Finite Group Databasebeta

← #11787783

Subgroups — #11787783

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic
3C3×#5240C211yesmaximal, characteristic, complemented
4#10591111C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#71817—31nomaximal
7#70045—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10#64157—24no—
11C2×#3748—22no—
12C2×#3748C2212yes—
13C3×#947C411yescharacteristic, complemented
14C3×#944C411yescharacteristic, complemented
15C3×#940C411yescharacteristic, complemented
16C3×#939—22no—
17C3×#936C411yescharacteristic, complemented
18C3×C4×#67—22no—
19C3×#926C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C3×#834—22no—
22#63569—24no—
23C3×#532—31no—
24#5832D311yescharacteristic
25#5819—31no—
26#5819—31no—
27#5819—61no—
28C3×#410—31no—
29#5240D311yescharacteristic, complemented
30#5236—32no—
31#5005—32no—
32#4532—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#3748—24no—
50#3748—22no—
51#3748D414yescomplemented
52C2×C3⋊(C3⋊C8)—24no—
53C2×C3⋊(C3⋊C8)—22no—
54C3×#217—22no—
55C3×#217—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3—22no—
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3C2×C411yescharacteristic
62C3×C4×Dic3C2×C411yescharacteristic
63#1884—91noSylow
64C2×C3×#41—21no—
65C2×C3×#41—31no—
66C2×C3×#41C2×D311yescharacteristic
67C2×C3×#41C2×D311yescharacteristic
68C2×#235C2×D311yescharacteristic
69C3×C4⋊Q8—31no—
70C3×#127—31no—
71C3×#124—31no—
72C3×#124—31no—
73C3×#121—62no—
74C3×C4×D4—62no—
75C3×#117—32no—
76C2×C3×C42—31no—
77#948—64no—
78#948—64no—
79#948—68no—
80#947Dic311yescharacteristic, complemented
81#944Dic311yescharacteristic, complemented
82#940Dic311yescharacteristic, complemented
83#939—22no—
84#936Dic311yescharacteristic, complemented
85C4×#67—22no—
86#926C2×D312yes—
87C2×C4×Dic3C2×D311yescharacteristic
88C2×#208—32no—
89C2×#208—32no—
90C2×#208—62no—
91C2×#208—64no—
92C2×#208—62no—
93C2×#208—62no—
94C3×#99—62no—
95#837—64no—
96#834—22no—
97#805—64no—
98C23×C32C22⋊C412yes—
99C23×C32C2×D411yescharacteristic
100C22×C3×D3—21no—
101C32×Q8—22no—
102C32×D4—24no—
103C32×D4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4C22⋊C412yes—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D412yes—
110C2×C32×C4#4112yes—
111C3×#67—44no—
112C3×#67—42no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—42no—
118C3×D12—22no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—22no—
122C3⋊(C3⋊C8)—24no—
123#568—91no—
124#532—31no—
125#421—92no—
126#410—31no—
127#339—92no—
128C3×#41—24no—
129C3×#41—24no—
130C3×#41—22no—
131C3×#41—22no—
132C3×#41—22no—
133C3×#41—22no—
134C3×#41—62no—
135C3×#41—62no—
136C2×C3×Q8—21no—
137C2×C3×Q8—31no—
138C2×C3×Q8C4×D311yescharacteristic
139C2×C3×Q8C2×Dic311yescharacteristic
140C2×C3×D4—21no—
141C2×C3×D4—22no—
142C2×C3×D4—31no—
143C2×C3×D4—62no—
144C2×C3×D4—61no—
145C2×C3×D4C4×D311yescharacteristic
146C2×C3×D4C2×Dic311yescharacteristic
147C2×C3×D4#6712yes—
148C2×C3×D4#6712yes—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4D1212yes—
154C22×C3×C4#6712yes—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—22no—
158C2×#67—21no—
159C22×Dic3—21no—
160#235—22no—
161#235—22no—
162C2×D12C2×Dic311yescharacteristic
163C2×C4×D3—21no—
164C2×Dic6C2×Dic311yescharacteristic
165C3×C4⋊C4—62no—
166C3×C4⋊C4—62no—
167C3×C22⋊C4—62no—
168C3×C22⋊C4—62no—
169C3×C22⋊C4—62no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—61no—
173C3×C42—62no—
174#217—22no—
175#217—22no—
176(C2×D3)⋊C4—22no—
177C4⋊Dic3—22no—
178Dic3⋊C4—22no—
179C4×Dic3—21no—
180C4×Dic3—22no—
181C4×Dic3C2×Dic311yescharacteristic
182C4×Dic3C2×Dic311yescharacteristic
183#208—34no—
184#208—34no—
185#208—64no—
186#208—64no—
187#208—68no—
188#208—64no—
189#208—64no—
190#208—62no—
191#208—62no—
192C2×C3⋊C8—68no—
193C2×C3⋊C8—64no—
194C2×C3⋊C8—64no—
195C2×C3⋊C8—64no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—62no—
198C22×C32—22no—
199C22×C32—41no—
200C22×C32—42no—
201C22×C32C2×C22⋊C411yescharacteristic
202C22×C32#12112yes—
203C2×C3×D3—42no—
204C2×C3×D3—41no—
205C32×C4—22no—
206C32×C4C4×D412yes—
207C32×C4#12011yescharacteristic
208C32×C4#12311yescharacteristic
209C3×Dic3—22no—
210C3×Dic3—41no—
211C3×Dic3—41no—
212C3×Dic3—82no—
213C2×#41—31no—
214C2×#41D3211yescharacteristic
215#131—184no—
216C2×M16—92no—
217C2×M16—182no—
218C4⋊Q8—31no—
219#127—31no—
220#124—31no—
221#124—31no—
222#121—62no—
223C4×D4—62no—
224#117—32no—
225C2×C42—31no—
226#104—184no—
227#99—62no—
228C23×C3—22no—
229C23×C3—21no—
230C23×C3—61no—
231C23×C3(C2×D3)⋊C412yes—
232C23×C3#21712yes—
233C23×C3C2×#6711yescharacteristic
234C23×C3C2×#6711yescharacteristic
235C22×D3—21no—
236C3×Q8—24no—
237C3×Q8—22no—
238C3×Q8—22no—
239C3×Q8—62no—
240C3×D4—28no—
241C3×D4—24no—
242C3×D4—24no—
243C3×D4—24no—
244C3×D4—22no—
245C3×D4—22no—
246C3×D4—62no—
247C3×D4—124no—
248C3×D4—122no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—22no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—122no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—122no—
267C2×C3×C4(C2×D3)⋊C412yes—
268C2×C3×C4#21712yes—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D412yes—
272C2×C3×C4D3×D412yes—
273C2×C3×C4#23712yes—
274C2×C3×C4#23712yes—
275C2×C3×C4C22×Dic311yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—44no—
278#67—42no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—42no—
283C2×Dic3—42no—
284D12—22no—
285C4×D3—41no—
286C4×D3—41no—
287Dic6—22no—
288C3⋊C8—68no—
289C3⋊C8—64no—
290C3⋊C8—64no—
291C2×C32—21no—
292C2×C32—22no—
293C2×C32—42no—
294C2×C32#38611yescharacteristic
295C3×D3—81no—
296#41—22no—
297#41—22no—
298#41—62no—
299#41—62no—
300C2×Q8—31no—
301C2×Q8D3×Dic311yescharacteristic
302C2×D4—31no—
303C2×D4—62no—
304C2×D4—61no—
305C2×D4D3×Dic311yescharacteristic
306C2×D4#62512yes—
307C22×C4—61no—
308C22×C4—61no—
309C22×C4#62612yes—
310C22×C4C2×D3211yescharacteristic
311M16—94no—
312M16—184no—
313M16—182no—
314C2×C8—184no—
315C2×C8—182no—
316C4⋊C4—62no—
317C4⋊C4—62no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C42—31no—
322C42—31no—
323C42—61no—
324C42—62no—
325C22×C3—24no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—22no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—81no—
335C22×C3—82no—
336C22×C3—122no—
337C22×C3—121no—
338C22×C3C2×(C2×D3)⋊C411yescharacteristic
339C22×C3#93912yes—
340C22×C3#93912yes—
341C22×C3C2×#21711yescharacteristic
342C2×D3—42no—
343C2×D3—41no—
344C3×C4—24no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—21no—
348C3×C4—22no—
349C3×C4—21no—
350C3×C4—62no—
351C3×C4—121no—
352C3×C4—121no—
353C3×C4—242no—
354C3×C4#67⋊C412yes—
355C3×C4#88211yescharacteristic
356C3×C4#88611yescharacteristic
357C3×C4D4×Dic312yes—
358C3×C4#93511yescharacteristic
359C3×C4#93711yescharacteristic
360Dic3—22no—
361Dic3—41no—
362Dic3—41no—
363Dic3—82no—
364C32#188411yescharacteristic, complemented, Sylow
365C23—61no—
366C23(C2×D3)⋊Dic312yes—
367C23C2×#62511yescharacteristic
368Q8—22no—
369Q8—62no—
370D4—24no—
371D4—22no—
372D4—62no—
373D4—124no—
374D4—122no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—122no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—122no—
384C2×C4(C2×D3)⋊Dic312yes—
385C2×C4C2×D3×Dic311yescharacteristic
386C2×C4#380512yes—
387C2×C4C2×#62611yescharacteristic
388C2×C4#381112yes—
389C8—184no—
390C2×C3—21no—
391C2×C3—22no—
392C2×C3—22no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—41no—
396C2×C3—42no—
397C2×C3—44no—
398C2×C3—42no—
399C2×C3—42no—
400C2×C3—241no—
401C2×C3#495811yescharacteristic
402C2×C3#522011yescharacteristic
403D3—81no—
404C22—22no—
405C22—41no—
406C22—42no—
407C22—122no—
408C22—121no—
409C22C2×(C2×D3)⋊Dic311yescharacteristic
410C22#6398012yes—
411C4—22no—
412C4—62no—
413C4—121no—
414C4—121no—
415C4—242no—
416C4#6396211yescharacteristic
417C4#67⋊Dic312yes—
418C4#6398111yescharacteristic
419C3—21no—
420C3#7004511yescharacteristic, complemented
421C3#7181711yescharacteristic, complemented
422C2—21no—
423C2—22no—
424C2—42no—
425C2—241no—
426C2#1059171311yescharacteristic
subgroupG/H
centerC4#63981
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
1. #10596290C2semidirect
3. C3×#5240C2semidirect
4. #10591111C2semidirect
5. #10589161C2semidirect
13. C3×#947C4semidirect
14. C3×#944C4semidirect
15. C3×#940C4semidirect
17. C3×#936C4semidirect
29. #5240D3semidirect
51. #3748D4semidirect
80. #947Dic3semidirect
81. #944Dic3semidirect
82. #940Dic3semidirect
84. #936Dic3semidirect
364. C32#1884semidirect
420. C3#70045semidirect
421. C3#71817semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#58322
C3×#52402
#105911112
#105891612
#718173
#700453