Finite Group Databasebeta

← #11895606

Subgroups — #11895606

Order 1152.

1044 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#10596152C211yesmaximal, characteristic
2#10596040C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic, complemented
4#10592884C211yesmaximal, characteristic, complemented
5Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592862C211yesmaximal, characteristic
7SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592755C211yesmaximal, characteristic, complemented
9C4×#3755C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592529C211yesmaximal, characteristic, complemented
12#10592499C211yesmaximal, characteristic, complemented
13#10592490C211yesmaximal, characteristic, complemented
14#10592465C211yesmaximal, characteristic, complemented
15#10592459C211yesmaximal, characteristic
16#80581—34nomaximal
17C2×C32×Q16C2211yescharacteristic
18C2×C32×SD16C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21#64156C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26#64149C2211yescharacteristic
27D4×C3⋊Dic3C2211yescharacteristic
28#64099—21no—
29#64099C2211yescharacteristic
30#64097—21no—
31#64097C2211yescharacteristic
32#64095—21no—
33#64094—21no—
34#64092—21no—
35#64090—21no—
36C4×C4⋊(C3⋊D3)C2211yescharacteristic
37#64079—21no—
38#64079C2211yescharacteristic
39C4×#634—21no—
40C4×#634C2211yescharacteristic
41C32×C4⋊C8C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63645C2211yescharacteristic
52#63644C2211yescharacteristic
53#63641C2211yescharacteristic
54#63641C2211yescharacteristic
55C8×C3⋊Dic3C2211yescharacteristic
56C8×C3⋊Dic3C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60#5681—34no—
61#5569—34no—
62C3×#464D314yescomplemented
63#5185—34no—
64Dic3×Q16—34no—
65#5163—34no—
66Dic3×SD16—34no—
67#5056—34no—
68C4×#215—34no—
69#4847—34no—
70#4830—34no—
71#4800—34no—
72#4791—34no—
73#4766—34no—
74#4760—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C2×#638—21no—
79C2×#638—21no—
80C22×C3⋊Dic3—21no—
81C2×C4⋊(C3⋊D3)C2311yescharacteristic
82C2×C4×C3⋊D3—21no—
83C2×#634—21no—
84C2×#634D411yescharacteristic
85C32×Q16—22no—
86C32×SD16—22no—
87C2×C32×C8C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C22⋊C4—21no—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94C32×C42C2311yescharacteristic
95#3757—21no—
96#3755—22no—
97#3752—21no—
98#3752—21no—
99#3752—21no—
100C4⋊(C3⋊Dic3)—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)D411yescharacteristic
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#3750D411yescharacteristic
113#3750D411yescharacteristic
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3365—91noSylow
122C2×C3×Q16C2×D314yes—
123C2×C3×SD16C2×D314yes—
124C3×#124C2×D314yes—
125C3×C4×Q8C2×D314yes—
126#947—34no—
127Q8×Dic3—34no—
128Q8×Dic3—34no—
129Q8×Dic3—34no—
130C2×#215—34no—
131#940—34no—
132D4×Dic3—34no—
133#890—34no—
134#890—64no—
135#888—34no—
136#888—64no—
137#886—64no—
138#885—64no—
139#883—64no—
140#67⋊C4—64no—
141C4×D12—34no—
142#870—34no—
143#870—64no—
144C4×Dic6—34no—
145C4×Dic6—64no—
146C3×C4⋊C8C2×D314yes—
147C3×#103C2×D314yes—
148C3×#102C2×D314yes—
149#835—34no—
150#835—34no—
151#835—34no—
152#832—34no—
153#832—34no—
154#821—34no—
155#821—34no—
156#818—34no—
157#817—34no—
158Dic3⋊C8—34no—
159Dic3⋊C8—34no—
160C8×Dic3—34no—
161C8×Dic3—34no—
162#809—34no—
163#808—34no—
164C4×C3⋊C8—34no—
165C23×C32—21no—
166C22×C3⋊D3—21no—
167C32×Q8—21no—
168C32×Q8—21no—
169C32×Q8—21no—
170C32×Q8#4112yes—
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179#638—42no—
180#638—81no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—81no—
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)—21no—
191C4×C3⋊D3—81no—
192#634—22no—
193#634—42no—
194C32×C8—21no—
195C32×C8—21no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198#559—91no—
199#557—91no—
200#488—91no—
201#488—91no—
202#486—91no—
203#478—91no—
204#478—91no—
205#475—91no—
206#464—91no—
207#464C3⋊D311yescharacteristic, complemented
208#460—91no—
209C8×Q8—91no—
210C4×Q16—91no—
211C4×SD16—91no—
212C4×SD16—91no—
213C2×C3×Q8C22×D314yes—
214C2×C3×Q8C22×D314yes—
215C2×C3×D4C22×D314yes—
216C2×#67—64no—
217C2×#67—64no—
218C22×Dic3—64no—
219C2×D12—34no—
220C2×C4×D3—64no—
221C2×Dic6—34no—
222C2×Dic6—64no—
223C3×Q16—28no—
224C3×SD16—28no—
225C2×C3×C8C22×D314yes—
226C2×C3×C8C22×D314yes—
227C3×C4⋊C4—24no—
228C3×C4⋊C4C22×D314yes—
229C3×C22⋊C4—24no—
230C3×C22⋊C4—24no—
231C3×C42—24no—
232C3×C42C22×D314yes—
233#217—64no—
234#215—68no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—64no—
238C4⋊Dic3—34no—
239C4⋊Dic3—34no—
240C4⋊Dic3—34no—
241C4⋊Dic3—34no—
242C4⋊Dic3—64no—
243C4⋊Dic3—64no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246Dic3⋊C4—34no—
247Dic3⋊C4—34no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252C4×Dic3—34no—
253C4×Dic3—34no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C2×C3⋊C8—34no—
258C2×C3⋊C8—34no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C2×C3⋊D3—41no—
266C32×C4—22no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4—41no—
270C32×C4—41no—
271C32×C4C2×#4111yescharacteristic
272C32×C42−1+411yescharacteristic
273C3⋊Dic3—21no—
274C3⋊Dic3—21no—
275C3⋊Dic3—21no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3—41no—
279C3⋊Dic3#13512yes—
280C2×Q16C2×C3⋊D311yescharacteristic
281C2×SD16—91no—
282C2×SD16C2×C3⋊D311yescharacteristic
283C4⋊Q8—91no—
284C4⋊Q8—181no—
285#127—91no—
286#125—91no—
287#125—91no—
288#125—181no—
289#125—181no—
290#124—91no—
291#124—181no—
292#124C2×C3⋊D311yescharacteristic
293#123—181no—
294#123—181no—
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—91no—
299C4×Q8—181no—
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⋊C8C2×C3⋊D311yescharacteristic
310#103—91no—
311#103—91no—
312#103—91no—
313#103C2×C3⋊D311yescharacteristic
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102—91no—
319#102C2×C3⋊D311yescharacteristic
320C4×C8—91no—
321C4×C8—91no—
322C4×C8—91no—
323C23×C3—24no—
324C22×D3—64no—
325C3×Q8—24no—
326C3×Q8—24no—
327C3×Q8—24no—
328C3×Q8#23718yes—
329C3×D4—24no—
330C3×D4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4D3×D414yes—
335C2×C3×C4D3×D414yes—
336C2×C3×C4C23×D314yes—
337#67—128no—
338#67—244no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—244no—
347D12—64no—
348D12—64no—
349C4×D3—244no—
350Dic6—68no—
351Dic6—128no—
352C3×C8—24no—
353C3×C8—24no—
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32—81no—
357C2×C32#54811yescharacteristic
358C2×C32C2×#13511yescharacteristic
359C2×C32#57711yescharacteristic
360C3⋊D3—81no—
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8C22×C3⋊D311yescharacteristic
364C2×Q8C22×C3⋊D311yescharacteristic
365C2×D4—91no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4C22×C3⋊D311yescharacteristic
369C22×C4—181no—
370C22×C4—181no—
371Q16—22no—
372SD16—22no—
373SD16—182no—
374C2×C8—91no—
375C2×C8—91no—
376C2×C8C22×C3⋊D311yescharacteristic
377C2×C8C22×C3⋊D311yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4C22×C3⋊D311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—21no—
401C42—91no—
402C42—91no—
403C42—181no—
404C42—181no—
405C42—181no—
406C42C22×C3⋊D311yescharacteristic
407C22×C3—44no—
408C22×C3—44no—
409C22×C3—44no—
410C22×C3C2×D3×D414yes—
411C2×D3—124no—
412C2×D3—124no—
413C2×D3—124no—
414C3×C4—24no—
415C3×C4—24no—
416C3×C4—28no—
417C3×C4—44no—
418C3×C4—44no—
419C3×C4C2×#23714yes—
420C3×C4#101014yes—
421Dic3—38no—
422Dic3—64no—
423Dic3—64no—
424Dic3—64no—
425Dic3—124no—
426Dic3—124no—
427Dic3—124no—
428C32#336511yescharacteristic, complemented, Sylow
429C23—21no—
430C23—181no—
431Q8—21no—
432Q8—21no—
433Q8—21no—
434Q8—182no—
435Q8—362no—
436Q8#383012yes—
437D4—21no—
438D4—21no—
439D4—181no—
440D4—181no—
441D4—362no—
442D4—721no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—721no—
454C2×C4—721no—
455C2×C4D4×C3⋊D311yescharacteristic
456C2×C4D4×C3⋊D311yescharacteristic
457C2×C4C23×C3⋊D311yescharacteristic
458C8—21no—
459C8—21no—
460C8—181no—
461C8—181no—
462C2×C3—84no—
463C2×C3#559814yes—
464C2×C3D3×#13514yes—
465C2×C3#577814yes—
466D3—244no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—361no—
471C22—361no—
472C22—361no—
473C22C2×D4×C3⋊D311yescharacteristic
474C4—21no—
475C4—21no—
476C4—22no—
477C4—41no—
478C4—41no—
479C4—92no—
480C4—181no—
481C4—181no—
482C4—181no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4C2×#383011yescharacteristic
487C4#6436711yescharacteristic
488C3#8058114yescomplemented
489C2—81no—
490C2—721no—
491C2#1059606911yescharacteristic
492C2C3⋊D3×#13511yescharacteristic
493C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radical#64149C22
hypercenter#464C3⋊D3
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #10596040C2semidirect
3. C32×#464C2semidirect
4. #10592884C2semidirect
5. Q16×C3⋊Dic3C2semidirect
7. SD16×C3⋊Dic3C2semidirect
8. #10592755C2semidirect
9. C4×#3755C2semidirect
10. #10592546C2semidirect
11. #10592529C2semidirect
12. #10592499C2semidirect
13. #10592490C2semidirect
14. #10592465C2semidirect
62. C3×#464D3semidirect
207. #464C3⋊D3semidirect
428. C32#3365semidirect
488. C3#80581semidirect

Maximal subgroups

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

subgroupindex
#105961522
#105960402
C32×#4642
#105928842
Q16×C3⋊Dic32
#105928622
SD16×C3⋊Dic32
#105927552
C4×#37552
#105925462
#105925292
#105924992
#105924902
#105924652
#105924592
#805813