Finite Group Databasebeta

← #11787782

Subgroups — #11787782

Order 1152.

743 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3#10592939C211yesmaximal, characteristic, complemented
4#10591110C212yesmaximal, complemented
5#10589162C212yesmaximal, complemented
6#72021—31nomaximal
7#71817—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10#64135C2212yes—
11C3×#948—24no—
12C3×#947C411yescharacteristic, complemented
13C3×#944C411yescharacteristic, complemented
14C3×#940C411yescharacteristic, complemented
15C3×#939—22no—
16C3×#936C411yescharacteristic, complemented
17C3×C4×#67—22no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208—22no—
20C2×C3×#208C2212yes—
21#63661—22no—
22#63568—24no—
23C3×#568—31no—
24C3×#532—31no—
25#5832D311yescharacteristic
26#5819D311yescharacteristic, complemented
27#5240—31no—
28#5240—31no—
29#5240—61no—
30#5236—32no—
31#5139—32no—
32#4555—32no—
33#4523—32no—
34C32×#41—22no—
35C32×#41—22no—
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4C2×C411yescharacteristic
38C2×C32×D4D412yes—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—22no—
42C2×C3×#67—21no—
43C22×C3×Dic3—21no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6C2×C411yescharacteristic
49#3757—22no—
50C4⋊(C3⋊Dic3)—22no—
51C4×C3⋊Dic3—22no—
52C3×#217—22no—
53C3×(C2×D3)⋊C4—22no—
54C3×Dic3⋊C4—22no—
55C3×C4×Dic3—21no—
56C3×C4×Dic3C2×C411yescharacteristic
57C3×C4×Dic3C2×C411yescharacteristic
58C3×#208—24no—
59C3×#208—22no—
60C3×#208D414yescomplemented
61C2×C3×C3⋊C8—24no—
62C2×C3×C3⋊C8—22no—
63#1884—91noSylow
64C2×C3×#41—21no—
65C2×C3×#41—31no—
66C2×C3×#41C2×D311yescharacteristic
67C2×C3×#41C2×D311yescharacteristic
68C2×#235C2×D311yescharacteristic
69C3×#131—64no—
70C2×C3×M16—32no—
71C2×C3×M16—62no—
72C3×C4⋊Q8—31no—
73C3×#127—31no—
74C3×#124—31no—
75C3×#124—31no—
76C3×#121—62no—
77C3×C4×D4—62no—
78C2×C3×C42—31no—
79#948—24no—
80#947Dic311yescharacteristic, complemented
81#944Dic311yescharacteristic, complemented
82#940Dic311yescharacteristic, complemented
83#939—22no—
84#936Dic311yescharacteristic, complemented
85C4×#67—22no—
86#926—32no—
87#926—32no—
88#926—62no—
89C2×C4×Dic3C2×D311yescharacteristic
90C2×#208—22no—
91C2×#208C2×D312yes—
92#837—64no—
93#834—64no—
94#834—62no—
95#834—62no—
96#825—64no—
97C23×C32C22⋊C412yes—
98C23×C32C2×D411yescharacteristic
99C22×C3×D3—21no—
100C32×Q8—22no—
101C32×D4—24no—
102C32×D4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4C22⋊C412yes—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4112yes—
110C2×C3⋊Dic3—42no—
111C3×#67—44no—
112C3×#67—42no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×C4×D3—41no—
119C3×C4×D3—41no—
120C3×Dic6—22no—
121C3×C3⋊C8—24no—
122#568—31no—
123#532—31no—
124#421—92no—
125#410—91no—
126#339—92no—
127C3×#41—22no—
128C3×#41—22no—
129C3×#41—22no—
130C3×#41—22no—
131C3×#41—42no—
132C3×#41—42no—
133C3×#41—62no—
134C3×#41—62no—
135C2×C3×Q8—21no—
136C2×C3×Q8—31no—
137C2×C3×Q8C4×D311yescharacteristic
138C2×C3×Q8C2×Dic311yescharacteristic
139C2×C3×D4—21no—
140C2×C3×D4—22no—
141C2×C3×D4—31no—
142C2×C3×D4—62no—
143C2×C3×D4—61no—
144C2×C3×D4C4×D311yescharacteristic
145C2×C3×D4D1212yes—
146C2×C3×D4C2×Dic311yescharacteristic
147C2×C3×D4#6712yes—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4#6712yes—
153C22×C3×C4#6712yes—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—22no—
157C2×#67—21no—
158C22×Dic3—21no—
159#235—22no—
160#235—22no—
161C2×D12C2×Dic311yescharacteristic
162C2×C4×D3—21no—
163C2×Dic6C2×Dic311yescharacteristic
164C3×M16—34no—
165C3×M16—64no—
166C3×M16—62no—
167C2×C3×C8—64no—
168C2×C3×C8—62no—
169C3×C4⋊C4—62no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—62no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—61no—
175#217—22no—
176#217—64no—
177#217—62no—
178#217—62no—
179(C2×D3)⋊C4—22no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—122no—
183Dic3⋊C4—22no—
184C4×Dic3—21no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3—122no—
188C4×Dic3C2×Dic311yescharacteristic
189C4×Dic3C2×Dic311yescharacteristic
190#208—24no—
191#208—22no—
192#208#6714yescomplemented
193C2×C3⋊C8—24no—
194C2×C3⋊C8—22no—
195C22×C32—22no—
196C22×C32—41no—
197C22×C32—42no—
198C22×C32C2×C22⋊C411yescharacteristic
199C22×C32#12112yes—
200C2×C3×D3—42no—
201C2×C3×D3—41no—
202C32×C4—22no—
203C32×C4C4×D412yes—
204C32×C4#12011yescharacteristic
205C32×C4#12311yescharacteristic
206C3⋊Dic3—82no—
207C3×Dic3—22no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C2×#41—31no—
211C2×#41D3211yescharacteristic
212#131—64no—
213C2×M16—32no—
214C2×M16—62no—
215C4⋊Q8—31no—
216#127—31no—
217#124—31no—
218#124—31no—
219#121—62no—
220C4×D4—62no—
221#117—92no—
222C2×C42—31no—
223#104—184no—
224#99—182no—
225C23×C3—22no—
226C23×C3—21no—
227C23×C3—61no—
228C23×C3(C2×D3)⋊C412yes—
229C23×C3#21712yes—
230C23×C3C2×D1211yescharacteristic
231C23×C3C2×#6711yescharacteristic
232C22×D3—21no—
233C3×Q8—22no—
234C3×Q8—22no—
235C3×Q8—42no—
236C3×Q8—62no—
237C3×D4—24no—
238C3×D4—24no—
239C3×D4—22no—
240C3×D4—22no—
241C3×D4—42no—
242C3×D4—44no—
243C3×D4—62no—
244C3×D4—124no—
245C3×D4—122no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—122no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4(C2×D3)⋊C412yes—
264C2×C3×C4#21712yes—
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4#23512yes—
267C2×C3×C4D3×D412yes—
268C2×C3×C4#23712yes—
269C2×C3×C4C22×Dic311yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6712yes—
273#67—44no—
274#67—42no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—42no—
279C2×Dic3—124no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282D12—22no—
283C4×D3—41no—
284C4×D3—41no—
285Dic6—22no—
286C3×C8—64no—
287C3⋊C8—24no—
288C2×C32—21no—
289C2×C32—22no—
290C2×C32—42no—
291C2×C32#38611yescharacteristic
292C3×D3—81no—
293#41—22no—
294#41—22no—
295#41—62no—
296#41—62no—
297C2×Q8—31no—
298C2×Q8D3×Dic311yescharacteristic
299C2×D4—31no—
300C2×D4—62no—
301C2×D4—61no—
302C2×D4D3×Dic311yescharacteristic
303C2×D4#62612yes—
304C22×C4—61no—
305C22×C4—61no—
306C22×C4#62512yes—
307C22×C4C2×D3211yescharacteristic
308M16—34no—
309M16—64no—
310M16—62no—
311C2×C8—64no—
312C2×C8—62no—
313C4⋊C4—62no—
314C4⋊C4—182no—
315C22⋊C4—62no—
316C22⋊C4—62no—
317C22⋊C4—182no—
318C42—31no—
319C42—31no—
320C42—61no—
321C42—182no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—22no—
326C22×C3—42no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—81no—
332C22×C3—82no—
333C22×C3—122no—
334C22×C3—121no—
335C22×C3C2×(C2×D3)⋊C411yescharacteristic
336C22×C3#93012yes—
337C22×C3#93912yes—
338C22×C3C2×#21711yescharacteristic
339C2×D3—42no—
340C2×D3—41no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—22no—
345C3×C4—21no—
346C3×C4—42no—
347C3×C4—62no—
348C3×C4—121no—
349C3×C4—121no—
350C3×C4C4×#6712yes—
351C3×C4#92911yescharacteristic
352C3×C4D4×Dic312yes—
353C3×C4#93511yescharacteristic
354C3×C4#93711yescharacteristic
355C3×C4#95311yescharacteristic
356Dic3—22no—
357Dic3—41no—
358Dic3—41no—
359Dic3—242no—
360Dic3—242no—
361Dic3—244no—
362C32#188411yescharacteristic, complemented, Sylow
363C23—61no—
364C23(C2×D3)⋊Dic312yes—
365C23C2×#62611yescharacteristic
366Q8—22no—
367Q8—62no—
368D4—24no—
369D4—22no—
370D4—62no—
371D4—124no—
372D4—122no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—122no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—362no—
382C2×C4(C2×D3)⋊Dic312yes—
383C2×C4C2×D3×Dic311yescharacteristic
384C2×C4#380412yes—
385C2×C4C2×#62511yescharacteristic
386C2×C4D3×#6712yes—
387C8—64no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—22no—
392C2×C3—21no—
393C2×C3—42no—
394C2×C3—41no—
395C2×C3—42no—
396C2×C3—42no—
397C2×C3—82no—
398C2×C3—241no—
399C2×C3#521311yescharacteristic
400C2×C3#522011yescharacteristic
401D3—81no—
402C22—22no—
403C22—41no—
404C22—42no—
405C22—122no—
406C22—121no—
407C22C2×(C2×D3)⋊Dic311yescharacteristic
408C22#6397812yes—
409C4—22no—
410C4—62no—
411C4—121no—
412C4—121no—
413C4—722no—
414C4#6396111yescharacteristic
415C4Dic3×#6712yes—
416C4#6397611yescharacteristic
417C3—21no—
418C3#7181711yescharacteristic, complemented
419C3#7202111yescharacteristic, complemented
420C2—21no—
421C2—22no—
422C2—42no—
423C2—241no—
424C2#1059171011yescharacteristic
subgroupG/H
centerC4#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radicalC3×#5832C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. #10592939C2semidirect
4. #10591110C2semidirect
5. #10589162C2semidirect
12. C3×#947C4semidirect
13. C3×#944C4semidirect
14. C3×#940C4semidirect
16. C3×#936C4semidirect
26. #5819D3semidirect
60. C3×#208D4semidirect
80. #947Dic3semidirect
81. #944Dic3semidirect
82. #940Dic3semidirect
84. #936Dic3semidirect
192. #208#67semidirect
362. C32#1884semidirect
418. C3#71817semidirect
419. C3#72021semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
C3×#58192
#105929392
#105911102
#105891622
#720213
#718173