Finite Group Databasebeta

← #11775088

Subgroups — #11775088

Order 1152.

520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic
2#10591242C211yesmaximal, characteristic
3#10591053C211yesmaximal, characteristic
4#10589404C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic
8#71835—31nomaximal
9#68309—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×Q8×Dic3C411yescharacteristic, complemented
12C3×#944C411yescharacteristic, complemented
13C3×#924C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#889—21no—
16C3×#888C411yescharacteristic, complemented
17C3×#887—21no—
18C3×#887C411yescharacteristic, complemented
19C3×#878—21no—
20C3×#877—21no—
21C2×Dic3⋊Dic3—21no—
22C2×Dic32—21no—
23#63658C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29C3×#533—31no—
30#5622D311yescharacteristic
31C4×C4⋊Dic3—31no—
32#4925—31no—
33#4718—31no—
34#4649—31no—
35C3×#328—31no—
36#4538—31no—
37#4538—31no—
38#4538—31no—
39#4538—31no—
40#4538—61no—
41#4538D311yescharacteristic
42#4467—31no—
43#4452—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—24no—
72Dic32—42no—
73#1503—91noSylow
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8—31no—
76C3×#125—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C2×D311yescharacteristic
82C3×C4×Q8—31no—
83C3×C4×Q8—31no—
84C3×C4×Q8—61no—
85C3×#117—61no—
86C2×C3×C42—31no—
87Q8×Dic3Dic311yescharacteristic, complemented
88#944Dic311yescharacteristic, complemented
89C2×C4⋊Dic3—61no—
90#924C2×D311yescharacteristic
91C2×Dic3⋊C4—61no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3C2×D311yescharacteristic
95#889—21no—
96#888Dic311yescharacteristic, complemented
97#887—21no—
98#887Dic311yescharacteristic, complemented
99#878—21no—
100#877—21no—
101C3×C22⋊C8—31no—
102C3×#95—31no—
103C3⋊#95—31no—
104C3⋊#95—31no—
105C3⋊#95—61no—
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111Dic3⋊C8—61no—
112C8×Dic3—61no—
113C4⋊(C3⋊C8)—61no—
114C4×C3⋊C8—61no—
115C23×C32C2×D411yescharacteristic
116C32×Q8—41no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3SD1612yes—
136C2×C3×Dic3Q1612yes—
137C3×Dic6—42no—
138C3×Dic6—41no—
139C3⋊(C3⋊C8)—41no—
140C3×C3⋊C8—41no—
141#533—31no—
142#431—91no—
143C4×C4⋊C4—91no—
144#328—31no—
145#328—91no—
146#328—91no—
147#328—91no—
148C2×C3×Q8—21no—
149C2×C3×Q8—31no—
150C2×C3×Q8—61no—
151C2×C3×Q8C4×D311yescharacteristic
152C2×C3×Q8C2×Dic311yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—121no—
163C22×Dic3#6711yescharacteristic
164C22×Dic3#6711yescharacteristic
165C2×Dic6—21no—
166C2×Dic6C2×Dic311yescharacteristic
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4C4×D311yescharacteristic
180C3×C4⋊C4C2×Dic311yescharacteristic
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—41no—
184C3×C22⋊C4—61no—
185C3×C42—31no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—61no—
190C3×C42—61no—
191#217—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3—64no—
194C4⋊Dic3C2×Dic311yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—64no—
201C4×Dic3—21no—
202C4×Dic3—21no—
203C4×Dic3—122no—
204C4×Dic3—122no—
205C4×Dic3C2×Dic311yescharacteristic
206C4×Dic3C2×Dic311yescharacteristic
207C4×Dic3#6711yescharacteristic
208C4×Dic3#6711yescharacteristic
209C2×C3⋊C8—21no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—121no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32C2×SD1611yescharacteristic
217C22×C32C2×Q1611yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4—41no—
222C3⋊Dic3—42no—
223C3×Dic3—21no—
224C3×Dic3—42no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C3×Dic3#10312yes—
228C3×Dic3#10312yes—
229C3×Dic3#10412yes—
230C4⋊Q8—31no—
231C4⋊Q8—31no—
232#125—61no—
233C22⋊Q8—31no—
234C22⋊Q8—61no—
235C22⋊Q8D3211yescharacteristic
236C4×Q8—31no—
237C4×Q8—31no—
238C4×Q8—61no—
239#117—61no—
240C2×C4⋊C4—181no—
241C2×C42—31no—
242C2×C42—181no—
243C4⋊C8—181no—
244C22⋊C8—31no—
245C22⋊C8—91no—
246C4×C8—181no—
247#95—31no—
248#95—91no—
249C23×C3—21no—
250C23×C3D3×D411yescharacteristic
251C23×C3C2×#6711yescharacteristic
252C3×Q8—41no—
253C3×Q8—41no—
254C3×Q8—81no—
255C3×Q8—121no—
256C3×Q8—122no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—31no—
266C2×C3×C4—32no—
267C2×C3×C4—32no—
268C2×C3×C4—31no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—81no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C22×Dic311yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—122no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—241no—
298C2×Dic3—241no—
299C2×Dic3#21512yes—
300C2×Dic3#21612yes—
301C2×Dic3#21711yescharacteristic
302C2×Dic3#21711yescharacteristic
303C2×Dic3#21711yescharacteristic
304C2×Dic3#21711yescharacteristic
305Dic6—42no—
306Dic6—41no—
307C3×C8—121no—
308C3⋊C8—41no—
309C3⋊C8—121no—
310C3⋊C8—121no—
311C3⋊C8—241no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#41011yescharacteristic
315C2×C32C2×#10311yescharacteristic
316C2×C32C2×#10411yescharacteristic
317C2×Q8—31no—
318C2×Q8—61no—
319C2×Q8D3×Dic311yescharacteristic
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—61no—
323C22×C4—181no—
324C22×C4C2×D3211yescharacteristic
325C2×C8—61no—
326C2×C8—181no—
327C4⋊C4—21no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—184no—
336C4⋊C4D3×Dic311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—61no—
339C42—31no—
340C42—31no—
341C42—31no—
342C42—31no—
343C42—61no—
344C42—61no—
345C42—362no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3D3×C22⋊C411yescharacteristic
356C22×C3D3×SD1611yescharacteristic
357C22×C3D3×Q1611yescharacteristic
358C22×C3C2×#21511yescharacteristic
359C22×C3C2×#21611yescharacteristic
360C22×C3C2×#21711yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—32no—
366C3×C4—32no—
367C3×C4—32no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—61no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—122no—
378C3×C4—121no—
379C3×C4—121no—
380Dic3—21no—
381Dic3—42no—
382Dic3—41no—
383Dic3—41no—
384Dic3—122no—
385Dic3—122no—
386Dic3—242no—
387Dic3#83512yes—
388Dic3#83512yes—
389Dic3#83712yes—
390C32#150311yescharacteristic, complemented, Sylow
391C23D3×#6711yescharacteristic
392Q8—41no—
393Q8—121no—
394Q8—122no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—32no—
398C2×C4—32no—
399C2×C4—31no—
400C2×C4—31no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—182no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4C2×D3×Dic311yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C8—121no—
416C8—361no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3#474011yescharacteristic
427C2×C3D3×#10311yescharacteristic
428C2×C3D3×#10411yescharacteristic
429C2×C3C2×#83511yescharacteristic
430C2×C3C2×#83711yescharacteristic
431C2×C3#524011yescharacteristic
432C22—21no—
433C22—21no—
434C22D3×#21511yescharacteristic
435C22D3×#21611yescharacteristic
436C22D3×#21711yescharacteristic
437C4—21no—
438C4—21no—
439C4—32no—
440C4—32no—
441C4—32no—
442C4—41no—
443C4—41no—
444C4—61no—
445C4—122no—
446C4—121no—
447C4—121no—
448C4—362no—
449C3—21no—
450C3#6830911yescharacteristic, complemented
451C3#7183511yescharacteristic, complemented
452C2—21no—
453C2—21no—
454C2#1059152811yescharacteristic
455C2D3×#83511yescharacteristic
456C2D3×#83711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
11. C3×Q8×Dic3C4semidirect
12. C3×#944C4semidirect
16. C3×#888C4semidirect
18. C3×#887C4semidirect
87. Q8×Dic3Dic3semidirect
88. #944Dic3semidirect
96. #888Dic3semidirect
98. #887Dic3semidirect
390. C32#1503semidirect
450. C3#68309semidirect
451. C3#71835semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
#105912422
#105910532
#105894042
C3×#45382
#105891532
#105891522
#718353
#683093