
375D4×C37—81no—
376D4×C37—81no—
377D4×C37—81no—
378D4×C37—81no—
379D4×C37—81no—
380D4×C37—81no—
381D4×C37—81no—
382D4×C37—81no—
383D4×C37—84no—
384C2×C4×C37—21no—
385C2×C4×C37—21no—
386C2×C4×C37—22no—
387C2×C4×C37—21no—
388C2×C4×C37—21no—
389C2×C4×C37—21no—
390C2×C4×C37—21no—
391C2×C4×C37—21no—
392C2×C4×C37—21no—
393C2×C4×C37—21no—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—21no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37—41no—
409C2×C4×C37—81no—
410C2×C4×C37—81no—
411C2×C4×C37—81no—
412C2×C4×C37—81no—
413C2×C4×C37—81no—
414C2×C4×C37—81no—
415C2×C4×C37—81no—
416C2×C4×C37—81no—
417C2×C4×C37#12011yescharacteristic
418C2×C4×C37#12011yescharacteristic
419C2×C4×C37#12011yescharacteristic
420C2×C4×C37#12011yescharacteristic
421C2×C4×C37C22×D411yescharacteristic
422C2×C4×C37C22×D411yescharacteristic
423C8×C37—41no—
424C8×C37—41no—
425C8×C37—41no—
426C8×C37—41no—
427#18434C3711yesmaximal, characteristic, direct product factor, Sylow
428C22×C37—21no—
429C22×C37—21no—
430C22×C37—41no—
431C22×C37—41no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—41no—
437C22×C37—41no—
438C22×C37—41no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37—81no—
449C22×C37—81no—
450C22×C37—81no—
451C22×C37—162no—
452C22×C37C2×#12011yescharacteristic
453C22×C37#57611yescharacteristic
454C22×C37#57711yescharacteristic
455C4×C37—21no—
456C4×C37—21no—
457C4×C37—21no—
458C4×C37—21no—
459C4×C37—21no—
460C4×C37—21no—
461C4×C37—42no—
462C4×C37—41no—
463C4×C37—41no—
464C4×C37—41no—
465C4×C37—41no—
466C4×C37—41no—
467C4×C37—41no—
468C4×C37—41no—
469C4×C37—41no—
470C4×C37—81no—
471C4×C37—81no—
472#3560C2×C3711yescharacteristic, complemented
473#3213C2×C3711yescharacteristic, complemented
474#3211C2×C3711yescharacteristic, complemented
475#2662C2×C3711yescharacteristic, complemented
476#1606C2×C3711yescharacteristic, complemented
477#1604C2×C3711yescharacteristic, complemented
478#1603C2×C3711yescharacteristic, complemented
479#1601C2×C3711yescharacteristic, complemented
480#1600C2×C3711yescharacteristic, complemented
481#1598C2×C3711yescharacteristic, complemented
482#1597C2×C3711yescharacteristic, complemented
483#1595C2×C3711yescharacteristic, complemented
484#1509C2×C3711yescharacteristic, complemented
485#1502C2×C3711yescharacteristic, complemented
486#1473C2×C3711yescharacteristic, complemented
487C2×C37—21no—
488C2×C37—21no—
489C2×C37—81no—
490C2×C37—81no—
491C2×C37—81no—
492C2×C37—81no—
493C2×C37—161no—
494C2×C37#301211yescharacteristic
495C2×C37#301811yescharacteristic
496C2×C37#302711yescharacteristic
497#563—21no—
498#560—21no—
499#553—21no—
500#553—21no—
501#551—21no—
502#547—21no—
503#546—21no—
504#546—21no—
505#542—21no—
506#539—21no—
507#539C22×C3711yescharacteristic
508#538—21no—
509#538—21no—
510#538C22×C3711yescharacteristic
511#537C22×C3711yescharacteristic
512#534C22×C3711yescharacteristic
513#532C22×C3711yescharacteristic
514#529C22×C3711yescharacteristic
515C2×#126C22×C3711yescharacteristic
516C2×#124C22×C3711yescharacteristic, complemented
517#496—21no—
518#495—21no—
519#489—21no—
520#488—21no—
521#464—21no—
522#463—21no—
523#463—21no—
524#463—21no—
525#451C22×C3711yescharacteristic, complemented
526#450C22×C3711yescharacteristic, complemented
527#448C22×C3711yescharacteristic
528#448C22×C3711yescharacteristic
529#448C22×C3711yescharacteristic, complemented
530#447C22×C3711yescharacteristic
531#447C22×C3711yescharacteristic
532#447C22×C3711yescharacteristic, complemented
533#432C22×C3711yescharacteristic, complemented
534#431C22×C3711yescharacteristic, complemented
535#396—21no—
536#395C22×C3711yescharacteristic, complemented
537#394—21no—
538#394C22×C3711yescharacteristic, complemented
539#393C22×C3711yescharacteristic
540#392C22×C3711yescharacteristic
541#390—21no—
542#388—21no—
543C4×C4⋊C4C22×C3711yescharacteristic, complemented
544#328C22×C3711yescharacteristic, complemented
545#328C22×C3711yescharacteristic, complemented
546#327C22×C3711yescharacteristic
547#327C22×C3711yescharacteristic
548#327C22×C3711yescharacteristic
549#327C22×C3711yescharacteristic
550#327C22×C3711yescharacteristic, complemented
551#327C22×C3711yescharacteristic, complemented
552#324C22×C3711yescharacteristic, complemented
553#324C22×C3711yescharacteristic, complemented
554#323C22×C3711yescharacteristic
555#323C22×C3711yescharacteristic
556C37#1843411yescharacteristic, direct product factor, Sylow
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C3711yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C3711yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C3711yescharacteristic, complemented
573#127D4×C3711yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C3711yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C3711yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C3711yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C3711yescharacteristic
628#121C23×C3711yescharacteristic
629#121C23×C3711yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C3711yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C3711yescharacteristic, complemented
645C4×D4D4×C3711yescharacteristic, complemented
646C4×D4D4×C3711yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C3711yescharacteristic
653C2×C4⋊C4D4×C3711yescharacteristic
654C2×C4⋊C4C23×C3711yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C3711yescharacteristic
664C2×C22⋊C4D4×C3711yescharacteristic
665C2×C22⋊C4C23×C3711yescharacteristic
666C2×C42—21no—
667C2×C42C23×C3711yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C3711yescharacteristic
679C22⋊C8C23×C3711yescharacteristic
680C22⋊C8C23×C3711yescharacteristic
681C22⋊C8C23×C3711yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C3711yescharacteristic
687#95C23×C3711yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C3711yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C3711yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C3711yescharacteristic
722C2×D4C2×D4×C3711yescharacteristic
723C2×D4C2×D4×C3711yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C3711yescharacteristic
736C22×C4C2×D4×C3711yescharacteristic
737C22×C4C2×D4×C3711yescharacteristic
738C22×C4C2×D4×C3711yescharacteristic
739C22×C4C2×D4×C3711yescharacteristic
740C22×C4C24×C3711yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C3711yescharacteristic
773C4⋊C4C2×D4×C3711yescharacteristic
774C4⋊C4C2×D4×C3711yescharacteristic
775C4⋊C4C2×D4×C3711yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C3711yescharacteristic
814C42C2×D4×C3711yescharacteristic
815C42C2×D4×C3711yescharacteristic
816C42C2×D4×C3711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C3711yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C3711yescharacteristic
900C2×C4#120×C3711yescharacteristic
901C2×C4#120×C3711yescharacteristic
902C2×C4#120×C3711yescharacteristic
903C2×C4C22×D4×C3711yescharacteristic
904C2×C4C22×D4×C3711yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C3711yescharacteristic
934C22C37×#57611yescharacteristic
935C22C37×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C37×#301211yescharacteristic
961C2C37×#301811yescharacteristic
962C2C37×#302711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3560C2semidirect
2. C37×#3213C2semidirect
3. C37×#3211C2semidirect
4. C37×#2662C2semidirect
5. C37×#1606C2semidirect
6. C37×#1604C2semidirect
7. C37×#1603C2semidirect
8. C37×#1601C2semidirect
9. C37×#1600C2semidirect
10. C37×#1598C2semidirect
11. C37×#1597C2semidirect
12. C37×#1595C2semidirect
13. C37×#1509C2semidirect
14. C37×#1502C2semidirect
15. C37×#1473C2semidirect
35. C2×#124×C37C22semidirect
44. C37×#451C22semidirect
45. C37×#450C22semidirect
48. C37×#448C22semidirect
51. C37×#447C22semidirect
52. C37×#432C22semidirect
53. C37×#431C22semidirect
55. C37×#395C22semidirect
57. C37×#394C22semidirect
62. C4×C4⋊C4×C37C22semidirect
63. C37×#328C22semidirect
64. C37×#328C22semidirect
69. C37×#327C22semidirect
70. C37×#327C22semidirect
71. C37×#324C22semidirect
72. C37×#324C22semidirect
90. C4⋊Q8×C37D4semidirect
91. #127×C37D4semidirect
103. #125×C37D4semidirect
112. #124×C37D4semidirect
153. C4×Q8×C37D4semidirect
162. C4×D4×C37D4semidirect
163. C4×D4×C37D4semidirect
164. C4×D4×C37D4semidirect
427. #18434C37direct (N × H)
472. #3560C2×C37semidirect
473. #3213C2×C37semidirect
474. #3211C2×C37semidirect
475. #2662C2×C37semidirect
476. #1606C2×C37semidirect
477. #1604C2×C37semidirect
478. #1603C2×C37semidirect
479. #1601C2×C37semidirect
480. #1600C2×C37semidirect
481. #1598C2×C37semidirect
482. #1597C2×C37semidirect
483. #1595C2×C37semidirect
484. #1509C2×C37semidirect
485. #1502C2×C37semidirect
486. #1473C2×C37semidirect
516. C2×#124C22×C37semidirect
525. #451C22×C37semidirect
526. #450C22×C37semidirect
529. #448C22×C37semidirect
532. #447C22×C37semidirect
533. #432C22×C37semidirect
534. #431C22×C37semidirect
536. #395C22×C37semidirect
538. #394C22×C37semidirect
543. C4×C4⋊C4C22×C37semidirect
544. #328C22×C37semidirect
545. #328C22×C37semidirect
550. #327C22×C37semidirect
551. #327C22×C37semidirect
552. #324C22×C37semidirect
553. #324C22×C37semidirect
556. C37#18434direct (N × H)
572. C4⋊Q8D4×C37semidirect
573. #127D4×C37semidirect
585. #125D4×C37semidirect
594. #124D4×C37semidirect
635. C4×Q8D4×C37semidirect
644. C4×D4D4×C37semidirect
645. C4×D4D4×C37semidirect
646. C4×D4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35602
C37×#32132
C37×#32112
C37×#26622
C37×#16062
C37×#16042
C37×#16032
C37×#16012
C37×#16002
C37×#15982
C37×#15972
C37×#15952
C37×#15092
C37×#15022
C37×#14732
#1843437