Finite Group Databasebeta

← C37×#12687 #22633940

Subgroups — C37×#12687 #22633940

Order 9472.

2508 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C37C211yesmaximal, characteristic
2C2×C37×AΣL(1,𝔽16)C214yesmaximal, complemented
3C37×#1783C211yesmaximal, characteristic, complemented
4C37×#1781C211yesmaximal, characteristic, complemented
5C26×C37C411yescharacteristic, complemented
6C23×D4×C37—21no—
7C23×D4×C37C2211yescharacteristic
8C2×#120×C37—21no—
9C2×#120×C37—21no—
10C2×#120×C37—28no—
11C2×#120×C37C412yescomplemented
12C2×#120×C37C2212yes—
13C22×C22⋊C4×C37—21no—
14C22×C22⋊C4×C37C411yescharacteristic, complemented
15C2×#100×C37—21no—
16C2×#100×C37C2212yescomplemented
17C2×#99×C37—21no—
18C2×#99×C37C2212yescomplemented
19C37×#407—21no—
20C37×#379—21no—
21C37×AΣL(1,𝔽16)—28no—
22C25×C37—21no—
23C25×C37—21no—
24C25×C37—24no—
25C25×C37—48no—
26C25×C37—42no—
27C25×C37—42no—
28C25×C37C2×C411yescharacteristic
29C25×C37C2×C412yes—
30C25×C37D411yescharacteristic
31C22×D4×C37—28no—
32C22×D4×C37—22no—
33C22×D4×C37—22no—
34C22×D4×C37—24no—
35C22×D4×C37—42no—
36C22×D4×C37—42no—
37C22×D4×C37—48no—
38C22×D4×C37C2×C411yescharacteristic
39C22×D4×C37D411yescharacteristic
40C22×D4×C37D411yescharacteristic
41C22×D4×C37C2311yescharacteristic
42C23×C4×C37—21no—
43C23×C4×C37D411yescharacteristic
44C2×M16×C37—22no—
45#120×C37—28no—
46#120×C37—28no—
47#120×C37—24no—
48#120×C37—24no—
49#120×C37—24no—
50#120×C37D418yes—
51C2×C22⋊C4×C37—28no—
52C2×C22⋊C4×C37—21no—
53C2×C22⋊C4×C37—22no—
54C2×C22⋊C4×C37—22no—
55C2×C22⋊C4×C37—24no—
56C2×C22⋊C4×C37—22no—
57C2×C22⋊C4×C37—42no—
58C2×C22⋊C4×C37C2×C412yes—
59#100×C37—24no—
60#100×C37—42no—
61#99×C37—24no—
62#99×C37—42no—
63C22⋊C8×C37—42no—
64C24×C37—24no—
65C24×C37—28no—
66C24×C37—22no—
67C24×C37—22no—
68C24×C37—22no—
69C24×C37—22no—
70C24×C37—24no—
71C24×C37—22no—
72C24×C37—22no—
73C24×C37—22no—
74C24×C37—41no—
75C24×C37—44no—
76C24×C37—48no—
77C24×C37—42no—
78C24×C37—42no—
79C24×C37—44no—
80C24×C37—42no—
81C24×C37—48no—
82C24×C37—432no—
83C24×C37—416no—
84C24×C37—42no—
85C24×C37—44no—
86C24×C37—48no—
87C24×C37—416no—
88C24×C37—432no—
89C24×C37—48no—
90C24×C37—42no—
91C24×C37—42no—
92C24×C37C22⋊C411yescharacteristic
93C24×C37C22⋊C411yescharacteristic
94C24×C37C22⋊C411yescharacteristic
95C24×C37C22⋊C414yescomplemented
96C24×C37C22×C411yescharacteristic
97C24×C37C2×D411yescharacteristic
98C2×D4×C37—28no—
99C2×D4×C37—22no—
100C2×D4×C37—22no—
101C2×D4×C37—22no—
102C2×D4×C37—22no—
103C2×D4×C37—28no—
104C2×D4×C37—22no—
105C2×D4×C37—41no—
106C2×D4×C37—41no—
107C2×D4×C37—41no—
108C2×D4×C37—41no—
109C2×D4×C37—41no—
110C2×D4×C37—41no—
111C2×D4×C37—416no—
112C2×D4×C37—48no—
113C2×D4×C37—48no—
114C2×D4×C37—432no—
115C2×D4×C37C2×D414yes—
116C22×C4×C37—24no—
117C22×C4×C37—22no—
118C22×C4×C37—22no—
119C22×C4×C37—22no—
120C22×C4×C37—41no—
121C22×C4×C37—44no—
122C22×C4×C37—42no—
123C22×C4×C37C22⋊C411yescharacteristic
124C22×C4×C37C2×D411yescharacteristic
125M16×C37—42no—
126M16×C37—42no—
127C2×C8×C37—42no—
128C22⋊C4×C37—28no—
129C22⋊C4×C37—24no—
130C22⋊C4×C37—22no—
131C22⋊C4×C37—28no—
132C22⋊C4×C37—42no—
133C22⋊C4×C37—42no—
134C22⋊C4×C37—84no—
135C22⋊C4×C37C22⋊C414yescomplemented
136C23×C37—24no—
137C23×C37—21no—
138C23×C37—21no—
139C23×C37—216no—
140C23×C37—28no—
141C23×C37—28no—
142C23×C37—21no—
143C23×C37—24no—
144C23×C37—21no—
145C23×C37—21no—
146C23×C37—21no—
147C23×C37—21no—
148C23×C37—21no—
149C23×C37—21no—
150C23×C37—21no—
151C23×C37—21no—
152C23×C37—44no—
153C23×C37—42no—
154C23×C37—48no—
155C23×C37—44no—
156C23×C37—42no—
157C23×C37—48no—
158C23×C37—48no—
159C23×C37—48no—
160C23×C37—416no—
161C23×C37—44no—
162C23×C37—48no—
163C23×C37—44no—
164C23×C37—48no—
165C23×C37—48no—
166C23×C37—416no—
167C23×C37—48no—
168C23×C37—44no—
169C23×C37—42no—
170C23×C37—42no—
171C23×C37—48no—
172C23×C37—48no—
173C23×C37—416no—
174C23×C37—416no—
175C23×C37—464no—
176C23×C37—464no—
177C23×C37—48no—
178C23×C37—416no—
179C23×C37—48no—
180C23×C37—44no—
181C23×C37—42no—
182C23×C37—42no—
183C23×C37—44no—
184C23×C37—82no—
185C23×C37—84no—
186C23×C37#9912yes—
187C23×C37#9912yes—
188C23×C37C2×C22⋊C411yescharacteristic
189C23×C37C2×C22⋊C412yes—
190C23×C37#12012yes—
191D4×C37—44no—
192D4×C37—44no—
193D4×C37—44no—
194D4×C37—416no—
195D4×C37—416no—
196D4×C37—44no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—21no—
200C2×C4×C37—24no—
201C2×C4×C37—21no—
202C2×C4×C37—21no—
203C2×C4×C37—44no—
204C2×C4×C37—48no—
205C2×C4×C37—44no—
206C2×C4×C37—82no—
207C2×C4×C37—84no—
208C2×C4×C37#12012yes—
209C8×C37—82no—
210#12687C3711yesmaximal, characteristic, direct product factor, Sylow
211C22×C37—24no—
212C22×C37—24no—
213C22×C37—22no—
214C22×C37—22no—
215C22×C37—22no—
216C22×C37—28no—
217C22×C37—22no—
218C22×C37—22no—
219C22×C37—22no—
220C22×C37—42no—
221C22×C37—42no—
222C22×C37—42no—
223C22×C37—42no—
224C22×C37—44no—
225C22×C37—432no—
226C22×C37—416no—
227C22×C37—48no—
228C22×C37—42no—
229C22×C37—42no—
230C22×C37—48no—
231C22×C37—48no—
232C22×C37—416no—
233C22×C37—432no—
234C22×C37—42no—
235C22×C37—48no—
236C22×C37—42no—
237C22×C37—42no—
238C22×C37—44no—
239C22×C37—42no—
240C22×C37—41no—
241C22×C37—81no—
242C22×C37—88no—
243C22×C37—81no—
244C22×C37AΣL(1,𝔽16)14yescomplemented
245C22×C37#37911yescharacteristic
246C22×C37C2×#9911yescharacteristic
247C22×C37C2×#9911yescharacteristic
248C4×C37—22no—
249C4×C37—44no—
250C4×C37—41no—
251C4×C37—162no—
252C22×#120C2×C3711yescharacteristic
253C2×AΣL(1,𝔽16)C2×C3714yescomplemented
254#1783C2×C3711yescharacteristic, complemented
255#1781C2×C3711yescharacteristic, complemented
256C2×C37—21no—
257C2×C37—24no—
258C2×C37—21no—
259C2×C37—42no—
260C2×C37—48no—
261C2×C37—42no—
262C2×C37—42no—
263C2×C37—81no—
264C2×C37#178111yescharacteristic
265C2×C37C2×AΣL(1,𝔽16)12yes—
266C26C4×C3711yescharacteristic, complemented
267C23×D4—21no—
268C23×D4C22×C3711yescharacteristic
269C2×#120—21no—
270C2×#120—21no—
271C2×#120—28no—
272C2×#120C4×C3712yescomplemented
273C2×#120C22×C3712yes—
274C22×C22⋊C4—21no—
275C22×C22⋊C4C4×C3711yescharacteristic, complemented
276C2×#100—21no—
277C2×#100C22×C3712yescomplemented
278C2×#99—21no—
279C2×#99C22×C3712yescomplemented
280#407—21no—
281#379—21no—
282AΣL(1,𝔽16)—28no—
283C37#1268711yescharacteristic, direct product factor, Sylow
284C25—21no—
285C25—21no—
286C25—24no—
287C25—48no—
288C25—42no—
289C25—42no—
290C25C2×C4×C3711yescharacteristic
291C25C2×C4×C3712yes—
292C25D4×C3711yescharacteristic
293C22×D4—28no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—24no—
297C22×D4—42no—
298C22×D4—42no—
299C22×D4—48no—
300C22×D4C2×C4×C3711yescharacteristic
301C22×D4D4×C3711yescharacteristic
302C22×D4D4×C3711yescharacteristic
303C22×D4C23×C3711yescharacteristic
304C23×C4—21no—
305C23×C4D4×C3711yescharacteristic
306C2×M16—22no—
307#120—28no—
308#120—28no—
309#120—24no—
310#120—24no—
311#120—24no—
312#120D4×C3718yes—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C2×C4×C3712yes—
321#100—24no—
322#100—42no—
323#99—24no—
324#99—42no—
325C22⋊C8—42no—
326C24—24no—
327C24—28no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—41no—
337C24—44no—
338C24—48no—
339C24—42no—
340C24—42no—
341C24—44no—
342C24—42no—
343C24—48no—
344C24—432no—
345C24—416no—
346C24—42no—
347C24—44no—
348C24—48no—
349C24—416no—
350C24—432no—
351C24—48no—
352C24—42no—
353C24—42no—
354C24C22⋊C4×C3711yescharacteristic
355C24C22⋊C4×C3711yescharacteristic
356C24C22⋊C4×C3711yescharacteristic
357C24C22⋊C4×C3714yescomplemented
358C24C22×C4×C3711yescharacteristic
359C24C2×D4×C3711yescharacteristic
360C2×D4—28no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—416no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4—432no—
377C2×D4C2×D4×C3714yes—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4C22⋊C4×C3711yescharacteristic
386C22×C4C2×D4×C3711yescharacteristic
387M16—42no—
388M16—42no—
389C2×C8—42no—
390C22⋊C4—28no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—28no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—84no—
397C22⋊C4C22⋊C4×C3714yescomplemented
398C23—24no—
399C23—21no—
400C23—21no—
401C23—216no—
402C23—28no—
403C23—28no—
404C23—21no—
405C23—24no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—44no—
415C23—42no—
416C23—48no—
417C23—44no—
418C23—42no—
419C23—48no—
420C23—48no—
421C23—48no—
422C23—416no—
423C23—44no—
424C23—48no—
425C23—44no—
426C23—48no—
427C23—48no—
428C23—416no—
429C23—48no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—48no—
434C23—48no—
435C23—416no—
436C23—416no—
437C23—464no—
438C23—464no—
439C23—48no—
440C23—416no—
441C23—48no—
442C23—44no—
443C23—42no—
444C23—42no—
445C23—44no—
446C23—82no—
447C23—84no—
448C23#99×C3712yes—
449C23#99×C3712yes—
450C23C2×C22⋊C4×C3711yescharacteristic
451C23C2×C22⋊C4×C3712yes—
452C23#120×C3712yes—
453D4—44no—
454D4—44no—
455D4—44no—
456D4—416no—
457D4—416no—
458D4—44no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—82no—
469C2×C4—84no—
470C2×C4#120×C3712yes—
471C8—82no—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—28no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—432no—
487C22—416no—
488C22—48no—
489C22—42no—
490C22—42no—
491C22—48no—
492C22—48no—
493C22—416no—
494C22—432no—
495C22—42no—
496C22—48no—
497C22—42no—
498C22—42no—
499C22—44no—
500C22—42no—
501C22—41no—
502C22—81no—
503C22—88no—
504C22—81no—
505C22C37×AΣL(1,𝔽16)14yescomplemented
506C22C37×#37911yescharacteristic
507C22C2×#99×C3711yescharacteristic
508C22C2×#99×C3711yescharacteristic
509C4—22no—
510C4—44no—
511C4—41no—
512C4—162no—
513C2—21no—
514C2—24no—
515C2—21no—
516C2—42no—
517C2—48no—
518C2—42no—
519C2—42no—
520C2—81no—
521C2C37×#178111yescharacteristic
522C2C2×C37×AΣL(1,𝔽16)12yes—
subgroupG/H
center, socleC22×C37C2×#99
commutatorC24C22×C4×C37
Frattini, cosocleC22×D4C23×C37
prime radicalC22×#120×C37C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C24×C37 ◁ C23×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×AΣL(1,𝔽16)C2semidirect
3. C37×#1783C2semidirect
4. C37×#1781C2semidirect
5. C26×C37C4semidirect
11. C2×#120×C37C4semidirect
14. C22×C22⋊C4×C37C4semidirect
16. C2×#100×C37C22semidirect
18. C2×#99×C37C22semidirect
95. C24×C37C22⋊C4semidirect
135. C22⋊C4×C37C22⋊C4semidirect
210. #12687C37direct (N × H)
244. C22×C37AΣL(1,𝔽16)semidirect
253. C2×AΣL(1,𝔽16)C2×C37semidirect
254. #1783C2×C37semidirect
255. #1781C2×C37semidirect
266. C26C4×C37semidirect
272. C2×#120C4×C37semidirect
275. C22×C22⋊C4C4×C37semidirect
277. C2×#100C22×C37semidirect
279. C2×#99C22×C37semidirect
283. C37#12687direct (N × H)
357. C24C22⋊C4×C37semidirect
397. C22⋊C4C22⋊C4×C37semidirect
505. C22C37×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C372
C2×C37×AΣL(1,𝔽16)2
C37×#17832
C37×#17812
#1268737