Finite Group Databasebeta

← C2×#10590606 #11863631

Subgroups — C2×#10590606 #11863631

Order 1152.

1797 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 1797 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×#3797C211yesmaximal, characteristic, complemented
2C2×#64104C211yesmaximal, characteristic
3C22×#3717C212yesmaximal, complemented
4C2×C3×#810C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic, complemented
6#10590606C218yesmaximal, direct product factor
7C2×#4806—32nomaximal
8C22×C4⋊(C3⋊D3)—21no—
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2212yes—
12C22×#627—21no—
13C22×#624—21no—
14C2×#3797—22no—
15C2×#3797—28no—
16C2×#3797C2214yescomplemented
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752—21no—
19#64104—22no—
20#64104C2214yes—
21C22×C3×C3⋊C8C2212yes—
22C2×#3717—28no—
23C2×#3717C2218yescomplemented
24C3×#810C2218yescomplemented
25#63557C2214yescomplemented
26C22×D3×Q8—32no—
27C22×#215—32no—
28C22×#204—32no—
29C2×#895—32no—
30C2×#895—61no—
31C2×C3×#103—32no—
32C2×(C2×D3)⋊C8—32no—
33C2×#810D312yescomplemented
34#4806—316no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3D411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4⋊(C3⋊D3)—24no—
41C2×C4⋊(C3⋊D3)—24no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—44no—
44C2×C4⋊(C3⋊D3)C2312yes—
45C2×C4×C3⋊D3—24no—
46C2×C4×C3⋊D3D412yes—
47C2×C4×C3⋊D3C2312yes—
48C22×C3×Dic3—22no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—24no—
51C2×C3×Dic6D418yescomplemented
52C2×C3×Dic6C2314yes—
53C2×#627—28no—
54C2×#627—24no—
55C2×#624—28no—
56C2×#624—24no—
57#3797—216no—
58#3797—216no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4C2312yes—
61#3752—24no—
62C2×C3×C3⋊C8—24no—
63C2×C3×C3⋊C8C2314yes—
64#3717—216no—
65C2×#448—91noSylow
66C22×C3×Q8—32no—
67C2×D3×Q8—38no—
68C2×D3×Q8—64no—
69C2×D3×Q8—68no—
70C2×D3×Q8—68no—
71C22×D12—32no—
72C22×D12—61no—
73C22×D12—62no—
74C22×D12—62no—
75C22×C4×D3—32no—
76C22×C4×D3—61no—
77C22×C4×D3—62no—
78C22×Dic6—62no—
79C22×Dic6C2×D312yes—
80C22×C3×C8—32no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4C2×D312yes—
83C2×#215—38no—
84C2×#215—68no—
85C2×(C2×D3)⋊C4—62no—
86C2×(C2×D3)⋊C4—62no—
87C22×C3⋊C8C2×D312yes—
88C2×#204—38no—
89C2×#204—68no—
90#895—38no—
91#895—64no—
92#895—64no—
93#895—64no—
94C3×#103—38no—
95(C2×D3)⋊C8—38no—
96#810C2×D318yescomplemented
97C23×C32C2×D411yescharacteristic
98C22×C3⋊D3—22no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3—42no—
102C22×C3⋊D3—42no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3SD1614yescomplemented
105C22×C3⋊D3C2×D412yes—
106C2×C32×C4—22no—
107C2×C32×C4—42no—
108C2×C32×C4C2×D414yes—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2411yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3C2×D412yes—
113C4⋊(C3⋊D3)—24no—
114C4⋊(C3⋊D3)—48no—
115C4⋊(C3⋊D3)—42no—
116C4×C3⋊D3—24no—
117C4×C3⋊D3—24no—
118C2×C3×Dic3—28no—
119C2×C3×Dic3—24no—
120C3×Dic6—28no—
121C3×Dic6—24no—
122C3×Dic6C2×D418yescomplemented
123#627—216no—
124#624—216no—
125C3×C3⋊C8—24no—
126C23×Q8—91no—
127C22×SD16—92no—
128C2×#121—91no—
129#448—98no—
130C2×#103—32no—
131C2×C22⋊C8—91no—
132C23×D3—32no—
133C23×D3—61no—
134C23×D3—62no—
135C23×D3—62no—
136C2×C3×Q8—38no—
137C2×C3×Q8—34no—
138C2×C3×Q8—64no—
139C2×C3×Q8—62no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—21no—
143C22×C3×C4—62no—
144C22×C3×C4C22×D312yes—
145C22×Dic3—22no—
146C22×Dic3—32no—
147C22×Dic3—61no—
148D3×Q8—616no—
149D3×Q8—632no—
150D3×Q8—616no—
151C2×D12—34no—
152C2×D12—62no—
153C2×D12—64no—
154C2×D12—64no—
155C2×D12—68no—
156C2×D12—68no—
157C2×D12—62no—
158C2×D12—62no—
159C2×D12—124no—
160C2×D12—128no—
161C2×D12—128no—
162C2×C4×D3—34no—
163C2×C4×D3—34no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—68no—
167C2×C4×D3—616no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×C4×D3—124no—
171C2×Dic6—24no—
172C2×Dic6—22no—
173C2×Dic6—68no—
174C2×Dic6—616no—
175C2×Dic6D1218yescomplemented
176C2×Dic6C22×D314yes—
177C2×C3×C8—34no—
178C2×C3×C8—64no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4C22×D314yes—
183#215—616no—
184(C2×D3)⋊C4—68no—
185(C2×D3)⋊C4—68no—
186C2×C3⋊C8—24no—
187C2×C3⋊C8C22×D314yes—
188#204—616no—
189C22×C32#12012yes—
190C22×C32C2×SD1612yes—
191C22×C32#13712yes—
192C22×C32C22×D411yescharacteristic
193C2×C3⋊D3—22no—
194C2×C3⋊D3—22no—
195C2×C3⋊D3—28no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—84no—
200C2×C3⋊D3C2×SD1614yescomplemented
201C32×C4—42no—
202C32×C4#12012yes—
203C32×C4C22×D412yes—
204C3⋊Dic3—22no—
205C3×Dic3—28no—
206C22×Q8—32no—
207C22×Q8—94no—
208C22×Q8—181no—
209C22×Q8—182no—
210C22×Q8—188no—
211C22×D4—91no—
212C22×D4—181no—
213C23×C4—91no—
214C23×C4—181no—
215C2×SD16—98no—
216C2×SD16—188no—
217C22×C8—32no—
218#121—94no—
219#121—182no—
220C2×C4⋊C4D3211yescharacteristic
221C2×C22⋊C4—181no—
222#103—38no—
223C22⋊C8—94no—
224C23×C3—21no—
225C23×C3D3×D412yes—
226C22×D3—38no—
227C22×D3—34no—
228C22×D3—64no—
229C22×D3—62no—
230C22×D3—64no—
231C22×D3—64no—
232C22×D3—64no—
233C22×D3—64no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—124no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—124no—
240C22×D3—124no—
241C22×D3—124no—
242C3×Q8—38no—
243C3×Q8—68no—
244C3×Q8—64no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—21no—
248C2×C3×C4—24no—
249C2×C3×C4—21no—
250C2×C3×C4—44no—
251C2×C3×C4—44no—
252C2×C3×C4—68no—
253C2×C3×C4—64no—
254C2×C3×C4C2×D1214yes—
255C2×C3×C4D3×D414yes—
256C2×C3×C4D3×D412yes—
257C2×C3×C4C23×D312yes—
258C2×Dic3—28no—
259C2×Dic3—24no—
260C2×Dic3—34no—
261C2×Dic3—62no—
262C2×Dic3—64no—
263C2×Dic3—122no—
264D12—64no—
265D12—64no—
266D12—124no—
267D12—124no—
268D12—1216no—
269D12—1216no—
270D12—124no—
271C4×D3—632no—
272C4×D3—68no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—124no—
276C4×D3—124no—
277Dic6—28no—
278Dic6—24no—
279Dic6—632no—
280Dic6C2×D1218yescomplemented
281C3×C8—64no—
282C3⋊C8—24no—
283C2×C32#44814yescomplemented
284C2×C32C2×#12011yescharacteristic
285C2×C32C22×SD1611yescharacteristic
286C2×C32C2×#13711yescharacteristic
287C3⋊D3—24no—
288C3⋊D3—82no—
289C24—91no—
290C24—181no—
291C2×Q8—34no—
292C2×Q8—38no—
293C2×Q8—64no—
294C2×Q8—62no—
295C2×Q8—184no—
296C2×Q8—188no—
297C2×Q8—1816no—
298C2×Q8—1816no—
299C2×D4—92no—
300C2×D4—184no—
301C2×D4—184no—
302C2×D4—181no—
303C2×D4—364no—
304C22×C4—21no—
305C22×C4—62no—
306C22×C4—91no—
307C22×C4—92no—
308C22×C4—92no—
309C22×C4—184no—
310C22×C4—188no—
311C22×C4—184no—
312C22×C4C2×D3211yescharacteristic
313SD16—1816no—
314C2×C8—34no—
315C2×C8—64no—
316C4⋊C4—21no—
317C4⋊C4C2×D3212yes—
318C22⋊C4—184no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3#88214yes—
324C22×C3D3×SD1614yes—
325C22×C3#91814yes—
326C22×C3C2×D3×D412yes—
327C2×D3—38no—
328C2×D3—64no—
329C2×D3—64no—
330C2×D3—64no—
331C2×D3—616no—
332C2×D3—122no—
333C2×D3—122no—
334C2×D3—128no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—124no—
338C2×D3—124no—
339C2×D3—124no—
340C2×D3—124no—
341C2×D3—248no—
342C2×D3—248no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—44no—
346C3×C4—44no—
347C3×C4—68no—
348C3×C4#88214yes—
349C3×C4C22×D1212yes—
350C3×C4C2×D3×D412yes—
351Dic3—28no—
352Dic3—64no—
353Dic3—122no—
354C32C2×#44811yescharacteristic, complemented, Sylow
355C23—92no—
356C23—94no—
357C23—182no—
358C23—182no—
359C23—182no—
360C23—362no—
361C23—362no—
362C23—362no—
363C23#381111yescharacteristic
364Q8—38no—
365Q8—64no—
366Q8—68no—
367Q8—1816no—
368D4—184no—
369D4—368no—
370D4—362no—
371C2×C4—22no—
372C2×C4—42no—
373C2×C4—64no—
374C2×C4—68no—
375C2×C4—92no—
376C2×C4—1816no—
377C2×C4—182no—
378C2×C4—184no—
379C2×C4—184no—
380C2×C4D3×D1214yes—
381C2×C4#381111yescharacteristic
382C2×C4C22×D3211yescharacteristic
383C8—64no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—24no—
387C2×C3—21no—
388C2×C3#480618yescomplemented
389C2×C3C2×#88212yes—
390C2×C3C2×D3×SD1612yes—
391C2×C3C2×#91812yes—
392D3—68no—
393D3—124no—
394D3—244no—
395D3—244no—
396C22—94no—
397C22—182no—
398C22—188no—
399C22—182no—
400C22—362no—
401C22—362no—
402C22—362no—
403C22—724no—
404C22#6392312yes—
405C22#6393012yes—
406C22#6394512yes—
407C22C2×#381111yescharacteristic
408C4—42no—
409C4—68no—
410C4—182no—
411C4#6392312yes—
412C4C2×D3×D1212yes—
413C3—21no—
414C3C2×#480612yescomplemented
415C2—184no—
416C2—722no—
417C2#1059060614yesdirect product factor
418C2C2×#6392311yescharacteristic
419C2C2×#6393011yescharacteristic
420C2C2×#6394511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#64104C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#448
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
1. C22×#3797C2semidirect
3. C22×#3717C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63557C2semidirect
6. #10590606C2direct (N × H)
16. C2×#3797C22semidirect
23. C2×#3717C22semidirect
24. C3×#810C22semidirect
25. #63557C22semidirect
33. C2×#810D3semidirect
51. C2×C3×Dic6D4semidirect
96. #810C2×D3semidirect
104. C22×C3⋊D3SD16semidirect
122. C3×Dic6C2×D4semidirect
175. C2×Dic6D12semidirect
200. C2×C3⋊D3C2×SD16semidirect
280. Dic6C2×D12semidirect
283. C2×C32#448semidirect
354. C32C2×#448semidirect
388. C2×C3#4806semidirect
414. C3C2×#4806semidirect
417. C2#10590606direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#641042
C22×#37172
C2×C3×#8102
C2×#635572
#105906062
C2×#48063