Finite Group Databasebeta

← #11803816

Subgroups — #11803816

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic
2C2×#63837C212yesmaximal
3#10592349C211yesmaximal, characteristic
4C3×#4654C212yesmaximal
5#10591333C212yesmaximal
6#10591269C212yesmaximal
7#10591255C212yesmaximal
8#10591252C211yesmaximal, characteristic
9#10591236C212yesmaximal
10#74948—32nomaximal
11C22×#627C2212yes—
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C2×#3724C2211yescharacteristic
18C2×#3724C2211yescharacteristic
19C2×Dic3⋊Dic3C2212yes—
20C2×Dic32C2211yescharacteristic
21C2×Dic32C2212yes—
22C2×Dic32C2211yescharacteristic
23#63919C418yescomplemented
24#63837—28no—
25C32×#95C2211yescharacteristic
26#63658C2212yes—
27#63658C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×#888—32no—
35C2×#887—32no—
36C2×C4×Dic6—32no—
37C3×#387—32no—
38#4980—32no—
39#4978—32no—
40#4933—32no—
41#4655—32no—
42#4654D312yes—
43#4653—32no—
44#4652—32no—
45#4650—32no—
46#4650—61no—
47#4648—32no—
48#4646—32no—
49#4646—32no—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C2×#627—24no—
60C2×#627—24no—
61C2×#627C2×C418yes—
62#3750—24no—
63C4×C3⋊Dic3C2×C414yes—
64C3×C4⋊Dic3C2×C418yes—
65C3×Dic3⋊C4—24no—
66C3×C4×Dic3—24no—
67#3724C2×C414yes—
68#3724C2×C414yes—
69Dic3⋊Dic3—24no—
70Dic32—22no—
71Dic32—24no—
72Dic32D414yes—
73#2327—91noSylow
74C22×Dic6—32no—
75C22×Dic6—32no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C42—32no—
79C2×C4⋊Dic3—32no—
80C2×C4⋊Dic3C2×D312yes—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—62no—
87C2×Dic3⋊C4C2×D312yes—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3C2×D312yes—
95#888—316no—
96#887—68no—
97C4×Dic6—68no—
98C3×#95—21no—
99C3×#95—32no—
100C3×#95—32no—
101C3×#95—32no—
102C3×#95C2×D312yes—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—62no—
113C3⋊#95—61no—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C3⋊#95C2×D312yes—
117C23×C32C2411yescharacteristic
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C22×C412yes—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C22×C412yes—
128C2×C3⋊Dic3C22×C412yes—
129C2×C3⋊Dic3C2×D412yes—
130C2×C3⋊Dic3#4112yes—
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×Dic3C22×C414yes—
141C2×C3×Dic3C22×C414yes—
142C2×C3×Dic3C2×D414yes—
143#627—216no—
144C2×C4⋊Q8—91no—
145C2×C4×Q8—92no—
146#391—92no—
147#387—32no—
148#387—92no—
149#387—92no—
150#387—92no—
151#382—91no—
152#376—91no—
153C22×C3×C4—21no—
154C22×C3×C4—22no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4C22×D312yes—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D312yes—
162C22×Dic3—32no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—62no—
169C22×Dic3C22×D312yes—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D312yes—
173C2×Dic6—38no—
174C2×Dic6—38no—
175C2×Dic6—64no—
176C2×Dic6—64no—
177C2×Dic6—64no—
178C2×Dic6—64no—
179C3×C4⋊C4—38no—
180C3×C4⋊C4—64no—
181C3×C42—64no—
182C4⋊Dic3—64no—
183C4⋊Dic3C4×D318yes—
184Dic3⋊C4—24no—
185Dic3⋊C4—38no—
186Dic3⋊C4—38no—
187Dic3⋊C4—64no—
188Dic3⋊C4—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—124no—
191C4×Dic3—24no—
192C4×Dic3—38no—
193C4×Dic3—38no—
194C4×Dic3—64no—
195C4×Dic3—64no—
196C4×Dic3—64no—
197C4×Dic3—64no—
198C22×C32C23×C411yescharacteristic
199C22×C32C22×D411yescharacteristic
200C22×C32C2×#4111yescharacteristic
201C22×C322−1+412yes—
202C22×C322−1+412yes—
203C32×C4—22no—
204C32×C4—42no—
205C3⋊Dic3—22no—
206C3⋊Dic3—42no—
207C3⋊Dic3C4×D414yes—
208C3×Dic3—24no—
209C3×Dic3—24no—
210C3×Dic3—24no—
211C3×Dic3—42no—
212C22×Q8—92no—
213C4⋊Q8—98no—
214C4×Q8—188no—
215C2×C4⋊C4—32no—
216C2×C4⋊C4—32no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—92no—
221C2×C42—32no—
222C2×C42—91no—
223C2×C42—91no—
224C2×C42—92no—
225C2×C42—91no—
226#95—32no—
227#95—32no—
228#95—32no—
229#95—92no—
230#95—92no—
231#95—92no—
232#95—92no—
233#95—91no—
234#95D3211yescharacteristic
235C23×C3—21no—
236C23×C3C23×D312yes—
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—22no—
245C2×C3×C4—22no—
246C2×C3×C4—34no—
247C2×C3×C4—34no—
248C2×C3×C4—34no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
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×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4C2×C4×D314yes—
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—34no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3—122no—
292C2×Dic3C2×C4×D314yes—
293C2×Dic3C2×C4×D314yes—
294C2×Dic3D3×D414yes—
295Dic6—616no—
296Dic6—616no—
297C2×C32C2×C4×D411yescharacteristic
298C2×C32#51911yescharacteristic
299C2×C32#51911yescharacteristic
300C2×C32#53612yes—
301C2×C32#54112yes—
302C2×Q8—98no—
303C2×Q8—184no—
304C2×Q8—184no—
305C22×C4—32no—
306C22×C4—32no—
307C22×C4—32no—
308C22×C4—32no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—92no—
312C22×C4C2×D3212yes—
313C22×C4C2×D3211yescharacteristic
314C4⋊C4—38no—
315C4⋊C4—64no—
316C4⋊C4—94no—
317C4⋊C4—94no—
318C4⋊C4—184no—
319C4⋊C4—184no—
320C42—64no—
321C42—94no—
322C42—94no—
323C42—184no—
324C42—182no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3C22×C4×D312yes—
331C22×C3C2×D3×D412yes—
332C22×C3#100712yes—
333C22×C3D3×#4112yes—
334C22×C3#101012yes—
335C22×C3#101012yes—
336C22×C3#101012yes—
337C3×C4—24no—
338C3×C4—42no—
339C3×C4—42no—
340C3×C4—42no—
341C3×C4—64no—
342C3×C4—64no—
343C3×C4—64no—
344C3×C4—82no—
345C3×C4—122no—
346Dic3—24no—
347Dic3—24no—
348Dic3—24no—
349Dic3—38no—
350Dic3—42no—
351Dic3—64no—
352Dic3—64no—
353Dic3—122no—
354Dic3—122no—
355Dic3—122no—
356Dic3—242no—
357C32#232711yescharacteristic, complemented, Sylow
358C23C22×D3211yescharacteristic
359Q8—1816no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—34no—
365C2×C4—34no—
366C2×C4—34no—
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—92no—
379C2×C4—92no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4C4×D3212yes—
385C2×C3—22no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3#551612yes—
391C2×C3C4×D3×D412yes—
392C2×C3#557212yes—
393C2×C3#562812yes—
394C2×C3#564812yes—
395C2×C3#569612yes—
396C2×C3#570112yes—
397C22#6429712yes—
398C22C2×C4×D3211yescharacteristic
399C22#6430912yes—
400C22D32×D411yescharacteristic
401C22#6431911yescharacteristic
402C4—22no—
403C4—42no—
404C4—64no—
405C4—64no—
406C4—64no—
407C4—94no—
408C4—122no—
409C4—182no—
410C4—362no—
411C3—21no—
412C3#7494812yescomplemented
413C2#1059384811yescharacteristic
414C2#1059405612yes—
415C2#1059424511yescharacteristic
416C2#1059448812yes—
417C2#1059460511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
23. #63919C4semidirect
357. C32#2327semidirect
412. C3#74948semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#638372
#105923492
C3×#46542
#105913332
#105912692
#105912552
#105912522
#105912362
#749483