Finite Group Databasebeta

← #11805946

Subgroups — #11805946

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2#10592348C211yesmaximal, characteristic
3C3×#4655C212yesmaximal
4#10591396C211yesmaximal, characteristic
5#10591396C211yesmaximal, characteristic
6#10591359C211yesmaximal, characteristic
7C4×#3724C211yesmaximal, characteristic
8#10591262C212yesmaximal
9#10591257C211yesmaximal, characteristic
10#10591247C212yesmaximal
11#10591243C212yesmaximal
12#74963—32nomaximal
13C22×#627C2211yescharacteristic
14C2×#3750C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2212yes—
23C2×#3724C2211yescharacteristic
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×Dic32C2212yes—
27C2×Dic32C2212yes—
28#63838C418yescomplemented
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#887—32no—
38C3×#387—32no—
39#4980—32no—
40#4978—32no—
41#4975—32no—
42C4×Dic3⋊C4—32no—
43C4×Dic3⋊C4—32no—
44#4655D312yes—
45#4650—32no—
46#4650—32no—
47#4649—32no—
48#4649—32no—
49#4649—32no—
50#4649—61no—
51#4646—32no—
52#4646—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—
64C2×#627—22no—
65C2×#627—22no—
66C2×#627C2×C414yes—
67#3750—22no—
68#3750Q814yescomplemented
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3C2×C414yes—
72C3×C4⋊Dic3—42no—
73C3×Dic3⋊C4C2×C418yes—
74C3×C4×Dic3—42no—
75#3724—22no—
76#3724—22no—
77#3724—24no—
78#3724C2×C414yes—
79Dic32—42no—
80Dic32C2×C418yes—
81#2355—91noSylow
82C22×Dic6—32no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C42—32no—
86C2×C4⋊Dic3C2×D312yes—
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×C4×Dic3—32no—
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—61no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3C2×D312yes—
108#887—316no—
109C3×#95—21no—
110C3×#95—32no—
111C3×#95—32no—
112C3×#95—32no—
113C3×#95C2×D312yes—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—61no—
122C3⋊#95C2×D312yes—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C23×C32C2411yescharacteristic
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×C32×C4C2×Q812yes—
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⋊Dic3C2×Q812yes—
144C2×C3⋊Dic3#4112yes—
145C2×C3⋊Dic3#4112yes—
146C2×C3⋊Dic3#4112yes—
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×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3C22×C414yes—
158C2×C3×Dic3C22×C414yes—
159#627—28no—
160C2×C4×Q8—91no—
161#391—91no—
162#391—91no—
163#387—32no—
164#387—92no—
165#384—91no—
166#382—92no—
167C4×C4⋊C4—91no—
168C4×C4⋊C4—92no—
169C4×C4⋊C4—91no—
170C4×C4⋊C4—91no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C22×Dic3C22×D312yes—
192C22×Dic3C22×D312yes—
193C2×Dic6—38no—
194C2×Dic6—64no—
195C2×Dic6—64no—
196C3×C4⋊C4—38no—
197C3×C4⋊C4—122no—
198C3×C42—122no—
199C4⋊Dic3—42no—
200Dic3⋊C4—38no—
201Dic3⋊C4—38no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209Dic3⋊C4C4×D318yes—
210C4×Dic3—38no—
211C4×Dic3—38no—
212C4×Dic3—38no—
213C4×Dic3—42no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C4×Dic3—122no—
218C4×Dic3—122no—
219C4×Dic3—122no—
220C4×Dic3—122no—
221C22×C32C23×C411yescharacteristic
222C22×C32C22×Q811yescharacteristic
223C22×C32C2×#4111yescharacteristic
224C22×C32C2×#4111yescharacteristic
225C22×C32C2×#4111yescharacteristic
226C22×C32H(5,𝔽2)11yescharacteristic
227C22×C322−1+411yescharacteristic
228C32×C4—22no—
229C32×C4—22no—
230C32×C4—41no—
231C3⋊Dic3—22no—
232C3⋊Dic3—41no—
233C3⋊Dic3#11714yes—
234C3⋊Dic3C4×Q814yes—
235C3×Dic3—24no—
236C3×Dic3—24no—
237C3×Dic3—42no—
238C3×Dic3—42no—
239C22×Q8—91no—
240C4×Q8—98no—
241C2×C4⋊C4—32no—
242C2×C4⋊C4—32no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—91no—
249C2×C42—32no—
250C2×C42—92no—
251C2×C42—91no—
252C2×C42—91no—
253C2×C42—91no—
254C2×C42—92no—
255#95—32no—
256#95—32no—
257#95—32no—
258#95—92no—
259#95—92no—
260#95—92no—
261#95—91no—
262#95D3211yescharacteristic
263C23×C3—21no—
264C23×C3C23×D312yes—
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—22no—
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×C4—62no—
293C2×C3×C4C2×C4×D314yes—
294C2×C3×C4D3×Q814yes—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—34no—
306C2×Dic3—34no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—34no—
310C2×Dic3—34no—
311C2×Dic3—34no—
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—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3C2×C4×D314yes—
330C2×Dic3C2×C4×D314yes—
331Dic6—616no—
332C2×C32C2×#11711yescharacteristic
333C2×C32C2×C4×Q811yescharacteristic
334C2×C32#52011yescharacteristic
335C2×C32#55411yescharacteristic
336C2×C32#55611yescharacteristic
337C2×C32#55711yescharacteristic
338C2×C32#55911yescharacteristic
339C2×Q8—94no—
340C2×Q8—182no—
341C2×Q8—182no—
342C22×C4—32no—
343C22×C4—32no—
344C22×C4—32no—
345C22×C4—32no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4C2×D3211yescharacteristic
351C22×C4C2×D3211yescharacteristic
352C22×C4C2×D3211yescharacteristic
353C4⋊C4—38no—
354C4⋊C4—94no—
355C4⋊C4—94no—
356C4⋊C4—122no—
357C4⋊C4—182no—
358C4⋊C4—184no—
359C4⋊C4—182no—
360C4⋊C4—182no—
361C42—98no—
362C42—94no—
363C42—122no—
364C42—182no—
365C42—182no—
366C42—362no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3C22×C4×D312yes—
375C22×C3#100412yes—
376C22×C3C2×D3×Q812yes—
377C22×C3D3×#4112yes—
378C22×C3D3×#4112yes—
379C22×C3D3×#4112yes—
380C22×C3#101012yes—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4—64no—
388C3×C4—64no—
389C3×C4—122no—
390C3×C4—122no—
391Dic3—24no—
392Dic3—24no—
393Dic3—38no—
394Dic3—38no—
395Dic3—42no—
396Dic3—42no—
397Dic3—64no—
398Dic3—64no—
399Dic3—64no—
400Dic3—122no—
401Dic3—122no—
402Dic3—122no—
403C32#235511yescharacteristic, complemented, Sylow
404C23C22×D3211yescharacteristic
405Q8—188no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—34no—
414C2×C4—34no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—92no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4#379712yes—
438C2×C4C4×D3212yes—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3D3×#11712yes—
447C2×C3#554612yes—
448C2×C3C4×D3×Q812yes—
449C2×C3#563612yes—
450C2×C3#566412yes—
451C2×C3#568512yes—
452C2×C3#570212yes—
453C22C2×#379711yescharacteristic
454C22C2×C4×D3211yescharacteristic
455C22#6430611yescharacteristic
456C22#6430911yescharacteristic
457C22#6431211yescharacteristic
458C22#6431311yescharacteristic
459C22#6431911yescharacteristic
460C4—22no—
461C4—22no—
462C4—41no—
463C4—64no—
464C4—64no—
465C4—94no—
466C4—94no—
467C4—122no—
468C4—122no—
469C4—182no—
470C4—361no—
471C3—21no—
472C3#7496312yescomplemented
473C2C4×#379711yescharacteristic
474C2#1059405111yescharacteristic
475C2#1059416811yescharacteristic
476C2#1059425011yescharacteristic
477C2#1059432411yescharacteristic
478C2#1059457011yescharacteristic
479C2#1059460211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
28. #63838C4semidirect
68. #3750Q8semidirect
403. C32#2355semidirect
472. C3#74963semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105923482
C3×#46552
#105913962
#105913592
C4×#37242
#105912622
#105912572
#105912472
#105912432
#749633