Finite Group Databasebeta

← C2×#10593185 #11921928

Subgroups — C2×#10593185 #11921928

Order 1152.

736 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 71 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×A4×D12C211yesmaximal, characteristic
2C2×C3×A4⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic, complemented
4#10593185C214yesmaximal, direct product factor
5C2×#5414—31nomaximal
6C2×#5046—31nomaximal
7C22×D3×A4—21no—
8C2×C3×C4×A4C2211yescharacteristic
9A4×D12—21no—
10A4×D12C2212yes—
11C2×C3×SL(2,ℤ/4)—21no—
12C3×A4⋊Q8—21no—
13C3×A4⋊Q8C2212yescomplemented
14C2×#3715—41nomaximal
15C3⋊(A4⋊C8)C2212yescomplemented
16C23×D12D311yescharacteristic
17C2×D4×A4—31no—
18C2×A4⋊Q8D311yescharacteristic, complemented
19C2×C3×C22⋊Q8—31no—
20C22×#215—31no—
21C22×#215—31no—
22#5414—34no—
23C2×A4⋊C8—31no—
24C2×A4⋊C8—61no—
25C2×#830—31no—
26#5046—34no—
27#5046—34no—
28C2×#809—31no—
29C2×#809—31no—
30C22×C3×A4D411yescharacteristic
31C2×D3×A4—22no—
32C2×D3×A4—42no—
33C2×C3×D12—41no—
34C2×C3×Dic6—41no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37C3×SL(2,ℤ/4)—22no—
38C2×C3⋊(C3⋊C8)—41no—
39#3715—44no—
40C2×#450—91noSylow
41C24×D3—21no—
42C23×A4—61no—
43C22×C3×Q8—31no—
44C23×C3×C4C2×D311yescharacteristic
45C22×D12—21no—
46C22×D12—31no—
47C22×D12—31no—
48C22×D12—32no—
49C22×D12—61no—
50C22×D12—61no—
51C22×D12C2×D312yes—
52D4×A4—32no—
53D4×A4—61no—
54C2×C4×A4—21no—
55C2×C4×A4C2×D311yescharacteristic
56C2×SL(2,ℤ/4)—21no—
57A4⋊Q8—21no—
58A4⋊Q8C2×D312yescomplemented
59C3×C22⋊Q8—32no—
60C3×C22⋊Q8—32no—
61C3×C22⋊Q8—61no—
62C3×C22⋊Q8—61no—
63C2×C3×C4⋊C4—31no—
64C2×C3×C4⋊C4—61no—
65C2×C3×C22⋊C4—61no—
66C2×#215—34no—
67C2×#215—34no—
68C2×#215—62no—
69C2×#215—62no—
70C2×#215—62no—
71C2×#215—61no—
72C2×#215—61no—
73C2×#214—121no—
74C22×C3⋊C8—31no—
75C22×C3⋊C8—31no—
76A4⋊C8—32no—
77A4⋊C8—62no—
78#830—32no—
79#830—32no—
80#809—34no—
81#809—34no—
82C22×C3×D3—81no—
83C2×C3×A4SD1612yescomplemented
84C2×C3×A4C2×D411yescharacteristic
85D3×A4—42no—
86C2×C32×C4—41no—
87C2×C3×Dic3—81no—
88C3×D12—42no—
89C3×D12—81no—
90C3×Dic6—42no—
91C3×Dic6—81no—
92C3⋊(C3⋊C8)—42no—
93C23×D4—31no—
94C22×SD16—91no—
95C22×SD16—91no—
96C2×C22⋊Q8—31no—
97#450—94no—
98#450—94no—
99C2×#102—91no—
100C2×#102—91no—
101C2×C22⋊C8—91no—
102C24×C3#6711yescharacteristic
103C23×D3—22no—
104C23×D3—42no—
105C23×D3—61no—
106C23×D3—62no—
107C23×D3—61no—
108C23×D3—122no—
109C22×A4—21no—
110C22×A4—62no—
111C22×A4—122no—
112C22×A4#6711yescharacteristic
113C2×C3×Q8—32no—
114C2×C3×Q8—61no—
115C2×C3×Q8—61no—
116C2×C3×Q8—61no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×C3×D4—121no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C2×D12—32no—
129C2×D12—32no—
130C2×D12—32no—
131C2×D12—31no—
132C2×D12—32no—
133C2×D12—32no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—62no—
138C2×D12—64no—
139C2×D12—61no—
140C2×D12—62no—
141C2×D12—61no—
142C2×D12S411yescharacteristic
143C2×Dic6—41no—
144C4×A4—21no—
145C4×A4—21no—
146C4×A4#6711yescharacteristic
147C4×A4C22×D311yescharacteristic
148SL(2,ℤ/4)—22no—
149C3×C4⋊C4—32no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—62no—
152C3×C4⋊C4—62no—
153C3×C22⋊C4—62no—
154C3×C22⋊C4—62no—
155#215—68no—
156#215—64no—
157#215—64no—
158#214—124no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—32no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—121no—
166C2×C3⋊C8—241no—
167C22×C32—41no—
168C2×C3×D3—82no—
169C2×C3×D3—162no—
170C3×A4C2×SD1611yescharacteristic, complemented
171C32×C4—41no—
172C32×C4—41no—
173C3×Dic3—82no—
174C25—61no—
175C22×Q8—31no—
176C22×D4—32no—
177C22×D4—61no—
178C22×D4—91no—
179C22×D4—91no—
180C22×D4—92no—
181C22×D4—181no—
182C22×D4—181no—
183C23×C4D3211yescharacteristic
184C2×SD16—94no—
185C2×SD16—94no—
186C2×SD16—181no—
187C2×SD16—182no—
188C2×SD16—182no—
189C2×SD16—182no—
190C2×SD16—181no—
191C22×C8—91no—
192C22×C8—91no—
193C22⋊Q8—32no—
194C22⋊Q8—32no—
195C22⋊Q8—61no—
196C22⋊Q8—61no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—61no—
199C2×C22⋊C4—61no—
200#102—94no—
201#102—94no—
202C22⋊C8—92no—
203C22⋊C8—92no—
204C23×C3—31no—
205C23×C3—31no—
206C23×C3—32no—
207C23×C3—241no—
208C23×C3#21412yescomplemented
209C23×C3C2×#6711yescharacteristic
210C22×D3—21no—
211C22×D3—42no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—61no—
216C22×D3—62no—
217C22×D3—122no—
218C22×D3—122no—
219C22×D3—124no—
220C22×D3—124no—
221C22×D3—122no—
222C22×D3—122no—
223C22×D3—122no—
224C2×A4—22no—
225C2×A4—21no—
226C2×A4—122no—
227C2×A4#21512yescomplemented
228C2×A4C2×#6711yescharacteristic
229C3×Q8—62no—
230C3×Q8—62no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×D4—122no—
234C3×D4—241no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—41no—
243C2×C3×C4—61no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—81no—
247C2×C3×C4—122no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4C2×S411yescharacteristic
251C2×Dic3—81no—
252D12—21no—
253D12—34no—
254D12—32no—
255D12—62no—
256D12—62no—
257D12—62no—
258D12—61no—
259D12C2×S412yes—
260Dic6—42no—
261Dic6—81no—
262C3⋊C8—62no—
263C3⋊C8—62no—
264C3⋊C8—122no—
265C3⋊C8—242no—
266C2×C32—42no—
267C2×C32—41no—
268C3×D3—162no—
269C24—62no—
270C24—122no—
271C24—181no—
272C24—181no—
273C24—182no—
274C24—362no—
275C24#62511yescharacteristic
276C2×Q8—32no—
277C2×Q8—61no—
278C2×Q8—61no—
279C2×Q8—61no—
280C2×Q8—61no—
281C2×Q8—61no—
282C2×D4—31no—
283C2×D4—92no—
284C2×D4—92no—
285C2×D4—92no—
286C2×D4—92no—
287C2×D4—92no—
288C2×D4—91no—
289C2×D4—181no—
290C2×D4—181no—
291C2×D4—181no—
292C2×D4—182no—
293C2×D4—181no—
294C2×D4—181no—
295C2×D4—182no—
296C2×D4—184no—
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—31no—
300C22×C4—31no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4#62511yescharacteristic
304C22×C4C2×D3211yescharacteristic
305SD16—184no—
306SD16—188no—
307SD16—184no—
308C2×C8—92no—
309C2×C8—92no—
310C2×C8—181no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8—181no—
314C4⋊C4—32no—
315C4⋊C4—61no—
316C4⋊C4—62no—
317C4⋊C4—62no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22×C3—32no—
321C22×C3—31no—
322C22×C3—32no—
323C22×C3—32no—
324C22×C3—31no—
325C22×C3—31no—
326C22×C3—41no—
327C22×C3—61no—
328C22×C3—81no—
329C22×C3—242no—
330C22×C3—482no—
331C22×C3C2×#21411yescharacteristic, complemented
332C22×C3GL(2,ℤ/4)11yescharacteristic
333C2×D3—22no—
334C2×D3—42no—
335C2×D3—62no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—124no—
339C2×D3—124no—
340C2×D3—122no—
341C2×D3—122no—
342C2×D3—122no—
343A4—21no—
344A4C2×#21511yescharacteristic, complemented
345C3×C4—31no—
346C3×C4—31no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—81no—
350C3×C4—81no—
351C3×C4—122no—
352C3×C4—122no—
353C3×C4GL(2,ℤ/4)11yescharacteristic
354C3×C4C22×S411yescharacteristic
355Dic3—82no—
356C32—41noSylow
357C23—31no—
358C23—31no—
359C23—32no—
360C23—61no—
361C23—122no—
362C23—182no—
363C23—182no—
364C23—182no—
365C23—182no—
366C23—181no—
367C23—362no—
368C23—362no—
369C23—362no—
370C23—364no—
371C23—362no—
372C23—362no—
373C23—364no—
374C23#371512yescomplemented
375C23C2×#62511yescharacteristic
376Q8—62no—
377Q8—62no—
378Q8—121no—
379Q8—121no—
380D4—32no—
381D4—61no—
382D4—94no—
383D4—92no—
384D4—182no—
385D4—182no—
386D4—182no—
387D4—181no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—61no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—121no—
399C2×C4—122no—
400C2×C4—121no—
401C2×C4D3×S411yescharacteristic
402C8—182no—
403C8—182no—
404C2×C3—31no—
405C2×C3—31no—
406C2×C3—32no—
407C2×C3—41no—
408C2×C3—42no—
409C2×C3—81no—
410C2×C3—82no—
411C2×C3—482no—
412C2×C3#541412yescomplemented
413C2×C3C2×GL(2,ℤ/4)11yescharacteristic
414D3—42no—
415D3—122no—
416C22—32no—
417C22—31no—
418C22—31no—
419C22—31no—
420C22—32no—
421C22—32no—
422C22—61no—
423C22—62no—
424C22—122no—
425C22—182no—
426C22—362no—
427C22—362no—
428C22—364no—
429C22—362no—
430C22—362no—
431C22—364no—
432C22—362no—
433C22C2×#371511yescharacteristic, complemented
434C22#6420911yescharacteristic
435C4—31no—
436C4—31no—
437C4—122no—
438C4—122no—
439C4#6420911yescharacteristic
440C4C2×D3×S411yescharacteristic
441C3—41no—
442C3—81no—
443C3C2×#541411yescharacteristic, complemented
444C2—31no—
445C2—31no—
446C2—32no—
447C2—122no—
448C2—362no—
449C2#1059318512yesdirect product factor
450C2C2×#6420911yescharacteristic
subgroupG/H
centerC22#64209
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3#67
prime radicalC2×A4×D12C2
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×SD16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×A4⋊Q8C2semidirect
3. C2×C3⋊(A4⋊C8)C2semidirect
4. #10593185C2direct (N × H)
13. C3×A4⋊Q8C22semidirect
15. C3⋊(A4⋊C8)C22semidirect
18. C2×A4⋊Q8D3semidirect
58. A4⋊Q8C2×D3semidirect
83. C2×C3×A4SD16semidirect
170. C3×A4C2×SD16semidirect
208. C23×C3#214semidirect
227. C2×A4#215semidirect
331. C22×C3C2×#214semidirect
344. A4C2×#215semidirect
374. C23#3715semidirect
412. C2×C3#5414semidirect
433. C22C2×#3715semidirect
443. C3C2×#5414semidirect
449. C2#10593185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×D122
C2×C3×A4⋊Q82
C2×C3⋊(A4⋊C8)2
#105931852
C2×#54143
C2×#50463
C2×#37154