Finite Group Databasebeta

← #11808805

Subgroups — #11808805

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C3×#4932C211yesmaximal, characteristic, complemented
4#10591326C212yesmaximal, complemented
5#10591321C212yesmaximal
6#10591310C212yesmaximal, complemented
7C4×#3722C214yesmaximal, complemented
8#10591226C212yesmaximal, complemented
9#82492—31nomaximal
10#73419—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3752C2212yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—24no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6—24no—
23C2×#3722C2214yes—
24C2×#3722C2214yes—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27#63579C2214yes—
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×C4×D12—31no—
31C2×C4×D12—31no—
32C2×C4×D12—61no—
33C2×C4×Dic6D311yescharacteristic, complemented
34C3×#376—31no—
35#5231—32no—
36#4992—32no—
37#4991—32no—
38#4986—32no—
39C4×(C2×D3)⋊C4—34no—
40C4×(C2×D3)⋊C4—34no—
41#4932D311yescharacteristic, complemented
42#4674—32no—
43#4673—32no—
44#4672—32no—
45#4659—32no—
46C23×C3⋊D3C2312yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C2×C4⋊(C3⋊D3)—24no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—28no—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C2×C3×Dic6—22no—
59C2×C3×Dic6—24no—
60C32×C42D414yes—
61#3752—24no—
62C4⋊(C3⋊Dic3)—22no—
63C3×C4⋊Dic3—22no—
64C3×Dic3⋊C4—24no—
65C3×C4×Dic3—24no—
66C3×C4×Dic3—24no—
67#3722—28no—
68#3722—28no—
69#2398—91noSylow
70C22×C3×Q8—31no—
71C22×D12—31no—
72C22×D12—31no—
73C22×D12—61no—
74C22×C4×D3—32no—
75C22×C4×D3—32no—
76C22×C4×D3—62no—
77C22×Dic6C2×D311yescharacteristic
78C3×C4×Q8—64no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C42—21no—
82C2×C3×C42—32no—
83C2×C3×C42—32no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—34no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—34no—
91C2×(C2×D3)⋊C4—34no—
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4C2×D312yes—
98C2×C4×Dic3C2×D312yes—
99C2×C4×Dic3C2×D312yes—
100C4×D12—68no—
101C4×D12—64no—
102C4×D12—64no—
103C4×Dic6—24no—
104C3×#95—32no—
105C3×#95—32no—
106C3⋊#95—34no—
107C3⋊#95—34no—
108C3⋊#95—34no—
109C3⋊#95—34no—
110C3⋊#95C2×D312yes—
111C3⋊#95C2×D312yes—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3—22no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—24no—
116C22×C3⋊D3—24no—
117C22×C3⋊D3#4114yes—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D412yes—
123C2×C32×C4#4114yes—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—24no—
126C4⋊(C3⋊D3)—28no—
127C4×C3⋊D3—48no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3#4114yes—
136C3×Dic6—28no—
137C2×C4×Q8—31no—
138C2×C4×D4—91no—
139#400—92no—
140#397—92no—
141#394—92no—
142#393—92no—
143C4×C22⋊C4—94no—
144#376—31no—
145C23×D3—32no—
146C23×D3—32no—
147C23×D3—62no—
148C2×C3×Q8—64no—
149C2×C3×Q8—62no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—32no—
154C22×C3×C4—34no—
155C22×C3×C4—32no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—32no—
163C22×Dic3—32no—
164C22×Dic3—62no—
165C22×Dic3C22×D314yes—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D312yes—
168C2×D12—64no—
169C2×D12—64no—
170C2×D12—64no—
171C2×D12—68no—
172C2×D12—62no—
173C2×D12—62no—
174C2×C4×D3—68no—
175C2×C4×D3—64no—
176C2×C4×D3—68no—
177C2×C4×D3—68no—
178C2×C4×D3—64no—
179C2×C4×D3—128no—
180C2×Dic6—22no—
181C2×Dic6—24no—
182C3×C4⋊C4—64no—
183C3×C4⋊C4—62no—
184C3×C42—24no—
185C3×C42—64no—
186C3×C42—64no—
187C3×C42D1214yes—
188C3×C42#6714yes—
189(C2×D3)⋊C4—68no—
190(C2×D3)⋊C4—68no—
191(C2×D3)⋊C4—68no—
192(C2×D3)⋊C4—68no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—68no—
196C4⋊Dic3—22no—
197C4⋊Dic3—64no—
198C4⋊Dic3—62no—
199C4⋊Dic3—62no—
200Dic3⋊C4—24no—
201C4×Dic3—24no—
202C4×Dic3—24no—
203C22×C32C22×D411yescharacteristic
204C22×C32C2×#4112yes—
205C22×C32C2×#4112yes—
206C22×C32C2×#4112yes—
207C2×C3⋊D3—24no—
208C2×C3⋊D3—28no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—44no—
212C32×C4—22no—
213C32×C4—22no—
214C32×C4#12414yes—
215C3⋊Dic3—42no—
216C3×Dic3—24no—
217C3×Dic3—42no—
218C3×Dic3—44no—
219C22×Q8—31no—
220C22×D4—91no—
221C23×C4—92no—
222C4×Q8—64no—
223C4×D4—184no—
224C2×C4⋊C4—32no—
225C2×C4⋊C4—31no—
226C2×C4⋊C4—91no—
227C2×C22⋊C4—94no—
228C2×C22⋊C4—94no—
229C2×C22⋊C4—92no—
230C2×C42—32no—
231C2×C42—32no—
232C2×C42D3211yescharacteristic
233#95—32no—
234#95—32no—
235#95—94no—
236#95—94no—
237C23×C3—21no—
238C23×C3C23×D311yescharacteristic
239C23×C3C23×D311yescharacteristic
240C22×D3—34no—
241C22×D3—34no—
242C22×D3—64no—
243C22×D3—64no—
244C22×D3—64no—
245C22×D3—62no—
246C22×D3—64no—
247C22×D3—64no—
248C22×D3—64no—
249C22×D3—64no—
250C22×D3—62no—
251C22×D3—62no—
252C22×D3—62no—
253C22×D3—124no—
254C22×D3—124no—
255C3×Q8—68no—
256C2×C3×C4—24no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—34no—
266C2×C3×C4—42no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—64no—
271C2×C3×C4—64no—
272C2×C3×C4—64no—
273C2×C3×C4—64no—
274C2×C3×C4C2×D1212yes—
275C2×C3×C4C2×D1212yes—
276C2×C3×C4C2×D1212yes—
277C2×C3×C4#23514yes—
278C2×C3×C4#23914yes—
279C2×C3×C4C2×#6712yes—
280C2×C3×C4C2×#6712yes—
281C2×C3×C4C2×#6712yes—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—24no—
285C2×Dic3—24no—
286C2×Dic3—24no—
287C2×Dic3—24no—
288C2×Dic3—22no—
289C2×Dic3—64no—
290C2×Dic3—62no—
291C2×Dic3—64no—
292C2×Dic3—64no—
293C2×Dic3—62no—
294C2×Dic3—124no—
295C2×Dic3#23514yes—
296D12—616no—
297D12—68no—
298D12—68no—
299C4×D3—1216no—
300C4×D3—128no—
301C4×D3—128no—
302Dic6—28no—
303C2×C32#52511yescharacteristic
304C2×C32#52511yescharacteristic
305C2×C32C2×#12411yescharacteristic
306C2×C32#52914yes—
307C3⋊D3—44no—
308C24—92no—
309C2×Q8—64no—
310C2×Q8—62no—
311C2×D4—184no—
312C2×D4—182no—
313C22×C4—32no—
314C22×C4—34no—
315C22×C4—32no—
316C22×C4—92no—
317C22×C4—188no—
318C22×C4—184no—
319C22×C4C2×D3211yescharacteristic
320C22×C4C2×D3211yescharacteristic
321C22×C4C2×D3211yescharacteristic
322C4⋊C4—64no—
323C4⋊C4—62no—
324C4⋊C4—182no—
325C22⋊C4—188no—
326C22⋊C4—188no—
327C22⋊C4—184no—
328C42—64no—
329C42—64no—
330C42#62614yes—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3C22×D1211yescharacteristic
336C22×C3C2×#23512yes—
337C22×C3C2×#23512yes—
338C22×C3C2×#23912yes—
339C22×C3D3×#4112yes—
340C22×C3D3×#4112yes—
341C22×C3D3×#4112yes—
342C22×C3C22×#6711yescharacteristic
343C2×D3—68no—
344C2×D3—64no—
345C2×D3—68no—
346C2×D3—64no—
347C2×D3—68no—
348C2×D3—128no—
349C2×D3—124no—
350C2×D3—128no—
351C2×D3—124no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—124no—
355C2×D3—122no—
356C2×D3—122no—
357C2×D3—124no—
358C3×C4—24no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—24no—
364C3×C4—42no—
365C3×C4—64no—
366C3×C4—122no—
367C3×C4—124no—
368C3×C4#87514yes—
369C3×C4#94714yes—
370Dic3—24no—
371Dic3—44no—
372Dic3—42no—
373Dic3—124no—
374Dic3—122no—
375Dic3—122no—
376C32#239811yescharacteristic, complemented, Sylow
377C23—94no—
378C23—184no—
379C23—184no—
380C23—182no—
381C23—182no—
382C23C22×D3211yescharacteristic
383Q8—68no—
384D4—188no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—34no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—64no—
391C2×C4—64no—
392C2×C4—64no—
393C2×C4—64no—
394C2×C4—62no—
395C2×C4—184no—
396C2×C4—182no—
397C2×C4—368no—
398C2×C4#379914yes—
399C2×C4C2×#62612yes—
400C2×C4C2×#62612yes—
401C2×C4C2×#62612yes—
402C2×C3—21no—
403C2×C3—24no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3C2×#87511yescharacteristic
407C2×C3#552411yescharacteristic
408C2×C3#552411yescharacteristic
409C2×C3#552814yes—
410C2×C3#558014yes—
411C2×C3#579111yescharacteristic
412C2×C3C2×#94711yescharacteristic
413C2×C3#582811yescharacteristic
414D3—128no—
415D3—124no—
416D3—124no—
417C22—188no—
418C22—184no—
419C22—362no—
420C22—364no—
421C22—362no—
422C22C2×#379912yes—
423C22D3×#23512yes—
424C22#6430612yes—
425C22C22×#62611yescharacteristic
426C4—22no—
427C4—22no—
428C4—64no—
429C4—124no—
430C4—122no—
431C4—362no—
432C4#6386414yes—
433C3—21no—
434C3#7341911yescharacteristic, complemented
435C3#8249211yescharacteristic, complemented
436C2—364no—
437C2#1059393414yes—
438C2C2×#6386411yescharacteristic
439C2#1059502311yescharacteristic
440C2#1059503411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C3×#4932C2semidirect
4. #10591326C2semidirect
6. #10591310C2semidirect
7. C4×#3722C2semidirect
8. #10591226C2semidirect
33. C2×C4×Dic6D3semidirect
41. #4932D3semidirect
376. C32#2398semidirect
434. C3#73419semidirect
435. C3#82492semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×Dic62
C3×#49322
#105913262
#105913212
#105913102
C4×#37222
#105912262
#824923
#734193