Finite Group Databasebeta

← C2×#10591358 #11808349

Subgroups — C2×#10591358 #11808349

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#10591358C218yesmaximal, direct product factor
7C2×#4983—31nomaximal
8C2×#4661—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2212yes—
14C2×#3750—24no—
15C2×#3750C2214yes—
16C2×C3×C4⋊Dic3—24no—
17C2×C3×C4⋊Dic3C2214yes—
18C2×Dic3⋊Dic3—28no—
19C2×Dic3⋊Dic3C2218yes—
20C3×C3⋊#95C2214yes—
21#63579C2218yes—
22C22×C3×C4⋊C4—31no—
23C22×C4⋊Dic3—32no—
24C22×C4⋊Dic3D311yescharacteristic
25C22×Dic3⋊C4—31no—
26C22×Dic3⋊C4—31no—
27C22×Dic3⋊C4—32no—
28C22×Dic3⋊C4—61no—
29C2×C3×#95—31no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95D311yescharacteristic
33#4983—38no—
34#4661—38no—
35C24×C32C2311yescharacteristic
36C22×C32×C4—24no—
37C22×C32×C4D414yes—
38C22×C32×C4C2312yes—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—24no—
43C22×C3⋊Dic3D414yes—
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2312yes—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3Q818yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2314yes—
54#3750—28no—
55C3×C4⋊Dic3—28no—
56Dic3⋊Dic3—216no—
57C2×#398—91noSylow
58C23×C3×C4—21no—
59C23×C3×C4—32no—
60C23×C3×C4—32no—
61C23×C3×C4C2×D311yescharacteristic
62C23×C3×C4C2×D311yescharacteristic
63C23×Dic3—31no—
64C23×Dic3—31no—
65C23×Dic3—31no—
66C23×Dic3—31no—
67C23×Dic3—61no—
68C23×Dic3—61no—
69C23×Dic3C2×D312yes—
70C23×Dic3C2×D312yes—
71C2×C3×C4⋊C4—34no—
72C2×C3×C4⋊C4—64no—
73C2×C4⋊Dic3—24no—
74C2×C4⋊Dic3—38no—
75C2×C4⋊Dic3—68no—
76C2×C4⋊Dic3C2×D314yes—
77C2×Dic3⋊C4—34no—
78C2×Dic3⋊C4—34no—
79C2×Dic3⋊C4—38no—
80C2×Dic3⋊C4—64no—
81C2×Dic3⋊C4—68no—
82C2×Dic3⋊C4—68no—
83C2×Dic3⋊C4—64no—
84C2×Dic3⋊C4—64no—
85C3×#95—34no—
86C3⋊#95—38no—
87C3⋊#95—38no—
88C3⋊#95C2×D314yes—
89C23×C32C2×D412yes—
90C23×C32C2×D412yes—
91C23×C32C2×Q814yes—
92C23×C32#4114yes—
93C23×C32#4112yes—
94C23×C32C2411yescharacteristic
95C2×C32×C4—28no—
96C2×C32×C4—24no—
97C2×C32×C4C2×D414yes—
98C2×C3⋊Dic3—28no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—44no—
104C2×C3⋊Dic3C2×D414yes—
105C2×C3×Dic3—216no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—48no—
112C2×C3×Dic3C2×Q818yes—
113C22×C4⋊C4—31no—
114C22×C4⋊C4—92no—
115C22×C4⋊C4—91no—
116#398—98no—
117C2×#95—31no—
118C2×#95—92no—
119C24×C3—21no—
120C24×C3C22×D311yescharacteristic
121C24×C3C22×D311yescharacteristic
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4—22no—
126C22×C3×C4—38no—
127C22×C3×C4—34no—
128C22×C3×C4—34no—
129C22×C3×C4—44no—
130C22×C3×C4—64no—
131C22×C3×C4—64no—
132C22×C3×C4—64no—
133C22×C3×C4—64no—
134C22×C3×C4—64no—
135C22×C3×C4D1214yes—
136C22×C3×C4#6714yes—
137C22×C3×C4C22×D312yes—
138C22×C3×C4C22×D312yes—
139C22×Dic3—24no—
140C22×Dic3—24no—
141C22×Dic3—24no—
142C22×Dic3—24no—
143C22×Dic3—24no—
144C22×Dic3—34no—
145C22×Dic3—34no—
146C22×Dic3—32no—
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—32no—
150C22×Dic3—62no—
151C22×Dic3—64no—
152C22×Dic3—62no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—62no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159C22×Dic3—64no—
160C22×Dic3—62no—
161C22×Dic3—64no—
162C22×Dic3—64no—
163C22×Dic3—62no—
164C22×Dic3—124no—
165C22×Dic3Dic618yes—
166C22×Dic3C22×D314yes—
167C22×Dic3C22×D314yes—
168C3×C4⋊C4—68no—
169C4⋊Dic3—28no—
170C4⋊Dic3—616no—
171Dic3⋊C4—616no—
172Dic3⋊C4—616no—
173Dic3⋊C4—68no—
174Dic3⋊C4—68no—
175C22×C32#12114yes—
176C22×C32C22⋊Q818yes—
177C22×C32#12314yes—
178C22×C32#12518yes—
179C22×C32C4⋊Q814yes—
180C22×C32C22×D411yescharacteristic
181C22×C32C22×D411yescharacteristic
182C22×C32C22×Q812yes—
183C22×C32C2×#4112yes—
184C22×C32C2×#4111yescharacteristic
185C32×C4—24no—
186C3⋊Dic3—24no—
187C3⋊Dic3—42no—
188C3×Dic3—28no—
189C3×Dic3—44no—
190C23×C4—32no—
191C23×C4—32no—
192C23×C4—91no—
193C23×C4—91no—
194C23×C4D3211yescharacteristic
195C2×C4⋊C4—34no—
196C2×C4⋊C4—64no—
197C2×C4⋊C4—98no—
198C2×C4⋊C4—94no—
199C2×C4⋊C4—188no—
200C2×C4⋊C4—184no—
201#95—34no—
202#95—98no—
203C23×C3—21no—
204C23×C3—24no—
205C23×C3—22no—
206C23×C3—22no—
207C23×C3—24no—
208C23×C3—22no—
209C23×C3C2×Dic614yes—
210C23×C3C2×D1212yes—
211C23×C3#23514yes—
212C23×C3D3×D412yes—
213C23×C3D3×D412yes—
214C23×C3#23712yes—
215C23×C3#23714yes—
216C23×C3D3×Q814yes—
217C23×C3#23912yes—
218C23×C3C2×#6712yes—
219C23×C3C23×D311yescharacteristic
220C23×C3C23×D311yescharacteristic
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—38no—
227C2×C3×C4—44no—
228C2×C3×C4—48no—
229C2×C3×C4—616no—
230C2×C3×C4—64no—
231C2×C3×C4—64no—
232C2×C3×C4—64no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—128no—
236C2×C3×C4C2×D1214yes—
237C2×C3×C4C2×#6714yes—
238C2×Dic3—216no—
239C2×Dic3—24no—
240C2×Dic3—24no—
241C2×Dic3—24no—
242C2×Dic3—24no—
243C2×Dic3—24no—
244C2×Dic3—34no—
245C2×Dic3—34no—
246C2×Dic3—48no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—616no—
251C2×Dic3—68no—
252C2×Dic3—68no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—64no—
258C2×Dic3—62no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—62no—
262C2×Dic3—124no—
263C2×Dic3—128no—
264C2×Dic3—124no—
265C2×Dic3—124no—
266C2×Dic3C2×Dic618yes—
267C2×C32#39818yescomplemented
268C2×C32C2×#12111yescharacteristic
269C2×C32C2×C22⋊Q812yes—
270C2×C32C2×#12311yescharacteristic
271C2×C32C2×#12512yes—
272C2×C32C2×C4⋊Q811yescharacteristic
273C24C2×D3211yescharacteristic
274C22×C4—24no—
275C22×C4—34no—
276C22×C4—38no—
277C22×C4—34no—
278C22×C4—64no—
279C22×C4—64no—
280C22×C4—64no—
281C22×C4—64no—
282C22×C4—64no—
283C22×C4—92no—
284C22×C4—94no—
285C22×C4—92no—
286C22×C4—182no—
287C22×C4—182no—
288C22×C4—184no—
289C22×C4—182no—
290C22×C4#62614yes—
291C22×C4C2×D3212yes—
292C4⋊C4—68no—
293C4⋊C4—1816no—
294C4⋊C4—188no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—28no—
301C22×C3—24no—
302C22×C3—28no—
303C22×C3—24no—
304C22×C3—24no—
305C22×C3#86914yes—
306C22×C3#87818yes—
307C22×C3#88614yes—
308C22×C3#88918yes—
309C22×C3#89018yes—
310C22×C3#89514yes—
311C22×C3#89618yes—
312C22×C3#92914yes—
313C22×C3#93814yes—
314C22×C3#94414yes—
315C22×C3C22×Dic612yes—
316C22×C3C22×D1211yescharacteristic
317C22×C3C2×#23512yes—
318C22×C3C2×D3×D411yescharacteristic
319C22×C3C2×D3×D411yescharacteristic
320C22×C3C2×#23711yescharacteristic
321C22×C3C2×#23712yes—
322C22×C3C2×D3×Q812yes—
323C22×C3C2×#23911yescharacteristic
324C22×C3C22×#6711yescharacteristic
325C3×C4—24no—
326C3×C4—24no—
327C3×C4—44no—
328C3×C4—68no—
329C3×C4—124no—
330Dic3—28no—
331Dic3—44no—
332Dic3—68no—
333Dic3—64no—
334Dic3—64no—
335Dic3—124no—
336Dic3—122no—
337Dic3—122no—
338C32C2×#39811yescharacteristic, complemented, Sylow
339C23D3×Dic614yes—
340C23#379612yes—
341C23#380212yes—
342C23#380414yes—
343C23C2×#62612yes—
344C23C22×D3211yescharacteristic
345C2×C4—24no—
346C2×C4—28no—
347C2×C4—38no—
348C2×C4—64no—
349C2×C4—64no—
350C2×C4—616no—
351C2×C4—64no—
352C2×C4—64no—
353C2×C4—64no—
354C2×C4—94no—
355C2×C4—128no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—188no—
359C2×C4—184no—
360C2×C4—182no—
361C2×C4—364no—
362C2×C4C2×#62614yes—
363C2×C3—22no—
364C2×C3—21no—
365C2×C3—22no—
366C2×C3—28no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3#466118yescomplemented
370C2×C3#498318yescomplemented
371C2×C3C2×#86911yescharacteristic
372C2×C3C2×#87812yes—
373C2×C3C2×#88611yescharacteristic
374C2×C3C2×#88912yes—
375C2×C3C2×#89012yes—
376C2×C3C2×#89511yescharacteristic
377C2×C3C2×#89612yes—
378C2×C3C2×#92911yescharacteristic
379C2×C3C2×#93811yescharacteristic
380C2×C3C2×#94411yescharacteristic
381C22#6384618yes—
382C22#6386614yes—
383C22#6389918yes—
384C22#6391614yes—
385C22#6396614yes—
386C22C2×D3×Dic612yes—
387C22C2×#379611yescharacteristic
388C22C2×#380211yescharacteristic
389C22C2×#380412yes—
390C22C22×#62611yescharacteristic
391C4—24no—
392C4—68no—
393C4—124no—
394C4—184no—
395C4—362no—
396C3—21no—
397C3C2×#466111yescharacteristic, complemented
398C3C2×#498311yescharacteristic, complemented
399C2#1059135818yesdirect product factor
400C2C2×#6384612yes—
401C2C2×#6386611yescharacteristic
402C2C2×#6389912yes—
403C2C2×#6391611yescharacteristic
404C2C2×#6396611yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591358C2direct (N × H)
267. C2×C32#398semidirect
338. C32C2×#398semidirect
369. C2×C3#4661semidirect
370. C2×C3#4983semidirect
397. C3C2×#4661semidirect
398. C3C2×#4983semidirect
399. C2#10591358direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C22×C3×C4⋊Dic32
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105913582
C2×#49833
C2×#46613