Finite Group Databasebeta

← C2×#10591715 #11808488

Subgroups — C2×#10591715 #11808488

Order 1152.

2153 conjugacy classes of subgroups.

The subgroup lattice has 428 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
4C22×Dic3⋊Dic3C212yesmaximal, complemented
5#10591715C218yesmaximal, direct product factor
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#4949—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
19C2×Dic3⋊Dic3—28no—
20C2×Dic3⋊Dic3C2218yescomplemented
21#63579C2214yescomplemented
22C22×C3×C22⋊C4—32no—
23C22×#217—32no—
24C22×#217—61no—
25C22×#217D312yes—
26C22×C4⋊Dic3—32no—
27C22×Dic3⋊C4—32no—
28C22×Dic3⋊C4—32no—
29C2×C3⋊#95—32no—
30#4949—316no—
31C24×C32—22no—
32C24×C32—24no—
33C24×C32—22no—
34C24×C32—24no—
35C24×C32Q814yes—
36C24×C32C2312yes—
37C24×C32C2311yescharacteristic
38C22×C3⋊Dic3—24no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3D414yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2312yes—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3D418yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2314yes—
52#3757—28no—
53C3×#217—216no—
54#3724—28no—
55Dic3⋊Dic3—216no—
56C2×#399—91noSylow
57C25×C3—21no—
58C25×C3C2×D312yes—
59C23×C3×C4—32no—
60C23×C3×C4—32no—
61C23×Dic3—32no—
62C23×Dic3—32no—
63C23×Dic3—61no—
64C23×Dic3—61no—
65C23×Dic3C2×D312yes—
66C23×Dic3C2×D312yes—
67C2×C3×C22⋊C4—38no—
68C2×C3×C22⋊C4—68no—
69C2×#217—28no—
70C2×#217—38no—
71C2×#217—64no—
72C2×#217—68no—
73C2×#217—68no—
74C2×#217C2×D318yes—
75C2×C4⋊Dic3—38no—
76C2×C4⋊Dic3—68no—
77C2×Dic3⋊C4—38no—
78C2×Dic3⋊C4—38no—
79C2×Dic3⋊C4—68no—
80C2×Dic3⋊C4—68no—
81C3⋊#95—38no—
82C23×C32—28no—
83C23×C32—22no—
84C23×C32—22no—
85C23×C32—216no—
86C23×C32—24no—
87C23×C32—24no—
88C23×C32—44no—
89C23×C32—48no—
90C23×C32—44no—
91C23×C32C2×D412yes—
92C23×C32C2×D414yes—
93C23×C32C2×Q814yes—
94C23×C32C2×Q812yes—
95C23×C32#4114yes—
96C23×C32#4112yes—
97C23×C32C2411yescharacteristic
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—28no—
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—24no—
102C2×C3⋊Dic3—44no—
103C2×C3⋊Dic3C2×D414yes—
104C2×C3×Dic3—216no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—48no—
111C2×C3×Dic3C2×D418yes—
112C22×C4⋊C4—91no—
113C22×C4⋊C4—92no—
114C22×C22⋊C4—32no—
115C22×C22⋊C4—91no—
116#399—98no—
117C2×#95—91no—
118C24×C3—24no—
119C24×C3—24no—
120C24×C3—24no—
121C24×C3—24no—
122C24×C3—24no—
123C24×C3—24no—
124C24×C3—24no—
125C24×C3—24no—
126C24×C3—24no—
127C24×C3—22no—
128C24×C3—21no—
129C24×C3—44no—
130C24×C3—44no—
131C24×C3Dic618yes—
132C24×C3C22×D314yes—
133C24×C3C22×D312yes—
134C22×C3×C4—38no—
135C22×C3×C4—34no—
136C22×C3×C4—34no—
137C22×C3×C4—64no—
138C22×C3×C4—64no—
139C22×C3×C4—64no—
140C22×C3×C4—64no—
141C22×C3×C4—64no—
142C22×Dic3—24no—
143C22×Dic3—24no—
144C22×Dic3—24no—
145C22×Dic3—24no—
146C22×Dic3—24no—
147C22×Dic3—38no—
148C22×Dic3—34no—
149C22×Dic3—34no—
150C22×Dic3—64no—
151C22×Dic3—62no—
152C22×Dic3—62no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C22×Dic3—64no—
158C22×Dic3—64no—
159C22×Dic3—124no—
160C22×Dic3—124no—
161C22×Dic3#6718yes—
162C22×Dic3C22×D314yes—
163C22×Dic3C22×D314yes—
164C3×C22⋊C4—616no—
165#217—216no—
166#217—616no—
167#217—616no—
168C4⋊Dic3—616no—
169Dic3⋊C4—616no—
170Dic3⋊C4—616no—
171C22×C32—24no—
172C22×C32—28no—
173C22×C32—42no—
174C22×C32—44no—
175C22×C32—42no—
176C22×C32—416no—
177C22×C32C22⋊Q814yes—
178C22×C32C22⋊Q818yes—
179C22×C32#12314yes—
180C22×C32#12318yes—
181C22×C32#12714yes—
182C22×C32C22×D411yescharacteristic
183C22×C32C22×D412yes—
184C22×C32C22×Q811yescharacteristic
185C22×C32C2×#4112yes—
186C22×C32C2×#4111yescharacteristic
187C3⋊Dic3—24no—
188C3⋊Dic3—42no—
189C3×Dic3—28no—
190C3×Dic3—44no—
191C25D3211yescharacteristic
192C23×C4—32no—
193C23×C4—32no—
194C23×C4—91no—
195C23×C4—91no—
196C2×C4⋊C4—94no—
197C2×C4⋊C4—98no—
198C2×C4⋊C4—188no—
199C2×C4⋊C4—184no—
200C2×C22⋊C4—38no—
201C2×C22⋊C4—68no—
202C2×C22⋊C4—94no—
203C2×C22⋊C4—184no—
204#95—94no—
205C23×C3—24no—
206C23×C3—24no—
207C23×C3—216no—
208C23×C3—216no—
209C23×C3—216no—
210C23×C3—216no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—24no—
214C23×C3—24no—
215C23×C3—24no—
216C23×C3—24no—
217C23×C3—21no—
218C23×C3—24no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—24no—
222C23×C3—24no—
223C23×C3—22no—
224C23×C3—44no—
225C23×C3—44no—
226C23×C3—416no—
227C23×C3—416no—
228C23×C3—48no—
229C23×C3—48no—
230C23×C3—48no—
231C23×C3—48no—
232C23×C3—48no—
233C23×C3—48no—
234C23×C3C2×Dic618yes—
235C23×C3C2×Dic614yes—
236C23×C3#23514yes—
237C23×C3D3×D414yes—
238C23×C3D3×D414yes—
239C23×C3#23714yes—
240C23×C3#23714yes—
241C23×C3C2×#6714yes—
242C23×C3C23×D312yes—
243C2×C3×C4—38no—
244C2×C3×C4—616no—
245C2×C3×C4—64no—
246C2×C3×C4—64no—
247C2×C3×C4—64no—
248C2×C3×C4—64no—
249C2×C3×C4—64no—
250C2×C3×C4—128no—
251C2×Dic3—216no—
252C2×Dic3—24no—
253C2×Dic3—24no—
254C2×Dic3—24no—
255C2×Dic3—24no—
256C2×Dic3—24no—
257C2×Dic3—38no—
258C2×Dic3—48no—
259C2×Dic3—64no—
260C2×Dic3—616no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C2×Dic3—124no—
268C2×Dic3—128no—
269C2×Dic3—124no—
270C2×Dic3—128no—
271C2×Dic3—128no—
272C2×Dic3C2×#6718yes—
273C2×C32—44no—
274C2×C32#39918yescomplemented
275C2×C32C2×C22⋊Q811yescharacteristic
276C2×C32C2×C22⋊Q812yes—
277C2×C32C2×#12311yescharacteristic
278C2×C32C2×#12312yes—
279C2×C32C2×#12711yescharacteristic
280C24—24no—
281C24—22no—
282C24—24no—
283C24—22no—
284C24#62714yes—
285C24C2×D3212yes—
286C24C2×D3211yescharacteristic
287C22×C4—34no—
288C22×C4—38no—
289C22×C4—34no—
290C22×C4—64no—
291C22×C4—64no—
292C22×C4—64no—
293C22×C4—64no—
294C22×C4—64no—
295C22×C4—92no—
296C22×C4—94no—
297C22×C4—92no—
298C22×C4—184no—
299C22×C4—184no—
300C22×C4—182no—
301C4⋊C4—1816no—
302C4⋊C4—188no—
303C22⋊C4—616no—
304C22⋊C4—188no—
305C22×C3—28no—
306C22×C3—28no—
307C22×C3—28no—
308C22×C3—28no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—28no—
315C22×C3—28no—
316C22×C3—24no—
317C22×C3—24no—
318C22×C3—24no—
319C22×C3—48no—
320C22×C3—48no—
321C22×C3—44no—
322C22×C3—44no—
323C22×C3—432no—
324C22×C3—432no—
325C22×C3—44no—
326C22×C3—44no—
327C22×C3—44no—
328C22×C3—44no—
329C22×C3#87818yes—
330C22×C3#87818yes—
331C22×C3#88318yes—
332C22×C3#88318yes—
333C22×C3#92418yes—
334C22×C3#93518yes—
335C22×C3#94018yes—
336C22×C3C22×Dic612yes—
337C22×C3C2×#23512yes—
338C22×C3C2×D3×D412yes—
339C22×C3C2×D3×D412yes—
340C22×C3C2×#23712yes—
341C22×C3C2×#23712yes—
342C22×C3C22×#6712yes—
343C3×C4—68no—
344C3×C4—124no—
345Dic3—28no—
346Dic3—44no—
347Dic3—68no—
348Dic3—124no—
349Dic3—124no—
350Dic3—124no—
351C32C2×#39911yescharacteristic, complemented, Sylow
352C23—24no—
353C23—22no—
354C23—24no—
355C23—22no—
356C23—216no—
357C23—28no—
358C23—48no—
359C23—44no—
360C23—44no—
361C23#380414yes—
362C23#380512yes—
363C23C2×#62714yes—
364C23C2×#62712yes—
365C23D3×#6714yes—
366C23#381112yes—
367C23C22×D3211yescharacteristic
368C2×C4—38no—
369C2×C4—64no—
370C2×C4—64no—
371C2×C4—616no—
372C2×C4—64no—
373C2×C4—64no—
374C2×C4—64no—
375C2×C4—94no—
376C2×C4—128no—
377C2×C4—184no—
378C2×C4—188no—
379C2×C4—184no—
380C2×C4—182no—
381C2×C4—364no—
382C2×C3—22no—
383C2×C3—22no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—28no—
388C2×C3—48no—
389C2×C3—48no—
390C2×C3#4949116yescomplemented
391C2×C3C2×#87812yes—
392C2×C3C2×#87812yes—
393C2×C3C2×#88312yes—
394C2×C3C2×#88312yes—
395C2×C3C2×#92412yes—
396C2×C3C2×#93512yes—
397C2×C3C2×#94012yes—
398C22—28no—
399C22—24no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—416no—
404C22#6396418yes—
405C22#6396918yes—
406C22#6397514yes—
407C22#6397914yes—
408C22#6398214yes—
409C22C2×#380412yes—
410C22C2×#380511yescharacteristic
411C22C22×#62711yescharacteristic
412C22C2×D3×#6712yes—
413C22C2×#381111yescharacteristic
414C4—68no—
415C4—124no—
416C4—184no—
417C4—362no—
418C3—21no—
419C3C2×#494912yescomplemented
420C2—44no—
421C2#1059171518yesdirect product factor
422C2C2×#6396412yes—
423C2C2×#6396912yes—
424C2C2×#6397511yescharacteristic
425C2C2×#6397911yescharacteristic
426C2C2×#6398211yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
Fitting, prime radicalC25×C32C22
socleC24×C32C23
hypercenterC25D32
hypocenterC32C2×#399
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. C22×Dic3⋊Dic3C2semidirect
5. #10591715C2direct (N × H)
6. C2×#63579C2semidirect
18. C2×#3724C22semidirect
20. C2×Dic3⋊Dic3C22semidirect
21. #63579C22semidirect
274. C2×C32#399semidirect
351. C32C2×#399semidirect
390. C2×C3#4949semidirect
419. C3C2×#4949semidirect
421. C2#10591715direct (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
C22×Dic3⋊Dic32
#105917152
C2×#635792
C2×#49493