Finite Group Databasebeta

← #11803221

Subgroups — #11803221

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic
3C3×#4933C212yesmaximal
4#10591256C212yesmaximal
5#10591252C211yesmaximal, characteristic
6#10591248C212yesmaximal
7#10591245C212yesmaximal
8#10591236C212yesmaximal
9#10591192C212yesmaximal
10#74946—32nomaximal
11C22×#627C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×#3724C2211yescharacteristic
19C2×Dic3⋊Dic3C2212yes—
20C2×Dic32C2212yes—
21C2×Dic32C2212yes—
22#63838C418yescomplemented
23#63658C2212yes—
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28#63579C2212yes—
29#63579C2212yes—
30#63579C2211yescharacteristic
31#63579C2211yescharacteristic
32#63579C2212yes—
33C2×#887—32no—
34C3×#387—32no—
35#4980—32no—
36#4977—32no—
37#4976—32no—
38#4933D312yes—
39C4×Dic3⋊C4—32no—
40C4×Dic3⋊C4—61no—
41#4652—32no—
42#4651—32no—
43#4651—32no—
44#4650—32no—
45#4648—32no—
46#4647—32no—
47#4646—32no—
48#4646—32no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C2×#627—24no—
59C2×#627C2×C414yes—
60C32×C42—41no—
61#3750—24no—
62C4×C3⋊Dic3—41no—
63C4×C3⋊Dic3C2×C414yes—
64C3×Dic3⋊C4—42no—
65C3×Dic3⋊C4C2×C418yes—
66#3724C2×C414yes—
67Dic3⋊Dic3—42no—
68Dic32—24no—
69Dic32C2×C418yes—
70#2320—91noSylow
71C22×Dic6—32no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C42—21no—
75C2×C3×C42C2×D312yes—
76C2×C4⋊Dic3—32no—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—32no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—62no—
82C2×Dic3⋊C4C2×D312yes—
83C2×Dic3⋊C4C2×D312yes—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—32no—
87C2×C4×Dic3—32no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3—61no—
92#887—316no—
93C3×#95—32no—
94C3×#95—32no—
95C3×#95—32no—
96C3×#95—32no—
97C3⋊#95—32no—
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—62no—
108C3⋊#95C2×D312yes—
109C3⋊#95C2×D312yes—
110C3⋊#95C2×D312yes—
111C3⋊#95C2×D312yes—
112C23×C32C2411yescharacteristic
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4C22×C412yes—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C22×C412yes—
124C2×C3⋊Dic3C22×C412yes—
125C2×C3⋊Dic3#4114yes—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
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×Dic3C22×C414yes—
137C2×C3×Dic3C22×C414yes—
138#627—28no—
139C2×C4×Q8—91no—
140#391—92no—
141#389—92no—
142#387—32no—
143#387—92no—
144#383—92no—
145#382—92no—
146C4×C4⋊C4—91no—
147#376—91no—
148C22×C3×C4—21no—
149C22×C3×C4—22no—
150C22×C3×C4—32no—
151C22×C3×C4—32no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D312yes—
156C22×C3×C4C22×D312yes—
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—62no—
164C22×Dic3C22×D312yes—
165C22×Dic3C22×D312yes—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C2×Dic6—38no—
169C2×Dic6—64no—
170C2×Dic6—64no—
171C3×C4⋊C4—38no—
172C3×C4⋊C4—122no—
173C3×C42—42no—
174C3×C42—42no—
175C4⋊Dic3—122no—
176Dic3⋊C4—38no—
177Dic3⋊C4—42no—
178Dic3⋊C4—64no—
179Dic3⋊C4—64no—
180Dic3⋊C4—68no—
181Dic3⋊C4—122no—
182Dic3⋊C4C4×D318yes—
183C4×Dic3—38no—
184C4×Dic3—38no—
185C4×Dic3—38no—
186C4×Dic3—64no—
187C4×Dic3—64no—
188C4×Dic3—64no—
189C4×Dic3—122no—
190C4×Dic3—122no—
191C22×C32C23×C411yescharacteristic
192C22×C32C2×#4112yes—
193C22×C32H(5,𝔽2)11yescharacteristic
194C22×C322−1+412yes—
195C22×C322−1+411yescharacteristic
196C32×C4—22no—
197C32×C4—42no—
198C3⋊Dic3—22no—
199C3⋊Dic3—42no—
200C3⋊Dic3#11714yes—
201C3×Dic3—24no—
202C3×Dic3—24no—
203C3×Dic3—42no—
204C3×Dic3—42no—
205C22×Q8—91no—
206C4×Q8—98no—
207C2×C4⋊C4—32no—
208C2×C4⋊C4—32no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4—92no—
212C2×C42—92no—
213C2×C42—91no—
214C2×C42—92no—
215C2×C42—91no—
216C2×C42D3211yescharacteristic
217#95—32no—
218#95—32no—
219#95—32no—
220#95—32no—
221#95—91no—
222#95—91no—
223#95—92no—
224#95—92no—
225#95—92no—
226#95—92no—
227C23×C3—21no—
228C23×C3C23×D312yes—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—24no—
234C2×C3×C4—22no—
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—34no—
242C2×C3×C4—34no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
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×C4C2×C4×D314yes—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—22no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—34no—
267C2×Dic3—34no—
268C2×Dic3—34no—
269C2×Dic3—34no—
270C2×Dic3—62no—
271C2×Dic3—64no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—64no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—122no—
285C2×Dic3C2×C4×D314yes—
286C2×Dic3C2×C4×D314yes—
287Dic6—616no—
288C2×C32C2×#11711yescharacteristic
289C2×C32#51911yescharacteristic
290C2×C32#52011yescharacteristic
291C2×C32#54112yes—
292C2×C32#54212yes—
293C2×Q8—94no—
294C2×Q8—184no—
295C22×C4—32no—
296C22×C4—32no—
297C22×C4—32no—
298C22×C4—32no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—92no—
302C22×C4C2×D3212yes—
303C22×C4C2×D3211yescharacteristic
304C4⋊C4—38no—
305C4⋊C4—94no—
306C4⋊C4—122no—
307C4⋊C4—184no—
308C4⋊C4—362no—
309C42—41no—
310C42—98no—
311C42—94no—
312C42—184no—
313C42—361no—
314C22×C3—22no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3C22×C4×D312yes—
320C22×C3#100412yes—
321C22×C3#100712yes—
322C22×C3D3×#4112yes—
323C22×C3D3×#4112yes—
324C22×C3#101012yes—
325C22×C3#101012yes—
326C3×C4—24no—
327C3×C4—24no—
328C3×C4—44no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4—64no—
332C3×C4—64no—
333C3×C4—122no—
334C3×C4—122no—
335Dic3—24no—
336Dic3—24no—
337Dic3—38no—
338Dic3—42no—
339Dic3—42no—
340Dic3—64no—
341Dic3—64no—
342Dic3—122no—
343Dic3—124no—
344Dic3—122no—
345Dic3—122no—
346C32#232011yescharacteristic, complemented, Sylow
347C23C22×D3211yescharacteristic
348Q8—188no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—34no—
355C2×C4—34no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—92no—
367C2×C4—94no—
368C2×C4—92no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4C4×D3212yes—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—22no—
377C2×C3—22no—
378C2×C3—21no—
379C2×C3D3×#11712yes—
380C2×C3#554612yes—
381C2×C3#557212yes—
382C2×C3#564012yes—
383C2×C3#566212yes—
384C2×C3#569612yes—
385C2×C3#570112yes—
386C22#6429712yes—
387C22#6429811yescharacteristic
388C22C2×C4×D3211yescharacteristic
389C22#6430612yes—
390C22#6433011yescharacteristic
391C4—22no—
392C4—42no—
393C4—64no—
394C4—64no—
395C4—94no—
396C4—122no—
397C4—122no—
398C4—182no—
399C4—362no—
400C3—21no—
401C3#7494612yescomplemented
402C2#1059384811yescharacteristic
403C2#1059394512yes—
404C2#1059399211yescharacteristic
405C2#1059487611yescharacteristic
406C2#1059496412yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2320
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. #63838C4semidirect
346. C32#2320semidirect
401. C3#74946semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
C4×#37502
C3×#49332
#105912562
#105912522
#105912482
#105912452
#105912362
#105911922
#749463