Finite Group Databasebeta

← C37×#19049 #22640302

Subgroups — C37×#19049 #22640302

Order 9472.

886 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3561C211yesmaximal, characteristic
2C37×#3215C211yesmaximal, characteristic, complemented
3C37×#3181C211yesmaximal, characteristic, complemented
4C37×#3162C211yesmaximal, characteristic, complemented
5C37×#1664C212yesmaximal, complemented
6C37×#1661C212yesmaximal, complemented
7C37×#1661C212yesmaximal, complemented
8C37×#1660C212yesmaximal, complemented
9C37×#1532C211yesmaximal, characteristic, complemented
10C37×#1531C211yesmaximal, characteristic, complemented
11C2×C37×#329C211yesmaximal, characteristic, complemented
12C37×#563C2212yes—
13C37×#562C2212yes—
14C37×#556—21no—
15C37×#551—22no—
16D4×Q8×C37—21no—
17C37×#548—21no—
18C37×#546—21no—
19C37×#543—21no—
20C37×#542—21no—
21C37×#542—22no—
22C37×#538—21no—
23C37×#536—21no—
24C37×#533C2211yescharacteristic
25C37×#533C2211yescharacteristic
26C37×#529C2211yescharacteristic
27C2×#124×C37C2211yescharacteristic
28C37×#501—21no—
29C37×#501—21no—
30C37×#501C2212yescomplemented
31C37×#501C2212yescomplemented
32C37×#501C2211yescharacteristic, complemented
33C37×#497C2212yes—
34C37×#497C2211yescharacteristic, complemented
35C37×#491C2211yescharacteristic, complemented
36C37×#489C2212yes—
37C37×#489C2211yescharacteristic, complemented
38C37×#467—21no—
39C37×#465—21no—
40C37×#464—22no—
41C37×#451—21no—
42C37×#450—21no—
43C37×#441—21no—
44C37×#440—21no—
45C37×#432C2211yescharacteristic
46C37×#427—22no—
47C2×#97×C37C2211yescharacteristic
48C2×#97×C37C2211yescharacteristic
49C37×#330C2212yescomplemented
50C37×#330C2212yescomplemented
51C37×#330C2212yescomplemented
52C37×#329C2212yes—
53C37×#329C2212yes—
54C37×#329C2212yescomplemented
55C2×#41×C37—21no—
56C22×Q8×C37—21no—
57C22×Q8×C37D411yescharacteristic
58C22×D4×C37D411yescharacteristic
59C2×Q16×C37—21no—
60C2×Q16×C37—22no—
61C2×SD16×C37—21no—
62C2×SD16×C37—22no—
63C22×C8×C37—21no—
64C22×C8×C37—21no—
65C4⋊Q8×C37—21no—
66C4⋊Q8×C37—22no—
67C4⋊Q8×C37D411yescharacteristic
68C4⋊Q8×C37D411yescharacteristic
69C4⋊Q8×C37C2311yescharacteristic
70C4⋊Q8×C37C2311yescharacteristic
71#126×C37—22no—
72#126×C37—22no—
73#126×C37—22no—
74#126×C37—21no—
75#125×C37—21no—
76#125×C37C2311yescharacteristic
77#125×C37C2312yes—
78#124×C37—21no—
79#124×C37—22no—
80#124×C37—22no—
81#124×C37—21no—
82#124×C37—21no—
83#124×C37D412yes—
84#124×C37C2312yes—
85#124×C37C2311yescharacteristic
86#123×C37—22no—
87#123×C37—22no—
88#123×C37—21no—
89#123×C37—22no—
90#123×C37—22no—
91C22⋊Q8×C37—22no—
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—21no—
94C22⋊Q8×C37—22no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37—22no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—21no—
102C22⋊Q8×C37—21no—
103C22⋊Q8×C37D411yescharacteristic
104#121×C37—21no—
105#121×C37—22no—
106#121×C37—22no—
107#121×C37D411yescharacteristic
108#120×C37—22no—
109C4×Q8×C37—21no—
110C4×Q8×C37—21no—
111C4×Q8×C37—21no—
112C4×Q8×C37—21no—
113C4×Q8×C37—21no—
114C4×Q8×C37D411yescharacteristic
115C4×D4×C37—22no—
116C4×D4×C37—21no—
117C4×D4×C37—22no—
118C4×D4×C37—21no—
119C4×D4×C37D411yescharacteristic
120#117×C37—22no—
121#117×C37—21no—
122#117×C37—21no—
123#117×C37D412yes—
124C2×C22⋊C4×C37—22no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C42×C37C2311yescharacteristic
128#107×C37—22no—
129#107×C37—22no—
130#107×C37—21no—
131#106×C37—22no—
132#106×C37—22no—
133#106×C37—21no—
134C4⋊C8×C37—21no—
135#103×C37—21no—
136#103×C37—22no—
137#103×C37—21no—
138#103×C37—21no—
139#102×C37—21no—
140#102×C37—22no—
141C22⋊C8×C37—21no—
142#97×C37—21no—
143#97×C37—21no—
144#97×C37C2312yes—
145#97×C37C2311yescharacteristic
146#97×C37C2311yescharacteristic
147#97×C37C2312yes—
148C24×C37—21no—
149#41×C37—82no—
150C2×Q8×C37—22no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—82no—
157C2×Q8×C37—81no—
158C2×Q8×C37C2×D411yescharacteristic
159C2×Q8×C37C2×D412yes—
160C2×D4×C37—21no—
161C2×D4×C37—22no—
162C2×D4×C37—22no—
163C2×D4×C37—21no—
164C2×D4×C37—81no—
165C2×D4×C37C2×D411yescharacteristic
166C2×D4×C37C2×D412yes—
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37C2×D411yescharacteristic
173C22×C4×C37C2×D411yescharacteristic
174C22×C4×C37C2×D411yescharacteristic
175Q16×C37—42no—
176Q16×C37—82no—
177SD16×C37—42no—
178SD16×C37—82no—
179C2×C8×C37—24no—
180C2×C8×C37—22no—
181C2×C8×C37—21no—
182C2×C8×C37—21no—
183C2×C8×C37—22no—
184C2×C8×C37—42no—
185C4⋊C4×C37—22no—
186C4⋊C4×C37—22no—
187C4⋊C4×C37—22no—
188C4⋊C4×C37—22no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—21no—
192C4⋊C4×C37—21no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—22no—
196C4⋊C4×C37—22no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—41no—
202C4⋊C4×C37—41no—
203C4⋊C4×C37C2×D411yescharacteristic
204C4⋊C4×C37C2×D411yescharacteristic
205C4⋊C4×C37C2×D412yes—
206C4⋊C4×C37C2×D412yes—
207C22⋊C4×C37—22no—
208C22⋊C4×C37—22no—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—22no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—21no—
213C22⋊C4×C37—22no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—21no—
217C22⋊C4×C37—21no—
218C22⋊C4×C37—22no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—21no—
221C22⋊C4×C37—21no—
222C22⋊C4×C37—41no—
223C42×C37—22no—
224C42×C37—22no—
225C42×C37—21no—
226C42×C37—41no—
227C42×C37C2×D411yescharacteristic
228C42×C37C2×D411yescharacteristic
229C42×C37C2×D411yescharacteristic
230C42×C37C2411yescharacteristic
231C23×C37—22no—
232C23×C37—21no—
233C23×C37—42no—
234C23×C37—81no—
235C23×C37—81no—
236C23×C37#12011yescharacteristic
237Q8×C37—41no—
238Q8×C37—42no—
239Q8×C37—42no—
240Q8×C37—42no—
241Q8×C37—41no—
242Q8×C37—42no—
243Q8×C37—41no—
244Q8×C37—81no—
245Q8×C37—82no—
246D4×C37—41no—
247D4×C37—42no—
248D4×C37—42no—
249D4×C37—42no—
250D4×C37—82no—
251D4×C37—82no—
252C2×C4×C37—22no—
253C2×C4×C37—21no—
254C2×C4×C37—22no—
255C2×C4×C37—21no—
256C2×C4×C37—22no—
257C2×C4×C37—22no—
258C2×C4×C37—21no—
259C2×C4×C37—41no—
260C2×C4×C37—41no—
261C2×C4×C37—42no—
262C2×C4×C37—41no—
263C2×C4×C37—41no—
264C2×C4×C37—81no—
265C2×C4×C37—82no—
266C2×C4×C37—82no—
267C2×C4×C37—82no—
268C2×C4×C37#12011yescharacteristic
269C2×C4×C37#12011yescharacteristic
270C2×C4×C37#12011yescharacteristic
271C2×C4×C37C22×D411yescharacteristic
272C2×C4×C37C22×D411yescharacteristic
273C2×C4×C37C22×D411yescharacteristic
274C8×C37—24no—
275C8×C37—22no—
276C8×C37—41no—
277C8×C37—42no—
278#19049C3711yesmaximal, characteristic, direct product factor, Sylow
279C22×C37—21no—
280C22×C37—21no—
281C22×C37—41no—
282C22×C37—42no—
283C22×C37—42no—
284C22×C37—41no—
285C22×C37—41no—
286C22×C37—42no—
287C22×C37—162no—
288C22×C37#45612yes—
289C22×C37C2×#12011yescharacteristic
290C4×C37—21no—
291C4×C37—21no—
292C4×C37—21no—
293C4×C37—21no—
294C4×C37—21no—
295C4×C37—21no—
296C4×C37—41no—
297C4×C37—41no—
298C4×C37—42no—
299C4×C37—41no—
300C4×C37—42no—
301C4×C37—42no—
302C4×C37—81no—
303C4×C37—81no—
304#3561C2×C3711yescharacteristic
305#3215C2×C3711yescharacteristic, complemented
306#3181C2×C3711yescharacteristic, complemented
307#3162C2×C3711yescharacteristic, complemented
308#1664C2×C3712yescomplemented
309#1661C2×C3712yescomplemented
310#1661C2×C3712yescomplemented
311#1660C2×C3712yescomplemented
312#1532C2×C3711yescharacteristic, complemented
313#1531C2×C3711yescharacteristic, complemented
314C2×#329C2×C3711yescharacteristic, complemented
315C2×C37—22no—
316C2×C37—81no—
317C2×C37—82no—
318C2×C37C2×#45611yescharacteristic
319C2×C37#301811yescharacteristic
320C2×C37#301911yescharacteristic
321#563C22×C3712yes—
322#562C22×C3712yes—
323#556—21no—
324#551—22no—
325D4×Q8—21no—
326#548—21no—
327#546—21no—
328#543—21no—
329#542—21no—
330#542—22no—
331#538—21no—
332#536—21no—
333#533C22×C3711yescharacteristic
334#533C22×C3711yescharacteristic
335#529C22×C3711yescharacteristic
336C2×#124C22×C3711yescharacteristic
337#501—21no—
338#501—21no—
339#501C22×C3712yescomplemented
340#501C22×C3712yescomplemented
341#501C22×C3711yescharacteristic, complemented
342#497C22×C3712yes—
343#497C22×C3711yescharacteristic, complemented
344#491C22×C3711yescharacteristic, complemented
345#489C22×C3712yes—
346#489C22×C3711yescharacteristic, complemented
347#467—21no—
348#465—21no—
349#464—22no—
350#451—21no—
351#450—21no—
352#441—21no—
353#440—21no—
354#432C22×C3711yescharacteristic
355#427—22no—
356C2×#97C22×C3711yescharacteristic
357C2×#97C22×C3711yescharacteristic
358#330C22×C3712yescomplemented
359#330C22×C3712yescomplemented
360#330C22×C3712yescomplemented
361#329C22×C3712yes—
362#329C22×C3712yes—
363#329C22×C3712yescomplemented
364C37#1904911yescharacteristic, direct product factor, Sylow
365C2×#41—21no—
366C22×Q8—21no—
367C22×Q8D4×C3711yescharacteristic
368C22×D4D4×C3711yescharacteristic
369C2×Q16—21no—
370C2×Q16—22no—
371C2×SD16—21no—
372C2×SD16—22no—
373C22×C8—21no—
374C22×C8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—22no—
377C4⋊Q8D4×C3711yescharacteristic
378C4⋊Q8D4×C3711yescharacteristic
379C4⋊Q8C23×C3711yescharacteristic
380C4⋊Q8C23×C3711yescharacteristic
381#126—22no—
382#126—22no—
383#126—22no—
384#126—21no—
385#125—21no—
386#125C23×C3711yescharacteristic
387#125C23×C3712yes—
388#124—21no—
389#124—22no—
390#124—22no—
391#124—21no—
392#124—21no—
393#124D4×C3712yes—
394#124C23×C3712yes—
395#124C23×C3711yescharacteristic
396#123—22no—
397#123—22no—
398#123—21no—
399#123—22no—
400#123—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8D4×C3711yescharacteristic
414#121—21no—
415#121—22no—
416#121—22no—
417#121D4×C3711yescharacteristic
418#120—22no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8D4×C3711yescharacteristic
425C4×D4—22no—
426C4×D4—21no—
427C4×D4—22no—
428C4×D4—21no—
429C4×D4D4×C3711yescharacteristic
430#117—22no—
431#117—21no—
432#117—21no—
433#117D4×C3712yes—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C42C23×C3711yescharacteristic
438#107—22no—
439#107—22no—
440#107—21no—
441#106—22no—
442#106—22no—
443#106—21no—
444C4⋊C8—21no—
445#103—21no—
446#103—22no—
447#103—21no—
448#103—21no—
449#102—21no—
450#102—22no—
451C22⋊C8—21no—
452#97—21no—
453#97—21no—
454#97C23×C3712yes—
455#97C23×C3711yescharacteristic
456#97C23×C3711yescharacteristic
457#97C23×C3712yes—
458C24—21no—
459#41—82no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—82no—
467C2×Q8—81no—
468C2×Q8C2×D4×C3711yescharacteristic
469C2×Q8C2×D4×C3712yes—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—81no—
475C2×D4C2×D4×C3711yescharacteristic
476C2×D4C2×D4×C3712yes—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4C2×D4×C3711yescharacteristic
483C22×C4C2×D4×C3711yescharacteristic
484C22×C4C2×D4×C3711yescharacteristic
485Q16—42no—
486Q16—82no—
487SD16—42no—
488SD16—82no—
489C2×C8—24no—
490C2×C8—22no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—22no—
494C2×C8—42no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C3711yescharacteristic
514C4⋊C4C2×D4×C3711yescharacteristic
515C4⋊C4C2×D4×C3712yes—
516C4⋊C4C2×D4×C3712yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—41no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—41no—
537C42C2×D4×C3711yescharacteristic
538C42C2×D4×C3711yescharacteristic
539C42C2×D4×C3711yescharacteristic
540C42C24×C3711yescharacteristic
541C23—22no—
542C23—21no—
543C23—42no—
544C23—81no—
545C23—81no—
546C23#120×C3711yescharacteristic
547Q8—41no—
548Q8—42no—
549Q8—42no—
550Q8—42no—
551Q8—41no—
552Q8—42no—
553Q8—41no—
554Q8—81no—
555Q8—82no—
556D4—41no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—82no—
561D4—82no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4#120×C3711yescharacteristic
579C2×C4#120×C3711yescharacteristic
580C2×C4#120×C3711yescharacteristic
581C2×C4C22×D4×C3711yescharacteristic
582C2×C4C22×D4×C3711yescharacteristic
583C2×C4C22×D4×C3711yescharacteristic
584C8—24no—
585C8—22no—
586C8—41no—
587C8—42no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—42no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—162no—
597C22C37×#45612yes—
598C22C2×#120×C3711yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—41no—
609C4—42no—
610C4—42no—
611C4—81no—
612C4—81no—
613C2—22no—
614C2—82no—
615C2—81no—
616C2C2×C37×#45611yescharacteristic
617C2C37×#301811yescharacteristic
618C2C37×#301911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3561C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3215C2semidirect
3. C37×#3181C2semidirect
4. C37×#3162C2semidirect
5. C37×#1664C2semidirect
6. C37×#1661C2semidirect
7. C37×#1661C2semidirect
8. C37×#1660C2semidirect
9. C37×#1532C2semidirect
10. C37×#1531C2semidirect
11. C2×C37×#329C2semidirect
30. C37×#501C22semidirect
31. C37×#501C22semidirect
32. C37×#501C22semidirect
34. C37×#497C22semidirect
35. C37×#491C22semidirect
37. C37×#489C22semidirect
49. C37×#330C22semidirect
50. C37×#330C22semidirect
51. C37×#330C22semidirect
54. C37×#329C22semidirect
278. #19049C37direct (N × H)
305. #3215C2×C37semidirect
306. #3181C2×C37semidirect
307. #3162C2×C37semidirect
308. #1664C2×C37semidirect
309. #1661C2×C37semidirect
310. #1661C2×C37semidirect
311. #1660C2×C37semidirect
312. #1532C2×C37semidirect
313. #1531C2×C37semidirect
314. C2×#329C2×C37semidirect
339. #501C22×C37semidirect
340. #501C22×C37semidirect
341. #501C22×C37semidirect
343. #497C22×C37semidirect
344. #491C22×C37semidirect
346. #489C22×C37semidirect
358. #330C22×C37semidirect
359. #330C22×C37semidirect
360. #330C22×C37semidirect
363. #329C22×C37semidirect
364. C37#19049direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35612
C37×#32152
C37×#31812
C37×#31622
C37×#16642
C37×#16612
C37×#16602
C37×#15322
C37×#15312
C2×C37×#3292
#1904937