Finite Group Databasebeta

← #11805950

Subgroups — #11805950

Order 1152.

1053 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2#10592674C211yesmaximal, characteristic
3C3×#4978C212yesmaximal
4#10591272C212yesmaximal
5#10591257C211yesmaximal, characteristic
6#10591247C212yesmaximal
7#10591243C212yesmaximal
8#10591243C212yesmaximal
9#10591236C212yesmaximal
10#74963—32nomaximal
11C22×#627C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2211yescharacteristic
21C2×#3724C2211yescharacteristic
22C2×Dic32C2212yes—
23C2×Dic32C2212yes—
24C2×Dic32C2212yes—
25#63838C418yescomplemented
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#887—32no—
34C3×#387—32no—
35#4980—32no—
36#4978D312yes—
37#4975—32no—
38#4975—61no—
39C4×Dic3⋊C4—32no—
40C4×Dic3⋊C4—32no—
41#4655—32no—
42#4650—32no—
43#4650—32no—
44#4649—32no—
45#4649—32no—
46#4649—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—22no—
59C2×#627—22no—
60C2×#627C2×C414yes—
61C32×C4⋊C4—41no—
62C4⋊(C3⋊Dic3)—41no—
63#3750—24no—
64#3750—24no—
65C4×C3⋊Dic3C2×C414yes—
66C3×Dic3⋊C4C2×C418yes—
67C3×C4×Dic3—42no—
68#3724—22no—
69#3724C2×C414yes—
70#3724Q814yescomplemented
71Dic32—24no—
72Dic32—42no—
73Dic32C2×C418yes—
74#2355—91noSylow
75C22×Dic6—32no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4C2×D312yes—
79C2×C3×C42—32no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—61no—
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—62no—
90C2×Dic3⋊C4—62no—
91C2×Dic3⋊C4C2×D312yes—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—61no—
100C2×C4×Dic3C2×D312yes—
101#887—316no—
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⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95C2×D312yes—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C23×C32C2411yescharacteristic
117C2×C32×C4—21no—
118C2×C32×C4—21no—
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⋊Dic3C22×C412yes—
127C2×C3⋊Dic3C22×C412yes—
128C2×C3⋊Dic3C2×Q812yes—
129C2×C3⋊Dic3#4112yes—
130C2×C3⋊Dic3#4112yes—
131C2×C3⋊Dic3#4112yes—
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×Q814yes—
144#627—28no—
145C2×C4×Q8—91no—
146#391—92no—
147#387—32no—
148#387—92no—
149#384—91no—
150#382—92no—
151C4×C4⋊C4—91no—
152C4×C4⋊C4—92no—
153C4×C4⋊C4—92no—
154C22×C3×C4—21no—
155C22×C3×C4—22no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D312yes—
174C2×Dic6—38no—
175C2×Dic6—64no—
176C2×Dic6—64no—
177C3×C4⋊C4—38no—
178C3×C4⋊C4—42no—
179C3×C4⋊C4—42no—
180C3×C42—122no—
181C4⋊Dic3—122no—
182C4⋊Dic3—122no—
183Dic3⋊C4—38no—
184Dic3⋊C4—38no—
185Dic3⋊C4—64no—
186Dic3⋊C4—64no—
187Dic3⋊C4—64no—
188Dic3⋊C4—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—124no—
191Dic3⋊C4—124no—
192Dic3⋊C4C4×D318yes—
193C4×Dic3—38no—
194C4×Dic3—38no—
195C4×Dic3—38no—
196C4×Dic3—42no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200C4×Dic3—122no—
201C4×Dic3—122no—
202C22×C32C23×C411yescharacteristic
203C22×C32C22×Q811yescharacteristic
204C22×C32C2×#4111yescharacteristic
205C22×C32C2×#4111yescharacteristic
206C22×C32C2×#4111yescharacteristic
207C22×C32H(5,𝔽2)11yescharacteristic
208C22×C322−1+411yescharacteristic
209C32×C4—22no—
210C32×C4—42no—
211C3⋊Dic3—42no—
212C3⋊Dic3#11714yes—
213C3⋊Dic3C4×Q814yes—
214C3×Dic3—24no—
215C3×Dic3—24no—
216C3×Dic3—24no—
217C3×Dic3—42no—
218C22×Q8—91no—
219C4×Q8—98no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4—91no—
222C2×C4⋊C4—91no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4—92no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4D3211yescharacteristic
228C2×C42—32no—
229C2×C42—92no—
230C2×C42—91no—
231C2×C42—92no—
232C2×C42—92no—
233#95—32no—
234#95—32no—
235#95—32no—
236#95—32no—
237#95—92no—
238#95—92no—
239#95—92no—
240C23×C3—21no—
241C23×C3C23×D312yes—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—34no—
254C2×C3×C4—34no—
255C2×C3×C4—34no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4C2×C4×D314yes—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—34no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—34no—
282C2×Dic3—34no—
283C2×Dic3—34no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3C2×C4×D314yes—
300C2×Dic3C2×C4×D314yes—
301C2×Dic3D3×Q814yes—
302Dic6—616no—
303C2×C32C2×#11711yescharacteristic
304C2×C32C2×C4×Q811yescharacteristic
305C2×C32#52011yescharacteristic
306C2×C32#55411yescharacteristic
307C2×C32#55611yescharacteristic
308C2×C32#55711yescharacteristic
309C2×C32#55911yescharacteristic
310C2×Q8—94no—
311C2×Q8—182no—
312C2×Q8—182no—
313C22×C4—32no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—32no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—92no—
320C22×C4C2×D3212yes—
321C22×C4C2×D3211yescharacteristic
322C4⋊C4—38no—
323C4⋊C4—41no—
324C4⋊C4—94no—
325C4⋊C4—94no—
326C4⋊C4—184no—
327C4⋊C4—184no—
328C4⋊C4—182no—
329C4⋊C4—361no—
330C42—98no—
331C42—94no—
332C42—122no—
333C42—184no—
334C42—362no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3C22×C4×D312yes—
343C22×C3#100412yes—
344C22×C3C2×D3×Q812yes—
345C22×C3D3×#4112yes—
346C22×C3D3×#4112yes—
347C22×C3D3×#4112yes—
348C22×C3#101012yes—
349C3×C4—24no—
350C3×C4—24no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—64no—
354C3×C4—64no—
355C3×C4—64no—
356C3×C4—82no—
357C3×C4—122no—
358Dic3—24no—
359Dic3—24no—
360Dic3—24no—
361Dic3—38no—
362Dic3—38no—
363Dic3—42no—
364Dic3—64no—
365Dic3—64no—
366Dic3—122no—
367Dic3—122no—
368Dic3—242no—
369C32#235511yescharacteristic, complemented, Sylow
370C23C22×D3211yescharacteristic
371Q8—188no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—34no—
378C2×C4—34no—
379C2×C4—34no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—92no—
390C2×C4—92no—
391C2×C4—92no—
392C2×C4—92no—
393C2×C4—92no—
394C2×C4—92no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4C4×D3212yes—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3D3×#11712yes—
407C2×C3#554612yes—
408C2×C3C4×D3×Q812yes—
409C2×C3#563612yes—
410C2×C3#566412yes—
411C2×C3#568512yes—
412C2×C3#570212yes—
413C22#6429811yescharacteristic
414C22C2×C4×D3211yescharacteristic
415C22#6431211yescharacteristic
416C22#6431211yescharacteristic
417C22D32×Q811yescharacteristic
418C22#6431911yescharacteristic
419C22#6433011yescharacteristic
420C4—22no—
421C4—42no—
422C4—64no—
423C4—64no—
424C4—64no—
425C4—94no—
426C4—94no—
427C4—122no—
428C4—362no—
429C3—21no—
430C3#7496312yescomplemented
431C2#1059431511yescharacteristic
432C2#1059436311yescharacteristic
433C2#1059448011yescharacteristic
434C2#1059460211yescharacteristic
435C2#1059487611yescharacteristic
436C2#1059521211yescharacteristic
437C2#1059537011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
25. #63838C4semidirect
70. #3724Q8semidirect
369. C32#2355semidirect
430. C3#74963semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105926742
C3×#49782
#105912722
#105912572
#105912472
#105912432
#105912362
#749633