Finite Group Databasebeta

← C2×#10593648 #11923036

Subgroups — C2×#10593648 #11923036

Order 1152.

850 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 99 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×C3×D4×A4C211yesmaximal, characteristic
2C2×#64259C211yesmaximal, characteristic, complemented
3#10593648C214yesmaximal, direct product factor
4C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
5C2×#5414—33nomaximal
6C2×#5218—31nomaximal
7C23×C3×A4—21no—
8C3×D4×A4—21no—
9C3×D4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)—21no—
12#64259—21no—
13#64259C2212yescomplemented
14C2×#3754—41nomaximal
15C3⋊(A4⋊C8)C2212yescomplemented
16C23×C3×D4D311yescharacteristic
17C2×D4×A4D313yes—
18C2×A4⋊Q8—33no—
19C22×#214—31no—
20C22×#214—31no—
21C2×#924—31no—
22#5414—312no—
23C2×A4⋊C8—33no—
24#5218—34no—
25#5218—34no—
26C2×#832—31no—
27C2×#832—31no—
28C2×#830—31no—
29C22×C3×A4—22no—
30C22×C3×A4—42no—
31C22×C3×A4D411yescharacteristic
32C2×C32×D4—41no—
33C2×#634—41no—
34C3×C4×A4D411yescharacteristic
35C3×C4×A4C2311yescharacteristic
36C3⋊SL(2,ℤ/4)—22no—
37#3754—44no—
38C2×C3⋊(C3⋊C8)—41no—
39C2×#450—91noSylow
40C25×C3—21no—
41C23×A4—23no—
42C22×C3×D4—21no—
43C22×C3×D4—31no—
44C22×C3×D4—31no—
45C22×C3×D4—32no—
46C22×C3×D4—61no—
47C22×C3×D4—61no—
48C22×C3×D4C2×D312yes—
49C23×C3×C4C2×D311yescharacteristic
50C22×Dic6—31no—
51D4×A4—23no—
52D4×A4C2×D316yes—
53C2×C4×A4C2×D313yes—
54C2×SL(2,ℤ/4)—63no—
55A4⋊Q8—36no—
56A4⋊Q8—63no—
57C2×#217—61no—
58C2×#214—34no—
59C2×#214—34no—
60C2×#214—62no—
61C2×#214—62no—
62C2×#214—62no—
63C2×#214—61no—
64C2×#214—61no—
65C2×#214—123no—
66C2×C4⋊Dic3—31no—
67#924—32no—
68#924—32no—
69#924—61no—
70#924—61no—
71C2×Dic3⋊C4—61no—
72C22×C3⋊C8—31no—
73C22×C3⋊C8—31no—
74A4⋊C8—36no—
75#832—34no—
76#832—34no—
77#830—32no—
78#830—32no—
79C23×C32—81no—
80C2×C3×A4—42no—
81C2×C3×A4SD1612yescomplemented
82C2×C3×A4C2×D411yescharacteristic
83C32×D4—42no—
84C32×D4—81no—
85C2×C32×C4—41no—
86C2×C3⋊Dic3—81no—
87#634—42no—
88#634—81no—
89C3⋊(C3⋊C8)—42no—
90C23×D4C3⋊D311yescharacteristic
91C22×SD16—91no—
92C22×SD16—91no—
93C2×C22⋊Q8—91no—
94#450—94no—
95#450—94no—
96C2×#102—91no—
97C2×#102—91no—
98C2×C22⋊C8—91no—
99C24×C3—22no—
100C24×C3—42no—
101C24×C3—61no—
102C24×C3—61no—
103C24×C3—62no—
104C24×C3—122no—
105C24×C3#6711yescharacteristic
106C22×A4—26no—
107C22×A4—46no—
108C22×A4#6713yes—
109C2×C3×D4—32no—
110C2×C3×D4—32no—
111C2×C3×D4—32no—
112C2×C3×D4—32no—
113C2×C3×D4—32no—
114C2×C3×D4—31no—
115C2×C3×D4—43no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—62no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×C3×D4—62no—
123C2×C3×D4—64no—
124C2×C3×D4S411yescharacteristic
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C22×C3×C4#6711yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—61no—
132C22×Dic3—61no—
133C2×Dic6—32no—
134C2×Dic6—61no—
135C2×Dic6—61no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139C2×Dic6—123no—
140C4×A4#6713yes—
141C4×A4C22×D313yes—
142SL(2,ℤ/4)—66no—
143#217—62no—
144#217—62no—
145#214—68no—
146#214—64no—
147#214—64no—
148#214—1212no—
149C4⋊Dic3—32no—
150C4⋊Dic3—61no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153C2×C3⋊C8—32no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—123no—
160C22×C32—41no—
161C22×C32—82no—
162C22×C32—162no—
163C3×A4C2×SD1611yescharacteristic, complemented
164C32×C4—41no—
165C32×C4—41no—
166C3⋊Dic3—82no—
167C25—21no—
168C22×Q8—91no—
169C22×D4—21no—
170C22×D4—31no—
171C22×D4—31no—
172C22×D4—32no—
173C22×D4—61no—
174C22×D4—61no—
175C22×D4C2×C3⋊D312yes—
176C23×C4C2×C3⋊D311yescharacteristic
177C2×SD16—94no—
178C2×SD16—94no—
179C2×SD16—182no—
180C2×SD16—182no—
181C2×SD16—182no—
182C2×SD16—181no—
183C2×SD16—181no—
184C22×C8—91no—
185C22×C8—91no—
186C22⋊Q8—92no—
187C22⋊Q8—92no—
188C22⋊Q8—181no—
189C22⋊Q8—181no—
190C2×C4⋊C4—91no—
191C2×C4⋊C4—181no—
192C2×C22⋊C4—181no—
193#102—94no—
194#102—94no—
195C22⋊C8—92no—
196C22⋊C8—92no—
197C23×C3—21no—
198C23×C3—31no—
199C23×C3—31no—
200C23×C3—32no—
201C23×C3—42no—
202C23×C3—62no—
203C23×C3—62no—
204C23×C3—62no—
205C23×C3—62no—
206C23×C3—61no—
207C23×C3—83no—
208C23×C3—122no—
209C23×C3—122no—
210C23×C3—122no—
211C23×C3—124no—
212C23×C3—122no—
213C23×C3—122no—
214C23×C3—124no—
215C23×C3#21412yescomplemented
216C23×C3C2×#6711yescharacteristic
217C2×A4—46no—
218C2×A4#21416yescomplemented
219C2×A4C2×#6713yes—
220C3×D4—21no—
221C3×D4—34no—
222C3×D4—32no—
223C3×D4—46no—
224C3×D4—62no—
225C3×D4—62no—
226C3×D4—62no—
227C3×D4—61no—
228C3×D4—83no—
229C3×D4C2×S412yes—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—43no—
238C2×C3×C4—61no—
239C2×C3×C4C2×S411yescharacteristic
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—121no—
243C2×Dic3—122no—
244C2×Dic3—121no—
245C2×Dic3—243no—
246Dic6—62no—
247Dic6—62no—
248Dic6—126no—
249Dic6—121no—
250Dic6—121no—
251Dic6—243no—
252C3⋊C8—62no—
253C3⋊C8—62no—
254C3⋊C8—126no—
255C2×C32—42no—
256C2×C32—41no—
257C2×C32—162no—
258C24—22no—
259C24—42no—
260C24—61no—
261C24—61no—
262C24—62no—
263C24—122no—
264C24#63811yescharacteristic
265C2×Q8—92no—
266C2×Q8—181no—
267C2×Q8—181no—
268C2×Q8—181no—
269C2×Q8—181no—
270C2×Q8—181no—
271C2×D4—32no—
272C2×D4—32no—
273C2×D4—32no—
274C2×D4—32no—
275C2×D4—32no—
276C2×D4—31no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—61no—
280C2×D4—62no—
281C2×D4—61no—
282C2×D4—61no—
283C2×D4—62no—
284C2×D4—64no—
285C2×D4C3⋊S411yescharacteristic
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—181no—
291C22×C4—181no—
292C22×C4#63811yescharacteristic
293C22×C4C22×C3⋊D311yescharacteristic
294SD16—188no—
295SD16—184no—
296SD16—184no—
297C2×C8—92no—
298C2×C8—92no—
299C2×C8—181no—
300C2×C8—181no—
301C2×C8—181no—
302C2×C8—181no—
303C4⋊C4—92no—
304C4⋊C4—181no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C22⋊C4—182no—
308C22⋊C4—182no—
309C22×C3—22no—
310C22×C3—32no—
311C22×C3—31no—
312C22×C3—32no—
313C22×C3—32no—
314C22×C3—31no—
315C22×C3—31no—
316C22×C3—42no—
317C22×C3—43no—
318C22×C3—61no—
319C22×C3—62no—
320C22×C3—86no—
321C22×C3—122no—
322C22×C3—122no—
323C22×C3—124no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3—124no—
327C22×C3—122no—
328C22×C3—166no—
329C22×C3C2×#21411yescharacteristic, complemented
330C22×C3GL(2,ℤ/4)11yescharacteristic
331A4C2×#21413yescomplemented
332C3×C4—31no—
333C3×C4—31no—
334C3×C4—43no—
335C3×C4—43no—
336C3×C4GL(2,ℤ/4)11yescharacteristic
337C3×C4C22×S411yescharacteristic
338Dic3—122no—
339Dic3—122no—
340Dic3—246no—
341C32—41noSylow
342C23—21no—
343C23—31no—
344C23—31no—
345C23—32no—
346C23—42no—
347C23—62no—
348C23—62no—
349C23—62no—
350C23—62no—
351C23—61no—
352C23—122no—
353C23—122no—
354C23—122no—
355C23—124no—
356C23—122no—
357C23—122no—
358C23—124no—
359C23#375412yescomplemented
360C23C2×#63811yescharacteristic
361Q8—182no—
362Q8—182no—
363Q8—361no—
364Q8—361no—
365D4—21no—
366D4—34no—
367D4—32no—
368D4—62no—
369D4—62no—
370D4—62no—
371D4—61no—
372D4C2×C3⋊S412yes—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—61no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—361no—
384C2×C4—362no—
385C2×C4—361no—
386C2×C4C2×C3⋊S411yescharacteristic
387C8—182no—
388C8—182no—
389C2×C3—31no—
390C2×C3—31no—
391C2×C3—32no—
392C2×C3—42no—
393C2×C3—46no—
394C2×C3—43no—
395C2×C3—122no—
396C2×C3—166no—
397C2×C3#541412yescomplemented
398C2×C3C2×GL(2,ℤ/4)11yescharacteristic
399C22—22no—
400C22—32no—
401C22—31no—
402C22—32no—
403C22—32no—
404C22—31no—
405C22—31no—
406C22—42no—
407C22—61no—
408C22—62no—
409C22—122no—
410C22—122no—
411C22—124no—
412C22—122no—
413C22—122no—
414C22—124no—
415C22—122no—
416C22C2×#375411yescharacteristic, complemented
417C22#6426911yescharacteristic
418C4—31no—
419C4—31no—
420C4—362no—
421C4—362no—
422C4#6426911yescharacteristic
423C4C22×C3⋊S411yescharacteristic
424C3—43no—
425C3C2×#541411yescharacteristic, complemented
426C2—31no—
427C2—31no—
428C2—32no—
429C2—42no—
430C2—122no—
431C2#1059364812yesdirect product factor
432C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×D4D3
socleC24×C3#67
prime radicalC2×C3×D4×A4C2
hypercenterC2×D4C3⋊S4
hypocenterC3×A4C2×SD16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×#64259C2semidirect
3. #10593648C2direct (N × H)
4. C2×C3⋊(A4⋊C8)C2semidirect
13. #64259C22semidirect
15. C3⋊(A4⋊C8)C22semidirect
81. C2×C3×A4SD16semidirect
163. C3×A4C2×SD16semidirect
215. C23×C3#214semidirect
218. C2×A4#214semidirect
329. C22×C3C2×#214semidirect
331. A4C2×#214semidirect
359. C23#3754semidirect
397. C2×C3#5414semidirect
416. C22C2×#3754semidirect
425. C3C2×#5414semidirect
431. C2#10593648direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×#642592
#105936482
C2×C3⋊(A4⋊C8)2
C2×#54143
C2×#52183
C2×#37544