Finite Group Databasebeta

← C37×#18366 #22639619

Subgroups — C37×#18366 #22639619

Order 9472.

1048 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3493C211yesmaximal, characteristic, complemented
2C37×#3217C212yesmaximal, complemented
3C37×#2619C211yesmaximal, characteristic, complemented
4C37×#1600C214yesmaximal, complemented
5C37×#1599C212yesmaximal, complemented
6C37×#1598C212yesmaximal, complemented
7C37×#1512C212yesmaximal, complemented
8C37×#1464C211yesmaximal, characteristic, complemented
9C37×#556—22no—
10C37×#555—22no—
11C37×#553—22no—
12C37×#552—22no—
13C37×#544C2211yescharacteristic
14C37×#538—21no—
15C37×#538C2212yes—
16C37×#537C2211yescharacteristic
17C2×#127×C37C2211yescharacteristic
18C37×#529—21no—
19C37×#529C2212yes—
20C37×#525—21no—
21C2×#121×C37—21no—
22C37×#520—21no—
23C2×#117×C37C2211yescharacteristic
24C37×#496—22no—
25C37×#490—22no—
26C37×#460—22no—
27C37×#459—22no—
28C37×#450C2214yes—
29C37×#447C2214yes—
30C37×#432C2212yes—
31C37×#394—21no—
32C37×#394C2212yes—
33C37×#392—21no—
34C37×#392C2212yes—
35C37×#390—21no—
36C37×#382C2211yescharacteristic
37C37×#328C2214yes—
38C37×#327C2214yes—
39C37×#324C2212yes—
40C37×#323C2212yes—
41C2×#41×C37—21no—
42C22×D4×C37—22no—
43C22×D4×C37—21no—
44C22×D4×C37—21no—
45C22×D4×C37C2312yes—
46C23×C4×C37D411yescharacteristic
47C2×SD16×C37—24no—
48C2×D8×C37—24no—
49C4⋊Q8×C37—22no—
50#127×C37—22no—
51#127×C37—22no—
52#126×C37—22no—
53#126×C37—22no—
54#126×C37—22no—
55#126×C37—22no—
56#125×C37—21no—
57#125×C37—22no—
58#125×C37D412yescomplemented
59#124×C37—21no—
60#124×C37—22no—
61#124×C37—22no—
62#124×C37D412yescomplemented
63#123×C37—22no—
64#123×C37—22no—
65#123×C37—22no—
66C22⋊Q8×C37—21no—
67C22⋊Q8×C37—21no—
68C22⋊Q8×C37—21no—
69C22⋊Q8×C37—22no—
70C22⋊Q8×C37C2312yes—
71#121×C37—21no—
72#121×C37—21no—
73#121×C37—22no—
74#121×C37—22no—
75#121×C37—22no—
76#121×C37—21no—
77#121×C37—44no—
78#121×C37C2312yes—
79#120×C37—22no—
80C4×Q8×C37—22no—
81C4×Q8×C37—21no—
82C4×Q8×C37D412yescomplemented
83C4×D4×C37—22no—
84C4×D4×C37—22no—
85C4×D4×C37—22no—
86C4×D4×C37—21no—
87C4×D4×C37—22no—
88C4×D4×C37—22no—
89C4×D4×C37D412yescomplemented
90#117×C37—22no—
91#117×C37—22no—
92#117×C37—21no—
93#117×C37—22no—
94#117×C37—22no—
95#117×C37—22no—
96C2×C4⋊C4×C37—22no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37D411yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C22⋊C4×C37—22no—
101C2×C22⋊C4×C37—22no—
102C2×C22⋊C4×C37—22no—
103C2×C22⋊C4×C37D411yescharacteristic
104C2×C22⋊C4×C37C2311yescharacteristic
105C2×C42×C37D411yescharacteristic
106C2×C42×C37C2311yescharacteristic
107C4⋊C8×C37—22no—
108#102×C37—24no—
109#102×C37—24no—
110C22⋊C8×C37C2314yes—
111#97×C37—22no—
112#95×C37—21no—
113#95×C37C2312yes—
114C24×C37—22no—
115C24×C37C2×D411yescharacteristic
116#41×C37—42no—
117#41×C37—42no—
118C2×Q8×C37—21no—
119C2×Q8×C37—21no—
120C2×Q8×C37C2×D412yes—
121C2×D4×C37—21no—
122C2×D4×C37—22no—
123C2×D4×C37—22no—
124C2×D4×C37—22no—
125C2×D4×C37—21no—
126C2×D4×C37—24no—
127C2×D4×C37—42no—
128C2×D4×C37—42no—
129C2×D4×C37—44no—
130C2×D4×C37—41no—
131C2×D4×C37—41no—
132C2×D4×C37—42no—
133C2×D4×C37—82no—
134C2×D4×C37—82no—
135C2×D4×C37—82no—
136C2×D4×C37—82no—
137C2×D4×C37C2×D412yes—
138C22×C4×C37—22no—
139C22×C4×C37—22no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—22no—
143C22×C4×C37—22no—
144C22×C4×C37—22no—
145C22×C4×C37—41no—
146C22×C4×C37C2×D411yescharacteristic
147C22×C4×C37C2×D411yescharacteristic
148C22×C4×C37C2×D411yescharacteristic
149C22×C4×C37C2×D411yescharacteristic
150C22×C4×C37C2×D411yescharacteristic
151C22×C4×C37C2411yescharacteristic
152SD16×C37—84no—
153D8×C37—84no—
154C2×C8×C37—24no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—22no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—22no—
159C4⋊C4×C37—21no—
160C4⋊C4×C37—21no—
161C4⋊C4×C37—22no—
162C4⋊C4×C37—22no—
163C4⋊C4×C37—22no—
164C4⋊C4×C37—22no—
165C4⋊C4×C37—22no—
166C4⋊C4×C37—22no—
167C4⋊C4×C37—42no—
168C4⋊C4×C37C2×D412yes—
169C4⋊C4×C37C2×D412yes—
170C22⋊C4×C37—22no—
171C22⋊C4×C37—22no—
172C22⋊C4×C37—22no—
173C22⋊C4×C37—22no—
174C22⋊C4×C37—22no—
175C22⋊C4×C37—22no—
176C22⋊C4×C37—22no—
177C22⋊C4×C37—22no—
178C22⋊C4×C37—22no—
179C22⋊C4×C37—22no—
180C22⋊C4×C37—22no—
181C22⋊C4×C37—44no—
182C22⋊C4×C37—82no—
183C22⋊C4×C37—82no—
184C42×C37—22no—
185C42×C37—22no—
186C42×C37—21no—
187C42×C37—21no—
188C42×C37—22no—
189C42×C37C2×D412yes—
190C42×C37C2×D412yes—
191C23×C37—21no—
192C23×C37—22no—
193C23×C37—21no—
194C23×C37—21no—
195C23×C37—41no—
196C23×C37—41no—
197C23×C37—42no—
198C23×C37—42no—
199C23×C37—42no—
200C23×C37—42no—
201C23×C37—42no—
202C23×C37—42no—
203C23×C37—42no—
204C23×C37C22×D411yescharacteristic
205Q8×C37—42no—
206Q8×C37—42no—
207Q8×C37—81no—
208D4×C37—42no—
209D4×C37—42no—
210D4×C37—44no—
211D4×C37—44no—
212D4×C37—42no—
213D4×C37—42no—
214D4×C37—82no—
215D4×C37—82no—
216D4×C37—84no—
217D4×C37—82no—
218D4×C37—81no—
219D4×C37—82no—
220D4×C37—88no—
221C2×C4×C37—21no—
222C2×C4×C37—21no—
223C2×C4×C37—21no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—22no—
227C2×C4×C37—21no—
228C2×C4×C37—22no—
229C2×C4×C37—22no—
230C2×C4×C37—41no—
231C2×C4×C37—41no—
232C2×C4×C37—42no—
233C2×C4×C37—42no—
234C2×C4×C37—44no—
235C2×C4×C37—41no—
236C2×C4×C37—41no—
237C2×C4×C37—42no—
238C2×C4×C37—42no—
239C2×C4×C37—42no—
240C2×C4×C37—82no—
241C2×C4×C37—82no—
242C2×C4×C37#12011yescharacteristic
243C2×C4×C37#12011yescharacteristic
244C2×C4×C37#12012yes—
245C2×C4×C37AGL(1,ℤ/8)12yes—
246C2×C4×C37C22×D412yes—
247C8×C37—44no—
248#18366C3711yesmaximal, characteristic, direct product factor, Sylow
249C22×C37—21no—
250C22×C37—21no—
251C22×C37—42no—
252C22×C37—41no—
253C22×C37—42no—
254C22×C37—42no—
255C22×C37—41no—
256C22×C37—42no—
257C22×C37—41no—
258C22×C37—81no—
259C22×C37—82no—
260C22×C37—82no—
261C22×C37—82no—
262C22×C37—82no—
263C22×C37—82no—
264C22×C37—82no—
265C22×C37—82no—
266C22×C37C2×#12011yescharacteristic
267C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C37#57511yescharacteristic
269C4×C37—22no—
270C4×C37—21no—
271C4×C37—21no—
272C4×C37—22no—
273C4×C37—22no—
274C4×C37—42no—
275C4×C37—41no—
276C4×C37—42no—
277C4×C37—41no—
278C4×C37—42no—
279C4×C37—82no—
280#3493C2×C3711yescharacteristic, complemented
281#3217C2×C3712yescomplemented
282#2619C2×C3711yescharacteristic, complemented
283#1600C2×C3714yescomplemented
284#1599C2×C3712yescomplemented
285#1598C2×C3712yescomplemented
286#1512C2×C3712yescomplemented
287#1464C2×C3711yescharacteristic, complemented
288C2×C37—21no—
289C2×C37—21no—
290C2×C37—82no—
291C2×C37—81no—
292C2×C37—162no—
293C2×C37#300611yescharacteristic
294C2×C37#302111yescharacteristic
295C2×C37#302711yescharacteristic
296#556—22no—
297#555—22no—
298#553—22no—
299#552—22no—
300#544C22×C3711yescharacteristic
301#538—21no—
302#538C22×C3712yes—
303#537C22×C3711yescharacteristic
304C2×#127C22×C3711yescharacteristic
305#529—21no—
306#529C22×C3712yes—
307#525—21no—
308C2×#121—21no—
309#520—21no—
310C2×#117C22×C3711yescharacteristic
311#496—22no—
312#490—22no—
313#460—22no—
314#459—22no—
315#450C22×C3714yes—
316#447C22×C3714yes—
317#432C22×C3712yes—
318#394—21no—
319#394C22×C3712yes—
320#392—21no—
321#392C22×C3712yes—
322#390—21no—
323#382C22×C3711yescharacteristic
324#328C22×C3714yes—
325#327C22×C3714yes—
326#324C22×C3712yes—
327#323C22×C3712yes—
328C37#1836611yescharacteristic, direct product factor, Sylow
329C2×#41—21no—
330C22×D4—22no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4C23×C3712yes—
334C23×C4D4×C3711yescharacteristic
335C2×SD16—24no—
336C2×D8—24no—
337C4⋊Q8—22no—
338#127—22no—
339#127—22no—
340#126—22no—
341#126—22no—
342#126—22no—
343#126—22no—
344#125—21no—
345#125—22no—
346#125D4×C3712yescomplemented
347#124—21no—
348#124—22no—
349#124—22no—
350#124D4×C3712yescomplemented
351#123—22no—
352#123—22no—
353#123—22no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—22no—
358C22⋊Q8C23×C3712yes—
359#121—21no—
360#121—21no—
361#121—22no—
362#121—22no—
363#121—22no—
364#121—21no—
365#121—44no—
366#121C23×C3712yes—
367#120—22no—
368C4×Q8—22no—
369C4×Q8—21no—
370C4×Q8D4×C3712yescomplemented
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4D4×C3712yescomplemented
378#117—22no—
379#117—22no—
380#117—21no—
381#117—22no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C3711yescharacteristic
387C2×C4⋊C4C23×C3711yescharacteristic
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4D4×C3711yescharacteristic
392C2×C22⋊C4C23×C3711yescharacteristic
393C2×C42D4×C3711yescharacteristic
394C2×C42C23×C3711yescharacteristic
395C4⋊C8—22no—
396#102—24no—
397#102—24no—
398C22⋊C8C23×C3714yes—
399#97—22no—
400#95—21no—
401#95C23×C3712yes—
402C24—22no—
403C24C2×D4×C3711yescharacteristic
404#41—42no—
405#41—42no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×D4×C3712yes—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—24no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—42no—
421C2×D4—82no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4C2×D4×C3712yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4C2×D4×C3711yescharacteristic
435C22×C4C2×D4×C3711yescharacteristic
436C22×C4C2×D4×C3711yescharacteristic
437C22×C4C2×D4×C3711yescharacteristic
438C22×C4C2×D4×C3711yescharacteristic
439C22×C4C24×C3711yescharacteristic
440SD16—84no—
441D8—84no—
442C2×C8—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4C2×D4×C3712yes—
457C4⋊C4C2×D4×C3712yes—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—44no—
470C22⋊C4—82no—
471C22⋊C4—82no—
472C42—22no—
473C42—22no—
474C42—21no—
475C42—21no—
476C42—22no—
477C42C2×D4×C3712yes—
478C42C2×D4×C3712yes—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—21no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C22×D4×C3711yescharacteristic
493Q8—42no—
494Q8—42no—
495Q8—81no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—44no—
500D4—42no—
501D4—42no—
502D4—82no—
503D4—82no—
504D4—84no—
505D4—82no—
506D4—81no—
507D4—82no—
508D4—88no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4#120×C3711yescharacteristic
531C2×C4#120×C3711yescharacteristic
532C2×C4#120×C3712yes—
533C2×C4AGL(1,ℤ/8)×C3712yes—
534C2×C4C22×D4×C3712yes—
535C8—44no—
536C22—21no—
537C22—21no—
538C22—42no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—41no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22C2×#120×C3711yescharacteristic
554C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
555C22C37×#57511yescharacteristic
556C4—22no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—22no—
561C4—42no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—82no—
567C2—21no—
568C2—21no—
569C2—81no—
570C2—82no—
571C2—162no—
572C2C37×#300611yescharacteristic
573C2C37×#302111yescharacteristic
574C2C37×#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×#3493C2semidirect
2. C37×#3217C2semidirect
3. C37×#2619C2semidirect
4. C37×#1600C2semidirect
5. C37×#1599C2semidirect
6. C37×#1598C2semidirect
7. C37×#1512C2semidirect
8. C37×#1464C2semidirect
58. #125×C37D4semidirect
62. #124×C37D4semidirect
82. C4×Q8×C37D4semidirect
89. C4×D4×C37D4semidirect
248. #18366C37direct (N × H)
280. #3493C2×C37semidirect
281. #3217C2×C37semidirect
282. #2619C2×C37semidirect
283. #1600C2×C37semidirect
284. #1599C2×C37semidirect
285. #1598C2×C37semidirect
286. #1512C2×C37semidirect
287. #1464C2×C37semidirect
328. C37#18366direct (N × H)
346. #125D4×C37semidirect
350. #124D4×C37semidirect
370. C4×Q8D4×C37semidirect
377. C4×D4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34932
C37×#32172
C37×#26192
C37×#16002
C37×#15992
C37×#15982
C37×#15122
C37×#14642
#1836637