Finite Group Databasebeta

← C37×#18361 #22639614

Subgroups — C37×#18361 #22639614

Order 9472.

930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3491C211yesmaximal, characteristic
2C37×#3238C212yesmaximal, complemented
3C37×#2621C211yesmaximal, characteristic, complemented
4C37×#1609C214yesmaximal, complemented
5C37×#1608C212yesmaximal, complemented
6C37×#1607C212yesmaximal
7C37×#1512C212yesmaximal, complemented
8C37×#1464C211yesmaximal, characteristic, complemented
9C37×#552—22no—
10C37×#552—22no—
11C37×#551—22no—
12C37×#551—22no—
13C37×#543C2211yescharacteristic
14C37×#539—21no—
15C37×#539C2212yes—
16C37×#534C2211yescharacteristic
17C2×C4⋊Q8×C37C2211yescharacteristic, complemented
18C37×#529—21no—
19C37×#529C2212yes—
20C2×#123×C37—21no—
21C2×C22⋊Q8×C37—21no—
22C37×#518—21no—
23C2×#117×C37C2211yescharacteristic
24C37×#501—22no—
25C37×#489—22no—
26C37×#483C2214yescomplemented
27C37×#480C2214yes—
28C37×#477—22no—
29C37×#476—22no—
30C37×#432C2212yescomplemented
31C37×#398—21no—
32C37×#398C2212yescomplemented
33C37×#397—21no—
34C37×#397C2212yes—
35C37×#391—21no—
36C37×#382C2211yescharacteristic, complemented
37C37×#328C2214yescomplemented
38C37×#327C2214yes—
39C37×#324C2212yescomplemented
40C37×#323C2212yes—
41C22×Q8×C37—21no—
42C22×D4×C37—21no—
43C23×C4×C37D411yescharacteristic
44C4⋊Q8×C37—22no—
45C4⋊Q8×C37—22no—
46#126×C37—22no—
47#126×C37—22no—
48#126×C37—22no—
49#126×C37—22no—
50#125×C37—21no—
51#125×C37—22no—
52#125×C37—22no—
53#125×C37D412yes—
54#124×C37—21no—
55#124×C37D412yes—
56#123×C37—22no—
57#123×C37—22no—
58#123×C37—22no—
59#123×C37—22no—
60#123×C37—22no—
61#123×C37—22no—
62#123×C37—22no—
63C22⋊Q8×C37—22no—
64C22⋊Q8×C37—22no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37—21no—
67C22⋊Q8×C37—22no—
68C22⋊Q8×C37—44no—
69C22⋊Q8×C37C2312yes—
70#121×C37—21no—
71#121×C37C2312yes—
72#120×C37—22no—
73C4×Q8×C37—21no—
74C4×Q8×C37D412yes—
75C4×D4×C37—21no—
76C4×D4×C37—22no—
77C4×D4×C37—22no—
78C4×D4×C37—22no—
79C4×D4×C37—22no—
80C4×D4×C37D412yes—
81#117×C37—22no—
82#117×C37—22no—
83#117×C37—22no—
84#117×C37—22no—
85#117×C37—22no—
86C2×C4⋊C4×C37—21no—
87C2×C4⋊C4×C37—21no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—22no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37D411yescharacteristic
92C2×C4⋊C4×C37C2312yes—
93C2×C4⋊C4×C37C2311yescharacteristic
94C2×C22⋊C4×C37—21no—
95C2×C22⋊C4×C37—21no—
96C2×C22⋊C4×C37—22no—
97C2×C22⋊C4×C37—21no—
98C2×C22⋊C4×C37—22no—
99C2×C22⋊C4×C37D411yescharacteristic
100C2×C22⋊C4×C37C2311yescharacteristic
101C2×C42×C37D411yescharacteristic
102C2×C42×C37C2311yescharacteristic
103#107×C37—24no—
104#106×C37—24no—
105C4⋊C8×C37—22no—
106#103×C37—24no—
107#102×C37—24no—
108C22⋊C8×C37C2314yes—
109#97×C37—22no—
110#95×C37—21no—
111#95×C37—22no—
112#95×C37—22no—
113#95×C37C2312yes—
114C24×C37—21no—
115C24×C37C2×D411yescharacteristic
116C2×Q8×C37—21no—
117C2×Q8×C37—42no—
118C2×Q8×C37—42no—
119C2×Q8×C37—41no—
120C2×Q8×C37—41no—
121C2×Q8×C37C2×D412yes—
122C2×D4×C37—22no—
123C2×D4×C37—22no—
124C2×D4×C37—21no—
125C2×D4×C37—42no—
126C2×D4×C37—42no—
127C2×D4×C37C2×D412yes—
128C22×C4×C37—21no—
129C22×C4×C37—22no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—22no—
133C22×C4×C37—21no—
134C22×C4×C37—21no—
135C22×C4×C37—22no—
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37—41no—
139C22×C4×C37C2×D411yescharacteristic
140C22×C4×C37C2×D411yescharacteristic
141C22×C4×C37C2×D411yescharacteristic
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2411yescharacteristic
145C2×C8×C37—24no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—22no—
149C4⋊C4×C37—22no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—22no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—22no—
156C4⋊C4×C37—22no—
157C4⋊C4×C37—22no—
158C4⋊C4×C37—24no—
159C4⋊C4×C37—42no—
160C4⋊C4×C37—44no—
161C4⋊C4×C37—42no—
162C4⋊C4×C37C2×D412yes—
163C4⋊C4×C37C2×D412yes—
164C22⋊C4×C37—22no—
165C22⋊C4×C37—22no—
166C22⋊C4×C37—22no—
167C22⋊C4×C37—22no—
168C22⋊C4×C37—22no—
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—44no—
177C42×C37—22no—
178C42×C37—21no—
179C42×C37—21no—
180C42×C37—22no—
181C42×C37C2×D412yes—
182C42×C37C2×D412yes—
183C23×C37—21no—
184C23×C37—21no—
185C23×C37—22no—
186C23×C37—41no—
187C23×C37—41no—
188C23×C37—42no—
189C23×C37—81no—
190C23×C37—81no—
191C23×C37AGL(1,ℤ/8)12yes—
192C23×C37C22×D411yescharacteristic
193Q8×C37—42no—
194Q8×C37—82no—
195Q8×C37—82no—
196Q8×C37—81no—
197D4×C37—42no—
198D4×C37—44no—
199D4×C37—42no—
200D4×C37—42no—
201D4×C37—81no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—21no—
205C2×C4×C37—21no—
206C2×C4×C37—22no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—21no—
210C2×C4×C37—21no—
211C2×C4×C37—21no—
212C2×C4×C37—41no—
213C2×C4×C37—41no—
214C2×C4×C37—42no—
215C2×C4×C37—42no—
216C2×C4×C37—42no—
217C2×C4×C37—41no—
218C2×C4×C37—41no—
219C2×C4×C37—42no—
220C2×C4×C37—42no—
221C2×C4×C37—42no—
222C2×C4×C37—42no—
223C2×C4×C37—42no—
224C2×C4×C37—42no—
225C2×C4×C37—82no—
226C2×C4×C37—81no—
227C2×C4×C37—82no—
228C2×C4×C37—81no—
229C2×C4×C37#12012yes—
230C2×C4×C37#12011yescharacteristic
231C2×C4×C37#12011yescharacteristic
232C2×C4×C37C22×D412yes—
233C8×C37—44no—
234#18361C3711yesmaximal, characteristic, direct product factor, Sylow
235C22×C37—21no—
236C22×C37—21no—
237C22×C37—22no—
238C22×C37—42no—
239C22×C37—41no—
240C22×C37—41no—
241C22×C37—42no—
242C22×C37—42no—
243C22×C37—42no—
244C22×C37—81no—
245C22×C37—162no—
246C22×C37C2×#12011yescharacteristic
247C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
248C22×C37#57511yescharacteristic
249C4×C37—21no—
250C4×C37—21no—
251C4×C37—22no—
252C4×C37—22no—
253C4×C37—41no—
254C4×C37—42no—
255C4×C37—41no—
256C4×C37—42no—
257C4×C37—41no—
258C4×C37—42no—
259C4×C37—82no—
260C4×C37—82no—
261#3491C2×C3711yescharacteristic
262#3238C2×C3712yescomplemented
263#2621C2×C3711yescharacteristic, complemented
264#1609C2×C3714yescomplemented
265#1608C2×C3712yescomplemented
266#1607C2×C3712yes—
267#1512C2×C3712yescomplemented
268#1464C2×C3711yescharacteristic, complemented
269C2×C37—21no—
270C2×C37—21no—
271C2×C37—42no—
272C2×C37—82no—
273C2×C37#300611yescharacteristic
274C2×C37#302211yescharacteristic
275C2×C37#302811yescharacteristic
276#552—22no—
277#552—22no—
278#551—22no—
279#551—22no—
280#543C22×C3711yescharacteristic
281#539—21no—
282#539C22×C3712yes—
283#534C22×C3711yescharacteristic
284C2×C4⋊Q8C22×C3711yescharacteristic, complemented
285#529—21no—
286#529C22×C3712yes—
287C2×#123—21no—
288C2×C22⋊Q8—21no—
289#518—21no—
290C2×#117C22×C3711yescharacteristic
291#501—22no—
292#489—22no—
293#483C22×C3714yescomplemented
294#480C22×C3714yes—
295#477—22no—
296#476—22no—
297#432C22×C3712yescomplemented
298#398—21no—
299#398C22×C3712yescomplemented
300#397—21no—
301#397C22×C3712yes—
302#391—21no—
303#382C22×C3711yescharacteristic, complemented
304#328C22×C3714yescomplemented
305#327C22×C3714yes—
306#324C22×C3712yescomplemented
307#323C22×C3712yes—
308C37#1836111yescharacteristic, direct product factor, Sylow
309C22×Q8—21no—
310C22×D4—21no—
311C23×C4D4×C3711yescharacteristic
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314#126—22no—
315#126—22no—
316#126—22no—
317#126—22no—
318#125—21no—
319#125—22no—
320#125—22no—
321#125D4×C3712yes—
322#124—21no—
323#124D4×C3712yes—
324#123—22no—
325#123—22no—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—21no—
335C22⋊Q8—22no—
336C22⋊Q8—44no—
337C22⋊Q8C23×C3712yes—
338#121—21no—
339#121C23×C3712yes—
340#120—22no—
341C4×Q8—21no—
342C4×Q8D4×C3712yes—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—21no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4D4×C3712yes—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4D4×C3711yescharacteristic
360C2×C4⋊C4C23×C3712yes—
361C2×C4⋊C4C23×C3711yescharacteristic
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4D4×C3711yescharacteristic
368C2×C22⋊C4C23×C3711yescharacteristic
369C2×C42D4×C3711yescharacteristic
370C2×C42C23×C3711yescharacteristic
371#107—24no—
372#106—24no—
373C4⋊C8—22no—
374#103—24no—
375#102—24no—
376C22⋊C8C23×C3714yes—
377#97—22no—
378#95—21no—
379#95—22no—
380#95—22no—
381#95C23×C3712yes—
382C24—21no—
383C24C2×D4×C3711yescharacteristic
384C2×Q8—21no—
385C2×Q8—42no—
386C2×Q8—42no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8C2×D4×C3712yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4C2×D4×C3712yes—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—41no—
407C22×C4C2×D4×C3711yescharacteristic
408C22×C4C2×D4×C3711yescharacteristic
409C22×C4C2×D4×C3711yescharacteristic
410C22×C4C2×D4×C3711yescharacteristic
411C22×C4C2×D4×C3711yescharacteristic
412C22×C4C24×C3711yescharacteristic
413C2×C8—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—42no—
428C4⋊C4—44no—
429C4⋊C4—42no—
430C4⋊C4C2×D4×C3712yes—
431C4⋊C4C2×D4×C3712yes—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—44no—
445C42—22no—
446C42—21no—
447C42—21no—
448C42—22no—
449C42C2×D4×C3712yes—
450C42C2×D4×C3712yes—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—81no—
458C23—81no—
459C23AGL(1,ℤ/8)×C3712yes—
460C23C22×D4×C3711yescharacteristic
461Q8—42no—
462Q8—82no—
463Q8—82no—
464Q8—81no—
465D4—42no—
466D4—44no—
467D4—42no—
468D4—42no—
469D4—81no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4#120×C3712yes—
498C2×C4#120×C3711yescharacteristic
499C2×C4#120×C3711yescharacteristic
500C2×C4C22×D4×C3712yes—
501C8—44no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—162no—
513C22C2×#120×C3711yescharacteristic
514C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
515C22C37×#57511yescharacteristic
516C4—21no—
517C4—21no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—82no—
527C4—82no—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—82no—
532C2C37×#300611yescharacteristic
533C2C37×#302211yescharacteristic
534C2C37×#302811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#534C22
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
2. C37×#3238C2semidirect
3. C37×#2621C2semidirect
4. C37×#1609C2semidirect
5. C37×#1608C2semidirect
7. C37×#1512C2semidirect
8. C37×#1464C2semidirect
17. C2×C4⋊Q8×C37C22semidirect
26. C37×#483C22semidirect
30. C37×#432C22semidirect
32. C37×#398C22semidirect
36. C37×#382C22semidirect
37. C37×#328C22semidirect
39. C37×#324C22semidirect
234. #18361C37direct (N × H)
262. #3238C2×C37semidirect
263. #2621C2×C37semidirect
264. #1609C2×C37semidirect
265. #1608C2×C37semidirect
267. #1512C2×C37semidirect
268. #1464C2×C37semidirect
284. C2×C4⋊Q8C22×C37semidirect
293. #483C22×C37semidirect
297. #432C22×C37semidirect
299. #398C22×C37semidirect
303. #382C22×C37semidirect
304. #328C22×C37semidirect
306. #324C22×C37semidirect
308. C37#18361direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34912
C37×#32382
C37×#26212
C37×#16092
C37×#16082
C37×#16072
C37×#15122
C37×#14642
#1836137