Finite Group Databasebeta

← #11783919

Subgroups — #11783919

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4#10591222C211yesmaximal, characteristic, complemented
5Dic3×#208C211yesmaximal, characteristic, complemented
6#10589161C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71643—31nomaximal
9#70354—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×Q8×Dic3C412yescomplemented
14C3×D4×Dic3—22no—
15C3×D4×Dic3C412yescomplemented
16C3×#926—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63664C414yescomplemented
23C3×#837C414yescomplemented
24#63579—22no—
25#63554—21no—
26Dic3×C3⋊C8—21no—
27C3×C4×#41—31no—
28Dic3×#41D311yescharacteristic
29C2×C3×#104—31no—
30C2×#837—31no—
31C2×#837—31no—
32C2×#837—61no—
33C2×#837D311yescharacteristic
34Dic3×M16—31no—
35#4932—31no—
36#4932—31no—
37C4×#208—31no—
38#4555—31no—
39#4532—31no—
40#4532—31no—
41#4523—31no—
42C32×#41—21no—
43C32×#41—21no—
44C32×#41C2×C412yes—
45C32×#41C2×C412yes—
46C2×C32×Q8C2×C411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4C2×C411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3D412yes—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3C2×C412yescomplemented
57#3748—21no—
58#3748C2×C412yescomplemented
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217—22no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3C2×C412yes—
64C3×C4×Dic3—21no—
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—21no—
76C2×C3×#41C2×D311yescharacteristic
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×M16—31no—
79C3×C4×Q8—32no—
80C3×C4×D4—32no—
81C3×C4×D4—62no—
82C3×#117—31no—
83C3×#117—61no—
84C2×C3×C42—31no—
85C2×C3×C42—31no—
86C2×C3×C42—61no—
87Q8×Dic3Dic312yescomplemented
88D4×Dic3—22no—
89D4×Dic3Dic312yescomplemented
90#926—21no—
91#926C2×D311yescharacteristic
92C2×C4×Dic3—21no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3C2×D311yescharacteristic
97C2×C4×Dic3C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102C3×#104—34no—
103#837—34no—
104#837—34no—
105#837—64no—
106#837Dic314yescomplemented
107C3⋊#95—62no—
108C3⋊#95—62no—
109#815—61no—
110C8×Dic3—61no—
111#803—61no—
112C4×C3⋊C8—61no—
113C23×C32—21no—
114C23×C32C2×D411yescharacteristic
115C32×Q8—21no—
116C32×Q8C4212yes—
117C32×D4—22no—
118C32×D4—22no—
119C32×D4—21no—
120C32×D4C4212yes—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—42no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—44no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3C22⋊C412yes—
138C2×C3×Dic3C22⋊C412yes—
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—22no—
141C4×#41—31no—
142C2×#104—31no—
143C2×#104—91no—
144C4×M16—91no—
145#376—91no—
146#339—91no—
147#339—91no—
148C3×#41—21no—
149C3×#41—21no—
150C3×#41—21no—
151C3×#41—21no—
152C3×#41—22no—
153C3×#41—22no—
154C3×#41—41no—
155C3×#41—41no—
156C3×#41C4×D312yes—
157C3×#41C4×D312yes—
158C3×#41C4×D312yes—
159C3×#41C2×Dic312yes—
160C2×C3×Q8—21no—
161C2×C3×Q8C4×D311yescharacteristic
162C2×C3×Q8C2×Dic311yescharacteristic
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—41no—
167C2×C3×D4C4×D311yescharacteristic
168C2×C3×D4C2×Dic311yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—32no—
173C22×C3×C4—41no—
174C22×C3×C4—62no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C22×Dic3—22no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3#6712yes—
184C3×M16—32no—
185C3×M16—61no—
186C2×C3×C8—61no—
187C3×C4⋊C4—32no—
188C3×C4⋊C4—62no—
189C3×C22⋊C4—62no—
190C3×C22⋊C4—61no—
191C3×C42—32no—
192C3×C42—31no—
193C3×C42—31no—
194C3×C42—32no—
195C3×C42—62no—
196C3×C42—61no—
197C3×C42—61no—
198#217—21no—
199#217—22no—
200C4⋊Dic3—22no—
201C4⋊Dic3C2×Dic312yes—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—22no—
205C4×Dic3—32no—
206C4×Dic3—32no—
207C4×Dic3—62no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—121no—
211C4×Dic3C2×Dic312yes—
212C4×Dic3C2×Dic312yescomplemented
213C4×Dic3#6711yescharacteristic
214C4×Dic3#6711yescharacteristic
215#208—21no—
216#208—32no—
217#208—32no—
218#208—62no—
219#208—61no—
220#208—61no—
221#208—121no—
222#208C2×Dic312yescomplemented
223C2×C3⋊C8—21no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—42no—
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32C4×D411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C32×C4—22no—
234C32×C4C2×C4211yescharacteristic
235C32×C4#11711yescharacteristic
236C32×C4C4×D411yescharacteristic
237C32×C4C4×D411yescharacteristic
238C3⋊Dic3—42no—
239C3×Dic3—22no—
240C3×Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C2×#41D3211yescharacteristic
244C2×M16—31no—
245C2×M16—91no—
246C4×Q8—32no—
247C4×D4—32no—
248C4×D4—62no—
249#117—31no—
250#117—61no—
251C2×C42—31no—
252C2×C42—31no—
253C2×C42—61no—
254C2×C42—91no—
255#104—34no—
256#104—94no—
257#97—181no—
258C4×C8—181no—
259#95—182no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—41no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C3×Q8—21no—
267C3×Q8—21no—
268C3×Q8—22no—
269C3×Q8—41no—
270C3×Q8C4×Dic312yes—
271C3×Q8C4×Dic312yes—
272C3×D4—22no—
273C3×D4—22no—
274C3×D4—22no—
275C3×D4—22no—
276C3×D4—21no—
277C3×D4—21no—
278C3×D4—22no—
279C3×D4—41no—
280C3×D4—42no—
281C3×D4—42no—
282C3×D4C4×Dic312yes—
283C3×D4C4×Dic312yes—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—41no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—122no—
304C2×C3×C4—124no—
305C2×C3×C4—122no—
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4C2×C4×D311yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4C22×Dic311yescharacteristic
316C2×C3×C4C22×Dic311yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—42no—
321C2×Dic3—44no—
322C2×Dic3—42no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—124no—
329C2×Dic3#21712yes—
330C2×Dic3#21712yes—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—62no—
334C3⋊C8—62no—
335C3⋊C8—122no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32—42no—
339C2×C32C4×C22⋊C411yescharacteristic
340C2×C32#42112yes—
341#41—21no—
342#41—21no—
343#41D3×Dic312yes—
344#41#62412yes—
345C2×Q8D3×Dic311yescharacteristic
346C2×D4—21no—
347C2×D4D3×Dic311yescharacteristic
348C22×C4—21no—
349C22×C4—32no—
350C22×C4—62no—
351C22×C4—61no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354M16—32no—
355M16—61no—
356M16—92no—
357M16—181no—
358C2×C8—61no—
359C2×C8—181no—
360C4⋊C4—32no—
361C4⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—61no—
364C42—32no—
365C42—31no—
366C42—31no—
367C42—32no—
368C42—62no—
369C42—61no—
370C42—61no—
371C42—92no—
372C42—181no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—82no—
385C22×C3D3×C22⋊C411yescharacteristic
386C22×C3#67⋊C411yescharacteristic
387C22×C3C4×#6711yescharacteristic
388C22×C3C4×#6711yescharacteristic
389C22×C3D4×Dic311yescharacteristic
390C22×C3C2×#21711yescharacteristic
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—62no—
399C3×C4—62no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4#87711yescharacteristic
403C3×C4#67⋊C411yescharacteristic
404C3×C4C2×C4×Dic311yescharacteristic
405C3×C4C2×C4×Dic311yescharacteristic
406C3×C4#92611yescharacteristic
407C3×C4C4×#6711yescharacteristic
408C3×C4C4×#6711yescharacteristic
409C3×C4D4×Dic311yescharacteristic
410Dic3—22no—
411Dic3—22no—
412Dic3—42no—
413Dic3—42no—
414Dic3—122no—
415Dic3—122no—
416Dic3—124no—
417C32#175911yescharacteristic, complemented, Sylow
418C23—21no—
419C23D3×#6711yescharacteristic
420Q8—21no—
421Q8Dic3212yes—
422D4—22no—
423D4—22no—
424D4—21no—
425D4Dic3212yes—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—122no—
434C2×C4—124no—
435C2×C4—122no—
436C2×C4—182no—
437C2×C4—362no—
438C2×C4C2×D3×Dic311yescharacteristic
439C2×C4C2×D3×Dic311yescharacteristic
440C2×C4#380411yescharacteristic
441C2×C4#380411yescharacteristic
442C2×C4C2×#62411yescharacteristic
443C2×C4D3×#6711yescharacteristic
444C8—62no—
445C8—182no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—42no—
455C2×C3—42no—
456C2×C3—82no—
457C2×C3#482112yes—
458C2×C3Dic3×C22⋊C411yescharacteristic
459C2×C3C4×#21711yescharacteristic
460C2×C3#523612yes—
461C22—22no—
462C22—22no—
463C22—42no—
464C22#6395211yescharacteristic
465C22D3×#21711yescharacteristic
466C22Dic3×#6711yescharacteristic
467C4—22no—
468C4—62no—
469C4—62no—
470C4—122no—
471C4—122no—
472C4—362no—
473C4#6395211yescharacteristic
474C4C2×Dic3211yescharacteristic
475C4#6395511yescharacteristic
476C4Dic3×#6711yescharacteristic
477C3—21no—
478C3#7035411yescharacteristic, complemented
479C3#7164311yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—42no—
483C2#1059167012yes—
484C2Dic3×#21711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591222C2semidirect
5. Dic3×#208C2semidirect
6. #10589161C2semidirect
7. #10589160C2semidirect
13. C3×Q8×Dic3C4semidirect
15. C3×D4×Dic3C4semidirect
22. #63664C4semidirect
23. C3×#837C4semidirect
56. C4×C3⋊Dic3C2×C4semidirect
58. #3748C2×C4semidirect
68. C3×C4×Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
87. Q8×Dic3Dic3semidirect
89. D4×Dic3Dic3semidirect
106. #837Dic3semidirect
212. C4×Dic3C2×Dic3semidirect
222. #208C2×Dic3semidirect
417. C32#1759semidirect
478. C3#70354semidirect
479. C3#71643semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×#636642
C2×C3×#8372
#105912222
Dic3×#2082
#105891612
#105891602
#716433
#703543