Finite Group Databasebeta

← C37×#18357 #22639610

Subgroups — C37×#18357 #22639610

Order 9472.

934 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×#3218C212yesmaximal, complemented
3C37×#2628C211yesmaximal, characteristic, complemented
4C37×#1603C214yesmaximal, complemented
5C37×#1602C212yesmaximal, complemented
6C37×#1601C212yesmaximal
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—
21C37×#518—21no—
22C2×#117×C37C2211yescharacteristic
23C37×#497—22no—
24C37×#491—22no—
25C37×#462—22no—
26C37×#461—22no—
27C37×#451C2214yescomplemented
28C37×#448C2214yes—
29C37×#432C2212yescomplemented
30C37×#400—21no—
31C37×#399—21no—
32C37×#395C2212yescomplemented
33C37×#393C2212yes—
34C37×#389—21no—
35C37×#382C2211yescharacteristic, complemented
36C37×#380—21no—
37C37×#328C2214yescomplemented
38C37×#327C2214yes—
39C37×#324C2212yescomplemented
40C37×#323C2212yes—
41C22×Q8×C37C2312yes—
42C22×D4×C37—21no—
43C23×C4×C37D411yescharacteristic
44C2×Q16×C37—24no—
45C2×SD16×C37—24no—
46C4⋊Q8×C37—22no—
47C4⋊Q8×C37—22no—
48#126×C37—22no—
49#126×C37—22no—
50#126×C37—22no—
51#126×C37—22no—
52#125×C37—21no—
53#125×C37—22no—
54#125×C37—22no—
55#125×C37D412yes—
56#124×C37—21no—
57#124×C37D412yes—
58#123×C37—22no—
59#123×C37—22no—
60#123×C37—22no—
61#123×C37—22no—
62#123×C37—22no—
63#123×C37—22no—
64#123×C37—22no—
65C22⋊Q8×C37—22no—
66C22⋊Q8×C37—22no—
67C22⋊Q8×C37—22no—
68C22⋊Q8×C37—21no—
69C22⋊Q8×C37—22no—
70C22⋊Q8×C37C2312yes—
71#121×C37—21no—
72#121×C37C2312yes—
73#120×C37—22no—
74C4×Q8×C37—21no—
75C4×Q8×C37D412yes—
76C4×D4×C37—21no—
77C4×D4×C37—22no—
78C4×D4×C37—22no—
79C4×D4×C37—22no—
80C4×D4×C37—22no—
81C4×D4×C37D412yes—
82#117×C37—22no—
83#117×C37—22no—
84#117×C37—22no—
85#117×C37—22no—
86#117×C37—22no—
87C2×C4⋊C4×C37—21no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—22no—
93C2×C4⋊C4×C37D411yescharacteristic
94C2×C4⋊C4×C37C2311yescharacteristic
95C2×C22⋊C4×C37—21no—
96C2×C22⋊C4×C37—21no—
97C2×C22⋊C4×C37—22no—
98C2×C22⋊C4×C37—21no—
99C2×C22⋊C4×C37—22no—
100C2×C22⋊C4×C37D411yescharacteristic
101C2×C22⋊C4×C37C2311yescharacteristic
102C2×C42×C37D411yescharacteristic
103C2×C42×C37C2311yescharacteristic
104C4⋊C8×C37—22no—
105#103×C37—24no—
106#103×C37—24no—
107C22⋊C8×C37C2314yes—
108#97×C37—22no—
109#95×C37—22no—
110#95×C37—21no—
111#95×C37—22no—
112#95×C37C2312yes—
113C24×C37—21no—
114C24×C37C2×D411yescharacteristic
115C2×Q8×C37—21no—
116C2×Q8×C37—24no—
117C2×Q8×C37—82no—
118C2×Q8×C37C2×D412yes—
119C2×D4×C37—22no—
120C2×D4×C37—22no—
121C2×D4×C37—21no—
122C2×D4×C37—42no—
123C2×D4×C37—42no—
124C2×D4×C37C2×D412yes—
125C22×C4×C37—21no—
126C22×C4×C37—22no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—22no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—41no—
136C22×C4×C37C2×D411yescharacteristic
137C22×C4×C37C2×D411yescharacteristic
138C22×C4×C37C2×D411yescharacteristic
139C22×C4×C37C2×D411yescharacteristic
140C22×C4×C37C2×D411yescharacteristic
141C22×C4×C37C2411yescharacteristic
142Q16×C37—84no—
143SD16×C37—84no—
144C2×C8×C37—24no—
145C4⋊C4×C37—22no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—22no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—22no—
152C4⋊C4×C37—22no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—22no—
155C4⋊C4×C37—22no—
156C4⋊C4×C37—22no—
157C4⋊C4×C37—42no—
158C4⋊C4×C37—41no—
159C4⋊C4×C37—41no—
160C4⋊C4×C37—42no—
161C4⋊C4×C37—82no—
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—82no—
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×C37#13712yes—
192C23×C37C22×D411yescharacteristic
193Q8×C37—42no—
194Q8×C37—44no—
195Q8×C37—44no—
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#12011yescharacteristic
230C2×C4×C37#12011yescharacteristic
231C2×C4×C37#12012yes—
232C2×C4×C37C22×D412yes—
233C8×C37—44no—
234#18357C3711yesmaximal, 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×#13711yescharacteristic
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#3218C2×C3712yescomplemented
263#2628C2×C3711yescharacteristic, complemented
264#1603C2×C3714yescomplemented
265#1602C2×C3712yescomplemented
266#1601C2×C3712yes—
267#1512C2×C3712yescomplemented
268#1464C2×C3711yescharacteristic, complemented
269C2×C37—21no—
270C2×C37—21no—
271C2×C37—42no—
272C2×C37—82no—
273C2×C37#300711yescharacteristic
274C2×C37#302211yescharacteristic
275C2×C37#302711yescharacteristic
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—
288#518—21no—
289C2×#117C22×C3711yescharacteristic
290#497—22no—
291#491—22no—
292#462—22no—
293#461—22no—
294#451C22×C3714yescomplemented
295#448C22×C3714yes—
296#432C22×C3712yescomplemented
297#400—21no—
298#399—21no—
299#395C22×C3712yescomplemented
300#393C22×C3712yes—
301#389—21no—
302#382C22×C3711yescharacteristic, complemented
303#380—21no—
304#328C22×C3714yescomplemented
305#327C22×C3714yes—
306#324C22×C3712yescomplemented
307#323C22×C3712yes—
308C37#1835711yescharacteristic, direct product factor, Sylow
309C22×Q8C23×C3712yes—
310C22×D4—21no—
311C23×C4D4×C3711yescharacteristic
312C2×Q16—24no—
313C2×SD16—24no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316#126—22no—
317#126—22no—
318#126—22no—
319#126—22no—
320#125—21no—
321#125—22no—
322#125—22no—
323#125D4×C3712yes—
324#124—21no—
325#124D4×C3712yes—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—22no—
332#123—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8—22no—
338C22⋊Q8C23×C3712yes—
339#121—21no—
340#121C23×C3712yes—
341#120—22no—
342C4×Q8—21no—
343C4×Q8D4×C3712yes—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—21no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4D4×C3712yes—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C3711yescharacteristic
362C2×C4⋊C4C23×C3711yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4D4×C3711yescharacteristic
369C2×C22⋊C4C23×C3711yescharacteristic
370C2×C42D4×C3711yescharacteristic
371C2×C42C23×C3711yescharacteristic
372C4⋊C8—22no—
373#103—24no—
374#103—24no—
375C22⋊C8C23×C3714yes—
376#97—22no—
377#95—22no—
378#95—21no—
379#95—22no—
380#95C23×C3712yes—
381C24—21no—
382C24C2×D4×C3711yescharacteristic
383C2×Q8—21no—
384C2×Q8—24no—
385C2×Q8—82no—
386C2×Q8C2×D4×C3712yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4C2×D4×C3712yes—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C2×D4×C3711yescharacteristic
406C22×C4C2×D4×C3711yescharacteristic
407C22×C4C2×D4×C3711yescharacteristic
408C22×C4C2×D4×C3711yescharacteristic
409C22×C4C24×C3711yescharacteristic
410Q16—84no—
411SD16—84no—
412C2×C8—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—42no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—42no—
429C4⋊C4—82no—
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—82no—
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—
459C23#137×C3712yes—
460C23C22×D4×C3711yescharacteristic
461Q8—42no—
462Q8—44no—
463Q8—44no—
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×C3711yescharacteristic
498C2×C4#120×C3711yescharacteristic
499C2×C4#120×C3712yes—
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×#137×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×#300711yescharacteristic
533C2C37×#302211yescharacteristic
534C2C37×#302711yescharacteristic
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×#3218C2semidirect
3. C37×#2628C2semidirect
4. C37×#1603C2semidirect
5. C37×#1602C2semidirect
7. C37×#1512C2semidirect
8. C37×#1464C2semidirect
17. C2×C4⋊Q8×C37C22semidirect
27. C37×#451C22semidirect
29. C37×#432C22semidirect
32. C37×#395C22semidirect
35. C37×#382C22semidirect
37. C37×#328C22semidirect
39. C37×#324C22semidirect
234. #18357C37direct (N × H)
262. #3218C2×C37semidirect
263. #2628C2×C37semidirect
264. #1603C2×C37semidirect
265. #1602C2×C37semidirect
267. #1512C2×C37semidirect
268. #1464C2×C37semidirect
284. C2×C4⋊Q8C22×C37semidirect
294. #451C22×C37semidirect
296. #432C22×C37semidirect
299. #395C22×C37semidirect
302. #382C22×C37semidirect
304. #328C22×C37semidirect
306. #324C22×C37semidirect
308. C37#18357direct (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×#32182
C37×#26282
C37×#16032
C37×#16022
C37×#16012
C37×#15122
C37×#14642
#1835737