Finite Group Databasebeta

← C2×#10590597 #11863585

Subgroups — C2×#10590597 #11863585

Order 1152.

2153 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 2153 conjugacy classes of subgroups — too many to draw. Only its 252 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
1C22×#3802C211yesmaximal, characteristic
2C2×#64106C211yesmaximal, characteristic, complemented
3C22×#3716C212yesmaximal, complemented
4C2×C3×#809C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic, complemented
6#10590597C218yesmaximal, direct product factor
7C2×#4776—32nomaximal
8C23×D32—21no—
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#634C2211yescharacteristic, complemented
11C22×C3×D12C2212yes—
12C22×#625—21no—
13C2×#3802—22no—
14C2×#3802—28no—
15C2×#3802C2214yes—
16C2×C32×C4⋊C4C2211yescharacteristic, complemented
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)—21no—
19#64106—22no—
20#64106C2214yescomplemented
21C22×C3×C3⋊C8C2212yescomplemented
22C2×#3716—28no—
23C2×#3716C2218yescomplemented
24C3×#809C2218yescomplemented
25#63557C2214yescomplemented
26C22×D3×D4—32no—
27C22×#214—32no—
28C22×#204—32no—
29C2×#897—32no—
30C2×#897—61no—
31C2×C3×#102—32no—
32C2×(C2×D3)⋊C8—32no—
33C2×#809D312yescomplemented
34#4776—316no—
35C23×C3⋊D3D411yescharacteristic
36C23×C3×D3—22no—
37C22×D32—28no—
38C22×D32—24no—
39C22×D32—44no—
40C22×D32—44no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C2×C4×C3⋊D3—24no—
46C2×C4×C3⋊D3D412yes—
47C2×C4×C3⋊D3C2312yes—
48C2×#634—24no—
49C2×#634—21no—
50C2×#634C2312yescomplemented
51C2×C3×D12—22no—
52C2×C3×D12—24no—
53C2×C3×D12D418yes—
54C2×C3×D12C2314yes—
55C2×#625—28no—
56C2×#625—24no—
57#3802—216no—
58#3802—216no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4C2312yescomplemented
61#3752—24no—
62C4⋊(C3⋊Dic3)—24no—
63C2×C3×C3⋊C8—24no—
64C2×C3×C3⋊C8C2314yescomplemented
65#3716—216no—
66C2×#450—91noSylow
67C24×D3—62no—
68C22×C3×D4—32no—
69C22×#67—62no—
70C2×D3×D4—38no—
71C2×D3×D4—64no—
72C2×D3×D4—68no—
73C2×D3×D4—68no—
74C22×D12C2×D312yes—
75C22×C4×D3—32no—
76C22×C4×D3—61no—
77C22×Dic6—32no—
78C22×Dic6—61no—
79C22×C3×C8—32no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4C2×D312yescomplemented
82C2×#214—38no—
83C2×#214—68no—
84C2×(C2×D3)⋊C4—62no—
85C2×(C2×D3)⋊C4—62no—
86C2×C4⋊Dic3—62no—
87C2×C4⋊Dic3—62no—
88C22×C3⋊C8C2×D312yescomplemented
89C2×#204—38no—
90C2×#204—68no—
91#897—38no—
92#897—64no—
93#897—64no—
94#897—64no—
95C3×#102—38no—
96(C2×D3)⋊C8—38no—
97#809C2×D318yescomplemented
98C23×C32C2×D411yescharacteristic
99C22×C3⋊D3—22no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3SD1614yescomplemented
102C22×C3⋊D3C2×D412yes—
103C22×C3×D3—28no—
104C22×C3×D3—24no—
105C22×C3×D3—44no—
106C22×C3×D3—44no—
107C2×D32—216no—
108C2×D32—48no—
109C2×D32—432no—
110C2×D32—48no—
111C2×C32×C4—22no—
112C2×C32×C4—42no—
113C2×C32×C4C2×D414yes—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2411yescharacteristic
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—42no—
119C2×C3⋊Dic3C2×D412yes—
120C4×C3⋊D3—24no—
121C4×C3⋊D3—24no—
122#634—24no—
123#634—42no—
124C3×D12—28no—
125C3×D12—24no—
126C3×D12C2×D418yes—
127#625—216no—
128C3×C3⋊C8—24no—
129C23×D4—91no—
130C22×SD16—92no—
131C2×C22⋊Q8—91no—
132#450—98no—
133C2×#102—32no—
134C2×C22⋊C8—91no—
135C24×C3—62no—
136C23×D3—22no—
137C23×D3—32no—
138C23×D3—61no—
139C23×D3—68no—
140C23×D3—616no—
141C23×D3—128no—
142C23×D3—128no—
143C2×C3×D4—38no—
144C2×C3×D4—34no—
145C2×C3×D4—64no—
146C2×C3×D4—62no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4C22×D312yes—
151C2×#67—68no—
152C2×#67—616no—
153C22×Dic3—32no—
154C22×Dic3—61no—
155C22×Dic3—62no—
156C22×Dic3—62no—
157D3×D4—616no—
158D3×D4—632no—
159D3×D4—616no—
160C2×D12—24no—
161C2×D12—22no—
162C2×D12D1218yes—
163C2×D12C22×D314yes—
164C2×C4×D3—34no—
165C2×C4×D3—34no—
166C2×C4×D3—62no—
167C2×C4×D3—62no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×C4×D3—124no—
171C2×Dic6—34no—
172C2×Dic6—62no—
173C2×Dic6—64no—
174C2×Dic6—64no—
175C2×Dic6—62no—
176C2×Dic6—62no—
177C2×Dic6—124no—
178C2×C3×C8—34no—
179C2×C3×C8—64no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4C22×D314yescomplemented
184#214—616no—
185(C2×D3)⋊C4—68no—
186(C2×D3)⋊C4—68no—
187C4⋊Dic3—68no—
188C4⋊Dic3—68no—
189C2×C3⋊C8—24no—
190C2×C3⋊C8C22×D314yescomplemented
191#204—616no—
192C22×C32#12012yes—
193C22×C32C2×SD1612yes—
194C22×C32AGL(1,ℤ/8)12yes—
195C22×C32C22×D411yescharacteristic
196C2×C3⋊D3—22no—
197C2×C3⋊D3—22no—
198C2×C3⋊D3—28no—
199C2×C3⋊D3C2×SD1614yescomplemented
200C2×C3×D3—28no—
201C2×C3×D3—44no—
202C2×C3×D3—44no—
203C2×C3×D3—416no—
204D32—432no—
205C32×C4—42no—
206C32×C4#12012yes—
207C32×C4C22×D412yes—
208C3⋊Dic3—22no—
209C3⋊Dic3—42no—
210C25—181no—
211C22×Q8—91no—
212C22×D4—32no—
213C22×D4—94no—
214C22×D4—182no—
215C22×D4—181no—
216C22×D4—188no—
217C23×C4—91no—
218C2×SD16—98no—
219C2×SD16—188no—
220C22×C8—32no—
221C22⋊Q8—94no—
222C22⋊Q8—182no—
223C2×C4⋊C4—181no—
224C2×C4⋊C4D3211yescharacteristic, complemented
225C2×C22⋊C4—181no—
226#102—38no—
227C22⋊C8—94no—
228C23×C3—21no—
229C23×C3—68no—
230C23×C3—64no—
231C23×C3—124no—
232C23×C3—124no—
233C23×C3D3×D412yes—
234C22×D3—28no—
235C22×D3—24no—
236C22×D3—38no—
237C22×D3—34no—
238C22×D3—44no—
239C22×D3—44no—
240C22×D3—64no—
241C22×D3—62no—
242C22×D3—632no—
243C22×D3—64no—
244C22×D3—64no—
245C22×D3—122no—
246C22×D3—122no—
247C22×D3—1216no—
248C22×D3—1216no—
249C22×D3—1264no—
250C3×D4—38no—
251C3×D4—68no—
252C3×D4—64no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—21no—
256C2×C3×C4—24no—
257C2×C3×C4—21no—
258C2×C3×C4—44no—
259C2×C3×C4—44no—
260C2×C3×C4C2×D1214yes—
261C2×C3×C4D3×D414yes—
262C2×C3×C4D3×D412yes—
263C2×C3×C4C23×D312yes—
264#67—632no—
265C2×Dic3—34no—
266C2×Dic3—62no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—122no—
271C2×Dic3—124no—
272C2×Dic3—124no—
273D12—28no—
274D12—24no—
275D12C2×D1218yes—
276C4×D3—68no—
277C4×D3—64no—
278C4×D3—64no—
279C4×D3—124no—
280C4×D3—124no—
281Dic6—64no—
282Dic6—64no—
283Dic6—124no—
284Dic6—124no—
285Dic6—124no—
286C3×C8—64no—
287C3⋊C8—24no—
288C2×C32#45014yescomplemented
289C2×C32C2×#12011yescharacteristic
290C2×C32C22×SD1611yescharacteristic
291C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
292C3⋊D3—24no—
293C3×D3—48no—
294C24—62no—
295C24—91no—
296C24—184no—
297C24—188no—
298C24—364no—
299C24—364no—
300C2×Q8—92no—
301C2×Q8—181no—
302C2×Q8—184no—
303C2×D4—34no—
304C2×D4—38no—
305C2×D4—64no—
306C2×D4—62no—
307C2×D4—184no—
308C2×D4—1816no—
309C2×D4—1816no—
310C2×D4—188no—
311C22×C4—21no—
312C22×C4—91no—
313C22×C4—92no—
314C22×C4—92no—
315C22×C4—184no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318SD16—1816no—
319C2×C8—34no—
320C2×C8—64no—
321C4⋊C4—21no—
322C4⋊C4—184no—
323C4⋊C4C2×D3212yescomplemented
324C22⋊C4—184no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—68no—
330C22×C3—124no—
331C22×C3—124no—
332C22×C3—1216no—
333C22×C3#88214yes—
334C22×C3#91114yes—
335C22×C3D3×SD1614yes—
336C22×C3C2×D3×D412yes—
337C2×D3—28no—
338C2×D3—38no—
339C2×D3—44no—
340C2×D3—44no—
341C2×D3—416no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—616no—
346C2×D3—122no—
347C2×D3—122no—
348C2×D3—128no—
349C2×D3—1264no—
350C3×C4—22no—
351C3×C4—22no—
352C3×C4—44no—
353C3×C4—44no—
354C3×C4#88214yes—
355C3×C4C22×D1212yes—
356C3×C4C2×D3×D412yes—
357Dic3—64no—
358Dic3—122no—
359Dic3—124no—
360Dic3—124no—
361C32C2×#45011yescharacteristic, complemented, Sylow
362C23—64no—
363C23—68no—
364C23—92no—
365C23—94no—
366C23—124no—
367C23—124no—
368C23—1816no—
369C23—182no—
370C23—182no—
371C23—368no—
372C23—368no—
373C23—3632no—
374C23#381111yescharacteristic
375Q8—184no—
376Q8—362no—
377D4—38no—
378D4—64no—
379D4—68no—
380D4—1816no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—92no—
384C2×C4—182no—
385C2×C4—184no—
386C2×C4—184no—
387C2×C4—182no—
388C2×C4—362no—
389C2×C4D3×D1214yes—
390C2×C4#381111yescharacteristic
391C2×C4C22×D3211yescharacteristic
392C8—64no—
393C2×C3—21no—
394C2×C3—24no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—128no—
398C2×C3#477618yescomplemented
399C2×C3C2×#88212yes—
400C2×C3C2×#91112yes—
401C2×C3C2×D3×SD1612yes—
402D3—48no—
403D3—68no—
404D3—124no—
405C22—68no—
406C22—94no—
407C22—124no—
408C22—1216no—
409C22—124no—
410C22—182no—
411C22—188no—
412C22—182no—
413C22—3632no—
414C22#6392312yes—
415C22#6392712yes—
416C22#6394012yes—
417C22C2×#381111yescharacteristic
418C4—42no—
419C4—182no—
420C4—362no—
421C4#6392312yes—
422C4C2×D3×D1212yes—
423C3—21no—
424C3C2×#477612yescomplemented
425C2—128no—
426C2—184no—
427C2#1059059714yesdirect product factor
428C2C2×#6392311yescharacteristic
429C2C2×#6392711yescharacteristic
430C2C2×#6394011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3802C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64106C2semidirect
3. C22×#3716C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63557C2semidirect
6. #10590597C2direct (N × H)
10. C22×#634C22semidirect
16. C2×C32×C4⋊C4C22semidirect
20. #64106C22semidirect
21. C22×C3×C3⋊C8C22semidirect
23. C2×#3716C22semidirect
24. C3×#809C22semidirect
25. #63557C22semidirect
33. C2×#809D3semidirect
50. C2×#634C23semidirect
60. C32×C4⋊C4C23semidirect
64. C2×C3×C3⋊C8C23semidirect
81. C2×C3×C4⋊C4C2×D3semidirect
88. C22×C3⋊C8C2×D3semidirect
97. #809C2×D3semidirect
101. C22×C3⋊D3SD16semidirect
183. C3×C4⋊C4C22×D3semidirect
190. C2×C3⋊C8C22×D3semidirect
199. C2×C3⋊D3C2×SD16semidirect
224. C2×C4⋊C4D32semidirect
288. C2×C32#450semidirect
323. C4⋊C4C2×D32semidirect
361. C32C2×#450semidirect
398. C2×C3#4776semidirect
424. C3C2×#4776semidirect
427. C2#10590597direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C2×#641062
C22×#37162
C2×C3×#8092
C2×#635572
#105905972
C2×#47763