Finite Group Databasebeta

← #11869015

Subgroups — #11869015

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596200C211yesmaximal, characteristic
2#10596043C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4#10592790C211yesmaximal, characteristic, complemented
5#10592721C211yesmaximal, characteristic, complemented
6#10592560C211yesmaximal, characteristic
7#10592559C211yesmaximal, characteristic
8#10592556C211yesmaximal, characteristic, complemented
9#10592553C211yesmaximal, characteristic, complemented
10#10592538C211yesmaximal, characteristic
11#10592528C211yesmaximal, characteristic, complemented
12#10592501C211yesmaximal, characteristic
13C3⋊D3×#103C211yesmaximal, characteristic
14#10592498C211yesmaximal, characteristic, complemented
15#10592492C211yesmaximal, characteristic, complemented
16#81013—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C32×C4⋊Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64155—21no—
21Q8×C3⋊Dic3C2211yescharacteristic
22#64153—21no—
23C2×#3743C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25#64105—21no—
26#64101—21no—
27#64101C2211yescharacteristic
28#64101C2211yescharacteristic
29C4⋊C4×C3⋊D3C2211yescharacteristic
30#64099C2211yescharacteristic
31#64098—21no—
32#64097C2211yescharacteristic
33#64096—21no—
34#64096C2211yescharacteristic
35#64081—21no—
36#64081C2211yescharacteristic
37#64079C2211yescharacteristic
38C4×#634—21no—
39C4×#634C2211yescharacteristic
40C32×#106C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63645C2211yescharacteristic
48#63644C2211yescharacteristic
49#63643C2211yescharacteristic
50#63643C2211yescharacteristic
51#63641C2211yescharacteristic
52#63641C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55#63635C2211yescharacteristic
56#63634C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5729—34no—
61#5572—34no—
62C3×#475D314yescomplemented
63#5091—34no—
64#5022—34no—
65#4861—34no—
66#4860—34no—
67#4857—34no—
68#4854—34no—
69#4839—34no—
70#4829—34no—
71#4802—34no—
72D3×#103—34no—
73#4799—34no—
74#4793—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8C2311yescharacteristic
77Q8×C3⋊D3—22no—
78Q8×C3⋊D3Q814yescomplemented
79C2×C4×C3⋊D3—21no—
80C2×C4×C3⋊D3—21no—
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×#634—21no—
83C2×#634—21no—
84C2×#634C2311yescharacteristic
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C4⋊C4C2311yescharacteristic
91C32×C4⋊C4C2311yescharacteristic
92C32×C42—21no—
93C32×C42C2311yescharacteristic
94#3752—21no—
95#3752—21no—
96#3752D411yescharacteristic
97#3752D411yescharacteristic
98C4⋊(C3⋊Dic3)—21no—
99C4⋊(C3⋊Dic3)—21no—
100C4⋊(C3⋊Dic3)C2311yescharacteristic
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750—21no—
104#3750—21no—
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⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—22no—
121C8×C3⋊D3—22no—
122#3082—91noSylow
123C2×D3×Q8—34no—
124C3×C4⋊Q8C2×D314yes—
125C3×C4×Q8C2×D314yes—
126#946—64no—
127Q8×Dic3—34no—
128#944—64no—
129C2×ΓL(1,𝔽25)—34no—
130C2×D3×C8—34no—
131#896—64no—
132#892—34no—
133#892—34no—
134#892—64no—
135D3×C4⋊C4—34no—
136#890—34no—
137#889—64no—
138#888—34no—
139#887—34no—
140#887—64no—
141#872—34no—
142#872—64no—
143#870—34no—
144C4×Dic6—34no—
145C4×Dic6—64no—
146C3×#106C2×D314yes—
147C3×#106C2×D314yes—
148C3×C4⋊C8C2×D314yes—
149C3×#103C2×D314yes—
150C3×#103C2×D314yes—
151#835—34no—
152#835—34no—
153#818—34no—
154#817—34no—
155#816—34no—
156#816—34no—
157Dic3⋊C8—34no—
158Dic3⋊C8—34no—
159#810—34no—
160#810—34no—
161#808—34no—
162#807—34no—
163#807—34no—
164#807—34no—
165C4⋊(C3⋊C8)—34no—
166C22×C3⋊D3C2×D411yescharacteristic
167C32×Q8—21no—
168C32×Q8—81no—
169C32×Q8C2×Q812yes—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
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⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4×C3⋊D3—24no—
185C4×C3⋊D3—81no—
186C4×C3⋊D3C2×Q812yes—
187C4×C3⋊D3#4112yes—
188#634—21no—
189#634—24no—
190#634—81no—
191#634C2×Q812yes—
192C32×C8—21no—
193C32×C8—21no—
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)—21no—
196#544—91no—
197#519—91no—
198#479—91no—
199#479—91no—
200#479—91no—
201#479—91no—
202#477—91no—
203#477—91no—
204#475—91no—
205#475C3⋊D311yescharacteristic, complemented
206#428—91no—
207#427—91no—
208#424—91no—
209#419—91no—
210C2×#103—91no—
211C2×C3×Q8—24no—
212C2×C3×Q8C22×D314yes—
213D3×Q8—316no—
214D3×Q8—68no—
215C2×C4×D3—34no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×Dic6—34no—
219C2×Dic6—64no—
220C2×Dic6—64no—
221C2×C3×C8C22×D314yes—
222C2×C3×C8C22×D314yes—
223C3×C4⋊C4—24no—
224C3×C4⋊C4—24no—
225C3×C4⋊C4C22×D314yes—
226C3×C4⋊C4C22×D314yes—
227C3×C4⋊C4C22×D314yes—
228C3×C42—24no—
229C3×C42C22×D314yes—
230(C2×D3)⋊C4—34no—
231(C2×D3)⋊C4—34no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—64no—
234C4⋊Dic3—34no—
235C4⋊Dic3—34no—
236C4⋊Dic3—34no—
237C4⋊Dic3—64no—
238C4⋊Dic3—64no—
239Dic3⋊C4—34no—
240Dic3⋊C4—34no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248C4×Dic3—34no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C4×Dic3—64no—
254C2×C3⋊C8—34no—
255C2×C3⋊C8—34no—
256ΓL(1,𝔽25)—68no—
257D3×C8—68no—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—21no—
260C2×C3⋊D3—21no—
261C2×C3⋊D3C22⋊Q812yes—
262C32×C4—22no—
263C32×C4—21no—
264C32×C4—21no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4C22×Q811yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3⋊Dic3—22no—
271C3⋊Dic3—21no—
272C3⋊Dic3—21no—
273C3⋊Dic3—41no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3⋊Dic3C22⋊Q812yes—
277C22×Q8—91no—
278C2×M16—91no—
279C22×C8—91no—
280C4⋊Q8—91no—
281C4⋊Q8—181no—
282C4⋊Q8C2×C3⋊D311yescharacteristic
283#125—91no—
284#125—91no—
285#125—181no—
286C22⋊Q8—181no—
287C22⋊Q8—181no—
288C4×Q8—91no—
289C4×Q8—91no—
290C4×Q8—91no—
291C4×Q8—181no—
292C4×Q8—181no—
293C4×Q8C2×C3⋊D311yescharacteristic
294#117—91no—
295#117—91no—
296#117—91no—
297#117—181no—
298#117—181no—
299C2×C4⋊C4—91no—
300#107—91no—
301#107—91no—
302#107—91no—
303#107—91no—
304#106—91no—
305#106—91no—
306#106C2×C3⋊D311yescharacteristic
307#106C2×C3⋊D311yescharacteristic
308C4⋊C8—91no—
309C4⋊C8—91no—
310C4⋊C8—91no—
311C4⋊C8C2×C3⋊D311yescharacteristic
312#103—91no—
313#103—91no—
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103C2×C3⋊D311yescharacteristic
319#103C2×C3⋊D311yescharacteristic
320C22×D3—34no—
321C3×Q8—24no—
322C3×Q8—84no—
323C3×Q8D3×Q818yes—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4D3×D414yes—
329C2×C3×C4D3×D414yes—
330C2×C3×C4C23×D314yes—
331C2×Dic3—34no—
332C2×Dic3—34no—
333C2×Dic3—34no—
334C2×Dic3—64no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C4×D3—38no—
339C4×D3—38no—
340C4×D3—616no—
341C4×D3—244no—
342Dic6—38no—
343Dic6—616no—
344Dic6—64no—
345Dic6—244no—
346C3×C8—24no—
347C3×C8—24no—
348C3⋊C8—64no—
349C3⋊C8—64no—
350C2×C32C2×C22⋊Q811yescharacteristic
351C2×C32#57711yescharacteristic
352C2×C32#57811yescharacteristic
353C3⋊D3—22no—
354C2×Q8—21no—
355C2×Q8—94no—
356C2×Q8—91no—
357C2×Q8—181no—
358C2×Q8—181no—
359C2×Q8—182no—
360C2×Q8C22×C3⋊D311yescharacteristic
361C22×C4—91no—
362C22×C4—181no—
363C22×C4—181no—
364M16—182no—
365C2×C8—91no—
366C2×C8—91no—
367C2×C8—182no—
368C2×C8C22×C3⋊D311yescharacteristic
369C2×C8C22×C3⋊D311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—91no—
373C4⋊C4—91no—
374C4⋊C4—91no—
375C4⋊C4—91no—
376C4⋊C4—91no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4C22×C3⋊D311yescharacteristic
387C4⋊C4C22×C3⋊D311yescharacteristic
388C4⋊C4C22×C3⋊D311yescharacteristic
389C22⋊C4—91no—
390C22⋊C4—91no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C42—21no—
394C42—91no—
395C42—181no—
396C42—181no—
397C42—181no—
398C42—181no—
399C42—181no—
400C42C22×C3⋊D311yescharacteristic
401C22×C3C2×D3×D414yes—
402C2×D3—38no—
403C2×D3—64no—
404C2×D3—64no—
405C3×C4—24no—
406C3×C4—24no—
407C3×C4—28no—
408C3×C4—44no—
409C3×C4—44no—
410C3×C4—44no—
411C3×C4C2×D3×Q814yes—
412C3×C4D3×#4114yes—
413Dic3—38no—
414Dic3—64no—
415Dic3—64no—
416Dic3—68no—
417Dic3—124no—
418Dic3—124no—
419Dic3—124no—
420C32#308211yescharacteristic, complemented, Sylow
421C23—91no—
422Q8—21no—
423Q8—81no—
424Q8—92no—
425Q8—184no—
426Q8—181no—
427Q8—721no—
428Q8Q8×C3⋊D312yes—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—91no—
434C2×C4—92no—
435C2×C4—92no—
436C2×C4—91no—
437C2×C4—91no—
438C2×C4—184no—
439C2×C4—181no—
440C2×C4—181no—
441C2×C4—181no—
442C2×C4—181no—
443C2×C4—721no—
444C2×C4D4×C3⋊D311yescharacteristic
445C2×C4D4×C3⋊D311yescharacteristic
446C2×C4C23×C3⋊D311yescharacteristic
447C8—21no—
448C8—21no—
449C8—181no—
450C8—181no—
451C2×C3D3×C22⋊Q814yes—
452C2×C3#576214yes—
453C2×C3#577914yes—
454D3—68no—
455C22—92no—
456C22—181no—
457C22—181no—
458C22C2×D4×C3⋊D311yescharacteristic
459C4—22no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—92no—
466C4—182no—
467C4—181no—
468C4—181no—
469C4—361no—
470C4—361no—
471C4—361no—
472C4C2×Q8×C3⋊D311yescharacteristic
473C4#41×C3⋊D311yescharacteristic
474C3#8101314yescomplemented
475C2—182no—
476C2C3⋊D3×C22⋊Q811yescharacteristic
477C2#1059623311yescharacteristic
478C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#475C3⋊D3
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C32×#475C2semidirect
4. #10592790C2semidirect
5. #10592721C2semidirect
8. #10592556C2semidirect
9. #10592553C2semidirect
11. #10592528C2semidirect
14. #10592498C2semidirect
15. #10592492C2semidirect
62. C3×#475D3semidirect
78. Q8×C3⋊D3Q8semidirect
205. #475C3⋊D3semidirect
420. C32#3082semidirect
474. C3#81013semidirect

Maximal subgroups

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

subgroupindex
#105962002
#105960432
C32×#4752
#105927902
#105927212
#105925602
#105925592
#105925562
#105925532
#105925382
#105925282
#105925012
C3⋊D3×#1032
#105924982
#105924922
#810133