Finite Group Databasebeta

← #11783908

Subgroups — #11783908

Order 1152.

695 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2#10591222C211yesmaximal, characteristic, complemented
3C2×#63569C211yesmaximal, characteristic
4C2×#63568C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#71643—31nomaximal
9#68729—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893C412yescomplemented
18C3×#887C412yescomplemented
19C3×#67⋊C4—22no—
20C3×#872—21no—
21C3×C42×D3—21no—
22#63579—22no—
23#63569C414yescomplemented
24#63568C414yescomplemented
25#63554—21no—
26Dic3×C3⋊C8—21no—
27C3×C4×#41—31no—
28#5522D311yescharacteristic
29C2×#837—31no—
30C2×#837—31no—
31C2×#825—31no—
32Dic3×M16—31no—
33#4932—31no—
34#4932—31no—
35C2×#805—31no—
36C4×#208—31no—
37C3×#339—31no—
38#4532—31no—
39#4532—31no—
40#4532—61no—
41#4532D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D412yes—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235C2×C412yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—22no—
54C2×C3×Dic6C2×C411yescharacteristic
55C32×C4⋊C4C2×C412yes—
56C32×C22⋊C4—21no—
57C32×C42—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3C2×C412yescomplemented
60#3748—21no—
61#3748C2×C412yescomplemented
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—22no—
64C3×Dic3⋊C4—22no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—22no—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3C2×C412yescomplemented
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74#1759—91noSylow
75C2×C3×#41—31no—
76C2×#235C2×D311yescharacteristic
77C2×C3×M16—31no—
78C3×C4×Q8—32no—
79C3×C4×D4—32no—
80C3×C4×D4—62no—
81C3×#117—21no—
82C3×#117—61no—
83C3×#117C2×D311yescharacteristic
84C3×#117C2×D311yescharacteristic
85C2×C3×C42—31no—
86C2×C3×C42—31no—
87C2×C3×C42—61no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3C2×D311yescharacteristic
92C2×C4×Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96C2×#208C2×D311yescharacteristic
97#893Dic312yescomplemented
98#887Dic312yescomplemented
99#67⋊C4—22no—
100#872—21no—
101C42×D3—21no—
102#837—34no—
103#837—34no—
104C3⋊#95—62no—
105C3⋊#95—62no—
106#825—34no—
107#815—61no—
108C8×Dic3—61no—
109#805—34no—
110#803—61no—
111C4×C3⋊C8—61no—
112C23×C32C2×D411yescharacteristic
113C22×C3×D3—21no—
114C2×C32×C4—22no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—42no—
123C3×#67—22no—
124C3×#67—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3C22⋊C412yes—
130C2×C3×Dic3C22⋊C412yes—
131C3×D12—21no—
132C3×D12C4212yes—
133C3×C4×D3—22no—
134C3×C4×D3—22no—
135C3×C4×D3—44no—
136C3×Dic6—21no—
137C3×Dic6C4212yes—
138C3⋊(C3⋊C8)—22no—
139C3×C3⋊C8—22no—
140C4×#41—31no—
141C2×#104—91no—
142C2×#104—91no—
143C4×M16—91no—
144#376—91no—
145#339—31no—
146#339—91no—
147C3×#41—32no—
148C3×#41—32no—
149C3×#41—61no—
150C3×#41—61no—
151C2×C3×Q8—31no—
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—62no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—21no—
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3#6712yes—
167#235—21no—
168#235—21no—
169#235C4×D312yes—
170#235C4×D312yes—
171C2×D12C2×Dic311yescharacteristic
172C2×C4×D3—21no—
173C2×C4×D3—22no—
174C2×Dic6C2×Dic311yescharacteristic
175C3×M16—32no—
176C3×M16—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—62no—
180C3×C4⋊C4C4×D312yes—
181C3×C4⋊C4C2×Dic312yes—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—62no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—32no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—32no—
192C3×C42—41no—
193C3×C42—62no—
194C3×C42—61no—
195(C2×D3)⋊C4—22no—
196Dic3⋊C4—22no—
197C4×Dic3—21no—
198C4×Dic3—22no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—62no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—121no—
205C4×Dic3C4×D312yescomplemented
206C4×Dic3C2×Dic312yes—
207C4×Dic3#6711yescharacteristic
208C4×Dic3#6711yescharacteristic
209#208—21no—
210#208—32no—
211#208—32no—
212#208—62no—
213#208—61no—
214#208—61no—
215#208—121no—
216#208C4×D312yescomplemented
217C2×C3⋊C8—21no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—121no—
221C22×C32—22no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32C4×D411yescharacteristic
224C22×C32C4×D411yescharacteristic
225C2×C3×D3—22no—
226C2×C3×D3—42no—
227C32×C4—42no—
228C32×C4C2×C4211yescharacteristic
229C32×C4#11711yescharacteristic
230C32×C4C4×D411yescharacteristic
231C32×C4C4×D411yescharacteristic
232C3⋊Dic3—42no—
233C3×Dic3—22no—
234C3×Dic3—22no—
235C3×Dic3—22no—
236C3×Dic3—42no—
237C2×#41—31no—
238C2×M16—31no—
239C2×M16—91no—
240C4×Q8—32no—
241C4×D4—32no—
242C4×D4—62no—
243#117—61no—
244#117D3211yescharacteristic
245C2×C42—31no—
246C2×C42—31no—
247C2×C42—61no—
248C2×C42—91no—
249#104—94no—
250#104—94no—
251#97—181no—
252C4×C8—181no—
253#95—182no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3D3×D411yescharacteristic
257C23×C3C2×#6711yescharacteristic
258C22×D3—21no—
259C3×Q8—32no—
260C3×Q8—61no—
261C3×D4—32no—
262C3×D4—62no—
263C3×D4—62no—
264C3×D4—61no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—32no—
274C2×C3×C4—32no—
275C2×C3×C4—42no—
276C2×C3×C4—61no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—124no—
281C2×C3×C4—122no—
282C2×C3×C4—122no—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23911yescharacteristic
293C2×C3×C4C22×Dic311yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—22no—
296#67—22no—
297C2×Dic3—21no—
298C2×Dic3—22no—
299C2×Dic3—42no—
300C2×Dic3—42no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—124no—
307C2×Dic3#21712yes—
308C2×Dic3#21712yes—
309D12—21no—
310D12C4×Dic312yes—
311C4×D3—22no—
312C4×D3—22no—
313C4×D3—44no—
314Dic6—21no—
315Dic6C4×Dic312yes—
316C3×C8—62no—
317C3⋊C8—22no—
318C3⋊C8—62no—
319C3⋊C8—62no—
320C3⋊C8—122no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32C4×C22⋊C411yescharacteristic
324C2×C32#42112yes—
325C3×D3—42no—
326#41—32no—
327#41—32no—
328#41—61no—
329#41—61no—
330C2×Q8—31no—
331C2×D4—31no—
332C2×D4—61no—
333C22×C4—32no—
334C22×C4—62no—
335C22×C4—61no—
336C22×C4—61no—
337C22×C4—181no—
338C22×C4C2×D3211yescharacteristic
339M16—32no—
340M16—61no—
341M16—92no—
342M16—181no—
343C2×C8—61no—
344C2×C8—181no—
345C4⋊C4—62no—
346C4⋊C4D3×Dic312yes—
347C22⋊C4—21no—
348C22⋊C4—62no—
349C42—21no—
350C42—32no—
351C42—31no—
352C42—31no—
353C42—32no—
354C42—62no—
355C42—61no—
356C42—92no—
357C42—181no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—42no—
364C22×C3—62no—
365C22×C3—122no—
366C22×C3D3×C22⋊C411yescharacteristic
367C22×C3#67⋊C411yescharacteristic
368C22×C3#89311yescharacteristic
369C22×C3C4×#6711yescharacteristic
370C22×C3C4×#6711yescharacteristic
371C22×C3C2×#21711yescharacteristic
372C2×D3—22no—
373C2×D3—42no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—42no—
379C3×C4—42no—
380C3×C4—62no—
381C3×C4—62no—
382C3×C4—62no—
383C3×C4—82no—
384C3×C4—122no—
385C3×C4C42×D311yescharacteristic
386C3×C4#67⋊C411yescharacteristic
387C3×C4#89211yescharacteristic
388C3×C4#89311yescharacteristic
389C3×C4C2×C4×Dic311yescharacteristic
390C3×C4#92611yescharacteristic
391C3×C4C4×#6711yescharacteristic
392C3×C4C4×#6711yescharacteristic
393Dic3—22no—
394Dic3—22no—
395Dic3—22no—
396Dic3—42no—
397Dic3—122no—
398Dic3—122no—
399Dic3—124no—
400C32#175911yescharacteristic, complemented, Sylow
401C23—61no—
402C23D3×#6711yescharacteristic
403Q8—32no—
404Q8—61no—
405D4—32no—
406D4—62no—
407D4—62no—
408D4—61no—
409C2×C4—22no—
410C2×C4—32no—
411C2×C4—32no—
412C2×C4—61no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—124no—
417C2×C4—122no—
418C2×C4—122no—
419C2×C4—182no—
420C2×C4—362no—
421C2×C4#379511yescharacteristic
422C2×C4#379911yescharacteristic
423C2×C4C4×D3211yescharacteristic
424C2×C4C4×D3211yescharacteristic
425C2×C4C2×D3×Dic311yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C8—62no—
428C8—182no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—22no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—122no—
438C2×C3#466611yescharacteristic
439C2×C3#482112yes—
440C2×C3C4×#21711yescharacteristic
441C2×C3#523612yes—
442D3—42no—
443C22—22no—
444C22—62no—
445C22—122no—
446C22#6387911yescharacteristic
447C22#6390411yescharacteristic
448C22D3×#21711yescharacteristic
449C4—42no—
450C4—62no—
451C4—62no—
452C4—62no—
453C4—122no—
454C4—362no—
455C4#6384111yescharacteristic
456C4C4×D3×Dic311yescharacteristic
457C4#6387911yescharacteristic
458C4#6390411yescharacteristic
459C3—21no—
460C3#6872911yescharacteristic, complemented
461C3#7164311yescharacteristic, complemented
462C2—21no—
463C2—21no—
464C2—122no—
465C2#1059123711yescharacteristic
466C2#1059167012yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10591222C2semidirect
5. Dic3×#208C2semidirect
6. #10589398C2semidirect
7. C3×#4532C2semidirect
17. C3×#893C4semidirect
18. C3×#887C4semidirect
23. #63569C4semidirect
24. #63568C4semidirect
41. #4532D3semidirect
59. C4×C3⋊Dic3C2×C4semidirect
61. #3748C2×C4semidirect
68. C3×C4×Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
97. #893Dic3semidirect
98. #887Dic3semidirect
205. C4×Dic3C4×D3semidirect
216. #208C4×D3semidirect
400. C32#1759semidirect
460. C3#68729semidirect
461. C3#71643semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
#105912222
C2×#635692
C2×#635682
Dic3×#2082
#105893982
C3×#45322
#716433
#687293