Finite Group Databasebeta

← #11802937

Subgroups — #11802937

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63883C211yesmaximal, characteristic
2C2×#63836C212yesmaximal
3#10592366C211yesmaximal, characteristic
4C3×#4647C212yesmaximal, complemented
5#10591367C212yesmaximal
6#10591330C212yesmaximal, complemented
7#10591325C211yesmaximal, characteristic
8#10591265C212yesmaximal, complemented
9#10591234C212yesmaximal, complemented
10#76195—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C2×#3752C2212yes—
15C2×#3750C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×#3722C2212yes—
25C2×Dic32C2212yes—
26#63883C418yescomplemented
27#63836—28no—
28C32×#95C2211yescharacteristic
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31#63579C2211yescharacteristic
32#63579C2212yes—
33#63579C2211yescharacteristic
34C2×#892—32no—
35C2×D3×C4⋊C4—32no—
36C2×#872—32no—
37C3×#389—32no—
38#4987—32no—
39#4987—32no—
40#4984—32no—
41#4976—32no—
42#4976—32no—
43#4972—32no—
44#4928—32no—
45#4667—32no—
46#4667—32no—
47#4667—61no—
48#4647—32no—
49#4647D312yescomplemented
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C2×C4×C3⋊D3—42no—
56C2×C4×C3⋊D3C2×C414yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C2×#624—42no—
62C2×#624C2×C414yes—
63C2×#624C2×C414yes—
64C2×#624D414yes—
65C2×#624Q814yes—
66#3752—24no—
67#3750—42no—
68C3×C4⋊Dic3—42no—
69C3×Dic3⋊C4—24no—
70C3×Dic3⋊C4—42no—
71C3×Dic3⋊C4C2×C418yes—
72C3×C4×Dic3—24no—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—42no—
75Dic3⋊Dic3C2×C418yes—
76#3722—24no—
77Dic32—24no—
78#2316—91noSylow
79C22×C4×D3—32no—
80C22×C4×D3—32no—
81C22×C4×D3—32no—
82C22×C4×D3—61no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C42—32no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4—32no—
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3—32no—
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—32no—
96C2×C4⋊Dic3C2×D312yes—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—62no—
103C2×Dic3⋊C4C2×D312yes—
104C2×Dic3⋊C4C2×D312yes—
105C2×Dic3⋊C4C2×D312yes—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3C2×D312yes—
109#892—68no—
110D3×C4⋊C4—316no—
111#872—68no—
112C3×#95—21no—
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—
122C23×C32C2411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3C22×C412yes—
126C22×C3⋊D3C2×D412yes—
127C22×C3⋊D3C2×Q812yes—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C22×C412yes—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3C22×C412yes—
138C4×C3⋊D3—44no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C22×C414yes—
148C2×C3×Dic3C22×C414yes—
149C2×C3×Dic3C2×D414yes—
150C2×C3×Dic3C2×Q814yes—
151#624—44no—
152#624C4⋊C4116yescomplemented
153C2×#117—92no—
154C22×C4⋊C4—91no—
155#389—32no—
156#389—92no—
157#389—92no—
158#389—92no—
159#380—92no—
160#380—91no—
161#380—91no—
162C23×D3—32no—
163C23×D3—61no—
164C22×C3×C4—21no—
165C22×C3×C4—22no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4C22×D312yes—
171C22×C3×C4C22×D312yes—
172C22×C3×C4C22×D312yes—
173C22×Dic3—32no—
174C22×Dic3—32no—
175C22×Dic3—32no—
176C22×Dic3—61no—
177C22×Dic3—62no—
178C22×Dic3C22×D312yes—
179C22×Dic3C22×D312yes—
180C22×Dic3C22×D312yes—
181C22×Dic3C22×D312yes—
182C2×C4×D3—38no—
183C2×C4×D3—38no—
184C2×C4×D3—38no—
185C2×C4×D3—38no—
186C2×C4×D3—38no—
187C2×C4×D3—64no—
188C2×C4×D3—122no—
189C2×C4×D3—122no—
190C2×C4×D3—122no—
191C2×C4×D3—122no—
192C2×C4×D3—124no—
193C3×C4⋊C4—38no—
194C3×C4⋊C4—64no—
195C3×C4⋊C4—122no—
196C3×C4⋊C4—122no—
197C3×C42—64no—
198(C2×D3)⋊C4—64no—
199(C2×D3)⋊C4—64no—
200(C2×D3)⋊C4—64no—
201(C2×D3)⋊C4—64no—
202(C2×D3)⋊C4—124no—
203C4⋊Dic3—38no—
204C4⋊Dic3—42no—
205C4⋊Dic3—64no—
206C4⋊Dic3—122no—
207Dic3⋊C4—24no—
208Dic3⋊C4—38no—
209Dic3⋊C4—42no—
210Dic3⋊C4—64no—
211Dic3⋊C4—122no—
212Dic3⋊C4—122no—
213Dic3⋊C4—122no—
214Dic3⋊C4—124no—
215Dic3⋊C4C4×D318yes—
216C4×Dic3—24no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C22×C32C23×C411yescharacteristic
220C22×C32C22×D411yescharacteristic
221C22×C32C22×Q811yescharacteristic
222C22×C32H(5,𝔽2)12yes—
223C22×C322−1+412yes—
224C2×C3⋊D3—22no—
225C2×C3⋊D3—22no—
226C2×C3⋊D3—24no—
227C2×C3⋊D3—24no—
228C2×C3⋊D3C2×C4⋊C414yes—
229C32×C4—22no—
230C32×C4—42no—
231C3⋊Dic3—22no—
232C3⋊Dic3—42no—
233C3×Dic3—24no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C3×Dic3C2×C4⋊C418yes—
237C23×C4—91no—
238C23×C4—91no—
239C23×C4—91no—
240#117—188no—
241C2×C4⋊C4—32no—
242C2×C4⋊C4—32no—
243C2×C4⋊C4—32no—
244C2×C4⋊C4—32no—
245C2×C4⋊C4—98no—
246C2×C4⋊C4—92no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—92no—
250C2×C22⋊C4—92no—
251C2×C22⋊C4—92no—
252C2×C42—32no—
253C2×C42—92no—
254#95—32no—
255#95—92no—
256#95—91no—
257#95—91no—
258#95—91no—
259#95D3211yescharacteristic
260C23×C3—21no—
261C23×C3C23×D312yes—
262C22×D3—34no—
263C22×D3—34no—
264C22×D3—34no—
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—62no—
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—122no—
273C22×D3—122no—
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—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—34no—
284C2×C3×C4—34no—
285C2×C3×C4—34no—
286C2×C3×C4—34no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
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×C4—62no—
299C2×C3×C4C2×C4×D314yes—
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—34no—
309C2×Dic3—62no—
310C2×Dic3—64no—
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—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3C2×C4×D314yes—
323C2×Dic3C2×C4×D314yes—
324C2×Dic3D3×D414yes—
325C2×Dic3D3×Q814yes—
326C4×D3—332no—
327C4×D3—128no—
328C4×D3—128no—
329C4×D3—128no—
330C2×C32C22×C4⋊C411yescharacteristic
331C2×C32#51811yescharacteristic
332C2×C32#51911yescharacteristic
333C2×C32#53712yes—
334C2×C32#54412yes—
335C3⋊D3—24no—
336C24—91no—
337C22×C4—32no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4—32no—
341C22×C4—94no—
342C22×C4—94no—
343C22×C4—94no—
344C22×C4—94no—
345C22×C4—91no—
346C22×C4—94no—
347C22×C4—92no—
348C22×C4—362no—
349C22×C4—362no—
350C22×C4C2×D3212yes—
351C22×C4C2×D3211yescharacteristic
352C4⋊C4—38no—
353C4⋊C4—64no—
354C4⋊C4—98no—
355C4⋊C4—122no—
356C4⋊C4—122no—
357C4⋊C4—184no—
358C4⋊C4—362no—
359C4⋊C4—362no—
360C22⋊C4—184no—
361C22⋊C4—184no—
362C42—64no—
363C42—184no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3C22×C4×D312yes—
370C22×C3C2×D3×D412yes—
371C22×C3#100412yes—
372C22×C3C2×D3×Q812yes—
373C22×C3#100712yes—
374C22×C3#100912yes—
375C22×C3#101012yes—
376C2×D3—38no—
377C2×D3—64no—
378C2×D3—64no—
379C2×D3—64no—
380C2×D3—64no—
381C2×D3—64no—
382C2×D3—64no—
383C2×D3—64no—
384C2×D3—122no—
385C2×D3—124no—
386C2×D3—122no—
387C2×D3—124no—
388C3×C4—24no—
389C3×C4—38no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—64no—
394C3×C4—82no—
395C3×C4—122no—
396C3×C4—122no—
397Dic3—24no—
398Dic3—42no—
399Dic3—42no—
400Dic3—64no—
401Dic3—64no—
402Dic3—122no—
403Dic3—122no—
404Dic3—242no—
405Dic3D3×C4⋊C418yes—
406C32#231611yescharacteristic, complemented, Sylow
407C23—92no—
408C23—92no—
409C23—92no—
410C23—182no—
411C23—182no—
412C23C22×D3211yescharacteristic
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—34no—
418C2×C4—34no—
419C2×C4—34no—
420C2×C4—34no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—916no—
430C2×C4—92no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—364no—
436C2×C4—364no—
437C2×C4C4×D3212yes—
438C2×C3—22no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3C2×D3×C4⋊C412yes—
444C2×C3#554512yes—
445C2×C3#557212yes—
446C2×C3#560812yes—
447C2×C3#562912yes—
448C2×C3#568912yes—
449C2×C3#572912yes—
450D3—68no—
451D3—124no—
452C22—94no—
453C22—184no—
454C22—182no—
455C22—184no—
456C22—182no—
457C22#6429712yes—
458C22C2×C4×D3211yescharacteristic
459C22D32×D411yescharacteristic
460C22#6431412yes—
461C22D32×Q811yescharacteristic
462C4—22no—
463C4—38no—
464C4—42no—
465C4—64no—
466C4—122no—
467C4—122no—
468C4—182no—
469C4—362no—
470C3—21no—
471C3#7619512yescomplemented
472C2—184no—
473C2#1059384811yescharacteristic
474C2#1059406912yes—
475C2#1059425611yescharacteristic
476C2#1059440012yes—
477C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2316
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C3×#4647C2semidirect
6. #10591330C2semidirect
8. #10591265C2semidirect
9. #10591234C2semidirect
26. #63883C4semidirect
49. #4647D3semidirect
152. #624C4⋊C4semidirect
406. C32#2316semidirect
471. C3#76195semidirect

Maximal subgroups

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

subgroupindex
C2×#638832
C2×#638362
#105923662
C3×#46472
#105913672
#105913302
#105913252
#105912652
#105912342
#761953