Finite Group Databasebeta

← #11896286

Subgroups — #11896286

Order 1152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2#10596056C211yesmaximal, characteristic
3#10592788C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592767C211yesmaximal, characteristic, complemented
6#10592766C211yesmaximal, characteristic
7#10592765C211yesmaximal, characteristic, complemented
8#10592762C211yesmaximal, characteristic, complemented
9#10592729C211yesmaximal, characteristic, complemented
10#10592727C211yesmaximal, characteristic, complemented
11#10592727C211yesmaximal, characteristic, complemented
12#10592726C211yesmaximal, characteristic
13#10592725C211yesmaximal, characteristic, complemented
14C4×#3755C211yesmaximal, characteristic, complemented
15#10592723C211yesmaximal, characteristic, complemented
16#83691—34nomaximal
17C32×C4⋊Q8—21no—
18C32×C4⋊Q8C2211yescharacteristic
19C32×#125—21no—
20C32×#125—21no—
21C32×#125C2211yescharacteristic
22C32×#125C2211yescharacteristic
23C32×C4×Q8—21no—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×Q8C2211yescharacteristic
28#64156—21no—
29C2×#3756C2211yescharacteristic
30C2×#3755C2211yescharacteristic
31C2×#3755C2211yescharacteristic
32#64103—21no—
33#64103—21no—
34#64102—21no—
35#64084C2211yescharacteristic
36#64084C2211yescharacteristic
37#64083C2211yescharacteristic
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C4×#634C2211yescharacteristic
41#63662C2211yescharacteristic
42#63637C2211yescharacteristic
43#63637C2211yescharacteristic
44#63637C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48#63636C2211yescharacteristic
49#63636C2211yescharacteristic
50#63636C2211yescharacteristic
51#63635C2211yescharacteristic
52#63635C2211yescharacteristic
53#63634C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
55C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
56C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
57#63630C2211yescharacteristic
58#63630C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60C3×#557D314yescomplemented
61#5585—34no—
62#5089—34no—
63#5084—34no—
64#5068—34no—
65#5067—34no—
66#5066—34no—
67#5063—34no—
68#5030—34no—
69#5028—34no—
70#5028—34no—
71#5027—34no—
72#5026—34no—
73C4×#215—34no—
74#5024—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8D411yescharacteristic
77C2×C32×Q8C2311yescharacteristic
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4⋊(C3⋊D3)C2311yescharacteristic
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×#634C2311yescharacteristic
85C32×C4⋊C4—21no—
86C32×C4⋊C4—21no—
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4D411yescharacteristic
94C32×C4⋊C4D411yescharacteristic
95C32×C4⋊C4D411yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C42—21no—
100C32×C42—21no—
101C32×C42—21no—
102C32×C42C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3756—22no—
106#3755—22no—
107#3755—22no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3371—91noSylow
122C3×C4⋊Q8—24no—
123C3×C4⋊Q8C2×D314yes—
124C3×#125—24no—
125C3×#125—24no—
126C3×#125C2×D314yes—
127C3×#125C2×D314yes—
128C3×C4×Q8—24no—
129C3×C4×Q8C2×D314yes—
130C3×C4×Q8C2×D314yes—
131C3×C4×Q8C2×D314yes—
132C3×C4×Q8C2×D314yes—
133#947—64no—
134C2×#216—34no—
135C2×#215—34no—
136C2×#215—34no—
137#894—64no—
138#894—64no—
139#893—64no—
140#875—34no—
141#875—34no—
142#874—34no—
143C4×D12—34no—
144C4×D12—34no—
145C4×Dic6—34no—
146#835—34no—
147#810—34no—
148#810—34no—
149#810—34no—
150#809—34no—
151#809—34no—
152#809—34no—
153#809—34no—
154#809—34no—
155#809—34no—
156#808—34no—
157#808—34no—
158#807—34no—
159C4⋊(C3⋊C8)—34no—
160C4⋊(C3⋊C8)—34no—
161C4⋊(C3⋊C8)—34no—
162#803—34no—
163#803—34no—
164C4×C3⋊C8—34no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C32×Q8—21no—
168C32×Q8—41no—
169C32×Q8—42no—
170C32×Q8#4112yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)—42no—
189C4⋊(C3⋊D3)—81no—
190C4×C3⋊D3—81no—
191C4×C3⋊D3—81no—
192#634—21no—
193#634—21no—
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)—21no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198#559—91no—
199#557C3⋊D311yescharacteristic, complemented
200#490—91no—
201#489—91no—
202#488—91no—
203#479—91no—
204#478—91no—
205#476—91no—
206#464—91no—
207#464—91no—
208#460—91no—
209#446—91no—
210#441—91no—
211#440—91no—
212C4×SD16—91no—
213C2×C3×Q8—24no—
214C2×C3×Q8#6714yes—
215C2×C3×Q8C22×D314yes—
216C2×D12—34no—
217C2×D12—34no—
218C2×D12—64no—
219C2×D12—64no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×Dic6—34no—
223C3×C4⋊C4—24no—
224C3×C4⋊C4—24no—
225C3×C4⋊C4—24no—
226C3×C4⋊C4—24no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—24no—
229C3×C4⋊C4—24no—
230C3×C4⋊C4—24no—
231C3×C4⋊C4#6714yes—
232C3×C4⋊C4#6714yes—
233C3×C4⋊C4#6714yes—
234C3×C4⋊C4C22×D314yes—
235C3×C4⋊C4C22×D314yes—
236C3×C4⋊C4C22×D314yes—
237C3×C42—24no—
238C3×C42—24no—
239C3×C42—24no—
240C3×C42C22×D314yes—
241C3×C42C22×D314yes—
242C3×C42C22×D314yes—
243#216—68no—
244#215—68no—
245#215—68no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—34no—
253Dic3⋊C4—64no—
254C4×Dic3—64no—
255C2×C3⋊C8—34no—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—34no—
258C2×C3⋊C8—34no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—41no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C2×C3⋊D3—41no—
266C32×C4—22no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—21no—
273C32×C4—41no—
274C32×C4—41no—
275C32×C4—41no—
276C32×C4C2×#4111yescharacteristic
277C32×C42−1+411yescharacteristic
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C2×Q16—91no—
281C2×SD16—91no—
282C2×SD16—91no—
283C4⋊Q8—21no—
284C4⋊Q8C2×C3⋊D311yescharacteristic
285#127—91no—
286#125—21no—
287#125—21no—
288#125C2×C3⋊D311yescharacteristic
289#125C2×C3⋊D311yescharacteristic
290#124—91no—
291#124—91no—
292#124—181no—
293#123—181no—
294#123—181no—
295C4×Q8—21no—
296C4×Q8—91no—
297C4×Q8C2×C3⋊D311yescharacteristic
298C4×Q8C2×C3⋊D311yescharacteristic
299C4×Q8C2×C3⋊D311yescharacteristic
300C4×Q8C2×C3⋊D311yescharacteristic
301C4×D4—91no—
302C4×D4—91no—
303C4×D4—181no—
304#107—91no—
305#106—91no—
306#106—91no—
307C4⋊C8—91no—
308C4⋊C8—91no—
309C4⋊C8—91no—
310#103—91no—
311#103—91no—
312#103—91no—
313#103—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102—91no—
319#102—91no—
320#97—91no—
321#97—91no—
322C4×C8—91no—
323C22×D3—64no—
324C22×D3—64no—
325C3×Q8—24no—
326C3×Q8—44no—
327C3×Q8—48no—
328C3×Q8#23918yes—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4C2×#6714yes—
334C2×C3×C4C2×#6714yes—
335C2×C3×C4C2×#6714yes—
336C2×C3×C4C2×#6714yes—
337C2×C3×C4C2×#6714yes—
338C2×C3×C4C2×#6714yes—
339C2×C3×C4C23×D314yes—
340C2×Dic3—64no—
341C2×Dic3—64no—
342D12—64no—
343D12—64no—
344D12—64no—
345D12—64no—
346D12—128no—
347D12—244no—
348C4×D3—244no—
349C4×D3—244no—
350Dic6—64no—
351Dic6—64no—
352C3⋊C8—64no—
353C3⋊C8—64no—
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32#54811yescharacteristic
357C2×C32#57511yescharacteristic
358C2×C32#57711yescharacteristic
359C3⋊D3—81no—
360C3⋊D3—81no—
361C2×Q8—21no—
362C2×Q8—91no—
363C2×Q8#63811yescharacteristic
364C2×Q8C22×C3⋊D311yescharacteristic
365C2×D4—91no—
366C2×D4—91no—
367C2×D4—181no—
368C2×D4—181no—
369C22×C4—181no—
370C22×C4—181no—
371Q16—182no—
372SD16—182no—
373SD16—182no—
374C2×C8—91no—
375C2×C8—91no—
376C2×C8—91no—
377C2×C8—91no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—91no—
387C4⋊C4—181no—
388C4⋊C4#63811yescharacteristic
389C4⋊C4#63811yescharacteristic
390C4⋊C4#63811yescharacteristic
391C4⋊C4C22×C3⋊D311yescharacteristic
392C4⋊C4C22×C3⋊D311yescharacteristic
393C4⋊C4C22×C3⋊D311yescharacteristic
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—181no—
404C42C22×C3⋊D311yescharacteristic
405C42C22×C3⋊D311yescharacteristic
406C42C22×C3⋊D311yescharacteristic
407C22×C3C22×#6714yes—
408C2×D3—124no—
409C2×D3—124no—
410C2×D3—124no—
411C2×D3—124no—
412C2×D3—124no—
413C2×D3—124no—
414C3×C4—28no—
415C3×C4—24no—
416C3×C4—24no—
417C3×C4—24no—
418C3×C4—24no—
419C3×C4—24no—
420C3×C4—24no—
421C3×C4—44no—
422C3×C4—44no—
423C3×C4—44no—
424C3×C4C2×#23914yes—
425C3×C4#100714yes—
426Dic3—124no—
427Dic3—124no—
428C32#337111yescharacteristic, complemented, Sylow
429C23—181no—
430C23—181no—
431Q8—21no—
432Q8—41no—
433Q8—42no—
434Q8—181no—
435Q8—181no—
436Q8#383212yes—
437D4—181no—
438D4—181no—
439D4—181no—
440D4—181no—
441D4—362no—
442D4—721no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—721no—
450C2×C4—721no—
451C2×C4C2×#63811yescharacteristic
452C2×C4C2×#63811yescharacteristic
453C2×C4C2×#63811yescharacteristic
454C2×C4C2×#63811yescharacteristic
455C2×C4C2×#63811yescharacteristic
456C2×C4C2×#63811yescharacteristic
457C2×C4C23×C3⋊D311yescharacteristic
458C8—181no—
459C8—181no—
460C8—181no—
461C8—181no—
462C2×C3#581714yes—
463C2×C3#582214yes—
464C2×C3#583714yes—
465D3—244no—
466D3—244no—
467C22—361no—
468C22—361no—
469C22—361no—
470C22—361no—
471C22—361no—
472C22—361no—
473C22C22×#63811yescharacteristic
474C4—22no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—361no—
485C4—361no—
486C4C2×#383211yescharacteristic
487C4#6436411yescharacteristic
488C3#8369114yescomplemented
489C2—721no—
490C2—721no—
491C2#1059628811yescharacteristic
492C2#1059629311yescharacteristic
493C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radical#64083C22
hypercenter#557C3⋊D3
hypocenterC32#3371
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. #10592788C2semidirect
4. #10592783C2semidirect
5. #10592767C2semidirect
7. #10592765C2semidirect
8. #10592762C2semidirect
9. #10592729C2semidirect
10. #10592727C2semidirect
11. #10592727C2semidirect
13. #10592725C2semidirect
14. C4×#3755C2semidirect
15. #10592723C2semidirect
60. C3×#557D3semidirect
199. #557C3⋊D3semidirect
428. C32#3371semidirect
488. C3#83691semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
#105960562
#105927882
#105927832
#105927672
#105927662
#105927652
#105927622
#105927292
#105927272
#105927262
#105927252
C4×#37552
#105927232
#836913