Finite Group Databasebeta

← C2×#10593180 #11921873

Subgroups — C2×#10593180 #11921873

Order 1152.

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

normal subgroups only

This group has 572 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×#64259C211yesmaximal, characteristic
2C2×C3×A4⋊Q8C211yesmaximal, characteristic
3C2×A4×C3⋊C8C211yesmaximal, characteristic
4#10593180C214yesmaximal, direct product factor
5C2×#5398—31nomaximal
6C2×#5051—31nomaximal
7C2×C3×C4×A4C2211yescharacteristic
8C2×C3⋊SL(2,ℤ/4)—21no—
9#64259—21no—
10#64259C2212yes—
11C2×C3×SL(2,ℤ/4)—21no—
12C3×A4⋊Q8—21no—
13C3×A4⋊Q8C2212yes—
14C2×#3719—41nomaximal
15A4×C3⋊C8C2212yes—
16C2×A4⋊Q8—31no—
17C2×A4⋊Q8—61no—
18C2×A4⋊Q8D311yescharacteristic
19C2×C3×C22⋊Q8—31no—
20C22×#216—31no—
21C2×#924—31no—
22C23×C3⋊C8D311yescharacteristic
23C2×C8×A4—31no—
24#5398—34no—
25C2×#835—31no—
26#5051—34no—
27#5051—34no—
28C2×#810—31no—
29C2×#807—31no—
30C22×C3×A4D411yescharacteristic
31C2×#634—41no—
32C2×C3×Dic6—41no—
33C3×C4×A4D411yescharacteristic
34C3×C4×A4C2311yescharacteristic
35C3⋊SL(2,ℤ/4)—22no—
36C3×SL(2,ℤ/4)—22no—
37C2×C3×C3⋊C8—41no—
38#3719—44no—
39C2×#467—91noSylow
40C22×C3×Q8—31no—
41C23×C3×C4C2×D311yescharacteristic
42C22×Dic6—31no—
43C2×C4×A4—21no—
44C2×C4×A4C2×D311yescharacteristic
45C2×SL(2,ℤ/4)—21no—
46C2×SL(2,ℤ/4)—62no—
47C2×SL(2,ℤ/4)—61no—
48A4⋊Q8—21no—
49A4⋊Q8—32no—
50A4⋊Q8—62no—
51A4⋊Q8—62no—
52A4⋊Q8—61no—
53A4⋊Q8C2×D312yes—
54C3×C22⋊Q8—32no—
55C3×C22⋊Q8—32no—
56C3×C22⋊Q8—61no—
57C3×C22⋊Q8—61no—
58C2×C3×C4⋊C4—31no—
59C2×C3×C4⋊C4—61no—
60C2×C3×C22⋊C4—61no—
61C2×#217—61no—
62C2×#216—34no—
63C2×#216—61no—
64C2×#216—62no—
65C2×#216—61no—
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—
74C22×C3⋊C8—32no—
75C22×C3⋊C8C2×D312yes—
76C2×Dic12—121no—
77C8×A4—32no—
78#835—34no—
79#810—34no—
80#807—34no—
81C2×C3×A4Q1612yescomplemented
82C2×C3×A4C2×D411yescharacteristic
83C2×C32×C4—41no—
84C2×C3⋊Dic3—81no—
85#634—42no—
86#634—81no—
87C2×C3×Dic3—81no—
88C3×Dic6—42no—
89C3×Dic6—81no—
90C3×C3⋊C8—42no—
91C22×Q16—91no—
92C23×C8—31no—
93C2×C22⋊Q8—31no—
94C2×C22⋊Q8—91no—
95#467—94no—
96#467—94no—
97C2×#107—91no—
98C2×#103—91no—
99C2×#103—91no—
100C24×C3D1211yescharacteristic
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—
109C22×C3×C4—31no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—61no—
114C22×C3×C4—61no—
115C22×C3×C4D1211yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C22×Dic3—61no—
118C22×Dic3—61no—
119C2×Dic6—32no—
120C2×Dic6—41no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6—121no—
127C2×Dic6—241no—
128C4×A4—21no—
129C4×A4—21no—
130C4×A4#6711yescharacteristic
131C4×A4C22×D311yescharacteristic
132SL(2,ℤ/4)—22no—
133SL(2,ℤ/4)—64no—
134SL(2,ℤ/4)—62no—
135C2×C3×C8—121no—
136C3×C4⋊C4—32no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—62no—
141C3×C22⋊C4—62no—
142#217—62no—
143#217—62no—
144#216—64no—
145#216—64no—
146C4⋊Dic3—32no—
147C4⋊Dic3—61no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—32no—
153C2×C3⋊C8—32no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8S411yescharacteristic
156Dic12—124no—
157C22×C32—41no—
158C3×A4C2×Q1611yescharacteristic, complemented
159C32×C4—41no—
160C32×C4—41no—
161C3⋊Dic3—82no—
162C3×Dic3—82no—
163C22×Q8—31no—
164C22×Q8—91no—
165C23×C4D3211yescharacteristic
166C2×Q16—94no—
167C2×Q16—181no—
168C2×Q16—182no—
169C2×Q16—181no—
170C22×C8—32no—
171C22×C8—91no—
172C22×C8—91no—
173C22×C8—92no—
174C22⋊Q8—32no—
175C22⋊Q8—32no—
176C22⋊Q8—61no—
177C22⋊Q8—61no—
178C22⋊Q8—92no—
179C22⋊Q8—92no—
180C22⋊Q8—181no—
181C22⋊Q8—181no—
182C2×C4⋊C4—31no—
183C2×C4⋊C4—61no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—181no—
186C2×C22⋊C4—61no—
187C2×C22⋊C4—181no—
188#107—94no—
189#103—94no—
190#103—94no—
191C23×C3—31no—
192C23×C3—31no—
193C23×C3—32no—
194C23×C3Dic1212yescomplemented
195C23×C3C2×D1211yescharacteristic
196C2×A4—22no—
197C2×A4—21no—
198C2×A4#21612yescomplemented
199C2×A4C2×#6711yescharacteristic
200C3×Q8—62no—
201C3×Q8—62no—
202C3×Q8—121no—
203C3×Q8—121no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—41no—
212C2×C3×C4—61no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—81no—
216C2×C3×C4—122no—
217C2×C3×C4—121no—
218C2×C3×C4—121no—
219C2×C3×C4C2×S411yescharacteristic
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—81no—
223C2×Dic3—121no—
224C2×Dic3—122no—
225C2×Dic3—121no—
226C2×Dic3—241no—
227C2×Dic3—242no—
228Dic6—42no—
229Dic6—62no—
230Dic6—62no—
231Dic6—81no—
232Dic6—122no—
233Dic6—121no—
234Dic6—121no—
235Dic6—242no—
236Dic6—241no—
237Dic6—242no—
238C3×C8—122no—
239C3⋊C8—32no—
240C3⋊C8C2×S412yes—
241C2×C32—42no—
242C2×C32—41no—
243C24#62611yescharacteristic
244C2×Q8—32no—
245C2×Q8—61no—
246C2×Q8—61no—
247C2×Q8—61no—
248C2×Q8—61no—
249C2×Q8—61no—
250C2×Q8—92no—
251C2×Q8—181no—
252C2×Q8—181no—
253C2×Q8—181no—
254C2×Q8—181no—
255C2×Q8—181no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—61no—
261C22×C4—61no—
262C22×C4—181no—
263C22×C4—181no—
264C22×C4#62611yescharacteristic
265C22×C4C2×D3211yescharacteristic
266Q16—184no—
267Q16—184no—
268C2×C8—31no—
269C2×C8—92no—
270C2×C8—92no—
271C2×C8—91no—
272C2×C8—92no—
273C2×C8—181no—
274C4⋊C4—32no—
275C4⋊C4—61no—
276C4⋊C4—62no—
277C4⋊C4—62no—
278C4⋊C4—92no—
279C4⋊C4—181no—
280C4⋊C4—182no—
281C4⋊C4—182no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—182no—
285C22⋊C4—182no—
286C22×C3—32no—
287C22×C3—31no—
288C22×C3—32no—
289C22×C3—32no—
290C22×C3—31no—
291C22×C3—31no—
292C22×C3—41no—
293C22×C3—61no—
294C22×C3—81no—
295C22×C3C2×Dic1211yescharacteristic, complemented
296C22×C3C4⋊S411yescharacteristic
297A4—21no—
298A4C2×#21611yescharacteristic, complemented
299C3×C4—31no—
300C3×C4—31no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—81no—
304C3×C4—81no—
305C3×C4—122no—
306C3×C4—122no—
307C3×C4C4⋊S411yescharacteristic
308C3×C4C22×S411yescharacteristic
309Dic3—82no—
310Dic3—122no—
311Dic3—122no—
312Dic3—242no—
313Dic3—244no—
314C32—41noSylow
315C23—31no—
316C23—31no—
317C23—32no—
318C23#371912yescomplemented
319C23C2×#62611yescharacteristic
320Q8—62no—
321Q8—62no—
322Q8—121no—
323Q8—121no—
324Q8—182no—
325Q8—182no—
326Q8—361no—
327Q8—361no—
328C2×C4—31no—
329C2×C4—31no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—61no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—121no—
339C2×C4—122no—
340C2×C4—121no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—361no—
344C2×C4—362no—
345C2×C4—361no—
346C2×C4D3×S411yescharacteristic
347C8—32no—
348C8—92no—
349C2×C3—31no—
350C2×C3—31no—
351C2×C3—32no—
352C2×C3—41no—
353C2×C3—42no—
354C2×C3—81no—
355C2×C3—82no—
356C2×C3#539812yescomplemented
357C2×C3C2×C4⋊S411yescharacteristic
358C22—32no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—32no—
363C22—32no—
364C22—61no—
365C22C2×#371911yescharacteristic, complemented
366C22#6420711yescharacteristic
367C4—31no—
368C4—31no—
369C4—122no—
370C4—122no—
371C4—362no—
372C4—362no—
373C4#6420711yescharacteristic
374C4C2×D3×S411yescharacteristic
375C3—41no—
376C3—81no—
377C3C2×#539811yescharacteristic, complemented
378C2—31no—
379C2—31no—
380C2—32no—
381C2#1059318012yesdirect product factor
382C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3D12
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. #10593180C2direct (N × H)
81. C2×C3×A4Q16semidirect
158. C3×A4C2×Q16semidirect
194. C23×C3Dic12semidirect
198. C2×A4#216semidirect
295. C22×C3C2×Dic12semidirect
298. A4C2×#216semidirect
318. C23#3719semidirect
356. C2×C3#5398semidirect
365. C22C2×#3719semidirect
377. C3C2×#5398semidirect
381. C2#10593180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642592
C2×C3×A4⋊Q82
C2×A4×C3⋊C82
#105931802
C2×#53983
C2×#50513
C2×#37194