Finite Group Databasebeta

← #11870562

Subgroups — #11870562

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2#10595950C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4#10592937C211yesmaximal, characteristic
5C4×#3756C211yesmaximal, characteristic, complemented
6#10592727C211yesmaximal, characteristic, complemented
7C4×#3755C211yesmaximal, characteristic, complemented
8#10592721C211yesmaximal, characteristic, complemented
9C4×#3754C211yesmaximal, characteristic, complemented
10#10592715C211yesmaximal, characteristic, complemented
11C4×#3753C211yesmaximal, characteristic, complemented
12#10592708C211yesmaximal, characteristic, complemented
13#10592702C211yesmaximal, characteristic, complemented
14#10592695C211yesmaximal, characteristic, complemented
15#10592624C211yesmaximal, characteristic, complemented
16#82528—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4—21no—
21C32×C4×D4—21no—
22C32×C4×D4C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24C32×#117—21no—
25C32×#117C2211yescharacteristic
26C2×C32×C42—21no—
27C2×C32×C42C2211yescharacteristic
28C2×#3756C2211yescharacteristic
29C2×#3755C2211yescharacteristic
30C2×#3754C2211yescharacteristic
31C2×#3753C2211yescharacteristic
32#64139C2211yescharacteristic
33#64138—21no—
34C4×#638—21no—
35#64133C2211yescharacteristic
36#64085—21no—
37#64084C2211yescharacteristic
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39#64081—21no—
40#64079C2211yescharacteristic
41C4×#634C2211yescharacteristic
42#63662C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47#63657C2211yescharacteristic
48#63637C2211yescharacteristic
49#63637C2211yescharacteristic
50#63636C2211yescharacteristic
51#63636C2211yescharacteristic
52#63635C2211yescharacteristic
53#63635C2211yescharacteristic
54#63634C2211yescharacteristic
55#63634C2211yescharacteristic
56C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
57C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
58C4×C3⋊(C3⋊C8)C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60C3×C4×#41D314yescomplemented
61#5479—34no—
62#5239—34no—
63#5238—34no—
64C4×#216—34no—
65#5028—34no—
66C4×#215—34no—
67#5022—34no—
68C4×#214—34no—
69#5016—34no—
70C4×#213—34no—
71#5009—34no—
72#5003—34no—
73#4996—34no—
74#4925—34no—
75C32×#41—22no—
76C32×#41—22no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4—21no—
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4D411yescharacteristic
84C22×C32×C4D411yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C2×#638—21no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×#634C2311yescharacteristic
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C22⋊C4—21no—
95C32×C22⋊C4—21no—
96C32×C22⋊C4—21no—
97C32×C42—21no—
98C32×C42—21no—
99C32×C42—21no—
100C32×C42D411yescharacteristic
101C32×C42D411yescharacteristic
102C32×C42C2311yescharacteristic
103C32×C42C2311yescharacteristic
104#3757—21no—
105#3756—22no—
106#3755—22no—
107#3754—22no—
108#3753—22no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3102—91noSylow
125C2×C3×#41C2×D314yes—
126C3×C4×Q8C2×D314yes—
127C3×C4×Q8C2×D314yes—
128C3×C4×D4—24no—
129C3×C4×D4—24no—
130C3×C4×D4C2×D314yes—
131C3×C4×D4C2×D314yes—
132C3×#117—24no—
133C3×#117C2×D314yes—
134C2×C3×C42—24no—
135C2×C3×C42C2×D314yes—
136C2×#216—34no—
137C2×#215—34no—
138C2×#214—34no—
139C2×#213—34no—
140#930—34no—
141#929—64no—
142C4×#67—64no—
143#924—34no—
144#876—64no—
145#875—34no—
146C4×D12—34no—
147#872—64no—
148#870—34no—
149C4×Dic6—34no—
150#835—34no—
151#835—34no—
152#832—34no—
153#832—34no—
154#830—34no—
155#830—34no—
156#810—34no—
157#810—34no—
158#809—34no—
159#809—34no—
160#808—34no—
161#808—34no—
162#807—34no—
163#807—34no—
164C4⋊(C3⋊C8)—34no—
165C4⋊(C3⋊C8)—34no—
166C4×C3⋊C8—34no—
167C4×C3⋊C8—34no—
168C23×C32—21no—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3—21no—
171C32×Q8—21no—
172C32×Q8#4112yes—
173C32×D4—24no—
174C32×D4—21no—
175C32×D4#4112yes—
176C2×C32×C4—24no—
177C2×C32×C4—21no—
178C2×C32×C4—22no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—41no—
184C2×C32×C4—42no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192#638—42no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—21no—
198C4×C3⋊D3—42no—
199#634—21no—
200#634—21no—
201C3⋊(C3⋊C8)—21no—
202C3⋊(C3⋊C8)—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#529—91no—
206C4×#41C3⋊D311yescharacteristic, complemented
207#485—91no—
208#482—91no—
209#479—91no—
210#478—91no—
211#464—91no—
212#463—91no—
213#452—91no—
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431—91no—
220C3×#41—28no—
221C3×#41—28no—
222C2×C3×Q8C22×D314yes—
223C2×C3×D4—24no—
224C2×C3×D4C22×D314yes—
225C22×C3×C4—24no—
226C22×C3×C4—24no—
227C22×C3×C4—24no—
228C22×C3×C4#6714yes—
229C22×C3×C4#6714yes—
230C22×C3×C4C22×D314yes—
231C2×#67—64no—
232C2×D12—34no—
233C2×C4×D3—64no—
234C2×Dic6—34no—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—24no—
237C3×C4⋊C4C22×D314yes—
238C3×C4⋊C4C22×D314yes—
239C3×C22⋊C4—24no—
240C3×C22⋊C4—24no—
241C3×C22⋊C4—24no—
242C3×C42—24no—
243C3×C42—24no—
244C3×C42—24no—
245C3×C42#6714yes—
246C3×C42#6714yes—
247C3×C42C22×D314yes—
248C3×C42C22×D314yes—
249#217—64no—
250#216—68no—
251#215—68no—
252#214—68no—
253#213—68no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264C4×Dic3—64no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—34no—
269C22×C32—21no—
270C22×C32—22no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4—22no—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4#13512yes—
287C32×C4C2×#4111yescharacteristic
288C32×C4C2×#4111yescharacteristic
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C2×#41C2×C3⋊D311yescharacteristic
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—181no—
298#125—91no—
299#124—91no—
300#123—181no—
301C22⋊Q8—91no—
302#121—91no—
303C4×Q8—91no—
304C4×Q8C2×C3⋊D311yescharacteristic
305C4×Q8C2×C3⋊D311yescharacteristic
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4C2×C3⋊D311yescharacteristic
311C4×D4C2×C3⋊D311yescharacteristic
312#117—21no—
313#117—181no—
314#117C2×C3⋊D311yescharacteristic
315C2×C42—21no—
316C2×C42C2×C3⋊D311yescharacteristic
317#107—91no—
318#107—91no—
319#106—91no—
320#106—91no—
321C4⋊C8—91no—
322C4⋊C8—91no—
323#103—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331C22⋊C8—91no—
332C22⋊C8—91no—
333C4×C8—91no—
334C4×C8—91no—
335C23×C3—24no—
336C23×C3C2×#6714yes—
337C22×D3—64no—
338C3×Q8—24no—
339C3×Q8#23518yes—
340C3×D4—216no—
341C3×D4—24no—
342C3×D4#23518yes—
343C2×C3×C4—216no—
344C2×C3×C4—24no—
345C2×C3×C4—28no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—44no—
351C2×C3×C4—48no—
352C2×C3×C4—48no—
353C2×C3×C4C2×#6714yes—
354C2×C3×C4C2×#6714yes—
355C2×C3×C4C2×#6714yes—
356C2×C3×C4C2×#6714yes—
357C2×C3×C4C2×#6714yes—
358C2×C3×C4C23×D314yes—
359#67—128no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363D12—64no—
364D12—64no—
365C4×D3—128no—
366Dic6—64no—
367Dic6—64no—
368C3⋊C8—64no—
369C3⋊C8—64no—
370C3⋊C8—64no—
371C3⋊C8—64no—
372C2×C32—41no—
373C2×C32—42no—
374C2×C32#52511yescharacteristic
375C2×C32C2×#13511yescharacteristic
376C2×C32#57511yescharacteristic
377C3⋊D3—81no—
378#41—22no—
379#41—22no—
380C2×Q8—91no—
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—21no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4C22×C3⋊D311yescharacteristic
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—181no—
390C22×C4#63811yescharacteristic
391C22×C4#63811yescharacteristic
392C22×C4C22×C3⋊D311yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—91no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4C22×C3⋊D311yescharacteristic
410C4⋊C4C22×C3⋊D311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—181no—
423C42#63811yescharacteristic
424C42#63811yescharacteristic
425C42C22×C3⋊D311yescharacteristic
426C42C22×C3⋊D311yescharacteristic
427C22×C3—24no—
428C22×C3—28no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3C22×#6714yes—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—24no—
438C3×C4—28no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4#95018yes—
445C3×C4C2×#23514yes—
446C3×C4C2×#23514yes—
447Dic3—124no—
448Dic3—124no—
449Dic3—124no—
450C32#310211yescharacteristic, complemented, Sylow
451C23—21no—
452C23—181no—
453C23C2×#63811yescharacteristic
454Q8—21no—
455Q8—181no—
456Q8—181no—
457Q8#382812yes—
458D4—24no—
459D4—21no—
460D4—181no—
461D4—181no—
462D4—362no—
463D4#382812yes—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—362no—
478C2×C4C2×#63811yescharacteristic
479C2×C4C2×#63811yescharacteristic
480C2×C4C2×#63811yescharacteristic
481C2×C4C2×#63811yescharacteristic
482C2×C4C2×#63811yescharacteristic
483C2×C4C23×C3⋊D311yescharacteristic
484C8—181no—
485C8—181no—
486C8—181no—
487C8—181no—
488C2×C3—44no—
489C2×C3—48no—
490C2×C3#579114yes—
491C2×C3C2×#95014yes—
492C2×C3#582214yes—
493D3—244no—
494C22—21no—
495C22—22no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—41no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22C22×#63811yescharacteristic
504C4—21no—
505C4—22no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4#6415912yes—
515C4C2×#382811yescharacteristic
516C4C2×#382811yescharacteristic
517C3#8252814yescomplemented
518C2—41no—
519C2—42no—
520C2—721no—
521C2#1059626211yescharacteristic
522C2C2×#6415911yescharacteristic
523C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
prime radical#10592937C2
hypercenterC4×#41C3⋊D3
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. #10595950C2semidirect
3. #10592938C2semidirect
5. C4×#3756C2semidirect
6. #10592727C2semidirect
7. C4×#3755C2semidirect
8. #10592721C2semidirect
9. C4×#3754C2semidirect
10. #10592715C2semidirect
11. C4×#3753C2semidirect
12. #10592708C2semidirect
13. #10592702C2semidirect
14. #10592695C2semidirect
15. #10592624C2semidirect
60. C3×C4×#41D3semidirect
206. C4×#41C3⋊D3semidirect
450. C32#3102semidirect
517. C3#82528semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
#105959502
#105929382
#105929372
C4×#37562
#105927272
C4×#37552
#105927212
C4×#37542
#105927152
C4×#37532
#105927082
#105927022
#105926952
#105926242
#825283