Finite Group Databasebeta

← #11784941

Subgroups — #11784941

Order 1152.

1175 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2#10592939C211yesmaximal, characteristic, complemented
3C3×#5234C211yesmaximal, characteristic, complemented
4#10591110C212yesmaximal, complemented
5#10591084C212yesmaximal, complemented
6#72146—31nomaximal
7#70010—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C3×#1010—22no—
10C3×#1009—22no—
11C3×D3×#41—24no—
12C3×#1007C412yescomplemented
13C3×#1004—22no—
14C3×#1004C412yescomplemented
15C2×C3×#235—22no—
16C2×C3×#235C2212yes—
17#64135C2212yescomplemented
18C2×C3×#208C2211yescharacteristic, complemented
19C22×C3×C3⋊C8C2211yescharacteristic, complemented
20#63661—22no—
21C3×#830—22no—
22#63568—24no—
23#63566—22no—
24#63563—22no—
25C3×#585—31no—
26#5964D311yescharacteristic
27C3×#408—31no—
28#5240—31no—
29#5240—31no—
30#5240—61no—
31#5236—32no—
32#5234D311yescharacteristic, complemented
33#5233—32no—
34#5139—32no—
35#5113—32no—
36C32×#41—22no—
37C32×#41—22no—
38C2×C32×Q8C2×C411yescharacteristic
39C2×C32×D4C2×C411yescharacteristic
40C2×C32×D4D412yes—
41C22×C32×C4D412yes—
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—24no—
44C2×C3×#67—22no—
45C3×#239—24no—
46C3×D3×Q8—24no—
47C3×#237—28no—
48C3×#237—24no—
49C3×D3×D4—28no—
50C3×D3×D4—24no—
51C3×#235—24no—
52C3×#235—24no—
53C3×#235—24no—
54C3×#235—22no—
55C3×#235—22no—
56C3×#235C2×C414yes—
57C3×#235D414yes—
58C2×C3×D12—22no—
59C2×C3×D12D412yes—
60C2×C3×C4×D3—24no—
61C2×C3×C4×D3—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6D412yes—
64#3757—22no—
65C4⋊(C3⋊Dic3)—22no—
66C4×C3⋊Dic3—22no—
67C3×#208—22no—
68C2×C3×C3⋊C8—22no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1794—91noSylow
72C3×2−1+4—32no—
73C3×2−1+4—62no—
74C3×H(5,𝔽2)—32no—
75C3×H(5,𝔽2)—62no—
76C3×H(5,𝔽2)—62no—
77C2×C3×#41—21no—
78C2×C3×#41—32no—
79C2×C3×#41—64no—
80C2×C3×#41—62no—
81C2×C3×#41C2×D311yescharacteristic
82C2×C3×#41C2×D311yescharacteristic
83#1010—22no—
84#1009—22no—
85D3×#41—24no—
86#1007Dic312yescomplemented
87#1004—22no—
88#1004Dic312yescomplemented
89C2×#235—22no—
90C2×#235C2×D312yes—
91C2×C3×M16—31no—
92C22×C3×C8—31no—
93#926—32no—
94#926—32no—
95#926—62no—
96C2×#208C2×D311yescharacteristic, complemented
97C22×C3⋊C8C2×D311yescharacteristic, complemented
98C3×C22⋊C8—62no—
99#837—64no—
100#835—62no—
101#834—64no—
102#834—62no—
103#834—62no—
104#832—62no—
105#830—22no—
106#825—64no—
107#821—62no—
108#816—62no—
109C23×C32C22⋊C412yes—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—24no—
112C22×C3×D3—22no—
113C32×Q8—22no—
114C32×D4—24no—
115C32×D4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4C22⋊C412yes—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—42no—
124C3×#67—28no—
125C3×#67—24no—
126C3×#67—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C3×D12—24no—
130C3×D12—22no—
131C3×D12C22⋊C414yes—
132C3×C4×D3—28no—
133C3×C4×D3—24no—
134C3×C4×D3—24no—
135C3×Dic6—24no—
136C3×Dic6—22no—
137C3×Dic6C22⋊C414yes—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140#585—31no—
141#421—92no—
142#416—92no—
143#410—91no—
144#408—31no—
145C3×#41—22no—
146C3×#41—22no—
147C3×#41—22no—
148C3×#41—22no—
149C3×#41—34no—
150C3×#41—34no—
151C3×#41—42no—
152C3×#41—42no—
153C3×#41—64no—
154C3×#41—64no—
155C3×#41—64no—
156C3×#41—68no—
157C3×#41—64no—
158C3×#41—64no—
159C3×#41—62no—
160C3×#41—62no—
161C2×C3×Q8—21no—
162C2×C3×Q8—32no—
163C2×C3×Q8—62no—
164C2×C3×Q8—64no—
165C2×C3×Q8C4×D311yescharacteristic
166C2×C3×Q8C2×Dic311yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4—22no—
169C2×C3×D4—32no—
170C2×C3×D4—62no—
171C2×C3×D4—64no—
172C2×C3×D4—68no—
173C2×C3×D4—64no—
174C2×C3×D4—62no—
175C2×C3×D4C4×D311yescharacteristic
176C2×C3×D4D1212yes—
177C2×C3×D4C2×Dic311yescharacteristic
178C2×C3×D4#6712yes—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—64no—
182C22×C3×C4—62no—
183C22×C3×C4#6712yes—
184C22×C3×C4#6712yes—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—24no—
188C2×#67—22no—
189#239—24no—
190D3×Q8—24no—
191#237—28no—
192#237—24no—
193D3×D4—28no—
194D3×D4—24no—
195#235—24no—
196#235—24no—
197#235—24no—
198#235—22no—
199#235—22no—
200#235C2×Dic314yes—
201#235#6714yes—
202C2×D12—22no—
203C2×D12#6712yes—
204C2×C4×D3—24no—
205C2×C4×D3—22no—
206C2×Dic6—22no—
207C2×Dic6#6712yes—
208C3×M16—62no—
209C2×C3×C8—62no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212#217—64no—
213#217—62no—
214#217—62no—
215C4⋊Dic3—62no—
216C4⋊Dic3—62no—
217C4⋊Dic3—122no—
218C4×Dic3—62no—
219C4×Dic3—62no—
220C4×Dic3—122no—
221#208—22no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C22×C32—22no—
226C22×C32—41no—
227C22×C32—42no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12012yes—
230C2×C3×D3—24no—
231C2×C3×D3—82no—
232C2×C3×D3—84no—
233C32×C4—22no—
234C32×C4C2×C22⋊C412yes—
235C32×C4#12011yescharacteristic
236C32×C4#12011yescharacteristic
237C3⋊Dic3—82no—
238C3×Dic3—24no—
2392−1+4—32no—
2402−1+4—62no—
241H(5,𝔽2)—32no—
242H(5,𝔽2)—62no—
243H(5,𝔽2)—62no—
244C2×#41—32no—
245C2×#41—64no—
246C2×#41—62no—
247C2×#41D3211yescharacteristic
248C2×M16—31no—
249C22×C8—31no—
250#117—92no—
251#104—184no—
252#103—182no—
253#102—182no—
254#99—182no—
255C22⋊C8—62no—
256C23×C3—22no—
257C23×C3—21no—
258C23×C3—64no—
259C23×C3—62no—
260C23×C3(C2×D3)⋊C412yes—
261C23×C3#21712yes—
262C23×C3C2×D1211yescharacteristic
263C23×C3C2×#6711yescharacteristic
264C22×D3—24no—
265C22×D3—22no—
266C3×Q8—22no—
267C3×Q8—22no—
268C3×Q8—34no—
269C3×Q8—42no—
270C3×Q8—64no—
271C3×Q8—62no—
272C3×D4—24no—
273C3×D4—24no—
274C3×D4—22no—
275C3×D4—22no—
276C3×D4—34no—
277C3×D4—42no—
278C3×D4—44no—
279C3×D4—64no—
280C3×D4—68no—
281C3×D4—64no—
282C3×D4—64no—
283C3×D4—62no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—68no—
296C2×C3×C4—64no—
297C2×C3×C4—62no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4(C2×D3)⋊C412yes—
301C2×C3×C4#21712yes—
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4D3×D412yes—
304C2×C3×C4D3×D412yes—
305C2×C3×C4C22×Dic311yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6712yes—
309C2×C3×C4C2×#6712yes—
310#67—28no—
311#67—24no—
312#67—24no—
313C2×Dic3—24no—
314C2×Dic3—22no—
315C2×Dic3—124no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318D12—24no—
319D12—22no—
320D12#21714yes—
321C4×D3—28no—
322C4×D3—24no—
323C4×D3—24no—
324Dic6—24no—
325Dic6—22no—
326Dic6#21714yes—
327C3×C8—121no—
328C3×C8—121no—
329C3⋊C8—41no—
330C3⋊C8—41no—
331C2×C32—22no—
332C2×C32—21no—
333C2×C32—42no—
334C2×C32#37911yescharacteristic
335C3×D3—44no—
336#41—22no—
337#41—22no—
338#41—34no—
339#41—34no—
340#41—64no—
341#41—64no—
342#41—64no—
343#41—68no—
344#41—64no—
345#41—64no—
346#41—62no—
347#41—62no—
348C2×Q8—32no—
349C2×Q8—62no—
350C2×Q8—64no—
351C2×Q8D3×Dic311yescharacteristic
352C2×D4—32no—
353C2×D4—62no—
354C2×D4—64no—
355C2×D4—68no—
356C2×D4—64no—
357C2×D4—62no—
358C2×D4D3×Dic311yescharacteristic
359C2×D4#62612yes—
360C22×C4—64no—
361C22×C4—62no—
362C22×C4#62512yes—
363C22×C4C2×D3211yescharacteristic
364M16—62no—
365C2×C8—61no—
366C2×C8—61no—
367C2×C8—62no—
368C4⋊C4—182no—
369C22⋊C4—182no—
370C42—182no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—42no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—64no—
381C22×C3—81no—
382C22×C3—82no—
383C22×C3—242no—
384C22×C3—244no—
385C22×C3#88212yes—
386C22×C3C2×(C2×D3)⋊C411yescharacteristic
387C22×C3C2×#21711yescharacteristic
388C22×C3#95312yes—
389C2×D3—24no—
390C2×D3—82no—
391C2×D3—84no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—64no—
399C3×C4D3×C22⋊C412yes—
400C3×C4#93711yescharacteristic
401C3×C4#93711yescharacteristic
402C3×C4C2×#21712yes—
403C3×C4#95311yescharacteristic
404C3×C4#95311yescharacteristic
405Dic3—24no—
406Dic3—242no—
407Dic3—242no—
408Dic3—244no—
409C32#179411yescharacteristic, complemented, Sylow
410C23—64no—
411C23—62no—
412C23(C2×D3)⋊Dic312yes—
413C23C2×#62611yescharacteristic
414Q8—22no—
415Q8—34no—
416Q8—64no—
417Q8—62no—
418D4—24no—
419D4—22no—
420D4—34no—
421D4—64no—
422D4—68no—
423D4—64no—
424D4—64no—
425D4—62no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—68no—
429C2×C4—64no—
430C2×C4—62no—
431C2×C4—64no—
432C2×C4—64no—
433C2×C4—362no—
434C2×C4(C2×D3)⋊Dic312yes—
435C2×C4C2×D3×Dic311yescharacteristic
436C2×C4C2×#62511yescharacteristic
437C2×C4D3×#6712yes—
438C2×C4D3×#6712yes—
439C8—121no—
440C8—121no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—42no—
447C2×C3—41no—
448C2×C3—42no—
449C2×C3—42no—
450C2×C3—82no—
451C2×C3—124no—
452C2×C3#495511yescharacteristic
453C2×C3#524711yescharacteristic
454D3—44no—
455C22—22no—
456C22—41no—
457C22—42no—
458C22—64no—
459C22—242no—
460C22—244no—
461C22C2×(C2×D3)⋊Dic311yescharacteristic
462C22#6397712yes—
463C4—22no—
464C4—64no—
465C4—722no—
466C4D3×#21712yes—
467C4#6397611yescharacteristic
468C4#6397611yescharacteristic
469C3—21no—
470C3#7001011yescharacteristic, complemented
471C3#7214611yescharacteristic, complemented
472C2—22no—
473C2—21no—
474C2—42no—
475C2—124no—
476C2#1059170611yescharacteristic
subgroupG/H
centerC4#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#379
prime radicalC3×#5964C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1794
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. #10592939C2semidirect
3. C3×#5234C2semidirect
4. #10591110C2semidirect
5. #10591084C2semidirect
12. C3×#1007C4semidirect
14. C3×#1004C4semidirect
17. #64135C22semidirect
18. C2×C3×#208C22semidirect
19. C22×C3×C3⋊C8C22semidirect
32. #5234D3semidirect
86. #1007Dic3semidirect
88. #1004Dic3semidirect
96. C2×#208C2×D3semidirect
97. C22×C3⋊C8C2×D3semidirect
409. C32#1794semidirect
470. C3#70010semidirect
471. C3#72146semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
#105929392
C3×#52342
#105911102
#105910842
#721463
#700103