Finite Group Databasebeta

← C37×#18141 #22639394

Subgroups — C37×#18141 #22639394

Order 9472.

1004 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3459C211yesmaximal, characteristic
2C37×#3092C212yesmaximal, complemented
3C37×#2487C211yesmaximal, characteristic, complemented
4C37×#1615C214yesmaximal, complemented
5C37×#1614C212yesmaximal, complemented
6C37×#1613C212yesmaximal, complemented
7C37×#1513C212yesmaximal, complemented
8C37×#1465C211yesmaximal, characteristic, complemented
9C37×#543C2211yescharacteristic
10C37×#539—22no—
11C37×#539C2212yes—
12C37×#538—22no—
13C37×#538—21no—
14C37×#534—21no—
15C37×#534C2211yescharacteristic
16C37×#529—22no—
17C37×#529—21no—
18C37×#525—22no—
19C37×#525C2212yes—
20C2×C4×D4×C37—21no—
21C2×C4×D4×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic, complemented
23C37×#484C2214yescomplemented
24C37×#483—22no—
25C37×#481C2214yes—
26C37×#480—22no—
27C37×#428—22no—
28C37×#417—22no—
29C37×#407C2212yescomplemented
30C37×#400C2212yescomplemented
31C37×#399C2212yes—
32C37×#389—21no—
33C37×#386—21no—
34C37×#385—21no—
35C37×#380—21no—
36C37×#380C2211yescharacteristic, complemented
37C37×#328C2214yescomplemented
38C37×#327C2214yes—
39C37×#324C2212yescomplemented
40C37×#323C2212yes—
41C2×#41×C37D412yes—
42C22×D4×C37—21no—
43C22×D4×C37D411yescharacteristic
44C23×C4×C37—21no—
45C23×C4×C37—21no—
46C23×C4×C37D411yescharacteristic
47C23×C4×C37C2311yescharacteristic
48C2×M16×C37—22no—
49#126×C37—22no—
50#126×C37—22no—
51#126×C37—22no—
52#125×C37—21no—
53#125×C37—22no—
54#124×C37—22no—
55#124×C37—21no—
56#123×C37—22no—
57#123×C37—22no—
58#123×C37—22no—
59#123×C37—22no—
60#123×C37—22no—
61#123×C37—22no—
62C22⋊Q8×C37—22no—
63C22⋊Q8×C37—22no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37D412yes—
67C22⋊Q8×C37C2312yes—
68#121×C37—22no—
69#121×C37—22no—
70#121×C37—22no—
71#121×C37—21no—
72#121×C37D412yes—
73#121×C37C2312yes—
74#120×C37—22no—
75#120×C37—22no—
76#120×C37—22no—
77C4×Q8×C37—21no—
78C4×D4×C37—21no—
79C4×D4×C37—22no—
80C4×D4×C37—22no—
81C4×D4×C37—22no—
82C4×D4×C37—22no—
83C4×D4×C37—22no—
84C4×D4×C37—22no—
85C4×D4×C37—22no—
86#117×C37—22no—
87#117×C37D412yes—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—22no—
90C2×C4⋊C4×C37—22no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—22no—
94C2×C4⋊C4×C37C2312yes—
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C22⋊C4×C37—21no—
97C2×C22⋊C4×C37—21no—
98C2×C22⋊C4×C37—21no—
99C2×C22⋊C4×C37—22no—
100C2×C22⋊C4×C37D411yescharacteristic
101C2×C22⋊C4×C37C2311yescharacteristic
102C2×C42×C37—21no—
103C2×C42×C37D411yescharacteristic
104#107×C37—24no—
105#106×C37—24no—
106#103×C37—24no—
107#102×C37—24no—
108C22⋊C8×C37—22no—
109C22⋊C8×C37C2314yes—
110#95×C37—22no—
111#95×C37—22no—
112#95×C37C2312yes—
113C24×C37—21no—
114C24×C37C2×D411yescharacteristic
115C24×C37C2×D411yescharacteristic
116#41×C37—44no—
117C2×Q8×C37—21no—
118C2×Q8×C37C2×D412yes—
119C2×D4×C37—22no—
120C2×D4×C37—22no—
121C2×D4×C37—22no—
122C2×D4×C37—22no—
123C2×D4×C37—21no—
124C2×D4×C37—22no—
125C2×D4×C37—22no—
126C2×D4×C37—41no—
127C2×D4×C37—42no—
128C2×D4×C37—42no—
129C2×D4×C37C2×D412yes—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—22no—
134C22×C4×C37—21no—
135C22×C4×C37—22no—
136C22×C4×C37—21no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—42no—
140C22×C4×C37—42no—
141C22×C4×C37—42no—
142C22×C4×C37—82no—
143C22×C4×C37—82no—
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146C22×C4×C37C2×D412yes—
147C22×C4×C37C2×D411yescharacteristic
148C22×C4×C37C2×D411yescharacteristic
149C22×C4×C37C2×D412yes—
150C22×C4×C37C2411yescharacteristic
151M16×C37—44no—
152C2×C8×C37—24no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—22no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—22no—
159C4⋊C4×C37—22no—
160C4⋊C4×C37—22no—
161C4⋊C4×C37—22no—
162C4⋊C4×C37—24no—
163C4⋊C4×C37—42no—
164C4⋊C4×C37—41no—
165C4⋊C4×C37—41no—
166C4⋊C4×C37—82no—
167C4⋊C4×C37C2×D412yes—
168C4⋊C4×C37C2×D412yes—
169C22⋊C4×C37—22no—
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—42no—
182C22⋊C4×C37—82no—
183C42×C37—22no—
184C42×C37—22no—
185C42×C37—21no—
186C42×C37—21no—
187C23×C37—21no—
188C23×C37—21no—
189C23×C37—21no—
190C23×C37—21no—
191C23×C37—22no—
192C23×C37—41no—
193C23×C37—41no—
194C23×C37—41no—
195C23×C37—41no—
196C23×C37—42no—
197C23×C37—81no—
198C23×C37—81no—
199C23×C37#12012yes—
200C23×C37#13712yes—
201C23×C37C22×D411yescharacteristic
202Q8×C37—42no—
203Q8×C37—81no—
204D4×C37—42no—
205D4×C37—44no—
206D4×C37—44no—
207D4×C37—42no—
208D4×C37—42no—
209D4×C37—82no—
210D4×C37—82no—
211D4×C37—81no—
212C2×C4×C37—22no—
213C2×C4×C37—24no—
214C2×C4×C37—21no—
215C2×C4×C37—22no—
216C2×C4×C37—21no—
217C2×C4×C37—22no—
218C2×C4×C37—21no—
219C2×C4×C37—22no—
220C2×C4×C37—21no—
221C2×C4×C37—21no—
222C2×C4×C37—42no—
223C2×C4×C37—41no—
224C2×C4×C37—42no—
225C2×C4×C37—42no—
226C2×C4×C37—44no—
227C2×C4×C37—41no—
228C2×C4×C37—41no—
229C2×C4×C37—42no—
230C2×C4×C37—42no—
231C2×C4×C37—42no—
232C2×C4×C37—42no—
233C2×C4×C37—42no—
234C2×C4×C37—42no—
235C2×C4×C37—81no—
236C2×C4×C37—81no—
237C2×C4×C37—82no—
238C2×C4×C37—81no—
239C2×C4×C37—84no—
240C2×C4×C37#12011yescharacteristic
241C2×C4×C37#12011yescharacteristic
242C2×C4×C37C22×D412yes—
243C8×C37—44no—
244#18141C3711yesmaximal, characteristic, direct product factor, Sylow
245C22×C37—21no—
246C22×C37—21no—
247C22×C37—22no—
248C22×C37—22no—
249C22×C37—22no—
250C22×C37—22no—
251C22×C37—42no—
252C22×C37—42no—
253C22×C37—42no—
254C22×C37—41no—
255C22×C37—41no—
256C22×C37—42no—
257C22×C37—42no—
258C22×C37—42no—
259C22×C37—81no—
260C22×C37—84no—
261C22×C37C2×#12011yescharacteristic
262C22×C37C2×#13711yescharacteristic
263C22×C37#57511yescharacteristic
264C4×C37—22no—
265C4×C37—21no—
266C4×C37—41no—
267C4×C37—42no—
268C4×C37—41no—
269C4×C37—42no—
270C4×C37—41no—
271C4×C37—42no—
272C4×C37—82no—
273C4×C37—82no—
274C4×C37#45812yes—
275#3459C2×C3711yescharacteristic
276#3092C2×C3712yescomplemented
277#2487C2×C3711yescharacteristic, complemented
278#1615C2×C3714yescomplemented
279#1614C2×C3712yescomplemented
280#1613C2×C3712yescomplemented
281#1513C2×C3712yescomplemented
282#1465C2×C3711yescharacteristic, complemented
283C2×C37—21no—
284C2×C37—21no—
285C2×C37—42no—
286C2×C37—42no—
287C2×C37—82no—
288C2×C37#300711yescharacteristic
289C2×C37#302111yescharacteristic
290C2×C37C2×#45811yescharacteristic
291#543C22×C3711yescharacteristic
292#539—22no—
293#539C22×C3712yes—
294#538—22no—
295#538—21no—
296#534—21no—
297#534C22×C3711yescharacteristic
298#529—22no—
299#529—21no—
300#525—22no—
301#525C22×C3712yes—
302C2×C4×D4—21no—
303C2×C4×D4C22×C3711yescharacteristic
304C22×C4⋊C4C22×C3711yescharacteristic, complemented
305#484C22×C3714yescomplemented
306#483—22no—
307#481C22×C3714yes—
308#480—22no—
309#428—22no—
310#417—22no—
311#407C22×C3712yescomplemented
312#400C22×C3712yescomplemented
313#399C22×C3712yes—
314#389—21no—
315#386—21no—
316#385—21no—
317#380—21no—
318#380C22×C3711yescharacteristic, complemented
319#328C22×C3714yescomplemented
320#327C22×C3714yes—
321#324C22×C3712yescomplemented
322#323C22×C3712yes—
323C37#1814111yescharacteristic, direct product factor, Sylow
324C2×#41D4×C3712yes—
325C22×D4—21no—
326C22×D4D4×C3711yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4D4×C3711yescharacteristic
330C23×C4C23×C3711yescharacteristic
331C2×M16—22no—
332#126—22no—
333#126—22no—
334#126—22no—
335#125—21no—
336#125—22no—
337#124—22no—
338#124—21no—
339#123—22no—
340#123—22no—
341#123—22no—
342#123—22no—
343#123—22no—
344#123—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8D4×C3712yes—
350C22⋊Q8C23×C3712yes—
351#121—22no—
352#121—22no—
353#121—22no—
354#121—21no—
355#121D4×C3712yes—
356#121C23×C3712yes—
357#120—22no—
358#120—22no—
359#120—22no—
360C4×Q8—21no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369#117—22no—
370#117D4×C3712yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4C23×C3712yes—
378C2×C4⋊C4C23×C3711yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4D4×C3711yescharacteristic
384C2×C22⋊C4C23×C3711yescharacteristic
385C2×C42—21no—
386C2×C42D4×C3711yescharacteristic
387#107—24no—
388#106—24no—
389#103—24no—
390#102—24no—
391C22⋊C8—22no—
392C22⋊C8C23×C3714yes—
393#95—22no—
394#95—22no—
395#95C23×C3712yes—
396C24—21no—
397C24C2×D4×C3711yescharacteristic
398C24C2×D4×C3711yescharacteristic
399#41—44no—
400C2×Q8—21no—
401C2×Q8C2×D4×C3712yes—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—41no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4C2×D4×C3712yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—82no—
426C22×C4—82no—
427C22×C4C2×D4×C3711yescharacteristic
428C22×C4C2×D4×C3711yescharacteristic
429C22×C4C2×D4×C3712yes—
430C22×C4C2×D4×C3711yescharacteristic
431C22×C4C2×D4×C3711yescharacteristic
432C22×C4C2×D4×C3712yes—
433C22×C4C24×C3711yescharacteristic
434M16—44no—
435C2×C8—24no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—42no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—82no—
450C4⋊C4C2×D4×C3712yes—
451C4⋊C4C2×D4×C3712yes—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—42no—
465C22⋊C4—82no—
466C42—22no—
467C42—22no—
468C42—21no—
469C42—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—81no—
481C23—81no—
482C23#120×C3712yes—
483C23#137×C3712yes—
484C23C22×D4×C3711yescharacteristic
485Q8—42no—
486Q8—81no—
487D4—42no—
488D4—44no—
489D4—44no—
490D4—42no—
491D4—42no—
492D4—82no—
493D4—82no—
494D4—81no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—81no—
519C2×C4—82no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4—84no—
523C2×C4#120×C3711yescharacteristic
524C2×C4#120×C3711yescharacteristic
525C2×C4C22×D4×C3712yes—
526C8—44no—
527C22—21no—
528C22—21no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—84no—
543C22C2×#120×C3711yescharacteristic
544C22C2×#137×C3711yescharacteristic
545C22C37×#57511yescharacteristic
546C4—22no—
547C4—21no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—42no—
552C4—41no—
553C4—42no—
554C4—82no—
555C4—82no—
556C4C37×#45812yes—
557C2—21no—
558C2—21no—
559C2—42no—
560C2—42no—
561C2—82no—
562C2C37×#300711yescharacteristic
563C2C37×#302111yescharacteristic
564C2C2×C37×#45811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3459C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3092C2semidirect
3. C37×#2487C2semidirect
4. C37×#1615C2semidirect
5. C37×#1614C2semidirect
6. C37×#1613C2semidirect
7. C37×#1513C2semidirect
8. C37×#1465C2semidirect
22. C22×C4⋊C4×C37C22semidirect
23. C37×#484C22semidirect
29. C37×#407C22semidirect
30. C37×#400C22semidirect
36. C37×#380C22semidirect
37. C37×#328C22semidirect
39. C37×#324C22semidirect
244. #18141C37direct (N × H)
276. #3092C2×C37semidirect
277. #2487C2×C37semidirect
278. #1615C2×C37semidirect
279. #1614C2×C37semidirect
280. #1613C2×C37semidirect
281. #1513C2×C37semidirect
282. #1465C2×C37semidirect
304. C22×C4⋊C4C22×C37semidirect
305. #484C22×C37semidirect
311. #407C22×C37semidirect
312. #400C22×C37semidirect
318. #380C22×C37semidirect
319. #328C22×C37semidirect
321. #324C22×C37semidirect
323. C37#18141direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34592
C37×#30922
C37×#24872
C37×#16152
C37×#16142
C37×#16132
C37×#15132
C37×#14652
#1814137