Finite Group Databasebeta

← #11801686

Subgroups — #11801686

Order 1152.

1517 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×#63874C212yesmaximal, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×C42×Dic3C211yesmaximal, characteristic, complemented
5#10591320C212yesmaximal
6C4×#3722C212yesmaximal, complemented
7#10591212C212yesmaximal, complemented
8#10591202C214yesmaximal, complemented
9#73617—31nomaximal
10#73299—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3752C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×#3724C2214yes—
24C2×#3722C2214yes—
25C2×#3722C2214yes—
26#63874—28no—
27C3×C3⋊#95C2212yes—
28#63579C2214yes—
29C2×C4×D12—31no—
30C2×C4×D12—31no—
31C2×C4×D12—61no—
32C2×#872—32no—
33C2×#872—32no—
34C3×C4×C4⋊C4—31no—
35C3×C43—31no—
36#4988—32no—
37#4972—32no—
38#4940—34no—
39#4939—32no—
40C4×(C2×D3)⋊C4—32no—
41C4×(C2×D3)⋊C4—32no—
42C4×C4⋊Dic3D311yescharacteristic, complemented
43C42×Dic3D311yescharacteristic, complemented
44#4928—32no—
45#4669—34no—
46C23×C3⋊D3C2312yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C2×C4⋊(C3⋊D3)—24no—
52C2×C4⋊(C3⋊D3)C2×C414yes—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3C2×C418yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C32×C42C2×C414yes—
60#3752C2×C418yes—
61C4⋊(C3⋊Dic3)C2×C414yes—
62C3×C4⋊Dic3—24no—
63C3×C4×Dic3—24no—
64C3×C4×Dic3—24no—
65C3×C4×Dic3—22no—
66C3×C4×Dic3—24no—
67C3×C4×Dic3D414yescomplemented
68#3724—28no—
69#3722—28no—
70#3722—28no—
71#2293—91noSylow
72C22×D12—31no—
73C22×D12—31no—
74C22×D12—61no—
75C22×C4×D3—32no—
76C22×C4×D3—32no—
77C22×C4×D3—62no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—21no—
80C2×C3×C42—31no—
81C2×C3×C42—32no—
82C2×C3×C42—31no—
83C2×C3×C42—32no—
84C2×C3×C42—32no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—34no—
91C2×(C2×D3)⋊C4—34no—
92C2×(C2×D3)⋊C4—34no—
93C2×(C2×D3)⋊C4—62no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D312yes—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—34no—
100C2×C4×Dic3C2×D312yes—
101C2×C4×Dic3C2×D311yescharacteristic
102C2×C4×Dic3C2×D312yes—
103C2×C4×Dic3C2×D312yes—
104C2×C4×Dic3C2×D311yescharacteristic
105C4×D12—38no—
106C4×D12—38no—
107C4×D12—68no—
108#872—68no—
109#872—68no—
110C3×#95—32no—
111C3⋊#95—34no—
112C3⋊#95—34no—
113C3⋊#95C2×D312yes—
114C23×C32C2411yescharacteristic
115C22×C3⋊D3—24no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—24no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3C22×C414yes—
120C2×C32×C4—22no—
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C2×D412yes—
125C2×C32×C4#4114yes—
126C2×C32×C4#4112yes—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C22×C414yes—
130C4⋊(C3⋊D3)—28no—
131C4×C3⋊D3—216no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3C2×D414yes—
140C2×C3×Dic3#4114yes—
141C2×C4×D4—91no—
142C2×#117—92no—
143#390—92no—
144#389—92no—
145#388—94no—
146C4×C4⋊C4—31no—
147C4×C22⋊C4—92no—
148C43—31no—
149C23×D3—32no—
150C23×D3—32no—
151C23×D3—62no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—34no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—62no—
167C22×Dic3C22×D314yes—
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C2×D12—34no—
171C2×D12—34no—
172C2×D12—64no—
173C2×D12—68no—
174C2×D12—64no—
175C2×D12—64no—
176C2×C4×D3—38no—
177C2×C4×D3—38no—
178C2×C4×D3—68no—
179C2×C4×D3—64no—
180C2×C4×D3—64no—
181C2×C4×D3—64no—
182C2×C4×D3—64no—
183C2×C4×D3—124no—
184C2×C4×D3—124no—
185C3×C4⋊C4—64no—
186C3×C42—24no—
187C3×C42—34no—
188C3×C42—64no—
189C3×C42—64no—
190C3×C42—64no—
191C3×C42—62no—
192C3×C42C4×D314yes—
193C3×C42C4×D314yes—
194(C2×D3)⋊C4—38no—
195(C2×D3)⋊C4—38no—
196(C2×D3)⋊C4—68no—
197(C2×D3)⋊C4—68no—
198(C2×D3)⋊C4—68no—
199(C2×D3)⋊C4—68no—
200(C2×D3)⋊C4—68no—
201C4⋊Dic3—24no—
202C4⋊Dic3—34no—
203C4⋊Dic3—34no—
204C4⋊Dic3—64no—
205Dic3⋊C4—68no—
206Dic3⋊C4—68no—
207C4×Dic3—24no—
208C4×Dic3—22no—
209C4×Dic3—24no—
210C4×Dic3—24no—
211C4×Dic3D1214yescomplemented
212C22×C32C23×C411yescharacteristic
213C22×C32C22×D411yescharacteristic
214C22×C32C2×#4112yes—
215C22×C32C2×#4111yescharacteristic
216C22×C32C2×#4112yes—
217C2×C3⋊D3—24no—
218C2×C3⋊D3—24no—
219C2×C3⋊D3—24no—
220C2×C3⋊D3—44no—
221C2×C3⋊D3—44no—
222C32×C4—22no—
223C32×C4#11714yescomplemented
224C32×C4C4×D414yes—
225C3⋊Dic3—24no—
226C3×Dic3—24no—
227C3×Dic3—24no—
228C3×Dic3—44no—
229C22×D4—91no—
230C23×C4—92no—
231C4×D4—98no—
232#117—188no—
233C2×C4⋊C4—32no—
234C2×C4⋊C4—91no—
235C2×C4⋊C4—94no—
236C2×C22⋊C4—92no—
237C2×C22⋊C4—94no—
238C2×C22⋊C4—94no—
239C2×C42—31no—
240C2×C42—32no—
241C2×C42—32no—
242C2×C42—32no—
243C2×C42—31no—
244C2×C42D3211yescharacteristic
245#95—32no—
246#95—94no—
247C23×C3—21no—
248C23×C3C23×D311yescharacteristic
249C23×C3C23×D311yescharacteristic
250C22×D3—34no—
251C22×D3—34no—
252C22×D3—64no—
253C22×D3—68no—
254C22×D3—62no—
255C22×D3—64no—
256C22×D3—62no—
257C22×D3—64no—
258C22×D3—64no—
259C22×D3—62no—
260C22×D3—62no—
261C22×D3—64no—
262C22×D3—122no—
263C22×D3—122no—
264C22×D3—124no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—24no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—34no—
274C2×C3×C4—34no—
275C2×C3×C4—42no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4C2×C4×D312yes—
284C2×C3×C4C2×C4×D312yes—
285C2×C3×C4C2×C4×D312yes—
286C2×C3×C4C2×C4×D312yes—
287C2×C3×C4C2×C4×D312yes—
288C2×C3×C4C2×C4×D312yes—
289C2×C3×C4C2×D1212yes—
290C2×C3×C4#23514yes—
291C2×C3×C4#23514yes—
292C2×C3×C4#23512yes—
293C2×C3×C4D3×D412yes—
294C2×C3×C4#23912yes—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3—24no—
302C2×Dic3—34no—
303C2×Dic3—34no—
304C2×Dic3—64no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3C2×D1214yes—
312C2×Dic3#23514yes—
313D12—616no—
314D12—68no—
315D12—68no—
316C4×D3—616no—
317C4×D3—616no—
318C4×D3—1216no—
319C2×C32C2×#11711yescharacteristic
320C2×C32C2×C4×D411yescharacteristic
321C2×C32C4×#4111yescharacteristic
322C2×C32#52912yes—
323C2×C32#53212yes—
324C3⋊D3—44no—
325C24—92no—
326C2×D4—94no—
327C2×D4—184no—
328C22×C4—32no—
329C22×C4—32no—
330C22×C4—34no—
331C22×C4—92no—
332C22×C4—98no—
333C22×C4—184no—
334C22×C4—184no—
335C22×C4C2×D3211yescharacteristic
336C22×C4C2×D3211yescharacteristic
337C22×C4C2×D3211yescharacteristic
338C4⋊C4—64no—
339C4⋊C4—94no—
340C4⋊C4—188no—
341C22⋊C4—98no—
342C22⋊C4—188no—
343C22⋊C4—188no—
344C42—34no—
345C42—64no—
346C42—64no—
347C42—62no—
348C42—64no—
349C42#62414yes—
350C22×C3—22no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3C22×C4×D311yescharacteristic
356C22×C3C22×C4×D311yescharacteristic
357C22×C3C22×D1211yescharacteristic
358C22×C3C2×#23512yes—
359C22×C3C2×#23512yes—
360C22×C3C2×#23511yescharacteristic
361C22×C3C2×#23512yes—
362C22×C3C2×D3×D411yescharacteristic
363C22×C3C2×#23911yescharacteristic
364C22×C3D3×#4112yes—
365C2×D3—68no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—64no—
371C2×D3—64no—
372C2×D3—124no—
373C2×D3—124no—
374C2×D3—128no—
375C2×D3—128no—
376C2×D3—124no—
377C2×D3—124no—
378C2×D3—124no—
379C2×D3—124no—
380C3×C4—22no—
381C3×C4—22no—
382C3×C4—24no—
383C3×C4—24no—
384C3×C4—42no—
385C3×C4—64no—
386C3×C4—64no—
387C3×C4—124no—
388C3×C4#87214yescomplemented
389C3×C4#87214yescomplemented
390C3×C4C4×D1214yes—
391C3×C4#89314yes—
392Dic3—24no—
393Dic3—24no—
394Dic3—44no—
395Dic3—64no—
396Dic3—64no—
397Dic3—124no—
398C32#229311yescharacteristic, complemented, Sylow
399C23—94no—
400C23—184no—
401C23—182no—
402C23—182no—
403C23—184no—
404C23C22×D3211yescharacteristic
405D4—188no—
406C2×C4—22no—
407C2×C4—34no—
408C2×C4—34no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—64no—
414C2×C4—64no—
415C2×C4—64no—
416C2×C4—94no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—1816no—
420C2×C4#379814yes—
421C2×C4#379912yes—
422C2×C4D3×D1212yes—
423C2×C4C2×#62412yes—
424C2×C4C2×#62412yes—
425C2×C4C2×#62412yes—
426C2×C3—21no—
427C2×C3—22no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—22no—
431C2×C3C2×#87211yescharacteristic
432C2×C3C2×#87211yescharacteristic
433C2×C3C2×C4×D1211yescharacteristic
434C2×C3C4×#23511yescharacteristic
435C2×C3#547712yes—
436C2×C3#547912yes—
437C2×C3C2×#89311yescharacteristic
438C2×C3#552211yescharacteristic
439C2×C3#554812yes—
440C2×C3#558012yes—
441D3—128no—
442D3—124no—
443D3—124no—
444C22—184no—
445C22—184no—
446C22—184no—
447C22—364no—
448C22—364no—
449C22C2×#379812yes—
450C22C2×#379911yescharacteristic
451C22C2×D3×D1211yescharacteristic
452C22D3×#23512yes—
453C22C22×#62411yescharacteristic
454C4—22no—
455C4—64no—
456C4—64no—
457C4—124no—
458C4—184no—
459C4#6387414yescomplemented
460C4#6389414yes—
461C3—21no—
462C3#7329911yescharacteristic, complemented
463C3#7361711yescharacteristic, complemented
464C2—364no—
465C2#1059387012yes—
466C2#1059396812yes—
467C2C2×#6387411yescharacteristic
468C2C2×#6389411yescharacteristic
469C2#1059495411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2293
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63874C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
4. C3×C42×Dic3C2semidirect
6. C4×#3722C2semidirect
7. #10591212C2semidirect
8. #10591202C2semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
42. C4×C4⋊Dic3D3semidirect
43. C42×Dic3D3semidirect
67. C3×C4×Dic3D4semidirect
211. C4×Dic3D12semidirect
223. C32×C4#117semidirect
388. C3×C4#872semidirect
389. C3×C4#872semidirect
398. C32#2293semidirect
459. C4#63874semidirect
462. C3#73299semidirect
463. C3#73617semidirect

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×#638742
C3×C4×C4⋊Dic32
C3×C42×Dic32
#105913202
C4×#37222
#105912122
#105912022
#736173
#732993