Finite Group Databasebeta

← #11803822

Subgroups — #11803822

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic
4#10592676C211yesmaximal, characteristic
5C3×#4973C211yesmaximal, characteristic
6#10591333C214yesmaximal
7#10591255C214yesmaximal
8#10591222C211yesmaximal, characteristic
9#10591220C211yesmaximal, characteristic
10#82456—31nomaximal
11#76485—31nomaximal
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C3×#887—24no—
22C2×#3724C2214yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic32C2212yes—
25#63873C418yescomplemented
26Dic3×Dic6—24no—
27#63658C2214yes—
28C3×C3⋊#95C2214yes—
29#63579C2212yes—
30#63579C2214yes—
31#63579C2212yes—
32C2×C3×C4×Q8—31no—
33C2×Q8×Dic3—31no—
34C2×#944—31no—
35C2×#944—31no—
36C2×#887D311yescharacteristic
37C2×C4×Dic6—31no—
38C3×#391—31no—
39#5229—31no—
40#4978—34no—
41#4977—31no—
42#4977—31no—
43#4977—61no—
44#4973D311yescharacteristic
45#4933—34no—
46#4932—31no—
47#4932—31no—
48#4929—31no—
49#4655—34no—
50#4652—34no—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2311yescharacteristic
59C22×C3×Dic3C2311yescharacteristic
60C2×C3×Dic6—22no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yes—
65C2×C3×Dic6C2×C414yes—
66C32×C4⋊C4—22no—
67C4⋊(C3⋊Dic3)—22no—
68C4×C3⋊Dic3C2×C414yes—
69C3×Dic3⋊C4—24no—
70C3×C4×Dic3—22no—
71C3×C4×Dic3—24no—
72C3×C4×Dic3D414yes—
73#3724C2×C4116yes—
74Dic3⋊Dic3—24no—
75Dic32—24no—
76#2327—91noSylow
77C22×C3×Q8—31no—
78C22×C3×Q8—31no—
79C22×Dic6C2×D311yescharacteristic
80C22×Dic6C2×D311yescharacteristic
81C3×C4×Q8—64no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C42—31no—
87C2×C3×C42—31no—
88C2×C3×C42—32no—
89Q8×Dic3—64no—
90#944—38no—
91#944—38no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—61no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4C2×D312yes—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D312yes—
106C2×C4×Dic3C2×D311yescharacteristic
107C2×C4×Dic3C2×D311yescharacteristic
108#887—24no—
109C4×Dic6—64no—
110C3×#95—34no—
111C3⋊#95—34no—
112C3⋊#95—34no—
113C3⋊#95—32no—
114C3⋊#95—34no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—34no—
119C3⋊#95—64no—
120C3⋊#95C2×D314yes—
121C23×C32C2411yescharacteristic
122C2×C32×C4—22no—
123C2×C32×C4—24no—
124C2×C32×C4C22×C412yes—
125C2×C32×C4C2×D412yes—
126C2×C32×C4#4112yes—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—24no—
131C2×C3⋊Dic3C22×C414yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3C22×C414yes—
142C2×C3×Dic3C22×C414yes—
143C2×C3×Dic3C2×D412yes—
144C2×C3×Dic3C2×D412yes—
145C3×Dic6—28no—
146C3×Dic6—28no—
147C2×C4⋊Q8—91no—
148C2×C4×Q8—31no—
149C2×C4×Q8—91no—
150#391—31no—
151#391—91no—
152#387—94no—
153#387—94no—
154#382—91no—
155#376—91no—
156C2×C3×Q8—34no—
157C2×C3×Q8—34no—
158C2×C3×Q8—62no—
159C2×C3×Q8—62no—
160C2×C3×Q8—62no—
161C2×C3×Q8—62no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D312yes—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—32no—
174C22×Dic3—32no—
175C22×Dic3—32no—
176C22×Dic3—32no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3C22×D312yes—
180C22×Dic3C22×D312yes—
181C22×Dic3C22×D312yes—
182C22×Dic3C22×D311yescharacteristic
183C22×Dic3C22×D311yescharacteristic
184C2×Dic6—22no—
185C2×Dic6—22no—
186C2×Dic6—22no—
187C2×Dic6—22no—
188C2×Dic6C4×D314yes—
189C2×Dic6C4×D314yes—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—42no—
193C3×C4⋊C4—64no—
194C3×C42—34no—
195C3×C42—64no—
196C3×C42—62no—
197C4⋊Dic3—62no—
198C4⋊Dic3—62no—
199C4⋊Dic3—64no—
200C4⋊Dic3—122no—
201Dic3⋊C4—24no—
202Dic3⋊C4—316no—
203Dic3⋊C4—316no—
204Dic3⋊C4—64no—
205C4×Dic3—22no—
206C4×Dic3—24no—
207C4×Dic3—34no—
208C4×Dic3—34no—
209C4×Dic3—64no—
210C4×Dic3—64no—
211C4×Dic3—64no—
212C4×Dic3#6714yes—
213C22×C32C23×C411yescharacteristic
214C22×C32C22×D411yescharacteristic
215C22×C32C2×#4111yescharacteristic
216C22×C322−1+412yes—
217C22×C322−1+412yes—
218C32×C4—42no—
219C32×C4C4×D414yes—
220C3⋊Dic3—24no—
221C3⋊Dic3—42no—
222C3×Dic3—24no—
223C3×Dic3—24no—
224C3×Dic3—22no—
225C3×Dic3—22no—
226C3×Dic3—42no—
227C22×Q8—31no—
228C22×Q8—31no—
229C4⋊Q8—98no—
230C4×Q8—64no—
231C4×Q8—184no—
232C2×C4⋊C4—32no—
233C2×C4⋊C4—94no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4D3211yescharacteristic
237C2×C42—31no—
238C2×C42—32no—
239C2×C42—31no—
240C2×C42—91no—
241C2×C42—92no—
242#95—34no—
243#95—92no—
244#95—92no—
245#95—94no—
246#95—94no—
247C23×C3—21no—
248C23×C3C23×D311yescharacteristic
249C23×C3C23×D311yescharacteristic
250C3×Q8—68no—
251C3×Q8—68no—
252C2×C3×C4—22no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—34no—
260C2×C3×C4—34no—
261C2×C3×C4—32no—
262C2×C3×C4—32no—
263C2×C3×C4—42no—
264C2×C3×C4—44no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4C2×C4×D312yes—
275C2×C3×C4C2×C4×D312yes—
276C2×C3×C4#23512yes—
277C2×C3×C4D3×D412yes—
278C2×C3×C4#23712yes—
279C2×C3×C4C2×#6712yes—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—64no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—62no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—124no—
304C2×Dic3C2×C4×D314yes—
305C2×Dic3C2×C4×D314yes—
306C2×Dic3C2×#6712yes—
307C2×Dic3C2×#6712yes—
308Dic6—28no—
309Dic6—28no—
310C2×C32C2×C4×D411yescharacteristic
311C2×C32#51912yes—
312C2×C32#53611yescharacteristic
313C2×C32#53611yescharacteristic
314C2×C32#54112yes—
315C2×Q8—34no—
316C2×Q8—34no—
317C2×Q8—62no—
318C2×Q8—62no—
319C2×Q8—62no—
320C2×Q8—62no—
321C22×C4—32no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—32no—
325C22×C4—32no—
326C22×C4—92no—
327C22×C4—92no—
328C22×C4C2×D3212yes—
329C22×C4C2×D3211yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—64no—
332C4⋊C4—916no—
333C4⋊C4—184no—
334C4⋊C4—182no—
335C42—34no—
336C42—64no—
337C42—62no—
338C42—94no—
339C42—184no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3C22×C4×D311yescharacteristic
346C22×C3C22×C4×D311yescharacteristic
347C22×C3C2×#23511yescharacteristic
348C22×C3C2×D3×D411yescharacteristic
349C22×C3C2×#23711yescharacteristic
350C22×C3#100712yes—
351C22×C3#100712yes—
352C22×C3#101012yes—
353C22×C3#101012yes—
354C22×C3C22×#6711yescharacteristic
355C3×C4—24no—
356C3×C4—42no—
357C3×C4—42no—
358C3×C4—62no—
359C3×C4—62no—
360C3×C4—64no—
361C3×C4—64no—
362C3×C4—82no—
363C3×C4—122no—
364C3×C4#67⋊C414yes—
365C3×C4C4×#6714yes—
366Dic3—24no—
367Dic3—24no—
368Dic3—22no—
369Dic3—22no—
370Dic3—42no—
371Dic3—64no—
372Dic3—64no—
373Dic3—124no—
374Dic3—122no—
375Dic3—122no—
376Dic3—242no—
377C32#232711yescharacteristic, complemented, Sylow
378C23C22×D3211yescharacteristic
379Q8—68no—
380Q8—68no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—34no—
384C2×C4—34no—
385C2×C4—32no—
386C2×C4—32no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—94no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—184no—
400C2×C4—182no—
401C2×C4#379512yes—
402C2×C4C4×D3212yes—
403C2×C4D3×#6712yes—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3C2×#67⋊C411yescharacteristic
410C2×C3#557212yes—
411C2×C3#557212yes—
412C2×C3#558312yes—
413C2×C3#562512yes—
414C2×C3#567511yescharacteristic
415C2×C3#572411yescharacteristic
416C2×C3C2×C4×#6711yescharacteristic
417C2×C3#581611yescharacteristic
418C2×C3#582511yescharacteristic
419C22C2×#379511yescharacteristic
420C22C2×C4×D3211yescharacteristic
421C22#6430912yes—
422C22#6431612yes—
423C22C2×D3×#6711yescharacteristic
424C4—42no—
425C4—62no—
426C4—64no—
427C4—64no—
428C4—62no—
429C4—122no—
430C4—184no—
431C4—362no—
432C4#6387914yes—
433C3—21no—
434C3#7648511yescharacteristic, complemented
435C3#8245611yescharacteristic, complemented
436C2#1059434512yes—
437C2#1059434712yes—
438C2C2×#6387911yescharacteristic
439C2#1059514711yescharacteristic
440C2#1059534011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
25. #63873C4semidirect
377. C32#2327semidirect
434. C3#76485semidirect
435. C3#82456semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×#638732
C2×Dic3×Dic62
#105926762
C3×#49732
#105913332
#105912552
#105912222
#105912202
#824563
#764853