Finite Group Databasebeta

← C2×#10593179 #11921869

Subgroups — C2×#10593179 #11921869

Order 1152.

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

normal subgroups only

This group has 724 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×C4⋊(C3⋊S4)C211yesmaximal, characteristic, complemented
2C2×C3×C4⋊S4C211yesmaximal, characteristic, complemented
3C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10593179C214yesmaximal, direct product factor
5C2×#5402—31nomaximal
6C2×#5038—31nomaximal
7C22×C3⋊S4—21no—
8C22×C3×S4—21no—
9C2×C3×C4×A4C2211yescharacteristic
10C4⋊(C3⋊S4)—21no—
11C4⋊(C3⋊S4)C2212yescomplemented
12C3×C4⋊S4—21no—
13C3×C4⋊S4C2212yescomplemented
14C2×#3714—41nomaximal
15A4×C3⋊C8C2212yescomplemented
16C2×C4⋊S4—31no—
17C2×C4⋊S4—61no—
18C2×C4⋊S4D311yescharacteristic, complemented
19C2×C3×#121—31no—
20C22×#213—31no—
21C2×#930—31no—
22C23×C3⋊C8D311yescharacteristic, complemented
23C2×C8×A4—31no—
24#5402—34no—
25C2×#832—31no—
26#5038—34no—
27#5038—34no—
28C2×#809—31no—
29C2×#807—31no—
30C22×C3×A4D411yescharacteristic
31C2×C3⋊S4—22no—
32C2×C3⋊S4—42no—
33C2×C3×S4—22no—
34C2×C3×S4—42no—
35C2×C4⋊(C3⋊D3)—41no—
36C2×C3×D12—41no—
37C3×C4×A4D411yescharacteristic
38C3×C4×A4C2311yescharacteristic
39C2×C3×C3⋊C8—41no—
40#3714—44no—
41C2×#466—91noSylow
42C22×S4—21no—
43C22×S4—62no—
44C22×S4—61no—
45C22×C3×D4—31no—
46C22×C3×D4—61no—
47C23×C3×C4C2×D311yescharacteristic
48C22×#67—61no—
49C22×D12—31no—
50C2×C4×A4—21no—
51C2×C4×A4C2×D311yescharacteristic
52C4⋊S4—21no—
53C4⋊S4—32no—
54C4⋊S4—62no—
55C4⋊S4—62no—
56C4⋊S4—61no—
57C4⋊S4C2×D312yescomplemented
58C3×#121—32no—
59C3×#121—32no—
60C3×#121—61no—
61C3×#121—61no—
62C2×C3×C4⋊C4—31no—
63C2×C3×C22⋊C4—61no—
64C2×#213—34no—
65C2×#213—61no—
66C2×#213—62no—
67C2×#213—61no—
68#930—32no—
69#930—32no—
70#930—61no—
71#930—61no—
72C2×(C2×D3)⋊C4—61no—
73C2×C4⋊Dic3—31no—
74C22×C3⋊C8—31no—
75C22×C3⋊C8—31no—
76C22×C3⋊C8—32no—
77C22×C3⋊C8C2×D312yescomplemented
78C2×D24—121no—
79C8×A4—32no—
80#832—34no—
81#809—34no—
82#807—34no—
83C22×C3⋊D3—81no—
84C22×C3×D3—81no—
85C2×C3×A4D812yescomplemented
86C2×C3×A4C2×D411yescharacteristic
87C3⋊S4—42no—
88C3×S4—42no—
89C2×C32×C4—41no—
90C4⋊(C3⋊D3)—42no—
91C4⋊(C3⋊D3)—81no—
92C3×D12—42no—
93C3×D12—81no—
94C3×C3⋊C8—42no—
95C22×D8—91no—
96C23×C8—31no—
97C2×#121—31no—
98C2×#121—91no—
99#466—94no—
100#466—94no—
101C2×#107—91no—
102C2×#102—91no—
103C2×#102—91no—
104C24×C3—61no—
105C24×C3D1211yescharacteristic
106C23×D3—61no—
107C22×A4—21no—
108C22×A4#6711yescharacteristic
109C2×S4—22no—
110C2×S4—42no—
111C2×S4—64no—
112C2×S4—62no—
113C2×S4—124no—
114C2×S4—122no—
115C2×C3×D4—32no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×C3×D4—62no—
121C2×C3×D4—62no—
122C2×C3×D4—61no—
123C2×C3×D4—122no—
124C2×C3×D4—122no—
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C22×C3×C4—61no—
130C22×C3×C4D1211yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C2×#67—62no—
133C2×#67—62no—
134C2×#67—122no—
135C2×#67—122no—
136C22×Dic3—61no—
137C2×D12—32no—
138C2×D12—41no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—121no—
145C2×D12—241no—
146C4×A4—21no—
147C4×A4—21no—
148C4×A4#6711yescharacteristic
149C4×A4C22×D311yescharacteristic
150C2×C3×C8—121no—
151C3×C4⋊C4—32no—
152C3×C4⋊C4—61no—
153C3×C22⋊C4—62no—
154C3×C22⋊C4—62no—
155#213—64no—
156#213—64no—
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—62no—
159C4⋊Dic3—32no—
160C4⋊Dic3—61no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—32no—
163C2×C3⋊C8—32no—
164C2×C3⋊C8—32no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8S411yescharacteristic, complemented
167D24—124no—
168C22×C32—41no—
169C2×C3⋊D3—82no—
170C2×C3⋊D3—162no—
171C2×C3×D3—82no—
172C2×C3×D3—162no—
173C3×A4C2×D811yescharacteristic, complemented
174C32×C4—41no—
175C32×C4—41no—
176C22×D4—31no—
177C22×D4—61no—
178C22×D4—91no—
179C22×D4—181no—
180C23×C4D3211yescharacteristic
181C2×D8—94no—
182C2×D8—181no—
183C2×D8—182no—
184C2×D8—181no—
185C22×C8—32no—
186C22×C8—91no—
187C22×C8—91no—
188C22×C8—92no—
189#121—32no—
190#121—32no—
191#121—61no—
192#121—61no—
193#121—92no—
194#121—92no—
195#121—181no—
196#121—181no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—91no—
199C2×C22⋊C4—61no—
200C2×C22⋊C4—181no—
201#107—94no—
202#102—94no—
203#102—94no—
204C23×C3—31no—
205C23×C3—31no—
206C23×C3—32no—
207C23×C3—62no—
208C23×C3—121no—
209C23×C3—122no—
210C23×C3—122no—
211C23×C3—121no—
212C23×C3D2412yescomplemented
213C23×C3C2×D1211yescharacteristic
214C22×D3—62no—
215C22×D3—81no—
216C22×D3—121no—
217C22×D3—122no—
218C22×D3—122no—
219C22×D3—121no—
220C22×D3—241no—
221C22×D3—242no—
222C2×A4—22no—
223C2×A4—21no—
224C2×A4#21312yescomplemented
225C2×A4C2×#6711yescharacteristic
226S4—42no—
227S4—124no—
228S4—122no—
229C3×D4—62no—
230C3×D4—62no—
231C3×D4—121no—
232C3×D4—124no—
233C3×D4—122no—
234C3×D4—122no—
235C3×D4—121no—
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—31no—
243C2×C3×C4—41no—
244C2×C3×C4—61no—
245C2×C3×C4—62no—
246C2×C3×C4—81no—
247C2×C3×C4—122no—
248C2×C3×C4C2×S411yescharacteristic
249#67—124no—
250#67—122no—
251#67—122no—
252C2×Dic3—62no—
253C2×Dic3—122no—
254D12—42no—
255D12—62no—
256D12—62no—
257D12—81no—
258D12—122no—
259D12—121no—
260D12—121no—
261D12—242no—
262D12—241no—
263D12—242no—
264C3×C8—122no—
265C3⋊C8—32no—
266C3⋊C8C2×S412yescomplemented
267C2×C32—41no—
268C2×C32—42no—
269C3⋊D3—162no—
270C3×D3—162no—
271C24—61no—
272C24—181no—
273C24#62611yescharacteristic
274C2×D4—32no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—62no—
280C2×D4—62no—
281C2×D4—61no—
282C2×D4—92no—
283C2×D4—122no—
284C2×D4—122no—
285C2×D4—181no—
286C2×D4—181no—
287C2×D4—181no—
288C2×D4—181no—
289C2×D4—182no—
290C2×D4—182no—
291C2×D4—181no—
292C2×D4—362no—
293C2×D4—362no—
294C22×C4—31no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—31no—
298C22×C4—61no—
299C22×C4—181no—
300C22×C4#62611yescharacteristic
301C22×C4C2×D3211yescharacteristic
302D8—184no—
303D8—184no—
304C2×C8—31no—
305C2×C8—92no—
306C2×C8—92no—
307C2×C8—91no—
308C2×C8—92no—
309C2×C8—181no—
310C4⋊C4—32no—
311C4⋊C4—61no—
312C4⋊C4—92no—
313C4⋊C4—181no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—182no—
317C22⋊C4—182no—
318C22×C3—32no—
319C22×C3—31no—
320C22×C3—31no—
321C22×C3—31no—
322C22×C3—32no—
323C22×C3—32no—
324C22×C3—41no—
325C22×C3—61no—
326C22×C3—81no—
327C22×C3—122no—
328C22×C3—122no—
329C22×C3—122no—
330C22×C3—242no—
331C22×C3—242no—
332C22×C3C2×D2411yescharacteristic, complemented
333C22×C3C4⋊S411yescharacteristic
334C2×D3—82no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—162no—
339C2×D3—242no—
340C2×D3—244no—
341C2×D3—242no—
342C2×D3—242no—
343C2×D3—482no—
344C2×D3—484no—
345A4—21no—
346A4C2×#21311yescharacteristic, complemented
347C3×C4—31no—
348C3×C4—31no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—81no—
352C3×C4—81no—
353C3×C4—122no—
354C3×C4C4⋊S411yescharacteristic
355C3×C4C22×S411yescharacteristic
356Dic3—122no—
357C32—41noSylow
358C23—31no—
359C23—31no—
360C23—32no—
361C23—62no—
362C23—121no—
363C23—122no—
364C23—122no—
365C23—121no—
366C23—182no—
367C23—361no—
368C23—362no—
369C23—362no—
370C23—361no—
371C23#371412yescomplemented
372C23C2×#62611yescharacteristic
373D4—62no—
374D4—62no—
375D4—121no—
376D4—124no—
377D4—122no—
378D4—122no—
379D4—121no—
380D4—182no—
381D4—182no—
382D4—361no—
383D4—364no—
384D4—362no—
385D4—362no—
386D4—361no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—61no—
395C2×C4—62no—
396C2×C4—122no—
397C2×C4—182no—
398C2×C4—362no—
399C2×C4D3×S411yescharacteristic
400C8—32no—
401C8—92no—
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#540212yescomplemented
411C2×C3C2×C4⋊S411yescharacteristic
412D3—162no—
413D3—242no—
414D3—482no—
415D3—484no—
416C22—32no—
417C22—31no—
418C22—31no—
419C22—31no—
420C22—32no—
421C22—32no—
422C22—61no—
423C22—122no—
424C22—122no—
425C22—122no—
426C22—242no—
427C22—242no—
428C22—362no—
429C22—362no—
430C22—362no—
431C22—722no—
432C22—722no—
433C22C2×#371411yescharacteristic, complemented
434C22#6420711yescharacteristic
435C4—31no—
436C4—31no—
437C4—122no—
438C4—362no—
439C4#6420711yescharacteristic
440C4C2×D3×S411yescharacteristic
441C3—41no—
442C3—81no—
443C3C2×#540211yescharacteristic, complemented
444C2—31no—
445C2—31no—
446C2—32no—
447C2—242no—
448C2—722no—
449C2#1059317912yesdirect product factor
450C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3D12
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×D8
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
1. C2×C4⋊(C3⋊S4)C2semidirect
2. C2×C3×C4⋊S4C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. #10593179C2direct (N × H)
11. C4⋊(C3⋊S4)C22semidirect
13. C3×C4⋊S4C22semidirect
15. A4×C3⋊C8C22semidirect
18. C2×C4⋊S4D3semidirect
22. C23×C3⋊C8D3semidirect
57. C4⋊S4C2×D3semidirect
77. C22×C3⋊C8C2×D3semidirect
85. C2×C3×A4D8semidirect
166. C2×C3⋊C8S4semidirect
173. C3×A4C2×D8semidirect
212. C23×C3D24semidirect
224. C2×A4#213semidirect
266. C3⋊C8C2×S4semidirect
332. C22×C3C2×D24semidirect
346. A4C2×#213semidirect
371. C23#3714semidirect
410. C2×C3#5402semidirect
433. C22C2×#3714semidirect
443. C3C2×#5402semidirect
449. C2#10593179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C2×C3×C4⋊S42
C2×A4×C3⋊C82
#105931792
C2×#54023
C2×#50383
C2×#37144