Finite Group Databasebeta

← #11803818

Subgroups — #11803818

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic
3C2×#63838C211yesmaximal, characteristic
4#10592347C211yesmaximal, characteristic
5C3×#4653C212yesmaximal
6#10591396C211yesmaximal, characteristic
7#10591396C211yesmaximal, characteristic
8#10591360C211yesmaximal, characteristic
9#10591270C212yesmaximal
10#10591249C212yesmaximal
11#10591193C212yesmaximal
12#74948—32nomaximal
13C22×#627C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×#3724C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic32C2212yes—
26#63919C418yescomplemented
27C4×#627—24no—
28#63838—24no—
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#888—32no—
40C2×#887—32no—
41C2×C4×Dic6—32no—
42C3×#387—32no—
43#4980—32no—
44#4978—32no—
45#4933—32no—
46#4655—32no—
47#4654—32no—
48#4653D312yes—
49#4652—32no—
50#4650—32no—
51#4648—32no—
52#4648—61no—
53#4646—32no—
54#4646—32no—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×#627—22no—
67C2×#627—22no—
68C2×#627—22no—
69C2×#627—22no—
70C2×#627C2×C414yes—
71C2×#627C2×C414yes—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3C2×C414yes—
74C4×C3⋊Dic3D414yes—
75C3×C4⋊Dic3C2×C418yes—
76C3×Dic3⋊C4—24no—
77C3×C4×Dic3—24no—
78#3724—22no—
79#3724—22no—
80#3724C2×C418yes—
81Dic3⋊Dic3—24no—
82Dic32—24no—
83#2327—91noSylow
84C22×Dic6—32no—
85C22×Dic6—32no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C4⋊C4—32no—
88C2×C3×C42—32no—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3C2×D312yes—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
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—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D312yes—
106#888—316no—
107#887—68no—
108C4×Dic6—68no—
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—32no—
122C3⋊#95—32no—
123C3⋊#95—61no—
124C3⋊#95—61no—
125C3⋊#95—61no—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C3⋊#95C2×D312yes—
129C23×C32C2411yescharacteristic
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D412yes—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3C22×C412yes—
147C2×C3⋊Dic3C22×C412yes—
148C2×C3⋊Dic3C2×D412yes—
149C2×C3⋊Dic3C2×D412yes—
150C2×C3⋊Dic3#4112yes—
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×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C22×C414yes—
162C2×C3×Dic3C22×C414yes—
163#627—28no—
164#627—28no—
165C2×C4⋊Q8—91no—
166C2×C4×Q8—91no—
167C2×C4×Q8—91no—
168#391—91no—
169#391—91no—
170#387—32no—
171#387—92no—
172#387—92no—
173#387—92no—
174#382—91no—
175#376—91no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D312yes—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C2×Dic6—38no—
199C2×Dic6—38no—
200C2×Dic6—64no—
201C2×Dic6—64no—
202C2×Dic6—64no—
203C2×Dic6—64no—
204C3×C4⋊C4—38no—
205C3×C4⋊C4—64no—
206C3×C42—64no—
207C4⋊Dic3—64no—
208C4⋊Dic3C4×D318yes—
209Dic3⋊C4—24no—
210Dic3⋊C4—38no—
211Dic3⋊C4—38no—
212Dic3⋊C4—64no—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215C4×Dic3—24no—
216C4×Dic3—38no—
217C4×Dic3—38no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C22×C32C23×C411yescharacteristic
225C22×C32C22×D411yescharacteristic
226C22×C32C2×#4111yescharacteristic
227C22×C322−1+411yescharacteristic
228C22×C322−1+411yescharacteristic
229C22×C322−1+411yescharacteristic
230C22×C322−1+411yescharacteristic
231C32×C4—22no—
232C32×C4—22no—
233C32×C4—41no—
234C3⋊Dic3—22no—
235C3⋊Dic3—22no—
236C3⋊Dic3—41no—
237C3⋊Dic3C4×D414yes—
238C3×Dic3—24no—
239C3×Dic3—24no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—91no—
243C22×Q8—91no—
244C4⋊Q8—98no—
245C4×Q8—184no—
246C4×Q8—184no—
247C2×C4⋊C4—32no—
248C2×C4⋊C4—32no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—92no—
253C2×C42—32no—
254C2×C42—91no—
255C2×C42—91no—
256C2×C42—92no—
257C2×C42—91no—
258#95—32no—
259#95—32no—
260#95—32no—
261#95—92no—
262#95—92no—
263#95—92no—
264#95—91no—
265#95—91no—
266#95—91no—
267#95D3211yescharacteristic
268C23×C3—21no—
269C23×C3C23×D312yes—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—34no—
281C2×C3×C4—34no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4C2×C4×D314yes—
299C2×C3×C4D3×D414yes—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—34no—
311C2×Dic3—34no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—34no—
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—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3C2×C4×D314yes—
335C2×Dic3C2×C4×D314yes—
336Dic6—616no—
337Dic6—616no—
338C2×C32C2×C4×D411yescharacteristic
339C2×C32#51911yescharacteristic
340C2×C32#51911yescharacteristic
341C2×C32#53611yescharacteristic
342C2×C32#53611yescharacteristic
343C2×C32#54111yescharacteristic
344C2×C32#54111yescharacteristic
345C2×Q8—94no—
346C2×Q8—94no—
347C2×Q8—182no—
348C2×Q8—182no—
349C2×Q8—182no—
350C2×Q8—182no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4C2×D3211yescharacteristic
360C22×C4C2×D3211yescharacteristic
361C22×C4C2×D3211yescharacteristic
362C4⋊C4—38no—
363C4⋊C4—64no—
364C4⋊C4—98no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—184no—
368C42—64no—
369C42—94no—
370C42—94no—
371C42—182no—
372C42—184no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3C22×C4×D312yes—
381C22×C3C2×D3×D412yes—
382C22×C3#100712yes—
383C22×C3D3×#4112yes—
384C22×C3#101012yes—
385C22×C3#101012yes—
386C22×C3#101012yes—
387C3×C4—24no—
388C3×C4—24no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—64no—
394C3×C4—64no—
395C3×C4—122no—
396C3×C4—122no—
397Dic3—24no—
398Dic3—24no—
399Dic3—38no—
400Dic3—42no—
401Dic3—42no—
402Dic3—64no—
403Dic3—64no—
404Dic3—64no—
405Dic3—122no—
406Dic3—122no—
407Dic3—122no—
408Dic3—122no—
409C32#232711yescharacteristic, complemented, Sylow
410C23C22×D3211yescharacteristic
411Q8—188no—
412Q8—188no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—34no—
421C2×C4—34no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—92no—
435C2×C4—92no—
436C2×C4—92no—
437C2×C4—181no—
438C2×C4—181no—
439C2×C4—181no—
440C2×C4—181no—
441C2×C4—181no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4C4×D3212yes—
445C2×C4#380212yes—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3#551612yes—
454C2×C3C4×D3×D412yes—
455C2×C3#557212yes—
456C2×C3#562812yes—
457C2×C3#564812yes—
458C2×C3#569612yes—
459C2×C3#570112yes—
460C22C2×C4×D3211yescharacteristic
461C22C2×#380211yescharacteristic
462C22#6430611yescharacteristic
463C22#6430911yescharacteristic
464C22#6430911yescharacteristic
465C22#6430911yescharacteristic
466C22#6431611yescharacteristic
467C4—22no—
468C4—22no—
469C4—41no—
470C4—64no—
471C4—64no—
472C4—94no—
473C4—122no—
474C4—122no—
475C4—182no—
476C4—182no—
477C4—361no—
478C3—21no—
479C3#7494812yescomplemented
480C2C4×#380211yescharacteristic
481C2#1059408411yescharacteristic
482C2#1059424511yescharacteristic
483C2#1059424911yescharacteristic
484C2#1059434711yescharacteristic
485C2#1059452911yescharacteristic
486C2#1059459911yescharacteristic
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
26. #63919C4semidirect
409. C32#2327semidirect
479. 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×C4×#6272
C2×#638382
#105923472
C3×#46532
#105913962
#105913602
#105912702
#105912492
#105911932
#749483