Finite Group Databasebeta

← C2×#10593182 #11921880

Subgroups — C2×#10593182 #11921880

Order 1152.

748 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 95 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×D3×A4C211yesmaximal, characteristic
2C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
3C2×C3×A4⋊C8C211yesmaximal, characteristic, complemented
4#10593182C214yesmaximal, direct product factor
5C2×#5409—31nomaximal
6C2×#4726—31nomaximal
7C22×D3×A4C411yescharacteristic
8C2×C3×C4×A4C2211yescharacteristic
9C2×Dic3×A4C411yescharacteristic
10C4×D3×A4C412yes—
11C4×D3×A4C2212yes—
12C2×#3711—41nomaximal
13C3⋊(A4⋊C8)C2212yescomplemented
14C3×A4⋊C8C2212yescomplemented
15C23×C4×D3D311yescharacteristic
16C22×C4×A4—31no—
17C22×ΓL(1,𝔽25)—31no—
18C22×ΓL(1,𝔽25)—31no—
19#5409—34no—
20C2×A4⋊C8—31no—
21C2×A4⋊C8—61no—
22C2×A4⋊C8D311yescharacteristic, complemented
23C2×C3×C22⋊C8—31no—
24C2×#830—31no—
25C2×(C2×D3)⋊C8—31no—
26C2×(C2×D3)⋊C8—31no—
27#4726—34no—
28#4726—34no—
29C22×C3×A4C2×C411yescharacteristic
30C2×D3×A4—22no—
31C2×D3×A4C2×C412yes—
32C2×C3×C4×D3—41no—
33C3×C4×A4C2×C411yescharacteristic
34C3×C4×A4C2311yescharacteristic
35Dic3×A4C2×C412yes—
36C2×C3⋊(C3⋊C8)—41no—
37C2×C3×C3⋊C8—41no—
38#3711—44no—
39C2×#407—91noSylow
40C24×D3Dic311yescharacteristic
41C23×A4—31no—
42C23×C3×C4C2×D311yescharacteristic
43C23×Dic3Dic311yescharacteristic
44C22×C4×D3—31no—
45C22×C4×D3—31no—
46C22×C4×D3—31no—
47C22×C4×D3—32no—
48C22×C4×D3—32no—
49C22×C4×D3—31no—
50C22×C4×D3Dic312yes—
51C22×C4×D3C2×D312yes—
52C2×C4×A4—21no—
53C2×C4×A4—31no—
54C2×C4×A4—32no—
55C2×C4×A4—32no—
56C2×C4×A4C2×D311yescharacteristic
57C22×C3×C8—31no—
58C22×C3×C8—31no—
59C2×#208—121no—
60C22×C3⋊C8—31no—
61C22×C3⋊C8—31no—
62C2×ΓL(1,𝔽25)—34no—
63C2×ΓL(1,𝔽25)—34no—
64C2×ΓL(1,𝔽25)—61no—
65C2×ΓL(1,𝔽25)—61no—
66C2×ΓL(1,𝔽25)—62no—
67C2×ΓL(1,𝔽25)—61no—
68C2×ΓL(1,𝔽25)—62no—
69C2×ΓL(1,𝔽25)—61no—
70A4⋊C8—32no—
71A4⋊C8—62no—
72A4⋊C8C2×D312yescomplemented
73C3×C22⋊C8—32no—
74C3×C22⋊C8—32no—
75#830—32no—
76#830—32no—
77(C2×D3)⋊C8—34no—
78(C2×D3)⋊C8—34no—
79C22×C3×D3—41no—
80C2×C3×A4M1612yescomplemented
81C2×C3×A4C22×C411yescharacteristic
82D3×A4—22no—
83C2×C32×C4—41no—
84C2×C3×Dic3—41no—
85C3×C4×D3—42no—
86C3×C4×D3—42no—
87C3⋊(C3⋊C8)—42no—
88C3×C3⋊C8—42no—
89C24×C4—31no—
90C22×M16—91no—
91C22×M16—91no—
92#407—94no—
93#407—94no—
94C2×C22⋊C8—31no—
95C2×C22⋊C8—91no—
96C2×C22⋊C8—91no—
97C2×C22⋊C8—91no—
98C24×C3C2×Dic311yescharacteristic
99C23×D3—22no—
100C23×D3—31no—
101C23×D3—31no—
102C23×D3—32no—
103C23×D3—62no—
104C23×D3C2×Dic312yes—
105C22×A4—21no—
106C22×A4—32no—
107C22×A4—62no—
108C22×A4C4×D311yescharacteristic
109C22×C3×C4—31no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—121no—
114C22×C3×C4C2×Dic311yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×Dic3—31no—
117C22×Dic3—31no—
118C22×Dic3—32no—
119C22×Dic3C2×Dic312yes—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—32no—
124C2×C4×D3—32no—
125C2×C4×D3—32no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—32no—
131C2×C4×D3—32no—
132C2×C4×D3—32no—
133C2×C4×D3—62no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—61no—
138C2×C4×D3S411yescharacteristic
139C4×A4—21no—
140C4×A4—21no—
141C4×A4—32no—
142C4×A4C4×D311yescharacteristic
143C4×A4C22×D311yescharacteristic
144C2×C3×C8—32no—
145C2×C3×C8—32no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150#208—124no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—32no—
153C2×C3⋊C8—41no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—121no—
159C2×C3⋊C8—241no—
160ΓL(1,𝔽25)—64no—
161ΓL(1,𝔽25)—64no—
162ΓL(1,𝔽25)—64no—
163ΓL(1,𝔽25)—64no—
164C22×C32—41no—
165C2×C3×D3—42no—
166C2×C3×D3—82no—
167C3×A4C2×M1611yescharacteristic, complemented
168C32×C4—41no—
169C32×C4—41no—
170C3×Dic3—42no—
171C25—31no—
172C23×C4—31no—
173C23×C4—32no—
174C23×C4—32no—
175C23×C4—91no—
176C23×C4—91no—
177C23×C4—92no—
178C23×C4—92no—
179C23×C4—91no—
180C23×C4—91no—
181C23×C4D3211yescharacteristic
182C2×M16—94no—
183C2×M16—94no—
184C2×M16—181no—
185C2×M16—182no—
186C2×M16—181no—
187C2×M16—182no—
188C2×M16—181no—
189C2×M16—181no—
190C22×C8—31no—
191C22×C8—31no—
192C22×C8—91no—
193C22×C8—91no—
194C22⋊C8—32no—
195C22⋊C8—32no—
196C22⋊C8—94no—
197C22⋊C8—94no—
198C22⋊C8—92no—
199C22⋊C8—92no—
200C23×C3—31no—
201C23×C3—31no—
202C23×C3—32no—
203C23×C3—121no—
204C23×C3#20812yescomplemented
205C23×C3C22×Dic311yescharacteristic
206C22×D3—22no—
207C22×D3—32no—
208C22×D3—34no—
209C22×D3—31no—
210C22×D3—32no—
211C22×D3—32no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—61no—
215C22×D3—62no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—62no—
219C22×D3SL(2,ℤ/4)11yescharacteristic
220C2×A4—22no—
221C2×A4—21no—
222C2×A4—62no—
223C2×A4ΓL(1,𝔽25)12yescomplemented
224C2×A4C2×C4×D311yescharacteristic
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—41no—
233C2×C3×C4—61no—
234C2×C3×C4—81no—
235C2×C3×C4—122no—
236C2×C3×C4—122no—
237C2×C3×C4—121no—
238C2×C3×C4C2×S411yescharacteristic
239C2×Dic3—31no—
240C2×Dic3—32no—
241C2×Dic3—32no—
242C2×Dic3—32no—
243C2×Dic3—61no—
244C2×Dic3SL(2,ℤ/4)11yescharacteristic
245C4×D3—32no—
246C4×D3—32no—
247C4×D3—32no—
248C4×D3—32no—
249C4×D3—32no—
250C4×D3—32no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3SL(2,ℤ/4)12yes—
254C4×D3C2×S412yes—
255C3×C8—62no—
256C3×C8—62no—
257C3⋊C8—42no—
258C3⋊C8—62no—
259C3⋊C8—62no—
260C3⋊C8—122no—
261C3⋊C8—242no—
262C2×C32—42no—
263C2×C32—41no—
264C3×D3—82no—
265C24—32no—
266C24—62no—
267C24—91no—
268C24—91no—
269C24—92no—
270C24—182no—
271C24D3×Dic311yescharacteristic
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—32no—
278C22×C4—92no—
279C22×C4—91no—
280C22×C4—92no—
281C22×C4—92no—
282C22×C4—92no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—92no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—92no—
289C22×C4—92no—
290C22×C4—92no—
291C22×C4—91no—
292C22×C4—92no—
293C22×C4—91no—
294C22×C4—181no—
295C22×C4—181no—
296C22×C4—181no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4D3×Dic311yescharacteristic
300C22×C4C2×D3211yescharacteristic
301M16—184no—
302M16—184no—
303M16—184no—
304M16—184no—
305C2×C8—32no—
306C2×C8—32no—
307C2×C8—61no—
308C2×C8—61no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—92no—
312C2×C8—92no—
313C2×C8—181no—
314C2×C8—181no—
315C2×C8—181no—
316C2×C8—181no—
317C22×C3—32no—
318C22×C3—31no—
319C22×C3—32no—
320C22×C3—32no—
321C22×C3—31no—
322C22×C3—31no—
323C22×C3—41no—
324C22×C3—61no—
325C22×C3—81no—
326C22×C3—122no—
327C22×C3—242no—
328C22×C3C2×#20811yescharacteristic, complemented
329C22×C3C2×SL(2,ℤ/4)11yescharacteristic
330C2×D3—22no—
331C2×D3—34no—
332C2×D3—32no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—64no—
336C2×D3—64no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3C2×SL(2,ℤ/4)12yes—
340A4—21no—
341A4C2×ΓL(1,𝔽25)11yescharacteristic, complemented
342C3×C4—31no—
343C3×C4—31no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—81no—
347C3×C4—81no—
348C3×C4—122no—
349C3×C4C2×SL(2,ℤ/4)11yescharacteristic
350C3×C4C22×S411yescharacteristic
351Dic3—32no—
352Dic3C2×SL(2,ℤ/4)12yes—
353C32—41noSylow
354C23—31no—
355C23—31no—
356C23—32no—
357C23—31no—
358C23—62no—
359C23—92no—
360C23—92no—
361C23—92no—
362C23—94no—
363C23—91no—
364C23—182no—
365C23—182no—
366C23—182no—
367C23—181no—
368C23—184no—
369C23—182no—
370C23—184no—
371C23#371112yescomplemented
372C23C2×D3×Dic311yescharacteristic
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—32no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—32no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—61no—
384C2×C4—92no—
385C2×C4—92no—
386C2×C4—92no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—92no—
390C2×C4—91no—
391C2×C4—92no—
392C2×C4—92no—
393C2×C4—92no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—181no—
397C2×C4D3×S411yescharacteristic
398C8—62no—
399C8—62no—
400C8—182no—
401C8—182no—
402C2×C3—31no—
403C2×C3—31no—
404C2×C3—32no—
405C2×C3—41no—
406C2×C3—42no—
407C2×C3—81no—
408C2×C3—82no—
409C2×C3—242no—
410C2×C3#540912yescomplemented
411C2×C3C22×SL(2,ℤ/4)11yescharacteristic
412D3—22no—
413D3—62no—
414C22—32no—
415C22—31no—
416C22—31no—
417C22—31no—
418C22—32no—
419C22—32no—
420C22—32no—
421C22—61no—
422C22—62no—
423C22—94no—
424C22—92no—
425C22—182no—
426C22—182no—
427C22—184no—
428C22—182no—
429C22—184no—
430C22—182no—
431C22C2×#371111yescharacteristic, complemented
432C22D3×SL(2,ℤ/4)11yescharacteristic
433C4—31no—
434C4—31no—
435C4—32no—
436C4—92no—
437C4D3×SL(2,ℤ/4)11yescharacteristic
438C4C2×D3×S411yescharacteristic
439C3—41no—
440C3—81no—
441C3C2×#540911yescharacteristic, complemented
442C2—31no—
443C2—31no—
444C2—32no—
445C2—62no—
446C2—182no—
447C2#1059318212yesdirect product factor
448C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutatorC2×C3×A4C22×C4
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3C2×Dic3
prime radicalC22×D3×A4C4
cosocleC3×C4×A4C23
hypocenterC3×A4C2×M16
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊(A4⋊C8)C2semidirect
3. C2×C3×A4⋊C8C2semidirect
4. #10593182C2direct (N × H)
13. C3⋊(A4⋊C8)C22semidirect
14. C3×A4⋊C8C22semidirect
22. C2×A4⋊C8D3semidirect
72. A4⋊C8C2×D3semidirect
80. C2×C3×A4M16semidirect
167. C3×A4C2×M16semidirect
204. C23×C3#208semidirect
223. C2×A4ΓL(1,𝔽25)semidirect
328. C22×C3C2×#208semidirect
341. A4C2×ΓL(1,𝔽25)semidirect
371. C23#3711semidirect
410. C2×C3#5409semidirect
431. C22C2×#3711semidirect
441. C3C2×#5409semidirect
447. C2#10593182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D3×A42
C2×C3⋊(A4⋊C8)2
C2×C3×A4⋊C82
#105931822
C2×#54093
C2×#47263
C2×#37114