Finite Group Databasebeta

← #11921897

Subgroups — #11921897

Order 1152.

744 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C3⋊S4C211yesmaximal, characteristic
2A4×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4#10593242C212yesmaximal
5Dic3×SL(2,ℤ/4)C212yesmaximal, complemented
6#85307—31nomaximal
7#73883—31nomaximal
8C22×C3⋊S4C2211yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
12C4×C3⋊S4C414yescomplemented
13C2×C3×SL(2,ℤ/4)C2212yes—
14#63849—41nomaximal
15C2×C4×S4—31no—
16C2×C4×S4—61no—
17C2×C4×#67—31no—
18C22×C4⋊Dic3D311yescharacteristic, complemented
19C2×#892—31no—
20A4×C4⋊C4—31no—
21(C2×S4)⋊C4—32no—
22C4⋊SL(2,ℤ/4)D311yescharacteristic, complemented
23C4×SL(2,ℤ/4)—32no—
24C3×#380—31no—
25#4987—31no—
26#4977—31no—
27Dic3×C4⋊C4—31no—
28#4958—32no—
29Dic3×C22⋊C4—32no—
30#4670—32no—
31#4655—32no—
32C22×C3×A4C2311yescharacteristic
33C2×C3⋊S4—21no—
34C2×C3⋊S4—21no—
35C2×C3⋊S4C2×C412yes—
36C2×C4×C3⋊D3—41no—
37C3×C4×A4C2×C412yes—
38Dic3×A4—22no—
39C3⋊SL(2,ℤ/4)C2×C412yes—
40C3×SL(2,ℤ/4)—22no—
41C3×C4⋊Dic3—41no—
42C3×C4⋊Dic3—41no—
43#3722—42no—
44Dic32—42no—
45#2352—91noSylow
46C22×S4—31no—
47C22×S4—61no—
48C23×C3×C4C2×D311yescharacteristic
49C22×#67—31no—
50C23×Dic3C2×D312yes—
51C22×C4×D3—31no—
52C2×C4×A4—21no—
53C2×C4×A4—32no—
54C2×C4×A4C2×D311yescharacteristic
55C2×SL(2,ℤ/4)—31no—
56C2×SL(2,ℤ/4)—61no—
57C2×SL(2,ℤ/4)C2×D312yes—
58C4×S4—34no—
59C4×S4—64no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C4⋊C4—31no—
62C2×C3×C22⋊C4—32no—
63C2×#217—31no—
64C4×#67—34no—
65C4×#67—34no—
66C2×(C2×D3)⋊C4—31no—
67C2×(C2×D3)⋊C4—32no—
68C2×(C2×D3)⋊C4—32no—
69C2×C4⋊Dic3—31no—
70C2×C4⋊Dic3—32no—
71C2×C4⋊Dic3—31no—
72C2×Dic3⋊C4—31no—
73C2×C4×Dic3—31no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—32no—
76#892—61no—
77#892—62no—
78#892—61no—
79#892—121no—
80C3×#95—32no—
81C3⋊#95—32no—
82C3⋊#95—32no—
83C3⋊#95—32no—
84C3⋊#95—32no—
85C22×C3⋊D3—41no—
86C2×C3×A4C22×C411yescharacteristic
87C2×C3×A4#4111yescharacteristic
88C2×C3×A4#4111yescharacteristic
89C3⋊S4—22no—
90C2×C32×C4—41no—
91C2×C3⋊Dic3—41no—
92C4×C3⋊D3—44no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—42no—
95C2×C4×D4—91no—
96C2×#117—91no—
97C22×C4⋊C4—31no—
98#388—92no—
99#387—92no—
100#386—92no—
101#382—91no—
102#380—31no—
103#380—91no—
104C4×C4⋊C4—91no—
105C4×C22⋊C4—92no—
106C24×C3C22×D311yescharacteristic
107C23×D3—31no—
108C22×A4—21no—
109C22×A4C22×D311yescharacteristic
110C2×S4—32no—
111C2×S4—62no—
112C2×S4—62no—
113C2×S4—62no—
114C2×S4—61no—
115C2×S4—61no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C22×C3×C4—32no—
119C22×C3×C4—32no—
120C22×C3×C4—32no—
121C22×C3×C4C4×D312yes—
122C2×#67—32no—
123C2×#67—32no—
124C2×#67—61no—
125C2×#67—61no—
126C2×#67—61no—
127C2×#67—61no—
128C22×Dic3—22no—
129C22×Dic3—31no—
130C22×Dic3—31no—
131C22×Dic3—31no—
132C22×Dic3—32no—
133C22×Dic3—32no—
134C22×Dic3—62no—
135C2×C4×D3—34no—
136C2×C4×D3—61no—
137C2×C4×D3—62no—
138C2×C4×D3—61no—
139C2×C4×D3—121no—
140C2×C4×D3—241no—
141C4×A4—22no—
142C4×A4—62no—
143C4×A4C4×D312yes—
144SL(2,ℤ/4)—22no—
145SL(2,ℤ/4)—32no—
146SL(2,ℤ/4)—62no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—62no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—121no—
151C3×C22⋊C4—62no—
152C3×C22⋊C4—62no—
153#217—32no—
154#217—32no—
155(C2×D3)⋊C4—34no—
156(C2×D3)⋊C4—62no—
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—122no—
159(C2×D3)⋊C4—122no—
160C4⋊Dic3—31no—
161C4⋊Dic3—32no—
162C4⋊Dic3—41no—
163C4⋊Dic3—61no—
164C4⋊Dic3S411yescharacteristic, complemented
165Dic3⋊C4—34no—
166C4×Dic3—34no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—122no—
170C4×Dic3—122no—
171C22×C32—41no—
172C2×C3⋊D3—42no—
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C3×A4#11711yescharacteristic, complemented
176C32×C4—42no—
177C3⋊Dic3—42no—
178C3×Dic3—82no—
179C3×Dic3—82no—
180C22×D4—91no—
181C23×C4—32no—
182C23×C4—91no—
183C23×C4D3211yescharacteristic
184C4×D4—94no—
185C4×D4—94no—
186#117—181no—
187#117—182no—
188#117—181no—
189C2×C4⋊C4—31no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—91no—
192C2×C4⋊C4—91no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—92no—
195C2×C22⋊C4—32no—
196C2×C22⋊C4—91no—
197C2×C22⋊C4—91no—
198C2×C22⋊C4—92no—
199C2×C22⋊C4—92no—
200C2×C42—91no—
201C2×C42—92no—
202C2×C42—92no—
203#95—32no—
204#95—92no—
205#95—92no—
206#95—92no—
207#95—92no—
208C23×C3—31no—
209C23×C3—31no—
210C23×C3—31no—
211C23×C3—31no—
212C23×C3C2×C4×D311yescharacteristic
213C23×C3#23711yescharacteristic
214C23×C3#23911yescharacteristic
215C22×D3—32no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—61no—
219C22×D3—61no—
220C22×D3—61no—
221C22×D3—61no—
222C22×D3—121no—
223C22×D3—241no—
224C2×A4—21no—
225C2×A4—21no—
226C2×A4—21no—
227C2×A4C2×C4×D311yescharacteristic
228C2×A4#23711yescharacteristic
229C2×A4#23911yescharacteristic
230S4—64no—
231S4—62no—
232C2×C3×C4—31no—
233C2×C3×C4—32no—
234C2×C3×C4—32no—
235C2×C3×C4—32no—
236C2×C3×C4—41no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4—81no—
245C2×C3×C4—122no—
246C2×C3×C4C2×S411yescharacteristic
247#67—62no—
248#67—62no—
249#67—62no—
250#67—62no—
251C2×Dic3—32no—
252C2×Dic3—32no—
253C2×Dic3—32no—
254C2×Dic3—32no—
255C2×Dic3—42no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—121no—
267C2×Dic3—241no—
268C2×Dic3C2×S412yes—
269C4×D3—64no—
270C4×D3—64no—
271C4×D3—124no—
272C4×D3—244no—
273C2×C32—41no—
274C2×C32—41no—
275C2×C32—41no—
276C3⋊D3—82no—
277C24—91no—
278C24C2×D3211yescharacteristic
279C2×D4—92no—
280C2×D4—92no—
281C2×D4—181no—
282C2×D4—181no—
283C2×D4—181no—
284C2×D4—181no—
285C22×C4—31no—
286C22×C4—31no—
287C22×C4—32no—
288C22×C4—32no—
289C22×C4—32no—
290C22×C4—62no—
291C22×C4—92no—
292C22×C4—94no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—92no—
297C22×C4—181no—
298C22×C4—182no—
299C22×C4—181no—
300C22×C4—182no—
301C22×C4#62412yes—
302C4⋊C4—31no—
303C4⋊C4—61no—
304C4⋊C4—62no—
305C4⋊C4—61no—
306C4⋊C4—92no—
307C4⋊C4—94no—
308C4⋊C4—91no—
309C4⋊C4—181no—
310C22⋊C4—62no—
311C22⋊C4—62no—
312C22⋊C4—94no—
313C22⋊C4—92no—
314C22⋊C4—92no—
315C22⋊C4—182no—
316C22⋊C4—182no—
317C22⋊C4—362no—
318C42—94no—
319C42—182no—
320C42—182no—
321C42—362no—
322C22×C3—31no—
323C22×C3—31no—
324C22×C3—31no—
325C22×C3—31no—
326C22×C3—31no—
327C22×C3—31no—
328C22×C3—31no—
329C22×C3—31no—
330C22×C3—31no—
331C22×C3—41no—
332C22×C3—61no—
333C22×C3—81no—
334C22×C3#89211yescharacteristic, complemented
335C22×C3C22×S411yescharacteristic
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3—122no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—242no—
345C2×D3—241no—
346C2×D3—241no—
347C2×D3—242no—
348C2×D3—242no—
349A4—21no—
350A4#89211yescharacteristic, complemented
351C3×C4—32no—
352C3×C4—42no—
353C3×C4—82no—
354C3×C4—122no—
355C3×C4—122no—
356C3×C4—242no—
357C3×C4C4×S412yes—
358Dic3—22no—
359Dic3—62no—
360Dic3—62no—
361Dic3—62no—
362Dic3—62no—
363Dic3—82no—
364Dic3—122no—
365Dic3—242no—
366C32—41noSylow
367C23—31no—
368C23—31no—
369C23—31no—
370C23—31no—
371C23—92no—
372C23—181no—
373C23—181no—
374C23—181no—
375C23—181no—
376C23—181no—
377C23—181no—
378C23#379611yescharacteristic
379C23#379611yescharacteristic
380C23C2×#62411yescharacteristic
381D4—182no—
382D4—182no—
383D4—182no—
384D4—182no—
385C2×C4—31no—
386C2×C4—32no—
387C2×C4—32no—
388C2×C4—32no—
389C2×C4—32no—
390C2×C4—61no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—92no—
398C2×C4—92no—
399C2×C4—92no—
400C2×C4—92no—
401C2×C4—184no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4—181no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—184no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4D3×S411yescharacteristic
414C2×C3—31no—
415C2×C3—31no—
416C2×C3—31no—
417C2×C3—31no—
418C2×C3—41no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—81no—
422C2×C3—81no—
423C2×C3—81no—
424C2×C3C2×C4×S411yescharacteristic
425C2×C3#591411yescharacteristic
426C2×C3#591911yescharacteristic
427D3—122no—
428D3—242no—
429D3—244no—
430C22—31no—
431C22—31no—
432C22—31no—
433C22—31no—
434C22—31no—
435C22—31no—
436C22—31no—
437C22—31no—
438C22—31no—
439C22—61no—
440C22—182no—
441C22—182no—
442C22—182no—
443C22—361no—
444C22—361no—
445C22—361no—
446C22—361no—
447C22#6384911yescharacteristic, complemented
448C22C2×D3×S411yescharacteristic
449C4—32no—
450C4—62no—
451C4—122no—
452C4—122no—
453C4—182no—
454C4—182no—
455C4—182no—
456C4—182no—
457C4(C3⋊S4)⋊C412yes—
458C3—41no—
459C3—81no—
460C3#8530711yescharacteristic, complemented
461C2—31no—
462C2—31no—
463C2—31no—
464C2—31no—
465C2—362no—
466C2#1059642011yescharacteristic
467C2#1059642511yescharacteristic
468C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
cosocleC22×C3×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4#117
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. A4×C4⋊Dic3C2semidirect
3. C3×C4⋊SL(2,ℤ/4)C2semidirect
5. Dic3×SL(2,ℤ/4)C2semidirect
12. C4×C3⋊S4C4semidirect
18. C22×C4⋊Dic3D3semidirect
22. C4⋊SL(2,ℤ/4)D3semidirect
164. C4⋊Dic3S4semidirect
175. C3×A4#117semidirect
334. C22×C3#892semidirect
350. A4#892semidirect
447. C22#63849semidirect
460. C3#85307semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
A4×C4⋊Dic32
C3×C4⋊SL(2,ℤ/4)2
#105932422
Dic3×SL(2,ℤ/4)2
#853073
#738833
#638494