Finite Group Databasebeta

← C2×#10591694 #11808309

Subgroups — C2×#10591694 #11808309

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic
2C22×C3×#217C212yesmaximal
3C22×#3724C211yesmaximal, characteristic, complemented
4C2×#63579C212yesmaximal, complemented
5C2×#63579C211yesmaximal, characteristic, complemented
6#10591694C218yesmaximal, direct product factor
7C2×#4952—32nomaximal
8C25×C32C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×#3757—24no—
14C2×#3757C2214yes—
15C2×C3×#217—28no—
16C2×C3×#217C2218yes—
17C2×#3724—24no—
18C2×#3724C2214yescomplemented
19#63579C2214yescomplemented
20#63579C2218yescomplemented
21C22×C3×C22⋊C4—32no—
22C22×#217—32no—
23C22×#217—61no—
24C22×#217D312yes—
25C22×Dic3⋊C4—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29#4952—316no—
30C24×C32—22no—
31C24×C32—22no—
32C24×C32—24no—
33C24×C32—24no—
34C24×C32D414yes—
35C24×C32C2312yes—
36C24×C32C2311yescharacteristic
37C22×C3⋊Dic3—24no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—24no—
40C22×C3⋊Dic3D414yes—
41C22×C3⋊Dic3C2312yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3×Dic3—24no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2314yes—
51#3757—28no—
52C3×#217—216no—
53#3724—28no—
54C2×#397—91noSylow
55C25×C3—21no—
56C25×C3C2×D312yes—
57C23×C3×C4—32no—
58C23×C3×C4—32no—
59C23×Dic3—32no—
60C23×Dic3—32no—
61C23×Dic3—61no—
62C23×Dic3—61no—
63C23×Dic3C2×D312yes—
64C23×Dic3C2×D312yes—
65C2×C3×C22⋊C4—38no—
66C2×C3×C22⋊C4—68no—
67C2×#217—28no—
68C2×#217—38no—
69C2×#217—64no—
70C2×#217—68no—
71C2×#217—68no—
72C2×#217C2×D318yes—
73C2×Dic3⋊C4—38no—
74C2×Dic3⋊C4—68no—
75C3⋊#95—38no—
76C3⋊#95—38no—
77C3⋊#95—38no—
78C23×C32—28no—
79C23×C32—22no—
80C23×C32—22no—
81C23×C32—216no—
82C23×C32—24no—
83C23×C32—24no—
84C23×C32—44no—
85C23×C32—44no—
86C23×C32—48no—
87C23×C32C2×D412yes—
88C23×C32C2×D414yes—
89C23×C32C2×D412yes—
90C23×C32#4114yes—
91C23×C32#4114yes—
92C23×C32#4112yes—
93C23×C32C2411yescharacteristic
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—28no—
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—44no—
99C2×C3⋊Dic3C2×D414yes—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—48no—
107C2×C3×Dic3—48no—
108C22×C4⋊C4—91no—
109C22×C22⋊C4—32no—
110C22×C22⋊C4—91no—
111#397—98no—
112C2×#95—92no—
113C2×#95—91no—
114C24×C3—24no—
115C24×C3—24no—
116C24×C3—24no—
117C24×C3—24no—
118C24×C3—24no—
119C24×C3—24no—
120C24×C3—24no—
121C24×C3—24no—
122C24×C3—24no—
123C24×C3—22no—
124C24×C3—21no—
125C24×C3—44no—
126C24×C3—44no—
127C24×C3#6718yes—
128C24×C3C22×D314yes—
129C24×C3C22×D312yes—
130C22×C3×C4—34no—
131C22×C3×C4—34no—
132C22×C3×C4—64no—
133C22×C3×C4—64no—
134C22×C3×C4—64no—
135C22×C3×C4—64no—
136C22×C3×C4—64no—
137C22×C3×C4—64no—
138C22×Dic3—24no—
139C22×Dic3—24no—
140C22×Dic3—24no—
141C22×Dic3—24no—
142C22×Dic3—24no—
143C22×Dic3—24no—
144C22×Dic3—38no—
145C22×Dic3—34no—
146C22×Dic3—34no—
147C22×Dic3—64no—
148C22×Dic3—62no—
149C22×Dic3—62no—
150C22×Dic3—64no—
151C22×Dic3—64no—
152C22×Dic3—64no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—124no—
157C22×Dic3—124no—
158C22×Dic3C22×D314yes—
159C22×Dic3C22×D314yes—
160C3×C22⋊C4—616no—
161#217—216no—
162#217—616no—
163#217—616no—
164Dic3⋊C4—616no—
165C22×C32—24no—
166C22×C32—28no—
167C22×C32—42no—
168C22×C32—42no—
169C22×C32—44no—
170C22×C32—416no—
171C22×C32#12114yes—
172C22×C32#12314yes—
173C22×C32#12318yes—
174C22×C32#12414yes—
175C22×C32#12618yes—
176C22×C32C22×D411yescharacteristic
177C22×C32C22×D411yescharacteristic
178C22×C32C2×#4112yes—
179C22×C32C2×#4112yes—
180C22×C32C2×#4111yescharacteristic
181C3⋊Dic3—24no—
182C3⋊Dic3—42no—
183C3×Dic3—44no—
184C3×Dic3—44no—
185C25D3211yescharacteristic
186C23×C4—32no—
187C23×C4—32no—
188C23×C4—91no—
189C23×C4—91no—
190C2×C4⋊C4—94no—
191C2×C4⋊C4—184no—
192C2×C22⋊C4—38no—
193C2×C22⋊C4—68no—
194C2×C22⋊C4—94no—
195C2×C22⋊C4—184no—
196#95—94no—
197#95—98no—
198C23×C3—24no—
199C23×C3—24no—
200C23×C3—216no—
201C23×C3—216no—
202C23×C3—216no—
203C23×C3—216no—
204C23×C3—24no—
205C23×C3—24no—
206C23×C3—24no—
207C23×C3—24no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—21no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—22no—
214C23×C3—22no—
215C23×C3—24no—
216C23×C3—22no—
217C23×C3—44no—
218C23×C3—44no—
219C23×C3—416no—
220C23×C3—48no—
221C23×C3—416no—
222C23×C3—48no—
223C23×C3—48no—
224C23×C3—48no—
225C23×C3—48no—
226C23×C3—48no—
227C23×C3#23514yes—
228C23×C3#23514yes—
229C23×C3D3×D414yes—
230C23×C3#23714yes—
231C23×C3#23714yes—
232C23×C3#23714yes—
233C23×C3C2×#6718yes—
234C23×C3C2×#6714yes—
235C23×C3C23×D312yes—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4—64no—
239C2×C3×C4—64no—
240C2×C3×C4—64no—
241C2×C3×C4—64no—
242C2×C3×C4—128no—
243C2×C3×C4—128no—
244C2×Dic3—24no—
245C2×Dic3—24no—
246C2×Dic3—24no—
247C2×Dic3—24no—
248C2×Dic3—24no—
249C2×Dic3—24no—
250C2×Dic3—38no—
251C2×Dic3—48no—
252C2×Dic3—48no—
253C2×Dic3—64no—
254C2×Dic3—616no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—124no—
262C2×Dic3—128no—
263C2×Dic3—124no—
264C2×Dic3—128no—
265C2×Dic3—128no—
266C2×C32—44no—
267C2×C32#39718yescomplemented
268C2×C32C2×#12111yescharacteristic
269C2×C32C2×#12311yescharacteristic
270C2×C32C2×#12312yes—
271C2×C32C2×#12411yescharacteristic
272C2×C32C2×#12612yes—
273C24—24no—
274C24—24no—
275C24—22no—
276C24—22no—
277C24#62514yes—
278C24C2×D3212yes—
279C24C2×D3211yescharacteristic
280C22×C4—34no—
281C22×C4—34no—
282C22×C4—64no—
283C22×C4—64no—
284C22×C4—64no—
285C22×C4—64no—
286C22×C4—64no—
287C22×C4—64no—
288C22×C4—92no—
289C22×C4—94no—
290C22×C4—92no—
291C22×C4—184no—
292C22×C4—184no—
293C22×C4—182no—
294C4⋊C4—188no—
295C22⋊C4—616no—
296C22⋊C4—188no—
297C22×C3—28no—
298C22×C3—28no—
299C22×C3—28no—
300C22×C3—28no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—24no—
307C22×C3—28no—
308C22×C3—28no—
309C22×C3—24no—
310C22×C3—24no—
311C22×C3—48no—
312C22×C3—44no—
313C22×C3—48no—
314C22×C3—44no—
315C22×C3—432no—
316C22×C3—432no—
317C22×C3—44no—
318C22×C3—44no—
319C22×C3—44no—
320C22×C3—44no—
321C22×C3#87918yes—
322C22×C3#87918yes—
323C22×C3#88318yes—
324C22×C3#88518yes—
325C22×C3#92918yes—
326C22×C3#93518yes—
327C22×C3#93918yes—
328C22×C3C2×#23512yes—
329C22×C3C2×#23512yes—
330C22×C3C2×D3×D412yes—
331C22×C3C2×#23712yes—
332C22×C3C2×#23712yes—
333C22×C3C2×#23712yes—
334C22×C3C22×#6712yes—
335C3×C4—124no—
336C3×C4—124no—
337Dic3—44no—
338Dic3—44no—
339Dic3—68no—
340Dic3—124no—
341Dic3—124no—
342Dic3—124no—
343C32C2×#39711yescharacteristic, complemented, Sylow
344C23—24no—
345C23—24no—
346C23—22no—
347C23—22no—
348C23—216no—
349C23—28no—
350C23—44no—
351C23—48no—
352C23—44no—
353C23#380414yes—
354C23#380414yes—
355C23#380512yes—
356C23C2×#62514yes—
357C23C2×#62512yes—
358C23#381112yes—
359C23C22×D3211yescharacteristic
360C2×C4—64no—
361C2×C4—64no—
362C2×C4—64no—
363C2×C4—64no—
364C2×C4—64no—
365C2×C4—64no—
366C2×C4—94no—
367C2×C4—128no—
368C2×C4—128no—
369C2×C4—184no—
370C2×C4—188no—
371C2×C4—184no—
372C2×C4—182no—
373C2×C4—364no—
374C2×C3—21no—
375C2×C3—22no—
376C2×C3—22no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—28no—
380C2×C3—48no—
381C2×C3—48no—
382C2×C3#4952116yescomplemented
383C2×C3C2×#87912yes—
384C2×C3C2×#87912yes—
385C2×C3C2×#88312yes—
386C2×C3C2×#88512yes—
387C2×C3C2×#92912yes—
388C2×C3C2×#93512yes—
389C2×C3C2×#93912yes—
390C22—28no—
391C22—24no—
392C22—42no—
393C22—44no—
394C22—42no—
395C22—416no—
396C22#6395314yes—
397C22#6395618yes—
398C22#6396118yes—
399C22#6397514yes—
400C22#6398014yes—
401C22C2×#380412yes—
402C22C2×#380412yes—
403C22C2×#380511yescharacteristic
404C22C22×#62511yescharacteristic
405C22C2×#381111yescharacteristic
406C4—124no—
407C4—124no—
408C4—184no—
409C4—362no—
410C3—21no—
411C3C2×#495212yescomplemented
412C2—44no—
413C2#1059169418yesdirect product factor
414C2C2×#6395311yescharacteristic
415C2C2×#6395612yes—
416C2C2×#6396112yes—
417C2C2×#6397511yescharacteristic
418C2C2×#6398011yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
Fitting, prime radicalC25×C32C22
socleC24×C32C23
hypercenterC25D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
3. C22×#3724C2semidirect
4. C2×#63579C2semidirect
5. C2×#63579C2semidirect
6. #10591694C2direct (N × H)
18. C2×#3724C22semidirect
19. #63579C22semidirect
20. #63579C22semidirect
267. C2×C32#397semidirect
343. C32C2×#397semidirect
382. C2×C3#4952semidirect
411. C3C2×#4952semidirect
413. C2#10591694direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37572
C22×C3×#2172
C22×#37242
C2×#635792
#105916942
C2×#49523