Finite Group Databasebeta

← #11897521

Subgroups — #11897521

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#10596010C211yesmaximal, characteristic, complemented
2D4×#634C211yesmaximal, characteristic, complemented
3C32×#442C211yesmaximal, characteristic
4#10592851C211yesmaximal, characteristic
5D8×C3⋊Dic3C211yesmaximal, characteristic
6#10592708C211yesmaximal, characteristic, complemented
7#10592707C211yesmaximal, characteristic, complemented
8#10592555C211yesmaximal, characteristic, complemented
9#10592554C211yesmaximal, characteristic, complemented
10#10592465C211yesmaximal, characteristic, complemented
11#10592460C211yesmaximal, characteristic, complemented
12#10592460C211yesmaximal, characteristic, complemented
13#10592458C211yesmaximal, characteristic, complemented
14#10592401C211yesmaximal, characteristic, complemented
15#10592400C211yesmaximal, characteristic, complemented
16#79855—34nomaximal
17C22×#634—21no—
18C2×C32×D8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25#64133—21no—
26#64133—21no—
27C2×#3750—21no—
28#64099C2211yescharacteristic
29#64097C2211yescharacteristic
30#64097C2211yescharacteristic
31#64097C2211yescharacteristic
32#64087—21no—
33#64087—21no—
34#64087—21no—
35#64087—21no—
36#64079C2211yescharacteristic
37#64078C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C32×#106C2211yescharacteristic
40C32×#102C2211yescharacteristic
41C32×#102C2211yescharacteristic
42C32×#97C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63645C2211yescharacteristic
48#63645C2211yescharacteristic
49#63644C2211yescharacteristic
50#63644C2211yescharacteristic
51#63642C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54C8×C3⋊Dic3C2211yescharacteristic
55#63635C2211yescharacteristic
56#63635C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5539—34no—
61D4×Dic6—34no—
62C3×#442D314yes—
63#5152—34no—
64Dic3×D8—34no—
65#5009—34no—
66#5008—34no—
67#4856—34no—
68#4855—34no—
69#4766—34no—
70#4761—34no—
71#4761—34no—
72#4759—34no—
73#4702—34no—
74#4701—34no—
75C2×C32×D4C2311yescharacteristic
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3—21no—
82C22×C3⋊Dic3—21no—
83C2×#634—21no—
84C2×#634—21no—
85C2×#634—21no—
86C2×#634—21no—
87C2×#634—44no—
88C2×#634D411yescharacteristic
89C32×D8Q814yescomplemented
90C2×C32×C8C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C22⋊C4—21no—
95C32×C22⋊C4—21no—
96C32×C42C2311yescharacteristic
97#3757—21no—
98#3757—21no—
99#3757—21no—
100#3757—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)D411yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
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—
122C2×C3×D8C2×D314yes—
123C3×C4×D4C2×D314yes—
124C3×C4×D4C2×D314yes—
125D4×Dic3—34no—
126D4×Dic3—34no—
127D4×Dic3—34no—
128D4×Dic3—34no—
129#924—64no—
130#924—64no—
131C2×Dic3⋊C4—64no—
132#890—34no—
133#888—34no—
134#888—34no—
135#888—34no—
136#878—64no—
137#878—64no—
138#878—64no—
139#878—64no—
140#870—34no—
141#869—34no—
142C4×Dic6—34no—
143C3×#106C2×D314yes—
144C3×#102C2×D314yes—
145C3×#102C2×D314yes—
146C3×#97C2×D314yes—
147#832—34no—
148#832—34no—
149#832—34no—
150#832—34no—
151#818—34no—
152#818—34no—
153#817—34no—
154#817—34no—
155#815—34no—
156Dic3⋊C8—34no—
157Dic3⋊C8—34no—
158C8×Dic3—34no—
159#808—34no—
160#808—34no—
161#808—34no—
162#807—34no—
163C4⋊(C3⋊C8)—34no—
164C23×C32—21no—
165C23×C32—21no—
166C32×D4—21no—
167C32×D4—21no—
168C32×D4C2×Q812yes—
169C32×D4C2×Q812yescomplemented
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4—81no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—42no—
182C2×C3⋊Dic3—42no—
183C2×C3⋊Dic3—42no—
184C2×C3⋊Dic3—81no—
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189#634—22no—
190#634—42no—
191#634—42no—
192#634—42no—
193#634—81no—
194C32×C8—21no—
195C32×C8C2×Q812yescomplemented
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198#554—91no—
199D4×Q8—91no—
200#501—91no—
201#501—91no—
202#498—91no—
203#478—91no—
204#478—91no—
205#476—91no—
206#476—91no—
207#476—91no—
208#474—91no—
209#446—91no—
210#442—91no—
211#442C3⋊D311yescharacteristic
212C4×D8—91no—
213C2×C3×D4C22×D314yes—
214C2×C3×D4C22×D314yes—
215C22×C3×C4—24no—
216C22×C3×C4—24no—
217C22×Dic3—64no—
218C22×Dic3—64no—
219C22×Dic3—64no—
220C22×Dic3—64no—
221C2×Dic6—34no—
222C2×Dic6—64no—
223C2×Dic6—64no—
224C2×Dic6—64no—
225C2×Dic6—64no—
226C2×Dic6—1216no—
227C3×D8Dic6116yescomplemented
228C2×C3×C8C22×D314yes—
229C2×C3×C8C22×D314yes—
230C3×C4⋊C4C22×D314yes—
231C3×C4⋊C4C22×D314yes—
232C3×C22⋊C4—24no—
233C3×C22⋊C4—24no—
234C3×C42C22×D314yes—
235#217—64no—
236#217—64no—
237#217—64no—
238#217—64no—
239C4⋊Dic3—34no—
240C4⋊Dic3—34no—
241C4⋊Dic3—34no—
242C4⋊Dic3—34no—
243C4⋊Dic3—34no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246Dic3⋊C4—34no—
247Dic3⋊C4—34no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
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—22no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32C22×D411yescharacteristic
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4C22×Q811yescharacteristic
270C32×C42−1+411yescharacteristic
271C3⋊Dic3—21no—
272C3⋊Dic3—21no—
273C3⋊Dic3—21no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3AGL(1,ℤ/8)12yes—
279C22×Q8—181no—
280C2×D8C2×C3⋊D311yescharacteristic
281C4⋊Q8—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284C4⋊Q8—91no—
285#125—91no—
286#125—91no—
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×D4C2×C3⋊D311yescharacteristic
299C4×D4C2×C3⋊D311yescharacteristic
300C2×C4⋊C4—181no—
301#107—91no—
302#107—91no—
303#107—91no—
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⋊C8—91no—
313#102—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102C2×C3⋊D311yescharacteristic
318#102C2×C3⋊D311yescharacteristic
319#97—91no—
320#97C2×C3⋊D311yescharacteristic
321C4×C8—91no—
322C23×C3—24no—
323C23×C3—24no—
324C3×D4—24no—
325C3×D4—24no—
326C3×D4C2×Dic618yes—
327C3×D4C2×Dic618yescomplemented
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—48no—
331C2×C3×C4—84no—
332C2×C3×C4D3×D414yes—
333C2×C3×C4D3×D414yes—
334C2×C3×C4C23×D314yes—
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—34no—
338C2×Dic3—34no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—128no—
344C2×Dic3—128no—
345C2×Dic3—128no—
346C2×Dic3—244no—
347Dic6—68no—
348Dic6—128no—
349Dic6—128no—
350Dic6—128no—
351Dic6—244no—
352C3×C8—24no—
353C3×C8C2×Dic618yescomplemented
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32—42no—
357C2×C32—42no—
358C2×C32D4×Q811yescharacteristic
359C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
360C2×C32#57711yescharacteristic
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8—181no—
364C2×Q8—181no—
365C2×Q8—181no—
366C2×Q8—364no—
367C2×D4C22×C3⋊D311yescharacteristic
368C2×D4C22×C3⋊D311yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—181no—
374C22×C4—181no—
375D8#63414yescomplemented
376C2×C8—91no—
377C2×C8—91no—
378C2×C8C22×C3⋊D311yescharacteristic
379C2×C8C22×C3⋊D311yescharacteristic
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—91no—
386C4⋊C4—91no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4C22×C3⋊D311yescharacteristic
396C4⋊C4C22×C3⋊D311yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C42—91no—
404C42—91no—
405C42C22×C3⋊D311yescharacteristic
406C22×C3—28no—
407C22×C3—28no—
408C22×C3—44no—
409C22×C3—44no—
410C22×C3—44no—
411C22×C3—44no—
412C22×C3C2×D3×D414yes—
413C3×C4—24no—
414C3×C4—24no—
415C3×C4—44no—
416C3×C4—44no—
417C3×C4C22×Dic614yes—
418C3×C4#101014yes—
419Dic3—38no—
420Dic3—64no—
421Dic3—64no—
422Dic3—64no—
423Dic3—124no—
424Dic3—124no—
425Dic3—124no—
426Dic3—124no—
427C32#338411yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430Q8—182no—
431Q8—362no—
432Q8—362no—
433Q8—362no—
434Q8—721no—
435D4—21no—
436D4—21no—
437D4C2×#63412yes—
438D4C2×#63412yescomplemented
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—91no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4—362no—
452C2×C4—362no—
453C2×C4—362no—
454C2×C4—721no—
455C2×C4D4×C3⋊D311yescharacteristic
456C2×C4D4×C3⋊D311yescharacteristic
457C2×C4C23×C3⋊D311yescharacteristic
458C8—21no—
459C8—181no—
460C8—181no—
461C8C2×#63412yescomplemented
462C2×C3—48no—
463C2×C3—48no—
464C2×C3D4×Dic614yes—
465C2×C3D3×AGL(1,ℤ/8)14yes—
466C2×C3#577514yes—
467C22—22no—
468C22—22no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22C2×D4×C3⋊D311yescharacteristic
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—92no—
479C4—181no—
480C4—181no—
481C4—181no—
482C4—361no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4C22×#63411yescharacteristic
487C4#6436711yescharacteristic
488C3#7985514yescomplemented
489C2—42no—
490C2—42no—
491C2D4×#63411yescharacteristic
492C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
493C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#442C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenter#442C3⋊D3
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10596010C2semidirect
2. D4×#634C2semidirect
6. #10592708C2semidirect
7. #10592707C2semidirect
8. #10592555C2semidirect
9. #10592554C2semidirect
10. #10592465C2semidirect
11. #10592460C2semidirect
12. #10592460C2semidirect
13. #10592458C2semidirect
14. #10592401C2semidirect
15. #10592400C2semidirect
89. C32×D8Q8semidirect
169. C32×D4C2×Q8semidirect
195. C32×C8C2×Q8semidirect
227. C3×D8Dic6semidirect
327. C3×D4C2×Dic6semidirect
353. C3×C8C2×Dic6semidirect
375. D8#634semidirect
427. C32#3384semidirect
438. D4C2×#634semidirect
461. C8C2×#634semidirect
488. C3#79855semidirect

Maximal subgroups

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

subgroupindex
#105960102
D4×#6342
C32×#4422
#105928512
D8×C3⋊Dic32
#105927082
#105927072
#105925552
#105925542
#105924652
#105924602
#105924582
#105924012
#105924002
#798553