Finite Group Databasebeta

← #11896028

Subgroups — #11896028

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596039C211yesmaximal, characteristic
2Q8×#634C211yesmaximal, characteristic, complemented
3C32×#441C211yesmaximal, characteristic, complemented
4#10592884C211yesmaximal, characteristic
5#10592881C211yesmaximal, characteristic, complemented
6#10592727C211yesmaximal, characteristic
7#10592719C211yesmaximal, characteristic, complemented
8#10592569C211yesmaximal, characteristic
9#10592553C211yesmaximal, characteristic, complemented
10#10592493C211yesmaximal, characteristic
11#10592491C211yesmaximal, characteristic, complemented
12#10592488C211yesmaximal, characteristic, complemented
13#10592487C211yesmaximal, characteristic
14#10592413C211yesmaximal, characteristic
15#10592400C211yesmaximal, characteristic, complemented
16#79815—34nomaximal
17C2×C32×Q16C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64156C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26#64107—21no—
27#64105—21no—
28#64102C2211yescharacteristic
29#64097—21no—
30#64097—21no—
31#64097C2211yescharacteristic
32#64097C2211yescharacteristic
33#64096C2211yescharacteristic
34#64085—21no—
35#64084C2211yescharacteristic
36#64081—21no—
37#64078—21no—
38#64078C2211yescharacteristic
39C4×#634—21no—
40C4×#634C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#97C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63643C2211yescharacteristic
50#63643C2211yescharacteristic
51#63642C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54C8×C3⋊Dic3C2211yescharacteristic
55#63637C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63635C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5568—34no—
61Q8×Dic6—34no—
62C3×#441D314yescomplemented
63#5185—34no—
64#5182—34no—
65#5028—34no—
66#5020—34no—
67#4870—34no—
68#4854—34no—
69#4794—34no—
70#4792—34no—
71#4789—34no—
72#4788—34no—
73#4714—34no—
74#4701—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3—21no—
79C2×#634—21no—
80C2×#634—21no—
81C2×#634—21no—
82C2×#634D411yescharacteristic
83C2×#634C2311yescharacteristic
84C32×Q16—22no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C4⋊C4C2311yescharacteristic
91C32×C42—21no—
92C32×C42—21no—
93C32×C42C2311yescharacteristic
94#3756—22no—
95#3755—22no—
96#3752—21no—
97#3752—21no—
98#3752—21no—
99#3752—21no—
100#3752—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
107#3750—21no—
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#3369—91noSylow
122C2×C3×Q16C2×D314yes—
123C3×C4×Q8C2×D314yes—
124C3×C4×Q8C2×D314yes—
125#947—34no—
126Q8×Dic3—34no—
127Q8×Dic3—34no—
128#944—34no—
129C2×#216—34no—
130C2×#215—34no—
131#898—64no—
132#896—64no—
133#893—34no—
134#888—34no—
135#888—34no—
136#888—64no—
137#888—64no—
138#887—34no—
139#876—64no—
140#875—34no—
141#872—64no—
142#869—34no—
143#869—64no—
144C4×Dic6—34no—
145C4×Dic6—64no—
146C3×#106C2×D314yes—
147C3×#103C2×D314yes—
148C3×#103C2×D314yes—
149C3×#97C2×D314yes—
150#835—34no—
151#835—34no—
152#821—34no—
153#821—34no—
154#816—34no—
155#816—34no—
156#815—34no—
157Dic3⋊C8—34no—
158Dic3⋊C8—34no—
159C8×Dic3—34no—
160#810—34no—
161#809—34no—
162#808—34no—
163#808—34no—
164C4⋊(C3⋊C8)—34no—
165C22×C3⋊D3—21no—
166C32×Q8—21no—
167C32×Q8—21no—
168C32×Q8—21no—
169C32×Q8#4112yes—
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⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4×C3⋊D3—42no—
187#634—22no—
188#634—21no—
189#634—21no—
190#634—81no—
191#634—81no—
192#634—81no—
193C32×C8—21no—
194C32×C8—21no—
195C3⋊(C3⋊C8)—21no—
196C3⋊(C3⋊C8)—21no—
197Q82—91no—
198#556—91no—
199#489—91no—
200#489—91no—
201#487—91no—
202#476—91no—
203#475—91no—
204#475—91no—
205#464—91no—
206#464—91no—
207#462—91no—
208#446—91no—
209#441—91no—
210#441C3⋊D311yescharacteristic, complemented
211C4×SD16—91no—
212C2×C3×Q8C22×D314yes—
213C2×C3×Q8C22×D314yes—
214C2×D12—34no—
215C2×C4×D3—64no—
216C2×Dic6—34no—
217C2×Dic6—34no—
218C2×Dic6—64no—
219C2×Dic6—64no—
220C2×Dic6—64no—
221C3×Q16—28no—
222C2×C3×C8C22×D314yes—
223C2×C3×C8C22×D314yes—
224C3×C4⋊C4—24no—
225C3×C4⋊C4—24no—
226C3×C4⋊C4C22×D314yes—
227C3×C4⋊C4C22×D314yes—
228C3×C42—24no—
229C3×C42—24no—
230C3×C42C22×D314yes—
231#216—68no—
232#215—68no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
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—64no—
242C4⋊Dic3—64no—
243C4⋊Dic3—64no—
244Dic3⋊C4—34no—
245Dic3⋊C4—34no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251C4×Dic3—34no—
252C4×Dic3—34no—
253C4×Dic3—64no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—34no—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—41no—
260C2×C3⋊D3—41no—
261C2×C3⋊D3—41no—
262C32×C4—22no—
263C32×C4—21no—
264C32×C4—21no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4C2×#4111yescharacteristic
269C32×C42−1+411yescharacteristic
270C3⋊Dic3—21no—
271C3⋊Dic3—21no—
272C3⋊Dic3—21no—
273C3⋊Dic3—41no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3⋊Dic3#13712yes—
277C2×Q16—91no—
278C2×Q16C2×C3⋊D311yescharacteristic
279C2×SD16—91no—
280C4⋊Q8—91no—
281C4⋊Q8—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284C4⋊Q8—181no—
285C4⋊Q8—181no—
286C4⋊Q8—181no—
287#126—181no—
288#126—181no—
289#124—91no—
290#124—91no—
291C22⋊Q8—181no—
292C4×Q8—91no—
293C4×Q8—91no—
294C4×Q8—91no—
295C4×Q8—91no—
296C4×Q8—181no—
297C4×Q8C2×C3⋊D311yescharacteristic
298C4×Q8C2×C3⋊D311yescharacteristic
299C4×D4—91no—
300#117—181no—
301#106—91no—
302#106—91no—
303#106C2×C3⋊D311yescharacteristic
304C4⋊C8—91no—
305C4⋊C8—91no—
306C4⋊C8—91no—
307#103—91no—
308#103—91no—
309#103—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#97—91no—
318#97C2×C3⋊D311yescharacteristic
319C4×C8—91no—
320C22×D3—64no—
321C3×Q8—24no—
322C3×Q8—24no—
323C3×Q8—24no—
324C3×Q8#23518yes—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4D3×D414yes—
330C2×C3×C4D3×D414yes—
331C2×C3×C4C23×D314yes—
332C2×Dic3—34no—
333C2×Dic3—34no—
334C2×Dic3—34no—
335C2×Dic3—34no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339D12—64no—
340D12—64no—
341C4×D3—128no—
342Dic6—68no—
343Dic6—64no—
344Dic6—64no—
345Dic6—244no—
346Dic6—244no—
347Dic6—244no—
348C3×C8—24no—
349C3×C8—24no—
350C3⋊C8—64no—
351C3⋊C8—64no—
352C2×C32#54811yescharacteristic
353C2×C32C2×#13711yescharacteristic
354C2×C32#57711yescharacteristic
355C3⋊D3—81no—
356C2×Q8—91no—
357C2×Q8—91no—
358C2×Q8—181no—
359C2×Q8—181no—
360C2×Q8—181no—
361C2×Q8C22×C3⋊D311yescharacteristic
362C2×Q8C22×C3⋊D311yescharacteristic
363C2×D4—91no—
364C22×C4—181no—
365Q16—22no—
366Q16—182no—
367SD16—182no—
368C2×C8—91no—
369C2×C8—91no—
370C2×C8C22×C3⋊D311yescharacteristic
371C2×C8C22×C3⋊D311yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—91no—
375C4⋊C4—91no—
376C4⋊C4—91no—
377C4⋊C4—91no—
378C4⋊C4—91no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4C22×C3⋊D311yescharacteristic
388C4⋊C4C22×C3⋊D311yescharacteristic
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C22⋊C4—181no—
394C42—21no—
395C42—21no—
396C42—91no—
397C42—91no—
398C42—181no—
399C42—181no—
400C42—181no—
401C42C22×C3⋊D311yescharacteristic
402C22×C3C2×D3×D414yes—
403C2×D3—124no—
404C2×D3—124no—
405C2×D3—124no—
406C3×C4—24no—
407C3×C4—24no—
408C3×C4—28no—
409C3×C4—44no—
410C3×C4—44no—
411C3×C4—44no—
412C3×C4C2×#23514yes—
413C3×C4#101014yes—
414Dic3—38no—
415Dic3—64no—
416Dic3—64no—
417Dic3—64no—
418Dic3—124no—
419Dic3—124no—
420Dic3—124no—
421C32#336911yescharacteristic, complemented, Sylow
422C23—181no—
423Q8—21no—
424Q8—21no—
425Q8—21no—
426Q8—182no—
427Q8—181no—
428Q8—181no—
429Q8—721no—
430Q8—721no—
431Q8—721no—
432Q8#382812yes—
433D4—181no—
434D4—181no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—91no—
442C2×C4—91no—
443C2×C4—181no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—362no—
447C2×C4D4×C3⋊D311yescharacteristic
448C2×C4D4×C3⋊D311yescharacteristic
449C2×C4C23×C3⋊D311yescharacteristic
450C8—21no—
451C8—21no—
452C8—181no—
453C8—181no—
454C2×C3#555214yes—
455C2×C3D3×#13714yes—
456C2×C3#577814yes—
457D3—244no—
458C22—361no—
459C22—361no—
460C22—361no—
461C22C2×D4×C3⋊D311yescharacteristic
462C4—21no—
463C4—21no—
464C4—22no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—92no—
469C4—181no—
470C4—181no—
471C4—181no—
472C4—361no—
473C4—361no—
474C4—361no—
475C4C2×#382811yescharacteristic
476C4#6436711yescharacteristic
477C3#7981514yescomplemented
478C2—721no—
479C2#1059602311yescharacteristic
480C2C3⋊D3×#13711yescharacteristic
481C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#441C3⋊D3
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. Q8×#634C2semidirect
3. C32×#441C2semidirect
5. #10592881C2semidirect
7. #10592719C2semidirect
9. #10592553C2semidirect
11. #10592491C2semidirect
12. #10592488C2semidirect
15. #10592400C2semidirect
62. C3×#441D3semidirect
210. #441C3⋊D3semidirect
421. C32#3369semidirect
477. C3#79815semidirect

Maximal subgroups

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

subgroupindex
#105960392
Q8×#6342
C32×#4412
#105928842
#105928812
#105927272
#105927192
#105925692
#105925532
#105924932
#105924912
#105924882
#105924872
#105924132
#105924002
#798153