Finite Group Databasebeta

← C2×#10593189 #11921938

Subgroups — C2×#10593189 #11921938

Order 1152.

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

normal subgroups only

This group has 624 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×Dic6C211yesmaximal, characteristic
2C2×C3×A4⋊Q8C211yesmaximal, characteristic
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic
4#10593189C214yesmaximal, direct product factor
5C2×#5416—31nomaximal
6C2×#5050—31nomaximal
7C2×C3×C4×A4C2211yescharacteristic
8C2×Dic3×A4—21no—
9A4×Dic6—21no—
10A4×Dic6C2212yes—
11C2×C3×SL(2,ℤ/4)—21no—
12C3×A4⋊Q8—21no—
13C3×A4⋊Q8C2212yes—
14C2×#3718—41nomaximal
15C3⋊(A4⋊C8)C2212yes—
16C23×Dic6D311yescharacteristic
17C2×Q8×A4—31no—
18C2×A4⋊Q8D311yescharacteristic
19C2×C3×C22⋊Q8—31no—
20C22×#216—31no—
21C22×#216—31no—
22#5416—34no—
23C2×A4⋊C8—31no—
24C2×A4⋊C8—61no—
25C2×#830—31no—
26#5050—34no—
27#5050—34no—
28C2×#810—31no—
29C2×#810—31no—
30C22×C3×A4D411yescharacteristic
31C2×C3×Dic6—41no—
32C2×C3×Dic6—41no—
33C3×C4×A4D411yescharacteristic
34C3×C4×A4C2311yescharacteristic
35Dic3×A4—22no—
36C3×SL(2,ℤ/4)—22no—
37C2×C3⋊(C3⋊C8)—41no—
38#3718—44no—
39C2×#451—91noSylow
40C22×C3×Q8—31no—
41C23×C3×C4C2×D311yescharacteristic
42C23×Dic3—21no—
43C22×Dic6—21no—
44C22×Dic6—31no—
45C22×Dic6—31no—
46C22×Dic6—32no—
47C22×Dic6—61no—
48C22×Dic6—61no—
49C22×Dic6C2×D312yes—
50Q8×A4—32no—
51Q8×A4—61no—
52C2×C4×A4—21no—
53C2×C4×A4—61no—
54C2×C4×A4C2×D311yescharacteristic
55C2×SL(2,ℤ/4)—21no—
56A4⋊Q8—21no—
57A4⋊Q8C2×D312yes—
58C3×C22⋊Q8—32no—
59C3×C22⋊Q8—32no—
60C3×C22⋊Q8—61no—
61C3×C22⋊Q8—61no—
62C2×C3×C4⋊C4—31no—
63C2×C3×C4⋊C4—61no—
64C2×C3×C22⋊C4—61no—
65C2×#216—34no—
66C2×#216—34no—
67C2×#216—62no—
68C2×#216—62no—
69C2×#216—62no—
70C2×#216—61no—
71C2×#216—61no—
72C2×#216—121no—
73C22×C3⋊C8—31no—
74C22×C3⋊C8—31no—
75A4⋊C8—32no—
76A4⋊C8—62no—
77#830—32no—
78#830—32no—
79#810—34no—
80#810—34no—
81C2×C3×A4Q1612yescomplemented
82C2×C3×A4C2×D411yescharacteristic
83C2×C32×C4—41no—
84C2×C3×Dic3—81no—
85C2×C3×Dic3—81no—
86C3×Dic6—42no—
87C3×Dic6—42no—
88C3×Dic6—81no—
89C3×Dic6—81no—
90C3⋊(C3⋊C8)—42no—
91C23×Q8—31no—
92C22×Q16—91no—
93C22×Q16—91no—
94C2×C22⋊Q8—31no—
95#451—94no—
96#451—94no—
97C2×#103—91no—
98C2×#103—91no—
99C2×C22⋊C8—91no—
100C24×C3#6711yescharacteristic
101C22×A4—21no—
102C22×A4#6711yescharacteristic
103C2×C3×Q8—32no—
104C2×C3×Q8—61no—
105C2×C3×Q8—61no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×C3×Q8—121no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—61no—
115C22×C3×C4—61no—
116C22×C3×C4#6711yescharacteristic
117C22×C3×C4C22×D311yescharacteristic
118C22×Dic3—22no—
119C22×Dic3—61no—
120C22×Dic3—62no—
121C22×Dic3—61no—
122C2×Dic6—32no—
123C2×Dic6—32no—
124C2×Dic6—32no—
125C2×Dic6—31no—
126C2×Dic6—32no—
127C2×Dic6—32no—
128C2×Dic6—41no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×Dic6—62no—
133C2×Dic6—64no—
134C2×Dic6—61no—
135C2×Dic6—62no—
136C2×Dic6—61no—
137C2×Dic6S411yescharacteristic
138C4×A4—21no—
139C4×A4—21no—
140C4×A4—62no—
141C4×A4#6711yescharacteristic
142C4×A4C22×D311yescharacteristic
143SL(2,ℤ/4)—22no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4—62no—
148C3×C22⋊C4—62no—
149C3×C22⋊C4—62no—
150#216—68no—
151#216—64no—
152#216—64no—
153#216—124no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—121no—
161C2×C3⋊C8—241no—
162C22×C32—41no—
163C3×A4C2×Q1611yescharacteristic, complemented
164C32×C4—41no—
165C32×C4—41no—
166C3×Dic3—82no—
167C3×Dic3—82no—
168C22×Q8—31no—
169C22×Q8—32no—
170C22×Q8—61no—
171C22×Q8—91no—
172C22×Q8—91no—
173C22×Q8—92no—
174C22×Q8—181no—
175C22×Q8—181no—
176C23×C4—61no—
177C23×C4D3211yescharacteristic
178C2×Q16—94no—
179C2×Q16—94no—
180C2×Q16—181no—
181C2×Q16—182no—
182C2×Q16—182no—
183C2×Q16—182no—
184C2×Q16—181no—
185C22×C8—91no—
186C22×C8—91no—
187C22⋊Q8—32no—
188C22⋊Q8—32no—
189C22⋊Q8—61no—
190C22⋊Q8—61no—
191C2×C4⋊C4—31no—
192C2×C4⋊C4—61no—
193C2×C22⋊C4—61no—
194#103—94no—
195#103—94no—
196C22⋊C8—92no—
197C22⋊C8—92no—
198C23×C3—31no—
199C23×C3—31no—
200C23×C3—32no—
201C23×C3#21612yescomplemented
202C23×C3C2×#6711yescharacteristic
203C2×A4—22no—
204C2×A4—21no—
205C2×A4#21612yescomplemented
206C2×A4C2×#6711yescharacteristic
207C3×Q8—62no—
208C3×Q8—62no—
209C3×Q8—122no—
210C3×Q8—121no—
211C3×Q8—121no—
212C3×Q8—241no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—31no—
220C2×C3×C4—41no—
221C2×C3×C4—61no—
222C2×C3×C4—62no—
223C2×C3×C4—62no—
224C2×C3×C4—81no—
225C2×C3×C4—122no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4—241no—
229C2×C3×C4C2×S411yescharacteristic
230C2×Dic3—21no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—61no—
235C2×Dic3—62no—
236C2×Dic3—81no—
237Dic6—21no—
238Dic6—34no—
239Dic6—32no—
240Dic6—42no—
241Dic6—62no—
242Dic6—62no—
243Dic6—62no—
244Dic6—61no—
245Dic6—81no—
246Dic6C2×S412yes—
247C3⋊C8—62no—
248C3⋊C8—62no—
249C3⋊C8—122no—
250C3⋊C8—242no—
251C2×C32—42no—
252C2×C32—41no—
253C24#62511yescharacteristic
254C2×Q8—32no—
255C2×Q8—31no—
256C2×Q8—61no—
257C2×Q8—61no—
258C2×Q8—61no—
259C2×Q8—61no—
260C2×Q8—61no—
261C2×Q8—92no—
262C2×Q8—92no—
263C2×Q8—92no—
264C2×Q8—92no—
265C2×Q8—92no—
266C2×Q8—91no—
267C2×Q8—181no—
268C2×Q8—181no—
269C2×Q8—181no—
270C2×Q8—182no—
271C2×Q8—181no—
272C2×Q8—181no—
273C2×Q8—182no—
274C2×Q8—184no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—61no—
280C22×C4—61no—
281C22×C4—62no—
282C22×C4—181no—
283C22×C4—182no—
284C22×C4—181no—
285C22×C4#62511yescharacteristic
286C22×C4C2×D3211yescharacteristic
287Q16—184no—
288Q16—188no—
289Q16—184no—
290C2×C8—92no—
291C2×C8—92no—
292C2×C8—181no—
293C2×C8—181no—
294C2×C8—181no—
295C2×C8—181no—
296C4⋊C4—32no—
297C4⋊C4—61no—
298C4⋊C4—62no—
299C4⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22×C3—32no—
303C22×C3—31no—
304C22×C3—32no—
305C22×C3—32no—
306C22×C3—31no—
307C22×C3—31no—
308C22×C3—41no—
309C22×C3—61no—
310C22×C3—81no—
311C22×C3C2×#21611yescharacteristic, complemented
312C22×C3GL(2,ℤ/4)11yescharacteristic
313A4—21no—
314A4C2×#21611yescharacteristic, complemented
315C3×C4—31no—
316C3×C4—31no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—81no—
320C3×C4—81no—
321C3×C4—122no—
322C3×C4—122no—
323C3×C4—242no—
324C3×C4GL(2,ℤ/4)11yescharacteristic
325C3×C4C22×S411yescharacteristic
326Dic3—22no—
327Dic3—62no—
328Dic3—82no—
329C32—41noSylow
330C23—31no—
331C23—31no—
332C23—32no—
333C23#371812yescomplemented
334C23C2×#62511yescharacteristic
335Q8—32no—
336Q8—62no—
337Q8—61no—
338Q8—62no—
339Q8—94no—
340Q8—92no—
341Q8—121no—
342Q8—121no—
343Q8—182no—
344Q8—182no—
345Q8—182no—
346Q8—181no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—121no—
359C2×C4—122no—
360C2×C4—121no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—182no—
364C2×C4—181no—
365C2×C4—182no—
366C2×C4D3×S411yescharacteristic
367C8—182no—
368C8—182no—
369C2×C3—31no—
370C2×C3—31no—
371C2×C3—32no—
372C2×C3—41no—
373C2×C3—42no—
374C2×C3—81no—
375C2×C3—82no—
376C2×C3#541612yescomplemented
377C2×C3C2×GL(2,ℤ/4)11yescharacteristic
378C22—32no—
379C22—31no—
380C22—31no—
381C22—31no—
382C22—32no—
383C22—32no—
384C22—61no—
385C22C2×#371811yescharacteristic, complemented
386C22#6420911yescharacteristic
387C4—31no—
388C4—31no—
389C4—62no—
390C4—122no—
391C4—122no—
392C4—182no—
393C4#6420911yescharacteristic
394C4C2×D3×S411yescharacteristic
395C3—41no—
396C3—81no—
397C3C2×#541611yescharacteristic, complemented
398C2—31no—
399C2—31no—
400C2—32no—
401C2#1059318912yesdirect product factor
402C2C2×#6420911yescharacteristic
subgroupG/H
centerC22#64209
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3#67
prime radicalC22×C3×A4D4
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×Q16
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
4. #10593189C2direct (N × H)
81. C2×C3×A4Q16semidirect
163. C3×A4C2×Q16semidirect
201. C23×C3#216semidirect
205. C2×A4#216semidirect
311. C22×C3C2×#216semidirect
314. A4C2×#216semidirect
333. C23#3718semidirect
376. C2×C3#5416semidirect
385. C22C2×#3718semidirect
397. C3C2×#5416semidirect
401. C2#10593189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×Dic62
C2×C3×A4⋊Q82
C2×C3⋊(A4⋊C8)2
#105931892
C2×#54163
C2×#50503
C2×#37184