Finite Group Databasebeta

← #11897527

Subgroups — #11897527

Order 1152.

1122 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
1#10596161C211yesmaximal, characteristic, complemented
2D4×#634C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4#10592763C211yesmaximal, characteristic, complemented
5#10592713C211yesmaximal, characteristic
6#10592589C211yesmaximal, characteristic, complemented
7#10592575C211yesmaximal, characteristic, complemented
8#10592569C211yesmaximal, characteristic, complemented
9#10592554C211yesmaximal, characteristic, complemented
10#10592541C211yesmaximal, characteristic, complemented
11#10592527C211yesmaximal, characteristic, complemented
12#10592484C211yesmaximal, characteristic
13#10592462C211yesmaximal, characteristic, complemented
14#10592460C211yesmaximal, characteristic, complemented
15#10592455C211yesmaximal, characteristic
16#81158—34nomaximal
17C22×#634—21no—
18C32×#125C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23#64133—21no—
24#64106—21no—
25#64105—21no—
26#64105—21no—
27#64102C2211yescharacteristic
28#64102C2211yescharacteristic
29C4⋊C4×C3⋊D3—21no—
30#64099C2211yescharacteristic
31#64097C2211yescharacteristic
32#64097C2211yescharacteristic
33#64097C2211yescharacteristic
34#64087—21no—
35#64087—21no—
36C4×C4⋊(C3⋊D3)C2211yescharacteristic
37#64078C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C32×#107C2211yescharacteristic
40C32×#106C2211yescharacteristic
41C32×C4⋊C8C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63659C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63644C2211yescharacteristic
48#63644C2211yescharacteristic
49#63642C2211yescharacteristic
50#63641C2211yescharacteristic
51#63641C2211yescharacteristic
52C8×C3⋊Dic3C2211yescharacteristic
53#63636C2211yescharacteristic
54#63635C2211yescharacteristic
55#63635C2211yescharacteristic
56#63635C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59#63630C2211yescharacteristic
60#5690—34no—
61D4×Dic6—34no—
62C3×#478D314yescomplemented
63#5064—34no—
64#5014—34no—
65#4890—34no—
66#4876—34no—
67#4870—34no—
68#4855—34no—
69#4842—34no—
70#4828—34no—
71#4785—34no—
72#4763—34no—
73#4761—34no—
74#4756—34no—
75C2×C32×D4C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3—21no—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—21no—
81C2×C4×C3⋊D3—21no—
82C2×C4×C3⋊D3—21no—
83C2×#634—21no—
84C2×#634—21no—
85C2×#634—21no—
86C2×#634—21no—
87C2×#634—44no—
88C2×#634D411yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C32×C4⋊C4—21no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C4⋊C4C2311yescharacteristic
96C32×C22⋊C4—21no—
97C32×C42C2311yescharacteristic
98#3757—21no—
99#3757—21no—
100#3753Q814yescomplemented
101#3752—21no—
102#3752—21no—
103#3752—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)D411yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750D411yescharacteristic
115#3750D411yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3384—91noSylow
121C22×Dic6—64no—
122C3×#125C2×D314yes—
123C3×C4×D4C2×D314yes—
124D4×Dic3—34no—
125D4×Dic3—34no—
126C2×#213—34no—
127#924—64no—
128#897—64no—
129#896—64no—
130#896—64no—
131#893—34no—
132#893—34no—
133D3×C4⋊C4—64no—
134#890—34no—
135#888—34no—
136#888—34no—
137#888—34no—
138#878—64no—
139#878—64no—
140C4×D12—34no—
141#869—34no—
142C4×Dic6—34no—
143C3×#107C2×D314yes—
144C3×#106C2×D314yes—
145C3×C4⋊C8C2×D314yes—
146C3×#102C2×D314yes—
147C3×#102C2×D314yes—
148#832—34no—
149#821—34no—
150#821—34no—
151#817—34no—
152#817—34no—
153#815—34no—
154Dic3⋊C8—34no—
155Dic3⋊C8—34no—
156C8×Dic3—34no—
157#809—34no—
158#808—34no—
159#808—34no—
160#808—34no—
161#807—34no—
162#807—34no—
163#803—34no—
164C23×C32—21no—
165C22×C3⋊D3—21no—
166C32×D4—21no—
167C32×D4C2×Q812yes—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—42no—
179C2×C3⋊Dic3—42no—
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)C2×Q812yescomplemented
186C4×C3⋊D3—42no—
187C4×C3⋊D3—81no—
188C4×C3⋊D3—81no—
189#634—22no—
190#634—42no—
191#634—42no—
192#634—42no—
193#634—81no—
194C32×C8—21no—
195C32×C8—21no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)C2×Q812yescomplemented
198#554—91no—
199D4×Q8—91no—
200#501—91no—
201#501—91no—
202#498—91no—
203#478—91no—
204#478C3⋊D311yescharacteristic, complemented
205#476—91no—
206#476—91no—
207#476—91no—
208#474—91no—
209#446—91no—
210#442—91no—
211#442—91no—
212C4×D8—91no—
213C2×C3×D4C22×D314yes—
214C22×C3×C4—24no—
215C22×Dic3—64no—
216C22×Dic3—64no—
217C2×D12—34no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×Dic6—34no—
222C2×Dic6—64no—
223C2×Dic6—64no—
224C2×Dic6—64no—
225C2×Dic6—64no—
226C2×Dic6—1216no—
227C2×C3×C8C22×D314yes—
228C2×C3×C8C22×D314yes—
229C3×C4⋊C4—24no—
230C3×C4⋊C4—24no—
231C3×C4⋊C4C22×D314yes—
232C3×C4⋊C4C22×D314yes—
233C3×C4⋊C4C22×D314yes—
234C3×C22⋊C4—24no—
235C3×C42C22×D314yes—
236#217—64no—
237#217—64no—
238#213—316no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242C4⋊Dic3—34no—
243C4⋊Dic3—34no—
244C4⋊Dic3—34no—
245C4⋊Dic3—34no—
246C4⋊Dic3—64no—
247C4⋊Dic3—64no—
248Dic3⋊C4—34no—
249Dic3⋊C4—34no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254C4×Dic3—34no—
255C4×Dic3—34no—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—34no—
258C22×C32—22no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4—41no—
270C32×C4C22×Q811yescharacteristic
271C32×C42−1+411yescharacteristic
272C3⋊Dic3—21no—
273C3⋊Dic3—21no—
274C3⋊Dic3—21no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3AGL(1,ℤ/8)12yes—
279C22×Q8—181no—
280C2×D8—91no—
281C4⋊Q8—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284C4⋊Q8—91no—
285#125—91no—
286#125C2×C3⋊D311yescharacteristic
287C22⋊Q8—181no—
288C22⋊Q8—181no—
289C22⋊Q8—181no—
290C22⋊Q8—181no—
291C22⋊Q8—181no—
292C22⋊Q8—181no—
293C4×Q8—91no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4—91no—
299C4×D4C2×C3⋊D311yescharacteristic
300C2×C4⋊C4—181no—
301#107—91no—
302#107—91no—
303#107C2×C3⋊D311yescharacteristic
304#106—91no—
305#106—91no—
306#106—91no—
307#106—91no—
308#106—91no—
309#106C2×C3⋊D311yescharacteristic
310C4⋊C8—91no—
311C4⋊C8—91no—
312C4⋊C8C2×C3⋊D311yescharacteristic
313#102—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102C2×C3⋊D311yescharacteristic
318#102C2×C3⋊D311yescharacteristic
319#97—91no—
320#97—91no—
321C4×C8—91no—
322C23×C3—24no—
323C22×D3—64no—
324C3×D4—24no—
325C3×D4D3×Q818yes—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—48no—
330C2×C3×C4D3×D414yes—
331C2×C3×C4D3×D414yes—
332C2×C3×C4C23×D314yes—
333C2×Dic3—34no—
334C2×Dic3—34no—
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—64no—
340C2×Dic3—128no—
341C2×Dic3—128no—
342D12—38no—
343D12—64no—
344C4×D3—128no—
345C4×D3—244no—
346C4×D3—244no—
347Dic6—68no—
348Dic6—128no—
349Dic6—128no—
350Dic6—128no—
351Dic6—244no—
352C3×C8—24no—
353C3×C8—24no—
354C3⋊C8—38no—
355C3⋊C8—64no—
356C2×C32—42no—
357C2×C32D4×Q811yescharacteristic
358C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
359C2×C32#57711yescharacteristic
360C3⋊D3—42no—
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8—181no—
364C2×Q8—181no—
365C2×Q8—181no—
366C2×Q8—364no—
367C2×D4—91no—
368C2×D4C22×C3⋊D311yescharacteristic
369C22×C4—21no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—181no—
374C22×C4—181no—
375D8—94no—
376C2×C8—91no—
377C2×C8—91no—
378C2×C8C22×C3⋊D311yescharacteristic
379C2×C8C22×C3⋊D311yescharacteristic
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—91no—
386C4⋊C4—91no—
387C4⋊C4—91no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4C22×C3⋊D311yescharacteristic
395C4⋊C4C22×C3⋊D311yescharacteristic
396C4⋊C4C22×C3⋊D311yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C42—91no—
404C42—91no—
405C42C22×C3⋊D311yescharacteristic
406C22×C3—28no—
407C22×C3—44no—
408C22×C3—44no—
409C22×C3C2×D3×D414yes—
410C2×D3—68no—
411C2×D3—124no—
412C2×D3—124no—
413C3×C4—24no—
414C3×C4—24no—
415C3×C4—44no—
416C3×C4—44no—
417C3×C4—44no—
418C3×C4C2×D3×Q814yes—
419C3×C4#101014yes—
420Dic3—38no—
421Dic3—64no—
422Dic3—64no—
423Dic3—64no—
424Dic3—124no—
425Dic3—124no—
426Dic3—124no—
427C32#338411yescharacteristic, complemented, Sylow
428C23—21no—
429C23—181no—
430Q8—182no—
431Q8—362no—
432Q8—362no—
433Q8—362no—
434Q8—721no—
435D4—21no—
436D4—92no—
437D4—181no—
438D4Q8×C3⋊D312yes—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—42no—
443C2×C4—91no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—362no—
451C2×C4—362no—
452C2×C4—362no—
453C2×C4—721no—
454C2×C4—721no—
455C2×C4D4×C3⋊D311yescharacteristic
456C2×C4D4×C3⋊D311yescharacteristic
457C2×C4C23×C3⋊D311yescharacteristic
458C8—21no—
459C8—21no—
460C8—92no—
461C8—181no—
462C2×C3—48no—
463C2×C3#563214yes—
464C2×C3#577014yes—
465C2×C3D3×AGL(1,ℤ/8)14yes—
466D3—128no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22—182no—
471C22—361no—
472C22—361no—
473C22C2×D4×C3⋊D311yescharacteristic
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—92no—
480C4—181no—
481C4—181no—
482C4—181no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4C2×Q8×C3⋊D311yescharacteristic
487C4#6436711yescharacteristic
488C3#8115814yescomplemented
489C2—42no—
490C2—362no—
491C2#1059610311yescharacteristic
492C2#1059624111yescharacteristic
493C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#478C3⋊D3
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10596161C2semidirect
2. D4×#634C2semidirect
3. C32×#478C2semidirect
4. #10592763C2semidirect
6. #10592589C2semidirect
7. #10592575C2semidirect
8. #10592569C2semidirect
9. #10592554C2semidirect
10. #10592541C2semidirect
11. #10592527C2semidirect
13. #10592462C2semidirect
14. #10592460C2semidirect
62. C3×#478D3semidirect
100. #3753Q8semidirect
185. C4⋊(C3⋊D3)C2×Q8semidirect
197. C3⋊(C3⋊C8)C2×Q8semidirect
204. #478C3⋊D3semidirect
427. C32#3384semidirect
488. C3#81158semidirect

Maximal subgroups

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

subgroupindex
#105961612
D4×#6342
C32×#4782
#105927632
#105927132
#105925892
#105925752
#105925692
#105925542
#105925412
#105925272
#105924842
#105924622
#105924602
#105924552
#811583