Finite Group Databasebeta

← C37×#19079 #22640332

Subgroups — C37×#19079 #22640332

Order 9472.

906 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3545C211yesmaximal, characteristic
2C37×#3181C212yesmaximal, complemented
3C37×#3140C211yesmaximal, characteristic, complemented
4C37×#1664C212yesmaximal, complemented
5C37×#1662C212yesmaximal, complemented
6C37×#1661C212yesmaximal, complemented
7C37×#1659C212yesmaximal, complemented
8C37×#1524C212yesmaximal, complemented
9C2×C37×#329C211yesmaximal, characteristic, complemented
10C37×#563C2211yescharacteristic
11C37×#562C2212yes—
12C37×H(3,𝔽4)C2211yescharacteristic
13C37×#555—21no—
14C37×#551—21no—
15C37×#551—22no—
16C37×#546—22no—
17C37×#542—22no—
18C37×#538—22no—
19C37×#536—21no—
20C37×#534—21no—
21C37×#533C2211yescharacteristic, complemented
22C37×#529C2212yes—
23C2×#124×C37C2211yescharacteristic
24C37×#501C2212yescomplemented
25C37×#497C2212yescomplemented
26C37×#491C2212yescomplemented
27C37×#489C2212yes—
28C37×#489C2212yescomplemented
29C37×#489C2212yescomplemented
30C37×#488—21no—
31C37×#488—21no—
32C37×#467—22no—
33C37×#465—22no—
34C37×#441—22no—
35C37×#440—22no—
36C37×#419—21no—
37C37×#418—21no—
38C4×M16×C37C2211yescharacteristic, complemented
39C2×#97×C37C2212yescomplemented
40C37×#330C2212yescomplemented
41C37×#330C2212yescomplemented
42C37×#329C2212yes—
43C37×#329C2212yescomplemented
44C37×#329C2212yescomplemented
45C37×#329C2211yescharacteristic, complemented
46C37×#329C2211yescharacteristic, complemented
47C2×#41×C37—21no—
48C22×Q8×C37D411yescharacteristic
49C22×D4×C37—21no—
50C22×D4×C37D411yescharacteristic
51C2×Q16×C37—22no—
52C2×SD16×C37—22no—
53C2×M16×C37—21no—
54C22×C8×C37—22no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37C2312yes—
58#126×C37—22no—
59#126×C37—22no—
60#126×C37—22no—
61#125×C37—21no—
62#125×C37C2312yes—
63#124×C37—21no—
64#124×C37—22no—
65#124×C37—21no—
66#124×C37—22no—
67#124×C37—22no—
68#124×C37D411yescharacteristic
69#124×C37D411yescharacteristic
70#124×C37C2311yescharacteristic
71#124×C37C2311yescharacteristic
72#124×C37C2312yes—
73#123×C37—21no—
74#123×C37—22no—
75#123×C37—22no—
76#123×C37—21no—
77#123×C37—22no—
78#123×C37—22no—
79#123×C37—22no—
80C22⋊Q8×C37—22no—
81C22⋊Q8×C37—22no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—22no—
85C22⋊Q8×C37D412yes—
86#121×C37—22no—
87#121×C37—22no—
88#121×C37—22no—
89#121×C37—22no—
90#121×C37D412yes—
91#120×C37—21no—
92#120×C37—22no—
93#120×C37—21no—
94#120×C37—22no—
95C4×Q8×C37—22no—
96C4×Q8×C37D412yes—
97C4×D4×C37—22no—
98C4×D4×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37D412yes—
101#117×C37—21no—
102#117×C37—22no—
103#117×C37—22no—
104#117×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—22no—
107C2×C22⋊C4×C37—22no—
108C2×C42×C37C2311yescharacteristic
109#107×C37—22no—
110#106×C37—22no—
111#103×C37—22no—
112#103×C37—22no—
113#103×C37—22no—
114#103×C37—22no—
115#103×C37—22no—
116#102×C37—22no—
117#102×C37—22no—
118#102×C37—22no—
119#97×C37—22no—
120#97×C37C2312yes—
121#97×C37C2312yes—
122#97×C37C2312yes—
123C4×C8×C37—21no—
124C24×C37—21no—
125C24×C37—21no—
126#41×C37—82no—
127C2×Q8×C37—21no—
128C2×Q8×C37—21no—
129C2×Q8×C37—22no—
130C2×Q8×C37—42no—
131C2×Q8×C37C2×D411yescharacteristic
132C2×Q8×C37C2×D411yescharacteristic
133C2×Q8×C37C2×D412yes—
134C2×D4×C37—22no—
135C2×D4×C37—22no—
136C2×D4×C37—22no—
137C2×D4×C37—21no—
138C2×D4×C37—22no—
139C2×D4×C37—21no—
140C2×D4×C37—42no—
141C2×D4×C37—82no—
142C2×D4×C37C2×D411yescharacteristic
143C2×D4×C37C2×D411yescharacteristic
144C2×D4×C37C2×D412yes—
145C22×C4×C37—21no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—21no—
149C22×C4×C37—22no—
150C22×C4×C37C2×D411yescharacteristic
151C22×C4×C37C2×D412yes—
152Q16×C37—44no—
153SD16×C37—44no—
154M16×C37—42no—
155C2×C8×C37—22no—
156C2×C8×C37—22no—
157C2×C8×C37—22no—
158C2×C8×C37—44no—
159C4⋊C4×C37—22no—
160C4⋊C4×C37—22no—
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—22no—
168C4⋊C4×C37—42no—
169C4⋊C4×C37C2×D412yes—
170C4⋊C4×C37C2×D412yes—
171C22⋊C4×C37—22no—
172C22⋊C4×C37—21no—
173C22⋊C4×C37—21no—
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—22no—
182C22⋊C4×C37—22no—
183C22⋊C4×C37—22no—
184C22⋊C4×C37—22no—
185C22⋊C4×C37—22no—
186C22⋊C4×C37—41no—
187C42×C37—21no—
188C42×C37—21no—
189C42×C37—22no—
190C42×C37—41no—
191C42×C37C2×D411yescharacteristic
192C42×C37C2×D412yes—
193C42×C37C2411yescharacteristic
194C23×C37—21no—
195C23×C37—22no—
196C23×C37—21no—
197C23×C37—42no—
198C23×C37—82no—
199C23×C37—81no—
200C23×C37—82no—
201C23×C37#12011yescharacteristic
202Q8×C37—42no—
203Q8×C37—41no—
204Q8×C37—41no—
205Q8×C37—42no—
206Q8×C37—42no—
207Q8×C37—81no—
208Q8×C37—81no—
209D4×C37—42no—
210D4×C37—41no—
211D4×C37—41no—
212D4×C37—44no—
213D4×C37—81no—
214D4×C37—82no—
215D4×C37—82no—
216D4×C37—82no—
217D4×C37—81no—
218C2×C4×C37—22no—
219C2×C4×C37—22no—
220C2×C4×C37—21no—
221C2×C4×C37—22no—
222C2×C4×C37—22no—
223C2×C4×C37—21no—
224C2×C4×C37—42no—
225C2×C4×C37—42no—
226C2×C4×C37—42no—
227C2×C4×C37—82no—
228C2×C4×C37—82no—
229C2×C4×C37—81no—
230C2×C4×C37—82no—
231C2×C4×C37#12012yes—
232C2×C4×C37#12011yescharacteristic
233C2×C4×C37C22×D412yes—
234C2×C4×C37C22×D411yescharacteristic
235C8×C37—24no—
236C8×C37—42no—
237C8×C37—42no—
238#19079C3711yesmaximal, characteristic, direct product factor, Sylow
239C22×C37—22no—
240C22×C37—42no—
241C22×C37—41no—
242C22×C37—41no—
243C22×C37—42no—
244C22×C37—42no—
245C22×C37—42no—
246C22×C37—42no—
247C22×C37—162no—
248C22×C37—162no—
249C22×C37#45512yes—
250C22×C37C2×#12011yescharacteristic
251C4×C37—21no—
252C4×C37—21no—
253C4×C37—22no—
254C4×C37—22no—
255C4×C37—41no—
256C4×C37—41no—
257C4×C37—42no—
258C4×C37—42no—
259C4×C37—42no—
260C4×C37—82no—
261#3545C2×C3711yescharacteristic
262#3181C2×C3712yescomplemented
263#3140C2×C3711yescharacteristic, complemented
264#1664C2×C3712yescomplemented
265#1662C2×C3712yescomplemented
266#1661C2×C3712yescomplemented
267#1659C2×C3712yescomplemented
268#1524C2×C3712yescomplemented
269C2×#329C2×C3711yescharacteristic, complemented
270C2×C37—22no—
271C2×C37—82no—
272C2×C37—81no—
273C2×C37—81no—
274C2×C37C2×#45511yescharacteristic
275C2×C37#301812yes—
276#563C22×C3711yescharacteristic
277#562C22×C3712yes—
278H(3,𝔽4)C22×C3711yescharacteristic
279#555—21no—
280#551—21no—
281#551—22no—
282#546—22no—
283#542—22no—
284#538—22no—
285#536—21no—
286#534—21no—
287#533C22×C3711yescharacteristic, complemented
288#529C22×C3712yes—
289C2×#124C22×C3711yescharacteristic
290#501C22×C3712yescomplemented
291#497C22×C3712yescomplemented
292#491C22×C3712yescomplemented
293#489C22×C3712yes—
294#489C22×C3712yescomplemented
295#489C22×C3712yescomplemented
296#488—21no—
297#488—21no—
298#467—22no—
299#465—22no—
300#441—22no—
301#440—22no—
302#419—21no—
303#418—21no—
304C4×M16C22×C3711yescharacteristic, complemented
305C2×#97C22×C3712yescomplemented
306#330C22×C3712yescomplemented
307#330C22×C3712yescomplemented
308#329C22×C3712yes—
309#329C22×C3712yescomplemented
310#329C22×C3712yescomplemented
311#329C22×C3711yescharacteristic, complemented
312#329C22×C3711yescharacteristic, complemented
313C37#1907911yescharacteristic, direct product factor, Sylow
314C2×#41—21no—
315C22×Q8D4×C3711yescharacteristic
316C22×D4—21no—
317C22×D4D4×C3711yescharacteristic
318C2×Q16—22no—
319C2×SD16—22no—
320C2×M16—21no—
321C22×C8—22no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8C23×C3712yes—
325#126—22no—
326#126—22no—
327#126—22no—
328#125—21no—
329#125C23×C3712yes—
330#124—21no—
331#124—22no—
332#124—21no—
333#124—22no—
334#124—22no—
335#124D4×C3711yescharacteristic
336#124D4×C3711yescharacteristic
337#124C23×C3711yescharacteristic
338#124C23×C3711yescharacteristic
339#124C23×C3712yes—
340#123—21no—
341#123—22no—
342#123—22no—
343#123—21no—
344#123—22no—
345#123—22no—
346#123—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8D4×C3712yes—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121D4×C3712yes—
358#120—21no—
359#120—22no—
360#120—21no—
361#120—22no—
362C4×Q8—22no—
363C4×Q8D4×C3712yes—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4D4×C3712yes—
368#117—21no—
369#117—22no—
370#117—22no—
371#117—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C42C23×C3711yescharacteristic
376#107—22no—
377#106—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#97—22no—
387#97C23×C3712yes—
388#97C23×C3712yes—
389#97C23×C3712yes—
390C4×C8—21no—
391C24—21no—
392C24—21no—
393#41—82no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—42no—
398C2×Q8C2×D4×C3711yescharacteristic
399C2×Q8C2×D4×C3711yescharacteristic
400C2×Q8C2×D4×C3712yes—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—82no—
409C2×D4C2×D4×C3711yescharacteristic
410C2×D4C2×D4×C3711yescharacteristic
411C2×D4C2×D4×C3712yes—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4C2×D4×C3711yescharacteristic
418C22×C4C2×D4×C3712yes—
419Q16—44no—
420SD16—44no—
421M16—42no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—44no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4C2×D4×C3712yes—
437C4⋊C4C2×D4×C3712yes—
438C22⋊C4—22no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—41no—
454C42—21no—
455C42—21no—
456C42—22no—
457C42—41no—
458C42C2×D4×C3711yescharacteristic
459C42C2×D4×C3712yes—
460C42C24×C3711yescharacteristic
461C23—21no—
462C23—22no—
463C23—21no—
464C23—42no—
465C23—82no—
466C23—81no—
467C23—82no—
468C23#120×C3711yescharacteristic
469Q8—42no—
470Q8—41no—
471Q8—41no—
472Q8—42no—
473Q8—42no—
474Q8—81no—
475Q8—81no—
476D4—42no—
477D4—41no—
478D4—41no—
479D4—44no—
480D4—81no—
481D4—82no—
482D4—81no—
483D4—82no—
484D4—82no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—82no—
495C2×C4—81no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4#120×C3712yes—
499C2×C4#120×C3711yescharacteristic
500C2×C4C22×D4×C3712yes—
501C2×C4C22×D4×C3711yescharacteristic
502C8—24no—
503C8—42no—
504C8—42no—
505C22—22no—
506C22—42no—
507C22—41no—
508C22—41no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—162no—
514C22—162no—
515C22C37×#45512yes—
516C22C2×#120×C3711yescharacteristic
517C4—21no—
518C4—21no—
519C4—22no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—82no—
527C2—22no—
528C2—81no—
529C2—82no—
530C2—81no—
531C2C2×C37×#45511yescharacteristic
532C2C37×#301812yes—
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3545C2
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×#3181C2semidirect
3. C37×#3140C2semidirect
4. C37×#1664C2semidirect
5. C37×#1662C2semidirect
6. C37×#1661C2semidirect
7. C37×#1659C2semidirect
8. C37×#1524C2semidirect
9. C2×C37×#329C2semidirect
21. C37×#533C22semidirect
24. C37×#501C22semidirect
25. C37×#497C22semidirect
26. C37×#491C22semidirect
28. C37×#489C22semidirect
29. C37×#489C22semidirect
38. C4×M16×C37C22semidirect
39. C2×#97×C37C22semidirect
40. C37×#330C22semidirect
41. C37×#330C22semidirect
43. C37×#329C22semidirect
44. C37×#329C22semidirect
45. C37×#329C22semidirect
46. C37×#329C22semidirect
238. #19079C37direct (N × H)
262. #3181C2×C37semidirect
263. #3140C2×C37semidirect
264. #1664C2×C37semidirect
265. #1662C2×C37semidirect
266. #1661C2×C37semidirect
267. #1659C2×C37semidirect
268. #1524C2×C37semidirect
269. C2×#329C2×C37semidirect
287. #533C22×C37semidirect
290. #501C22×C37semidirect
291. #497C22×C37semidirect
292. #491C22×C37semidirect
294. #489C22×C37semidirect
295. #489C22×C37semidirect
304. C4×M16C22×C37semidirect
305. C2×#97C22×C37semidirect
306. #330C22×C37semidirect
307. #330C22×C37semidirect
309. #329C22×C37semidirect
310. #329C22×C37semidirect
311. #329C22×C37semidirect
312. #329C22×C37semidirect
313. C37#19079direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35452
C37×#31812
C37×#31402
C37×#16642
C37×#16622
C37×#16612
C37×#16592
C37×#15242
C2×C37×#3292
#1907937