Finite Group Databasebeta

← #11808016

Subgroups — #11808016

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic
2C3×#4980C212yesmaximal
3#10591360C211yesmaximal, characteristic
4#10591360C211yesmaximal, characteristic
5#10591271C212yesmaximal
6#10591271C212yesmaximal
7#10591264C212yesmaximal
8#10591212C212yesmaximal
9#10591197C212yesmaximal
10#74978—32nomaximal
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64099C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2212yes—
21C2×#3724C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×#3724C2211yescharacteristic
24C2×Dic32C2212yes—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#890—32no—
34C2×#890—61no—
35C3×#387—32no—
36#4980D312yes—
37#4976—32no—
38#4972—32no—
39#4933—32no—
40#4928—32no—
41#4654—32no—
42#4654—32no—
43#4653—32no—
44#4653—32no—
45#4652—32no—
46#4650—32no—
47#4650—32no—
48#4647—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C32×C4⋊C4C2×C414yes—
59C4⋊(C3⋊Dic3)C2×C418yes—
60C4⋊(C3⋊Dic3)C2×C414yes—
61#3750C2×C418yes—
62C4×C3⋊Dic3C2×C414yes—
63C3×C4⋊Dic3—42no—
64C3×C4×Dic3—42no—
65#3724—41no—
66#3724—42no—
67#3724—41no—
68#3724—41no—
69#3724—41no—
70Dic32—42no—
71#2382—91noSylow
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C4⋊C4C2×D312yes—
75C2×C3×C42—32no—
76C2×C4⋊Dic3—32no—
77C2×C4⋊Dic3—32no—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—61no—
80C2×C4⋊Dic3—62no—
81C2×C4⋊Dic3C2×D312yes—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—62no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3C2×D312yes—
96#890—316no—
97#890—68no—
98C3×#95—32no—
99C3×#95—32no—
100C3×#95—32no—
101C3×#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95C2×D312yes—
111C3⋊#95C2×D312yes—
112C3⋊#95C2×D312yes—
113C3⋊#95C2×D312yes—
114C23×C32C2411yescharacteristic
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4C22×C412yes—
120C2×C32×C4C22×C414yes—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C22×C412yes—
128C2×C3⋊Dic3C22×C412yes—
129C2×C3⋊Dic3C22×C414yes—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
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×Dic3—22no—
142C2×#125—91no—
143#389—92no—
144#389—92no—
145#387—32no—
146#387—92no—
147#387—92no—
148#387—92no—
149#382—91no—
150#382—91no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D312yes—
159C22×C3×C4C22×D312yes—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—32no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—62no—
167C22×Dic3C22×D312yes—
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C22×Dic3C22×D312yes—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—122no—
173C3×C4⋊C4C4×D318yes—
174C3×C42—122no—
175C4⋊Dic3—38no—
176C4⋊Dic3—38no—
177C4⋊Dic3—38no—
178C4⋊Dic3—42no—
179C4⋊Dic3—68no—
180C4⋊Dic3—64no—
181Dic3⋊C4—38no—
182Dic3⋊C4—38no—
183Dic3⋊C4—68no—
184Dic3⋊C4—122no—
185Dic3⋊C4—122no—
186Dic3⋊C4—122no—
187Dic3⋊C4—122no—
188Dic3⋊C4—122no—
189Dic3⋊C4—122no—
190C4×Dic3—38no—
191C4×Dic3—42no—
192C4×Dic3—64no—
193C4×Dic3—122no—
194C4×Dic3—122no—
195C22×C32C23×C411yescharacteristic
196C22×C32H(5,𝔽2)11yescharacteristic
197C22×C32H(5,𝔽2)11yescharacteristic
198C22×C322−1+411yescharacteristic
199C22×C322−1+411yescharacteristic
200C22×C322−1+411yescharacteristic
201C22×C322−1+411yescharacteristic
202C32×C4—22no—
203C32×C4—24no—
204C3⋊Dic3—22no—
205C3⋊Dic3—24no—
206C3⋊Dic3—22no—
207C3×Dic3—42no—
208C3×Dic3—42no—
209C3×Dic3—42no—
210C3×Dic3—42no—
211#125—98no—
212C2×C4⋊C4—32no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4—92no—
215C2×C4⋊C4—92no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—92no—
221C2×C4⋊C4D3211yescharacteristic
222C2×C42—32no—
223C2×C42—91no—
224C2×C42—92no—
225#95—32no—
226#95—32no—
227#95—32no—
228#95—32no—
229#95—92no—
230#95—92no—
231#95—92no—
232#95—92no—
233C23×C3—21no—
234C23×C3C23×D312yes—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—24no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4C2×C4×D314yes—
260C2×C3×C4C2×C4×D314yes—
261C2×C3×C4C2×C4×D314yes—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—64no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—121no—
295C2×C32#51911yescharacteristic
296C2×C32#52011yescharacteristic
297C2×C32#52011yescharacteristic
298C2×C32#56211yescharacteristic
299C2×C32#56311yescharacteristic
300C2×C32#56311yescharacteristic
301C2×C32#56411yescharacteristic
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—32no—
305C22×C4—32no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—92no—
309C22×C4C2×D3211yescharacteristic
310C22×C4C2×D3212yes—
311C4⋊C4—98no—
312C4⋊C4—98no—
313C4⋊C4—94no—
314C4⋊C4—122no—
315C4⋊C4—361no—
316C4⋊C4—361no—
317C4⋊C4—361no—
318C4⋊C4—362no—
319C4⋊C4—361no—
320C4⋊C4#62414yes—
321C42—94no—
322C42—122no—
323C42—362no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3C22×C4×D312yes—
332C22×C3#100412yes—
333C22×C3#100712yes—
334C22×C3#100912yes—
335C22×C3#101012yes—
336C22×C3#101012yes—
337C22×C3#101012yes—
338C3×C4—24no—
339C3×C4—24no—
340C3×C4—24no—
341C3×C4—24no—
342C3×C4—44no—
343C3×C4—122no—
344C3×C4—122no—
345C3×C4—122no—
346C3×C4—122no—
347Dic3—42no—
348Dic3—42no—
349Dic3—42no—
350Dic3—42no—
351Dic3—64no—
352Dic3—64no—
353Dic3—64no—
354Dic3—64no—
355Dic3—122no—
356Dic3—124no—
357Dic3—122no—
358C32#238211yescharacteristic, complemented, Sylow
359C23C22×D3211yescharacteristic
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—62no—
367C2×C4—62no—
368C2×C4—62no—
369C2×C4—62no—
370C2×C4—62no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—92no—
377C2×C4—92no—
378C2×C4—94no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—181no—
385C2×C4C2×#62412yes—
386C2×C4C2×#62414yes—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3#551612yes—
395C2×C3#554612yes—
396C2×C3#557412yes—
397C2×C3#564612yes—
398C2×C3#566712yes—
399C2×C3C3⋊#56412yes—
400C2×C3#571212yes—
401C22#6429811yescharacteristic
402C22#6429811yescharacteristic
403C22#6430911yescharacteristic
404C22#6431311yescharacteristic
405C22#6431611yescharacteristic
406C22#6432011yescharacteristic
407C22C22×#62411yescharacteristic
408C4—22no—
409C4—24no—
410C4—122no—
411C4—122no—
412C4—122no—
413C4—122no—
414C4—182no—
415C4—184no—
416C4—182no—
417C3—21no—
418C3#7497812yescomplemented
419C2#1059435411yescharacteristic
420C2#1059449711yescharacteristic
421C2#1059450711yescharacteristic
422C2#1059458911yescharacteristic
423C2#1059482811yescharacteristic
424C2#1059521911yescharacteristic
425C2#1059535311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #64099C4semidirect
358. C32#2382semidirect
418. C3#74978semidirect

Maximal subgroups

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

subgroupindex
C2×#640992
C3×#49802
#105913602
#105912712
#105912642
#105912122
#105911972
#749783