Finite Group Databasebeta

← #11807191

Subgroups — #11807191

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63870C211yesmaximal, characteristic
2#10592348C211yesmaximal, characteristic
3C3×#4652C212yesmaximal
4#10591337C211yesmaximal, characteristic
5C4×#3724C211yesmaximal, characteristic
6#10591328C211yesmaximal, characteristic
7#10591257C211yesmaximal, characteristic
8#10591257C211yesmaximal, characteristic
9#10591251C212yesmaximal
10Dic3×Dic3⋊C4C212yesmaximal
11#10591234C212yesmaximal
12#74968—32nomaximal
13C2×#3750C2211yescharacteristic
14C2×#3750C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×#3724C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×#3724C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29#63870C418yescomplemented
30C32×#95C2211yescharacteristic
31#63658C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#889—32no—
38C3×#387—32no—
39#4976—32no—
40Dic3×C4⋊C4—32no—
41#4972—32no—
42C4×Dic3⋊C4—32no—
43C4×Dic3⋊C4—32no—
44#4654—32no—
45#4652—32no—
46#4652D312yes—
47#4649—32no—
48#4649—32no—
49#4649—32no—
50#4649—61no—
51#4647—32no—
52#4647—32no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64#3750—22no—
65#3750—22no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3—22no—
68C4×C3⋊Dic3C2×C414yes—
69C3×Dic3⋊C4—42no—
70C3×Dic3⋊C4C2×C418yes—
71C3×C4×Dic3—42no—
72#3724—22no—
73#3724C2×C414yes—
74#3724C2×C414yes—
75#3724Q814yes—
76Dic3⋊Dic3—24no—
77Dic3⋊Dic3C2×C418yes—
78Dic32—24no—
79Dic32—42no—
80#2370—91noSylow
81C2×C3×C4⋊C4—32no—
82C2×C3×C4⋊C4—32no—
83C2×C3×C42—32no—
84C2×C4⋊Dic3—32no—
85C2×C4⋊Dic3—32no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—61no—
95C2×Dic3⋊C4—61no—
96C2×Dic3⋊C4C2×D312yes—
97C2×Dic3⋊C4C2×D312yes—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D312yes—
109#889—316no—
110C3×#95—21no—
111C3×#95—32no—
112C3×#95—32no—
113C3×#95—32no—
114C3×#95C2×D312yes—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—61no—
121C3⋊#95C2×D312yes—
122C3⋊#95C2×D312yes—
123C3⋊#95C2×D312yes—
124C23×C32C2411yescharacteristic
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4C22×C412yes—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3C22×C412yes—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3⋊Dic3C2×Q812yes—
143C2×C3⋊Dic3#4112yes—
144C2×C3⋊Dic3#4112yes—
145C2×C3⋊Dic3#4112yes—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C22×C414yes—
156C2×C3×Dic3C22×C414yes—
157C2×C3×Dic3C2×Q814yes—
158C2×#125—91no—
159#389—91no—
160#389—92no—
161#389—91no—
162#387—32no—
163#387—92no—
164C4×C4⋊C4—91no—
165C4×C4⋊C4—91no—
166C4×C4⋊C4—91no—
167C4×C4⋊C4—92no—
168C4×C4⋊C4—91no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4C22×D312yes—
177C22×C3×C4C22×D312yes—
178C22×C3×C4C22×D312yes—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C3×C4⋊C4—38no—
192C3×C4⋊C4—122no—
193C3×C42—122no—
194C4⋊Dic3—38no—
195C4⋊Dic3—64no—
196Dic3⋊C4—38no—
197Dic3⋊C4—38no—
198Dic3⋊C4—38no—
199Dic3⋊C4—38no—
200Dic3⋊C4—42no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4C4×D318yes—
208C4×Dic3—38no—
209C4×Dic3—42no—
210C4×Dic3—64no—
211C4×Dic3—64no—
212C4×Dic3—64no—
213C4×Dic3—64no—
214C4×Dic3—64no—
215C4×Dic3—122no—
216C4×Dic3—122no—
217C4×Dic3—122no—
218C4×Dic3—122no—
219C22×C32C23×C411yescharacteristic
220C22×C32C22×Q811yescharacteristic
221C22×C32C2×#4111yescharacteristic
222C22×C32C2×#4111yescharacteristic
223C22×C32C2×#4111yescharacteristic
224C22×C32H(5,𝔽2)11yescharacteristic
225C22×C322−1+411yescharacteristic
226C32×C4—22no—
227C32×C4—41no—
228C32×C4—41no—
229C3⋊Dic3—22no—
230C3⋊Dic3—22no—
231C3⋊Dic3—22no—
232C3⋊Dic3C4×Q814yes—
233C3×Dic3—24no—
234C3×Dic3—24no—
235C3×Dic3—24no—
236C3×Dic3—42no—
237#125—98no—
238C2×C4⋊C4—32no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—91no—
248C2×C42—32no—
249C2×C42—91no—
250C2×C42—92no—
251C2×C42—91no—
252C2×C42—91no—
253C2×C42—92no—
254#95—32no—
255#95—32no—
256#95—32no—
257#95—92no—
258#95—92no—
259#95—91no—
260#95D3211yescharacteristic
261C23×C3—21no—
262C23×C3C23×D312yes—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—34no—
275C2×C3×C4—34no—
276C2×C3×C4—34no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4C2×C4×D314yes—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—34no—
303C2×Dic3—34no—
304C2×Dic3—34no—
305C2×Dic3—34no—
306C2×Dic3—34no—
307C2×Dic3—34no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3C2×C4×D314yes—
327C2×Dic3C2×C4×D314yes—
328C2×Dic3D3×Q814yes—
329C2×C32C2×C4×Q811yescharacteristic
330C2×C32C4×#4111yescharacteristic
331C2×C32#52011yescharacteristic
332C2×C32#55211yescharacteristic
333C2×C32#55311yescharacteristic
334C2×C32#55411yescharacteristic
335C2×C32#55711yescharacteristic
336C22×C4—32no—
337C22×C4—32no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4C2×D3211yescharacteristic
345C22×C4C2×D3211yescharacteristic
346C22×C4C2×D3211yescharacteristic
347C4⋊C4—38no—
348C4⋊C4—94no—
349C4⋊C4—94no—
350C4⋊C4—98no—
351C4⋊C4—94no—
352C4⋊C4—122no—
353C4⋊C4—182no—
354C4⋊C4—182no—
355C4⋊C4—182no—
356C4⋊C4—184no—
357C42—94no—
358C42—122no—
359C42—182no—
360C42—182no—
361C42—184no—
362C42—362no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3C22×C4×D312yes—
371C22×C3#100412yes—
372C22×C3C2×D3×Q812yes—
373C22×C3D3×#4112yes—
374C22×C3D3×#4112yes—
375C22×C3D3×#4112yes—
376C22×C3#101012yes—
377C3×C4—24no—
378C3×C4—42no—
379C3×C4—42no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4—64no—
384C3×C4—64no—
385C3×C4—64no—
386C3×C4—122no—
387Dic3—24no—
388Dic3—24no—
389Dic3—24no—
390Dic3—38no—
391Dic3—42no—
392Dic3—64no—
393Dic3—64no—
394Dic3—64no—
395Dic3—64no—
396Dic3—64no—
397Dic3—122no—
398Dic3—122no—
399C32#237011yescharacteristic, complemented, Sylow
400C23C22×D3211yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—34no—
410C2×C4—34no—
411C2×C4—34no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—92no—
424C2×C4—92no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4C4×D3212yes—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3#552212yes—
442C2×C3#554612yes—
443C2×C3C4×D3×Q812yes—
444C2×C3#563612yes—
445C2×C3#566112yes—
446C2×C3#568512yes—
447C2×C3#570812yes—
448C22C2×C4×D3211yescharacteristic
449C22#6430611yescharacteristic
450C22#6430611yescharacteristic
451C22#6430911yescharacteristic
452C22#6431211yescharacteristic
453C22#6431311yescharacteristic
454C22D32×Q811yescharacteristic
455C4—22no—
456C4—41no—
457C4—41no—
458C4—64no—
459C4—64no—
460C4—64no—
461C4—94no—
462C4—122no—
463C4—182no—
464C4—182no—
465C4—182no—
466C3—21no—
467C3#7496812yescomplemented
468C2#1059396611yescharacteristic
469C2#1059405111yescharacteristic
470C2#1059415511yescharacteristic
471C2#1059422911yescharacteristic
472C2#1059436311yescharacteristic
473C2#1059453411yescharacteristic
474C2#1059459711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2370
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
29. #63870C4semidirect
399. C32#2370semidirect
467. C3#74968semidirect

Maximal subgroups

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

subgroupindex
C2×#638702
#105923482
C3×#46522
#105913372
C4×#37242
#105913282
#105912572
#105912512
Dic3×Dic3⋊C42
#105912342
#749683