Finite Group Databasebeta

← #11775181

Subgroups — #11775181

Order 1152.

496 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic
2#10591239C211yesmaximal, characteristic
3#10591063C211yesmaximal, characteristic
4#10589404C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic
8#71836—31nomaximal
9#68310—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×Dic32—21no—
22#63658C2211yescharacteristic
23#63657C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#533—31no—
30#5622D311yescharacteristic
31#4932—31no—
32#4926—31no—
33#4719—31no—
34#4648—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—
71Dic32—24no—
72#1506—91noSylow
73C3×C4⋊Q8—31no—
74C3×C4⋊Q8—31no—
75C3×#125—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C4×Q8—31no—
82C3×C4×Q8—31no—
83C3×C4×Q8—61no—
84C3×#117—61no—
85C2×C3×C42—31no—
86Q8×Dic3Dic311yescharacteristic, complemented
87#944Dic311yescharacteristic, complemented
88#924C2×D311yescharacteristic
89C2×C4×Dic3—61no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3C2×D311yescharacteristic
92#889—21no—
93#888Dic311yescharacteristic, complemented
94#887—21no—
95#887Dic311yescharacteristic, complemented
96#878—21no—
97#877—21no—
98C3×C22⋊C8—31no—
99C3×#95—31no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#815—61no—
111Dic3⋊C8—61no—
112C4⋊(C3⋊C8)—61no—
113#803—61no—
114C23×C32C2×D411yescharacteristic
115C32×Q8—41no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C3×Dic6—42no—
137C3×Dic6—41no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#533—31no—
141#432—91no—
142#376—91no—
143#328—31no—
144#328—91no—
145#328—91no—
146#328—91no—
147C2×C3×Q8—21no—
148C2×C3×Q8—31no—
149C2×C3×Q8—61no—
150C2×C3×Q8C4×D311yescharacteristic
151C2×C3×Q8C2×Dic311yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—121no—
162C22×Dic3#6711yescharacteristic
163C22×Dic3#6711yescharacteristic
164C2×Dic6—21no—
165C2×Dic6C2×Dic311yescharacteristic
166C2×C3×C8—61no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4C4×D311yescharacteristic
179C3×C4⋊C4C2×Dic311yescharacteristic
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—41no—
183C3×C22⋊C4—61no—
184C3×C42—31no—
185C3×C42—31no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42—61no—
189C3×C42—61no—
190#217—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3C2×Dic311yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C4×Dic3—21no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C4×Dic3C2×Dic311yescharacteristic
203C4×Dic3C2×Dic311yescharacteristic
204C4×Dic3#6711yescharacteristic
205C4×Dic3#6711yescharacteristic
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32C2×C22⋊C411yescharacteristic
213C22×C32#13711yescharacteristic
214C22×C32#13711yescharacteristic
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—41no—
218C32×C4—41no—
219C3⋊Dic3—42no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—42no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3#10412yes—
227C4⋊Q8—31no—
228C4⋊Q8—31no—
229#125—61no—
230C22⋊Q8—31no—
231C22⋊Q8—61no—
232C22⋊Q8D3211yescharacteristic
233C4×Q8—31no—
234C4×Q8—31no—
235C4×Q8—61no—
236#117—61no—
237C2×C42—31no—
238C2×C42—181no—
239C4⋊C8—181no—
240C22⋊C8—31no—
241C22⋊C8—91no—
242#97—181no—
243#95—31no—
244#95—91no—
245#95—181no—
246C23×C3—21no—
247C23×C3D3×D411yescharacteristic
248C23×C3C2×#6711yescharacteristic
249C3×Q8—41no—
250C3×Q8—41no—
251C3×Q8—81no—
252C3×Q8—121no—
253C3×Q8—122no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—62no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—62no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4C22×Dic311yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—41no—
288C2×Dic3—41no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—122no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—241no—
297C2×Dic3—241no—
298C2×Dic3#21711yescharacteristic
299C2×Dic3#21711yescharacteristic
300C2×Dic3#21711yescharacteristic
301C2×Dic3#21711yescharacteristic
302Dic6—42no—
303Dic6—41no—
304C3×C8—121no—
305C3⋊C8—41no—
306C3⋊C8—121no—
307C3⋊C8—121no—
308C3⋊C8—241no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#41011yescharacteristic
312C2×C32#41911yescharacteristic
313C2×C32C2×#10411yescharacteristic
314C2×Q8—31no—
315C2×Q8—61no—
316C2×Q8D3×Dic311yescharacteristic
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—61no—
320C22×C4—181no—
321C22×C4C2×D3211yescharacteristic
322C2×C8—61no—
323C2×C8—181no—
324C4⋊C4—21no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4D3×Dic311yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—61no—
335C42—31no—
336C42—31no—
337C42—31no—
338C42—31no—
339C42—61no—
340C42—61no—
341C42—184no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3D3×C22⋊C411yescharacteristic
352C22×C3#91511yescharacteristic
353C22×C3#91811yescharacteristic
354C22×C3#94211yescharacteristic
355C22×C3#94211yescharacteristic
356C22×C3C2×#21711yescharacteristic
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—32no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—61no—
369C3×C4—61no—
370C3×C4—61no—
371C3×C4—81no—
372C3×C4—81no—
373C3×C4—122no—
374C3×C4—121no—
375C3×C4—121no—
376Dic3—21no—
377Dic3—21no—
378Dic3—21no—
379Dic3—42no—
380Dic3—41no—
381Dic3—41no—
382Dic3—122no—
383Dic3—122no—
384Dic3—242no—
385Dic3#83712yes—
386C32#150611yescharacteristic, complemented, Sylow
387C23D3×#6711yescharacteristic
388Q8—41no—
389Q8—121no—
390Q8—122no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—31no—
396C2×C4—31no—
397C2×C4—41no—
398C2×C4—62no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—62no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—182no—
407C2×C4—361no—
408C2×C4—361no—
409C2×C4C2×D3×Dic311yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C8—121no—
412C8—361no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3#474011yescharacteristic
423C2×C3#480211yescharacteristic
424C2×C3D3×#10411yescharacteristic
425C2×C3#522511yescharacteristic
426C2×C3C2×#83711yescharacteristic
427C2×C3#524011yescharacteristic
428C22—21no—
429C22—21no—
430C22#6394611yescharacteristic
431C22#6394811yescharacteristic
432C22D3×#21711yescharacteristic
433C4—21no—
434C4—21no—
435C4—32no—
436C4—41no—
437C4—41no—
438C4—61no—
439C4—61no—
440C4—61no—
441C4—122no—
442C4—121no—
443C4—121no—
444C4—362no—
445C3—21no—
446C3#6831011yescharacteristic, complemented
447C3#7183611yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2#1059152811yescharacteristic
451C2#1059155711yescharacteristic
452C2D3×#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#1506
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
86. Q8×Dic3Dic3semidirect
87. #944Dic3semidirect
93. #888Dic3semidirect
95. #887Dic3semidirect
386. C32#1506semidirect
446. C3#68310semidirect
447. C3#71836semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
#105912392
#105910632
#105894042
C3×#45382
#105891532
#105891522
#718363
#683103