Finite Group Databasebeta

← #11807840

Subgroups — #11807840

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic
2C3×#5229C212yesmaximal, complemented
3#10591355C211yesmaximal, characteristic
4#10591271C212yesmaximal, complemented
5#10591266C212yesmaximal
6#10591264C212yesmaximal, complemented
7#10591219C211yesmaximal, characteristic
8#10591202C212yesmaximal
9#10591197C212yesmaximal, complemented
10#76617—32nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13#64155C418yescomplemented
14C2×#3752C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2212yes—
20C2×#3724C2212yes—
21C2×#3722C2211yescharacteristic
22C2×#3722C2212yes—
23C2×#3722C2211yescharacteristic
24C2×Dic32C2212yes—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2211yescharacteristic
30#63579C2212yes—
31#63579C2212yes—
32#63579C2211yescharacteristic
33C2×#946—32no—
34C2×#946—61no—
35C3×#391—32no—
36#5229D312yescomplemented
37#4990—32no—
38#4976—32no—
39#4940—32no—
40#4933—32no—
41#4670—32no—
42#4669—32no—
43#4667—32no—
44#4664—32no—
45#4654—32no—
46#4653—32no—
47#4652—32no—
48#4647—32no—
49C23×C3⋊D3C2311yescharacteristic
50C2×C32×Q8—42no—
51C2×C32×Q8C2×C414yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2312yes—
56C2×C4×C3⋊D3—42no—
57C2×C4×C3⋊D3C2×C414yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62#3752C2×C418yes—
63C4⋊(C3⋊Dic3)C2×C414yes—
64#3750C2×C418yes—
65C3×C4⋊Dic3—42no—
66C3×C4×Dic3—42no—
67#3724—42no—
68#3724—42no—
69#3722—41no—
70#3722—41no—
71#3722—42no—
72Dic32—42no—
73#2378—91noSylow
74C22×C3×Q8—21no—
75C22×C3×Q8C2×D312yes—
76C22×C4×D3—32no—
77C22×C4×D3—61no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—32no—
80#946—316no—
81#946—68no—
82C2×(C2×D3)⋊C4—32no—
83C2×(C2×D3)⋊C4—32no—
84C2×(C2×D3)⋊C4—32no—
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—62no—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3C2×D312yes—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—62no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3C2×D312yes—
102C3×#95—32no—
103C3×#95—32no—
104C3×#95—32no—
105C3×#95—32no—
106C3⋊#95—32no—
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95C2×D312yes—
113C3⋊#95C2×D312yes—
114C3⋊#95C2×D312yes—
115C3⋊#95C2×D312yes—
116C23×C32C2411yescharacteristic
117C22×C3⋊D3—22no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3C22×C412yes—
122C32×Q8—44no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C22×C414yes—
127C2×C32×C4C22×C412yes—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C22×C412yes—
132C2×C3⋊Dic3C22×C414yes—
133C4×C3⋊D3—44no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
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×C22⋊Q8—91no—
147#391—32no—
148#389—92no—
149#388—92no—
150#388—92no—
151#387—92no—
152#387—92no—
153#381—91no—
154#380—91no—
155C23×D3—32no—
156C23×D3—61no—
157C2×C3×Q8—24no—
158C2×C3×Q8—42no—
159C2×C3×Q8—42no—
160C2×C3×Q8—44no—
161C2×C3×Q8C4×D318yes—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4C22×D312yes—
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D312yes—
171C22×Dic3—32no—
172C22×Dic3—32no—
173C22×Dic3—32no—
174C22×Dic3—61no—
175C22×Dic3—62no—
176C22×Dic3C22×D312yes—
177C22×Dic3C22×D312yes—
178C22×Dic3C22×D312yes—
179C22×Dic3C22×D312yes—
180C2×C4×D3—38no—
181C2×C4×D3—64no—
182C2×C4×D3—122no—
183C2×C4×D3—122no—
184C2×C4×D3—124no—
185C3×C4⋊C4—122no—
186C3×C42—122no—
187(C2×D3)⋊C4—38no—
188(C2×D3)⋊C4—38no—
189(C2×D3)⋊C4—68no—
190(C2×D3)⋊C4—122no—
191(C2×D3)⋊C4—122no—
192(C2×D3)⋊C4—122no—
193(C2×D3)⋊C4—122no—
194C4⋊Dic3—38no—
195C4⋊Dic3—42no—
196C4⋊Dic3—64no—
197Dic3⋊C4—38no—
198Dic3⋊C4—38no—
199Dic3⋊C4—68no—
200Dic3⋊C4—122no—
201Dic3⋊C4—122no—
202Dic3⋊C4—122no—
203Dic3⋊C4—122no—
204C4×Dic3—42no—
205C4×Dic3—122no—
206C4×Dic3—122no—
207C22×C32C23×C411yescharacteristic
208C22×C32H(5,𝔽2)12yes—
209C22×C32H(5,𝔽2)11yescharacteristic
210C22×C322−1+411yescharacteristic
211C22×C322−1+412yes—
212C2×C3⋊D3—22no—
213C2×C3⋊D3—22no—
214C2×C3⋊D3—22no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—42no—
217C32×C4—22no—
218C32×C4—24no—
219C3⋊Dic3—22no—
220C3⋊Dic3—24no—
221C3×Dic3—42no—
222C3×Dic3—42no—
223C3×Dic3—42no—
224C3×Dic3—42no—
225C22×Q8D3211yescharacteristic
226C23×C4—91no—
227C22⋊Q8—98no—
228C2×C4⋊C4—32no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—92no—
232C2×C4⋊C4—92no—
233C2×C22⋊C4—92no—
234C2×C22⋊C4—91no—
235C2×C22⋊C4—91no—
236C2×C22⋊C4—92no—
237C2×C42—32no—
238C2×C42—92no—
239#95—32no—
240#95—32no—
241#95—32no—
242#95—32no—
243#95—91no—
244#95—91no—
245#95—92no—
246#95—92no—
247C23×C3—21no—
248C23×C3C23×D312yes—
249C22×D3—34no—
250C22×D3—62no—
251C22×D3—64no—
252C22×D3—62no—
253C22×D3—62no—
254C22×D3—62no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—62no—
258C22×D3—122no—
259C22×D3—121no—
260C22×D3—121no—
261C3×Q8—48no—
262C3×Q8—48no—
263C2×C3×C4—24no—
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—24no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—62no—
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×C4—62no—
286C2×C3×C4C2×C4×D314yes—
287C2×C3×C4C2×C4×D314yes—
288C2×C3×C4C2×C4×D314yes—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—22no—
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—34no—
302C2×Dic3—34no—
303C2×Dic3—34no—
304C2×Dic3—62no—
305C2×Dic3—64no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C4×D3—128no—
316C4×D3—128no—
317C2×C32#51811yescharacteristic
318C2×C32#51911yescharacteristic
319C2×C32#52011yescharacteristic
320C2×C32#56212yes—
321C2×C32#56312yes—
322C3⋊D3—42no—
323C24—91no—
324C2×Q8—42no—
325C2×Q8#62414yes—
326C22×C4—32no—
327C22×C4—32no—
328C22×C4—32no—
329C22×C4—32no—
330C22×C4—92no—
331C22×C4—91no—
332C22×C4—94no—
333C22×C4—362no—
334C22×C4C2×D3211yescharacteristic
335C22×C4C2×D3212yes—
336C4⋊C4—98no—
337C4⋊C4—94no—
338C4⋊C4—122no—
339C4⋊C4—362no—
340C4⋊C4—362no—
341C22⋊C4—98no—
342C22⋊C4—361no—
343C22⋊C4—361no—
344C22⋊C4—362no—
345C42—122no—
346C42—362no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—22no—
352C22×C3C22×C4×D312yes—
353C22×C3#100412yes—
354C22×C3#100412yes—
355C22×C3#100712yes—
356C22×C3#100712yes—
357C22×C3#100912yes—
358C22×C3#101012yes—
359C2×D3—64no—
360C2×D3—64no—
361C2×D3—64no—
362C2×D3—64no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—124no—
366C2×D3—124no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C3×C4—24no—
372C3×C4—24no—
373C3×C4—24no—
374C3×C4—24no—
375C3×C4—44no—
376C3×C4—122no—
377C3×C4—122no—
378C3×C4—122no—
379C3×C4—122no—
380Dic3—42no—
381Dic3—42no—
382Dic3—42no—
383Dic3—42no—
384Dic3—64no—
385Dic3—64no—
386Dic3—64no—
387Dic3—122no—
388Dic3—124no—
389C32#237811yescharacteristic, complemented, Sylow
390C23—92no—
391C23—182no—
392C23—181no—
393C23—181no—
394C23—182no—
395C23C22×D3211yescharacteristic
396Q8—44no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
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—94no—
413C2×C4—92no—
414C2×C4—182no—
415C2×C4—182no—
416C2×C4—182no—
417C2×C4—364no—
418C2×C4C2×#62414yes—
419C2×C4C2×#62412yes—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3#548612yes—
426C2×C3#557212yes—
427C2×C3#557412yes—
428C2×C3#564612yes—
429C2×C3#564712yes—
430C2×C3#568412yes—
431C2×C3#573512yes—
432D3—124no—
433D3—124no—
434C22—182no—
435C22—182no—
436C22—182no—
437C22—362no—
438C22—362no—
439C22#6431512yes—
440C22#6431611yescharacteristic
441C22#6432011yescharacteristic
442C22C22×#62411yescharacteristic
443C22#6433012yes—
444C4—22no—
445C4—24no—
446C4—122no—
447C4—122no—
448C4—122no—
449C4—122no—
450C4—184no—
451C4—182no—
452C3—21no—
453C3#7661712yescomplemented
454C2—362no—
455C2#1059533911yescharacteristic
456C2#1059534512yes—
457C2#1059535311yescharacteristic
458C2#1059541712yes—
459C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC22×Q8D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5229C2semidirect
4. #10591271C2semidirect
6. #10591264C2semidirect
9. #10591197C2semidirect
13. #64155C4semidirect
36. #5229D3semidirect
389. C32#2378semidirect
453. C3#76617semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C3×#52292
#105913552
#105912712
#105912662
#105912642
#105912192
#105912022
#105911972
#766173