Finite Group Databasebeta

← #11896283

Subgroups — #11896283

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
1#10596192C211yesmaximal, characteristic, complemented
2#10596152C211yesmaximal, characteristic
3C32×#489C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592753C211yesmaximal, characteristic, complemented
6#10592499C211yesmaximal, characteristic, complemented
7#10592497C211yesmaximal, characteristic, complemented
8#10592495C211yesmaximal, characteristic, complemented
9#10592488C211yesmaximal, characteristic, complemented
10#10592465C211yesmaximal, characteristic, complemented
11#10592463C211yesmaximal, characteristic
12#10592461C211yesmaximal, characteristic
13#10592457C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592400C211yesmaximal, characteristic, complemented
16#81673—34nomaximal
17C32×C4⋊Q8C2211yescharacteristic
18C32×#124C2211yescharacteristic
19#64156C2211yescharacteristic
20Q8×C3⋊Dic3—21no—
21Q8×C3⋊Dic3C2211yescharacteristic
22#64153—21no—
23C2×#3756C2211yescharacteristic
24#64149C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28#64099C2211yescharacteristic
29#64099C2211yescharacteristic
30#64098—21no—
31#64098—21no—
32#64096C2211yescharacteristic
33#64096C2211yescharacteristic
34#64095—21no—
35#64094—21no—
36#64092—21no—
37#64090—21no—
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39C4×#634C2211yescharacteristic
40C4×#634C2211yescharacteristic
41C32×#103C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#97C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63645C2211yescharacteristic
50#63643C2211yescharacteristic
51#63642C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54C8×C3⋊Dic3C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63635C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5721—34no—
61#5681—34no—
62C3×#489D314yescomplemented
63#5084—34no—
64#5054—34no—
65#4800—34no—
66#4798—34no—
67#4796—34no—
68#4789—34no—
69#4766—34no—
70#4764—34no—
71#4762—34no—
72#4758—34no—
73#4710—34no—
74#4701—34no—
75C2×C32×Q8—21no—
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×#634D411yescharacteristic
84C2×#634C2311yescharacteristic
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4—21no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91C32×C22⋊C4—21no—
92C32×C42C2311yescharacteristic
93#3757—21no—
94#3756—22no—
95#3754—22no—
96#3752—21no—
97#3752—21no—
98#3752—21no—
99C4⋊(C3⋊Dic3)—21no—
100C4⋊(C3⋊Dic3)—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)D411yescharacteristic
103C4⋊(C3⋊Dic3)C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105#3750—21no—
106#3750—21no—
107#3750—21no—
108#3750—21no—
109#3750—21no—
110#3750D411yescharacteristic
111#3750D411yescharacteristic
112C4×C3⋊Dic3—21no—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3744—22no—
121#3371—91noSylow
122C3×C4⋊Q8C2×D314yes—
123C3×#124C2×D314yes—
124#947—34no—
125Q8×Dic3—34no—
126Q8×Dic3—64no—
127#944—64no—
128C2×#216—34no—
129#940—34no—
130D4×Dic3—34no—
131C2×#214—34no—
132C2×#204—34no—
133#890—34no—
134#890—34no—
135#889—64no—
136#889—64no—
137#887—34no—
138#887—34no—
139#886—64no—
140#885—64no—
141#883—64no—
142#67⋊C4—64no—
143C4×D12—34no—
144C4×Dic6—34no—
145C4×Dic6—34no—
146C3×#103C2×D314yes—
147C3×#103C2×D314yes—
148C3×#102C2×D314yes—
149C3×#102C2×D314yes—
150C3×#97C2×D314yes—
151#835—34no—
152#832—34no—
153#821—34no—
154#818—34no—
155#816—34no—
156#815—34no—
157Dic3⋊C8—34no—
158Dic3⋊C8—34no—
159C8×Dic3—34no—
160#809—34no—
161#809—34no—
162#808—34no—
163#808—34no—
164C4⋊(C3⋊C8)—34no—
165C23×C32—21no—
166C22×C3⋊D3—21no—
167C32×Q8—21no—
168C32×Q8—21no—
169C32×Q8—42no—
170C32×D4—21no—
171C32×D4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—42no—
179#638—81no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—81no—
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)—21no—
190C4×C3⋊D3—81no—
191#634—21no—
192#634—41no—
193#634#4112yes—
194C32×C8—21no—
195C32×C8—21no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198#559—91no—
199#557—91no—
200#490—91no—
201#489C3⋊D311yescharacteristic, complemented
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×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—34no—
223C2×C3×C8C22×D314yes—
224C2×C3×C8C22×D314yes—
225C3×C4⋊C4—24no—
226C3×C4⋊C4C22×D314yes—
227C3×C4⋊C4C22×D314yes—
228C3×C22⋊C4—24no—
229C3×C22⋊C4—24no—
230C3×C42C22×D314yes—
231#217—64no—
232#216—68no—
233#214—68no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—34no—
238C4⋊Dic3—34no—
239C4⋊Dic3—34no—
240C4⋊Dic3—64no—
241C4⋊Dic3—64no—
242C4⋊Dic3—64no—
243Dic3⋊C4—34no—
244Dic3⋊C4—34no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250C4×Dic3—34no—
251C4×Dic3—34no—
252C4×Dic3—64no—
253C4×Dic3—64no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—34no—
258#204—68no—
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—21no—
267C32×C4—21no—
268C32×C4—41no—
269C32×C4—41no—
270C32×C4—41no—
271C32×C4C2×#4111yescharacteristic
272C32×C42−1+411yescharacteristic
273C3⋊Dic3—22no—
274C3⋊Dic3—21no—
275C3⋊Dic3—21no—
276C3⋊Dic3—21no—
277C3⋊Dic3—21no—
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C2×Q16—91no—
281C2×SD16—91no—
282C2×SD16—91no—
283C4⋊Q8—181no—
284C4⋊Q8C2×C3⋊D311yescharacteristic
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—91no—
300C4×Q8—181no—
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#103C2×C3⋊D311yescharacteristic
313#103C2×C3⋊D311yescharacteristic
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102C2×C3⋊D311yescharacteristic
319#102C2×C3⋊D311yescharacteristic
320#97—91no—
321#97C2×C3⋊D311yescharacteristic
322C4×C8—91no—
323C23×C3—24no—
324C22×D3—64no—
325C3×Q8—24no—
326C3×Q8—24no—
327C3×Q8—48no—
328C3×D4—24no—
329C3×D4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4D3×D414yes—
334C2×C3×C4D3×D414yes—
335C2×C3×C4C23×D314yes—
336#67—128no—
337#67—244no—
338C2×Dic3—34no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—34no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—244no—
346D12—64no—
347D12—64no—
348C4×D3—244no—
349Dic6—38no—
350Dic6—64no—
351Dic6—124no—
352C3×C8—24no—
353C3×C8—24no—
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32—81no—
357C2×C32#54811yescharacteristic
358C2×C32#57511yescharacteristic
359C2×C32#57711yescharacteristic
360C3⋊D3—81no—
361C2×Q8—21no—
362C2×Q8—91no—
363C2×Q8—91no—
364C2×Q8C22×C3⋊D311yescharacteristic
365C2×D4—91no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4C22×C3⋊D311yescharacteristic
369C22×C4—181no—
370C22×C4—181no—
371Q16—182no—
372SD16—182no—
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—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4C22×C3⋊D311yescharacteristic
393C4⋊C4C22×C3⋊D311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—91no—
401C42—91no—
402C42—181no—
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—44no—
417C3×C4—44no—
418C3×C4—44no—
419C3×C4D3×#4114yes—
420C3×C4#101014yes—
421Dic3—68no—
422Dic3—64no—
423Dic3—64no—
424Dic3—64no—
425Dic3—64no—
426Dic3—124no—
427Dic3—124no—
428C32#337111yescharacteristic, complemented, Sylow
429C23—21no—
430C23—181no—
431Q8—21no—
432Q8—21no—
433Q8—42no—
434Q8—92no—
435Q8—181no—
436Q8—361no—
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#567714yes—
464C2×C3#577314yes—
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—41no—
477C4—41no—
478C4—41no—
479C4—182no—
480C4—181no—
481C4—181no—
482C4—181no—
483C4—181no—
484C4—361no—
485C4—361no—
486C4#41×C3⋊D311yescharacteristic
487C4#6436711yescharacteristic
488C3#8167314yescomplemented
489C2—81no—
490C2—721no—
491C2#1059614811yescharacteristic
492C2#1059624411yescharacteristic
493C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#489C2
socleC22×C32C22×D4
prime radical#64149C22
hypercenter#489C3⋊D3
hypocenterC32#3371
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10596192C2semidirect
3. C32×#489C2semidirect
4. #10592783C2semidirect
5. #10592753C2semidirect
6. #10592499C2semidirect
7. #10592497C2semidirect
8. #10592495C2semidirect
9. #10592488C2semidirect
10. #10592465C2semidirect
13. #10592457C2semidirect
14. #10592409C2semidirect
15. #10592400C2semidirect
62. C3×#489D3semidirect
201. #489C3⋊D3semidirect
428. C32#3371semidirect
488. C3#81673semidirect

Maximal subgroups

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

subgroupindex
#105961922
#105961522
C32×#4892
#105927832
#105927532
#105924992
#105924972
#105924952
#105924882
#105924652
#105924632
#105924612
#105924572
#105924092
#105924002
#816733