Finite Group Databasebeta

← #11887709

Subgroups — #11887709

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#548C211yesmaximal, characteristic
2#10596012C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10592927C211yesmaximal, characteristic, complemented
6C2×#63662C211yesmaximal, characteristic, complemented
7#10592755C211yesmaximal, characteristic, complemented
8#10592753C211yesmaximal, characteristic, complemented
9#10592750C211yesmaximal, characteristic, complemented
10#10592744C211yesmaximal, characteristic, complemented
11#10592740C211yesmaximal, characteristic, complemented
12#10592732C211yesmaximal, characteristic, complemented
13C4×#3756C211yesmaximal, characteristic, complemented
14#10592721C211yesmaximal, characteristic, complemented
15D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16#83534—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic
19C32×#124—21no—
20C32×#124C2211yescharacteristic
21C32×C22⋊Q8—21no—
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121—21no—
24C32×#121C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×D4—21no—
27C32×C4×D4C2211yescharacteristic
28C2×#3756C2211yescharacteristic
29C2×#3756C2211yescharacteristic
30#64144—21no—
31C2×#3754C2211yescharacteristic
32#64135C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34#64133C2211yescharacteristic
35#64133C2211yescharacteristic
36C22×C3⋊(C3⋊C8)C2211yescharacteristic
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38#64098—21no—
39#64088—21no—
40#64086—21no—
41#64079C2211yescharacteristic
42C4×#634C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63659C2211yescharacteristic
52#63657C2211yescharacteristic
53#63657C2211yescharacteristic
54#63637C2211yescharacteristic
55#63635C2211yescharacteristic
56#63634C2211yescharacteristic
57#63634C2211yescharacteristic
58C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60C3×#548D314yes—
61#5541—34no—
62#5239—34no—
63#5233—34no—
64#5228—34no—
65C2×#835—34no—
66#5056—34no—
67#5054—34no—
68#5051—34no—
69#5045—34no—
70#5041—34no—
71#5033—34no—
72C4×#216—34no—
73#5022—34no—
74D4×C3⋊C8—34no—
75C32×#41—22no—
76C32×#41—41no—
77C2×C32×Q8—21no—
78C2×C32×Q8—22no—
79C2×C32×Q8—41no—
80C2×C32×Q8C2311yescharacteristic
81C2×C32×Q8C2311yescharacteristic
82C2×C32×D4—21no—
83C2×C32×D4—21no—
84C2×C32×D4D411yescharacteristic
85C2×C32×D4C2311yescharacteristic
86C22×C32×C4—21no—
87C22×C32×C4—21no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3—21no—
91C2×#634C2311yescharacteristic
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C4⋊C4D411yescharacteristic
95C32×C4⋊C4C2311yescharacteristic
96C32×C22⋊C4—21no—
97C32×C22⋊C4—21no—
98C32×C22⋊C4—21no—
99C32×C22⋊C4—21no—
100C32×C22⋊C4D411yescharacteristic
101C32×C22⋊C4D411yescharacteristic
102C32×C42—21no—
103C32×C42C2311yescharacteristic
104#3757—21no—
105#3757—21no—
106#3757—21no—
107#3756—22no—
108#3756—41no—
109#3754—41no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)—41no—
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3300—91noSylow
128C2×C3×#41C2×D314yes—
129C22×C3×Q8C2×D314yes—
130C3×#124—24no—
131C3×#124C2×D314yes—
132C3×C22⋊Q8—24no—
133C3×C22⋊Q8C2×D314yes—
134C3×#121—24no—
135C3×#121C2×D314yes—
136C3×C4×Q8C2×D314yes—
137C3×C4×D4—24no—
138C3×C4×D4C2×D314yes—
139C2×#216—34no—
140C2×#216—34no—
141#935—64no—
142C2×#214—34no—
143#926—34no—
144C2×C4⋊Dic3—34no—
145#924—34no—
146#924—34no—
147C22×C3⋊C8—34no—
148C22×C3⋊C8—34no—
149#889—64no—
150#879—64no—
151#877—64no—
152#870—34no—
153C4×Dic6—34no—
154#835—34no—
155#835—34no—
156#835—34no—
157#835—34no—
158#835—34no—
159#835—34no—
160#832—34no—
161#832—34no—
162#832—34no—
163#830—34no—
164#830—34no—
165#810—34no—
166#808—34no—
167#807—34no—
168#807—34no—
169C4⋊(C3⋊C8)—34no—
170C4×C3⋊C8—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C23×C32C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—42no—
178C32×Q8#4112yes—
179C32×D4—22no—
180C32×D4—21no—
181C32×D4—21no—
182C32×D4—42no—
183C32×D4—42no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—42no—
192C2×C32×C4—42no—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—42no—
203#634—21no—
204#634—21no—
205C3⋊(C3⋊C8)—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#548C3⋊D311yescharacteristic
211#488—91no—
212#485—91no—
213#480—91no—
214#479—91no—
215#467—91no—
216#465—91no—
217#464—91no—
218#452—91no—
219#451—91no—
220C4×Q16—91no—
221C8×D4—91no—
222#416—91no—
223C2×#103—91no—
224C3×#41—28no—
225C3×#41—44no—
226C2×C3×Q8—24no—
227C2×C3×Q8—28no—
228C2×C3×Q8—44no—
229C2×C3×Q8C22×D314yes—
230C2×C3×Q8C22×D314yes—
231C2×C3×D4—24no—
232C2×C3×D4—24no—
233C2×C3×D4#6714yes—
234C2×C3×D4C22×D314yes—
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C22×C3×C4C22×D314yes—
238C22×C3×C4C22×D314yes—
239C22×Dic3—64no—
240C2×Dic6—34no—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—24no—
243C3×C4⋊C4#6714yes—
244C3×C4⋊C4C22×D314yes—
245C3×C22⋊C4—24no—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—24no—
248C3×C22⋊C4—24no—
249C3×C22⋊C4#6714yes—
250C3×C22⋊C4#6714yes—
251C3×C42—24no—
252C3×C42C22×D314yes—
253#217—64no—
254#217—64no—
255#217—64no—
256#216—68no—
257#216—124no—
258#214—124no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—124no—
275C2×C3⋊C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32#13512yes—
285C22×C32C22×D411yescharacteristic
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—22no—
289C32×C4—21no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4C2×#4111yescharacteristic
294C32×C4H(5,𝔽2)11yescharacteristic
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41C2×C3⋊D311yescharacteristic
300C22×Q8C2×C3⋊D311yescharacteristic
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C22×C8—91no—
305C22×C8—91no—
306#126—181no—
307#125—91no—
308#125—181no—
309#124—21no—
310#124C2×C3⋊D311yescharacteristic
311#123—181no—
312C22⋊Q8—21no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8C2×C3⋊D311yescharacteristic
316#121—21no—
317#121C2×C3⋊D311yescharacteristic
318C4×Q8—91no—
319C4×Q8C2×C3⋊D311yescharacteristic
320C4×D4—21no—
321C4×D4C2×C3⋊D311yescharacteristic
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341C4×C8—91no—
342C23×C3—24no—
343C23×C3C2×#6714yes—
344C23×C3C2×#6714yes—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—48no—
349C3×Q8#23718yes—
350C3×D4—28no—
351C3×D4—24no—
352C3×D4—24no—
353C3×D4—48no—
354C3×D4—48no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—48no—
363C2×C3×C4—48no—
364C2×C3×C4C2×#6714yes—
365C2×C3×C4C2×#6714yes—
366C2×C3×C4C2×#6714yes—
367C2×C3×C4C2×#6714yes—
368C2×C3×C4C23×D314yes—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—128no—
374Dic6—64no—
375Dic6—64no—
376C3⋊C8—64no—
377C3⋊C8—64no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—22no—
381C2×C32—41no—
382C2×C32—81no—
383C2×C32#54611yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57811yescharacteristic
386#41—22no—
387#41—41no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—41no—
391C2×Q8—91no—
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—21no—
395C2×D4—21no—
396C2×D4#63811yescharacteristic
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—181no—
401C22×C4C22×C3⋊D311yescharacteristic
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—182no—
404Q16—361no—
405SD16—361no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—361no—
411C2×C8—361no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4#63811yescharacteristic
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4#63811yescharacteristic
433C22⋊C4#63811yescharacteristic
434C42—21no—
435C42—181no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3—44no—
446C22×C3#95018yes—
447C22×C3C22×#6714yes—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—28no—
451C3×C4—24no—
452C3×C4—24no—
453C3×C4—44no—
454C3×C4—44no—
455C3×C4C2×#23714yes—
456C3×C4#100414yes—
457Dic3—124no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330011yescharacteristic, complemented, Sylow
462C23—21no—
463C23C2×#63811yescharacteristic
464C23C2×#63811yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—42no—
469Q8—181no—
470Q8—181no—
471Q8#383012yes—
472D4—22no—
473D4—21no—
474D4—21no—
475D4—42no—
476D4—42no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—362no—
491C2×C4C2×#63811yescharacteristic
492C2×C4C2×#63811yescharacteristic
493C2×C4C2×#63811yescharacteristic
494C2×C4C2×#63811yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—181no—
497C8—181no—
498C8—181no—
499C8—181no—
500C2×C3—28no—
501C2×C3—44no—
502C2×C3—84no—
503C2×C3#580614yes—
504C2×C3C2×#95014yes—
505C2×C3#583814yes—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22#6415912yes—
515C22C22×#63811yescharacteristic
516C4—21no—
517C4—21no—
518C4—22no—
519C4—21no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#383011yescharacteristic
528C4#6436111yescharacteristic
529C3#8353414yescomplemented
530C2—22no—
531C2—41no—
532C2—81no—
533C2#1059627711yescharacteristic
534C2C2×#6415911yescharacteristic
535C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
Fitting, prime radicalC32×#548C2
socleC22×C32C22×D4
hypercenter#548C3⋊D3
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
2. #10596012C2semidirect
3. #10592938C2semidirect
4. #10592932C2semidirect
5. #10592927C2semidirect
6. C2×#63662C2semidirect
7. #10592755C2semidirect
8. #10592753C2semidirect
9. #10592750C2semidirect
10. #10592744C2semidirect
11. #10592740C2semidirect
12. #10592732C2semidirect
13. C4×#3756C2semidirect
14. #10592721C2semidirect
15. D4×C3⋊(C3⋊C8)C2semidirect
461. C32#3300semidirect
529. C3#83534semidirect

Maximal subgroups

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

subgroupindex
C32×#5482
#105960122
#105929382
#105929322
#105929272
C2×#636622
#105927552
#105927532
#105927502
#105927442
#105927402
#105927322
C4×#37562
#105927212
D4×C3⋊(C3⋊C8)2
#835343