Finite Group Databasebeta

← #11800945

Subgroups — #11800945

Order 1152.

1405 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C2×#63844C212yesmaximal
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4C3×#4932C211yesmaximal, characteristic
5Dic3×C4⋊Dic3C212yesmaximal
6#10591257C212yesmaximal
7#10591252C212yesmaximal
8#10591243C214yesmaximal
9#73616—31nomaximal
10#73383—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C4×#634C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2214yes—
21C2×Dic32C2214yes—
22C2×Dic32C2214yes—
23#63844C4116yescomplemented
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2211yescharacteristic
28#63579C2214yes—
29C2×#887—32no—
30C2×C4×Dic6—31no—
31C2×C4×Dic6—31no—
32C2×C4×Dic6—32no—
33C2×C4×Dic6—61no—
34C3×C4×C4⋊C4—31no—
35C3×#376—31no—
36Dic3×C4⋊C4—32no—
37C4×C4⋊Dic3—32no—
38C4×C4⋊Dic3D311yescharacteristic
39#4932D311yescharacteristic
40C4×Dic3⋊C4—34no—
41#4649—34no—
42#4649—32no—
43#4649—32no—
44#4648—32no—
45#4648—32no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C2×#634C2×C414yes—
52C2×#634C2×C418yes—
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C32×C42C2×C414yes—
57C4⋊(C3⋊Dic3)C2×C414yes—
58#3750C2×C418yes—
59C4×C3⋊Dic3C2×C418yes—
60C3×C4⋊Dic3C2×C418yes—
61C3×C4×Dic3—42no—
62C3×C4×Dic3C2×C418yes—
63#3724C2×C4116yes—
64Dic32—44no—
65Dic32C2×C4116yes—
66#2276—91noSylow
67C22×Dic6—31no—
68C22×Dic6—31no—
69C22×Dic6—61no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C42—21no—
72C2×C3×C42—32no—
73C2×C3×C42—32no—
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C2×D311yescharacteristic
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—61no—
79C2×C4⋊Dic3C2×D312yes—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—34no—
84C2×Dic3⋊C4—62no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—32no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—34no—
90C2×C4×Dic3—34no—
91C2×C4×Dic3—62no—
92C2×C4×Dic3C2×D312yes—
93C2×C4×Dic3C2×D312yes—
94#887—316no—
95C4×Dic6—38no—
96C4×Dic6—38no—
97C4×Dic6—316no—
98C4×Dic6—68no—
99C3×#95—31no—
100C3×#95—32no—
101C3×#95—32no—
102C3×#95—31no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95C2×D311yescharacteristic
106C3⋊#95C2×D312yes—
107C3⋊#95C2×D311yescharacteristic
108C3⋊#95C2×D312yes—
109C23×C32C2411yescharacteristic
110C2×C32×C4—22no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C22×C412yes—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C22×C414yes—
116C2×C32×C4C22×C412yes—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3C22×C414yes—
120C2×C3⋊Dic3C22×C418yes—
121C2×C3⋊Dic3C22×C414yes—
122#634C42116yescomplemented
123C2×C3×Dic3—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3C22×C414yes—
130C2×C3×Dic3C22×C418yes—
131C2×C3×Dic3C22×C414yes—
132C2×C4×Q8—92no—
133C2×C4×Q8—91no—
134C4×C4⋊C4—31no—
135C4×C4⋊C4—92no—
136C4×C4⋊C4—94no—
137C4×C4⋊C4—92no—
138#376—31no—
139#376—92no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—32no—
144C22×C3×C4—34no—
145C22×C3×C4—32no—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×Dic3—32no—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158C22×Dic3C22×D312yes—
159C22×Dic3C22×D314yes—
160C22×Dic3C22×D312yes—
161C2×Dic6—38no—
162C2×Dic6—34no—
163C2×Dic6—34no—
164C2×Dic6—38no—
165C2×Dic6—64no—
166C2×Dic6—68no—
167C3×C4⋊C4—38no—
168C3×C42—24no—
169C3×C42—38no—
170C3×C42—122no—
171C3×C42C4×D314yes—
172C3×C42C4×D314yes—
173C4⋊Dic3—34no—
174C4⋊Dic3—34no—
175C4⋊Dic3—64no—
176C4⋊Dic3C4×D318yes—
177Dic3⋊C4—38no—
178Dic3⋊C4—38no—
179Dic3⋊C4—316no—
180Dic3⋊C4—316no—
181Dic3⋊C4—68no—
182C4×Dic3—38no—
183C4×Dic3—38no—
184C4×Dic3—316no—
185C4×Dic3—316no—
186C4×Dic3—42no—
187C4×Dic3—68no—
188C4×Dic3—124no—
189C4×Dic3—124no—
190C4×Dic3C4×D318yes—
191C22×C32C23×C412yes—
192C22×C32C23×C411yescharacteristic
193C22×C32H(5,𝔽2)11yescharacteristic
194C22×C322−1+411yescharacteristic
195C22×C322−1+412yes—
196C32×C4—22no—
197C32×C4—22no—
198C32×C4C2×C4214yes—
199C3⋊Dic3—24no—
200C3⋊Dic3C2×C4218yes—
201C3×Dic3—24no—
202C3×Dic3—24no—
203C3×Dic3—28no—
204C22×Q8—91no—
205C4×Q8—916no—
206C4×Q8—98no—
207C2×C4⋊C4—32no—
208C2×C4⋊C4—94no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—91no—
211C2×C42—32no—
212C2×C42—32no—
213C2×C42—94no—
214C2×C42—92no—
215C2×C42—94no—
216C2×C42D3211yescharacteristic
217#95—31no—
218#95—32no—
219#95—31no—
220#95—32no—
221#95—94no—
222C23×C3—21no—
223C23×C3C23×D311yescharacteristic
224C23×C3C23×D311yescharacteristic
225C2×C3×C4—24no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—24no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—34no—
237C2×C3×C4—38no—
238C2×C3×C4—34no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—64no—
244C2×C3×C4—64no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4C2×C4×D314yes—
248C2×C3×C4C2×C4×D314yes—
249C2×C3×C4C2×C4×D312yes—
250C2×C3×C4C2×C4×D312yes—
251C2×C3×C4C2×C4×D312yes—
252C2×C3×C4C2×C4×D312yes—
253C2×C3×C4C2×C4×D312yes—
254C2×C3×C4C2×C4×D312yes—
255C2×Dic3—24no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—24no—
261C2×Dic3—38no—
262C2×Dic3—38no—
263C2×Dic3—34no—
264C2×Dic3—34no—
265C2×Dic3—34no—
266C2×Dic3—34no—
267C2×Dic3—64no—
268C2×Dic3—68no—
269C2×Dic3—64no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—122no—
275C2×Dic3—122no—
276C2×Dic3C2×C4×D314yes—
277C2×Dic3C2×C4×D318yes—
278C2×Dic3C2×C4×D314yes—
279Dic6—316no—
280Dic6—316no—
281Dic6—616no—
282C2×C32C22×C4211yescharacteristic
283C2×C32#51911yescharacteristic
284C2×C32#51912yes—
285C2×C32#52011yescharacteristic
286C2×C32#52012yes—
287C2×Q8—98no—
288C2×Q8—94no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—34no—
292C22×C4—92no—
293C22×C4—92no—
294C22×C4C2×D3211yescharacteristic
295C22×C4C2×D3211yescharacteristic
296C22×C4C2×D3211yescharacteristic
297C4⋊C4—38no—
298C4⋊C4—916no—
299C4⋊C4—98no—
300C4⋊C4—94no—
301C42—38no—
302C42—916no—
303C42—98no—
304C42—122no—
305C42—364no—
306C42#62414yes—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3C22×C4×D312yes—
313C22×C3C22×C4×D312yes—
314C22×C3C22×C4×D311yescharacteristic
315C22×C3C22×C4×D311yescharacteristic
316C22×C3#100411yescharacteristic
317C22×C3#100711yescharacteristic
318C22×C3#100911yescharacteristic
319C22×C3#101011yescharacteristic
320C22×C3#101012yes—
321C22×C3#101012yes—
322C3×C4—24no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—24no—
328C3×C4—42no—
329C3×C4—68no—
330C3×C4—64no—
331C3×C4—64no—
332C3×C4C42×D314yes—
333C3×C4C42×D314yes—
334Dic3—24no—
335Dic3—24no—
336Dic3—28no—
337Dic3—38no—
338Dic3—38no—
339Dic3—68no—
340Dic3—64no—
341Dic3—64no—
342Dic3—124no—
343C32#227611yescharacteristic, complemented, Sylow
344C23C22×D3211yescharacteristic
345Q8—916no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—34no—
350C2×C4—34no—
351C2×C4—38no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—62no—
355C2×C4—64no—
356C2×C4—64no—
357C2×C4—62no—
358C2×C4—98no—
359C2×C4—94no—
360C2×C4—94no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4C4×D3214yes—
364C2×C4C2×#62412yes—
365C2×C4C2×#62412yes—
366C2×C4C2×#62412yes—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3C2×C42×D311yescharacteristic
373C2×C3C2×C42×D311yescharacteristic
374C2×C3#550411yescharacteristic
375C2×C3#551611yescharacteristic
376C2×C3#551611yescharacteristic
377C2×C3#551612yes—
378C2×C3#552312yes—
379C2×C3#552311yescharacteristic
380C2×C3#554612yes—
381C2×C3#557212yes—
382C22#6429711yescharacteristic
383C22#6429812yes—
384C22C2×C4×D3212yes—
385C22#6430711yescharacteristic
386C22C22×#62411yescharacteristic
387C4—22no—
388C4—22no—
389C4—64no—
390C4—64no—
391C4—68no—
392C4—98no—
393C4—184no—
394C4C4×#62414yes—
395C3—21no—
396C3#7338311yescharacteristic, complemented
397C3#7361611yescharacteristic, complemented
398C2#1059388512yes—
399C2#1059388712yes—
400C2#1059482811yescharacteristic
401C2C2×C4×#62411yescharacteristic
402C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2276
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. C4×#634C4semidirect
23. #63844C4semidirect
122. #634C42semidirect
343. C32#2276semidirect
396. C3#73383semidirect
397. C3#73616semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×#638442
C3×C4×C4⋊Dic32
C3×#49322
Dic3×C4⋊Dic32
#105912572
#105912522
#105912432
#736163
#733833