Finite Group Databasebeta

← #11803223

Subgroups — #11803223

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2#10592347C211yesmaximal, characteristic
3C3×#4652C212yesmaximal
4#10591396C211yesmaximal, characteristic
5#10591396C211yesmaximal, characteristic
6#10591337C211yesmaximal, characteristic
7C4×#3724C211yesmaximal, characteristic
8#10591328C211yesmaximal, characteristic
9#10591248C212yesmaximal
10#10591245C212yesmaximal
11#10591201C212yesmaximal
12#74946—32nomaximal
13C22×#627C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2211yescharacteristic
21C2×#3724C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic32C2212yes—
25#63838C418yescomplemented
26C32×#95C2211yescharacteristic
27#63658C2211yescharacteristic
28#63658C2211yescharacteristic
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#887—32no—
38C3×#387—32no—
39#4980—32no—
40#4977—32no—
41#4976—32no—
42#4933—32no—
43C4×Dic3⋊C4—32no—
44#4652D312yes—
45#4651—32no—
46#4651—32no—
47#4650—32no—
48#4648—32no—
49#4648—61no—
50#4647—32no—
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—
67C4×C3⋊Dic3—22no—
68C4×C3⋊Dic3—22no—
69C4×C3⋊Dic3C2×C414yes—
70C3×Dic3⋊C4—42no—
71C3×Dic3⋊C4C2×C418yes—
72C3×C4×Dic3—42no—
73#3724—22no—
74#3724—22no—
75#3724C2×C414yes—
76Dic3⋊Dic3—42no—
77Dic32C2×C418yes—
78#2320—91noSylow
79C22×Dic6—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C4⋊C4—32no—
82C2×C3×C42—32no—
83C2×C4⋊Dic3—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4C2×D312yes—
89C2×Dic3⋊C4C2×D312yes—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3—61no—
97C2×C4×Dic3—61no—
98C2×C4×Dic3C2×D312yes—
99#887—316no—
100C3×#95—21no—
101C3×#95—32no—
102C3×#95—32no—
103C3×#95—32no—
104C3×#95C2×D312yes—
105C3⋊#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95—61no—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C3⋊#95C2×D312yes—
122C23×C32C2411yescharacteristic
123C2×C32×C4—21no—
124C2×C32×C4—21no—
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×C4C22×C412yes—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
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⋊Dic3#4112yes—
143C2×C3⋊Dic3#4112yes—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
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×Dic3C22×C414yes—
155C2×C3×Dic3C22×C414yes—
156#627—28no—
157C2×C4×Q8—91no—
158#391—91no—
159#391—91no—
160#389—91no—
161#389—91no—
162#387—32no—
163#387—92no—
164#383—92no—
165#382—92no—
166C4×C4⋊C4—91no—
167#376—91no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D312yes—
177C22×C3×C4C22×D312yes—
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3C22×D312yes—
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D312yes—
190C2×Dic6—38no—
191C2×Dic6—64no—
192C2×Dic6—64no—
193C3×C4⋊C4—38no—
194C3×C4⋊C4—122no—
195C3×C42—122no—
196C4⋊Dic3—122no—
197Dic3⋊C4—38no—
198Dic3⋊C4—42no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201Dic3⋊C4—122no—
202Dic3⋊C4C4×D318yes—
203C4×Dic3—38no—
204C4×Dic3—38no—
205C4×Dic3—38no—
206C4×Dic3—42no—
207C4×Dic3—64no—
208C4×Dic3—64no—
209C4×Dic3—64no—
210C4×Dic3—64no—
211C4×Dic3—64no—
212C22×C32C23×C411yescharacteristic
213C22×C32C2×#4111yescharacteristic
214C22×C32C2×#4111yescharacteristic
215C22×C32H(5,𝔽2)11yescharacteristic
216C22×C322−1+411yescharacteristic
217C22×C322−1+411yescharacteristic
218C22×C322−1+411yescharacteristic
219C32×C4—22no—
220C32×C4—41no—
221C32×C4—41no—
222C3⋊Dic3—22no—
223C3⋊Dic3—41no—
224C3⋊Dic3—41no—
225C3⋊Dic3#11714yes—
226C3×Dic3—24no—
227C3×Dic3—24no—
228C3×Dic3—42no—
229C3×Dic3—42no—
230C22×Q8—91no—
231C4×Q8—98no—
232C2×C4⋊C4—32no—
233C2×C4⋊C4—32no—
234C2×C4⋊C4—91no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—92no—
238C2×C42—32no—
239C2×C42—92no—
240C2×C42—91no—
241C2×C42—91no—
242C2×C42—91no—
243#95—32no—
244#95—32no—
245#95—32no—
246#95—92no—
247#95—92no—
248#95—92no—
249#95—92no—
250#95—91no—
251#95—91no—
252#95—91no—
253#95D3211yescharacteristic
254C23×C3—21no—
255C23×C3C23×D312yes—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—34no—
268C2×C3×C4—34no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4C2×C4×D314yes—
286C2×Dic3—22no—
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—34no—
297C2×Dic3—34no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3C2×C4×D314yes—
321C2×Dic3C2×C4×D314yes—
322Dic6—616no—
323C2×C32C2×#11711yescharacteristic
324C2×C32#51911yescharacteristic
325C2×C32#52011yescharacteristic
326C2×C32#54111yescharacteristic
327C2×C32#54111yescharacteristic
328C2×C32#54211yescharacteristic
329C2×C32#54211yescharacteristic
330C2×Q8—94no—
331C2×Q8—182no—
332C2×Q8—182no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4—91no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4C2×D3211yescharacteristic
342C22×C4C2×D3211yescharacteristic
343C22×C4C2×D3211yescharacteristic
344C4⋊C4—38no—
345C4⋊C4—94no—
346C4⋊C4—122no—
347C4⋊C4—182no—
348C4⋊C4—182no—
349C4⋊C4—362no—
350C42—98no—
351C42—94no—
352C42—122no—
353C42—182no—
354C42—182no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3C22×C4×D312yes—
363C22×C3#100412yes—
364C22×C3#100712yes—
365C22×C3D3×#4112yes—
366C22×C3D3×#4112yes—
367C22×C3#101012yes—
368C22×C3#101012yes—
369C3×C4—24no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—64no—
376C3×C4—64no—
377C3×C4—122no—
378C3×C4—122no—
379Dic3—24no—
380Dic3—24no—
381Dic3—38no—
382Dic3—42no—
383Dic3—42no—
384Dic3—64no—
385Dic3—64no—
386Dic3—122no—
387Dic3—122no—
388Dic3—122no—
389Dic3—122no—
390Dic3—122no—
391C32#232011yescharacteristic, complemented, Sylow
392C23C22×D3211yescharacteristic
393Q8—188no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—34no—
403C2×C4—34no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—92no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—92no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4C4×D3212yes—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3D3×#11712yes—
435C2×C3#554612yes—
436C2×C3#557212yes—
437C2×C3#564012yes—
438C2×C3#566212yes—
439C2×C3#569612yes—
440C2×C3#570112yes—
441C22C2×C4×D3211yescharacteristic
442C22#6430611yescharacteristic
443C22#6430611yescharacteristic
444C22#6430911yescharacteristic
445C22#6430911yescharacteristic
446C22#6431311yescharacteristic
447C22#6431611yescharacteristic
448C4—22no—
449C4—41no—
450C4—41no—
451C4—64no—
452C4—64no—
453C4—94no—
454C4—122no—
455C4—122no—
456C4—182no—
457C4—361no—
458C4—361no—
459C3—21no—
460C3#7494612yescomplemented
461C2#1059399211yescharacteristic
462C2#1059405111yescharacteristic
463C2#1059422211yescharacteristic
464C2#1059424911yescharacteristic
465C2#1059434711yescharacteristic
466C2#1059456911yescharacteristic
467C2#1059459911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2320
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
25. #63838C4semidirect
391. C32#2320semidirect
460. C3#74946semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105923472
C3×#46522
#105913962
#105913372
C4×#37242
#105913282
#105912482
#105912452
#105912012
#749463