Finite Group Databasebeta

← C2×#10591203 #11808487

Subgroups — C2×#10591203 #11808487

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×#3752C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C212yesmaximal, complemented
3C22×#3724C211yesmaximal, characteristic, complemented
4C22×#3722C212yesmaximal
5C2×#63579C211yesmaximal, characteristic, complemented
6#10591203C218yesmaximal, direct product factor
7C2×#4993—32nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×#3752—24no—
14C2×#3752C2214yes—
15C2×C3×Dic3⋊C4—28no—
16C2×C3×Dic3⋊C4C2218yescomplemented
17C2×#3724—24no—
18C2×#3724C2214yescomplemented
19C2×#3722—28no—
20C2×#3722C2218yes—
21#63579C2214yescomplemented
22C22×C3×C4⋊C4—32no—
23C22×(C2×D3)⋊C4—32no—
24C22×(C2×D3)⋊C4—32no—
25C22×(C2×D3)⋊C4—32no—
26C22×(C2×D3)⋊C4—61no—
27C22×Dic3⋊C4—32no—
28C22×Dic3⋊C4D312yescomplemented
29C2×C3⋊#95—32no—
30#4993—316no—
31C24×C32C2311yescharacteristic
32C23×C3⋊D3—22no—
33C23×C3⋊D3—24no—
34C23×C3⋊D3—22no—
35C23×C3⋊D3—24no—
36C23×C3⋊D3Q814yes—
37C23×C3⋊D3C2312yes—
38C22×C32×C4—22no—
39C22×C32×C4—24no—
40C22×C32×C4C2312yes—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3D414yes—
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#3752—28no—
53C3×Dic3⋊C4—216no—
54#3724—28no—
55#3722—216no—
56C2×#399—91noSylow
57C24×D3—32no—
58C24×D3—61no—
59C23×C3×C4—21no—
60C23×C3×C4—32no—
61C23×C3×C4—32no—
62C23×C3×C4C2×D312yes—
63C23×Dic3—32no—
64C23×Dic3—61no—
65C23×Dic3C2×D312yes—
66C23×Dic3C2×D312yes—
67C2×C3×C4⋊C4—38no—
68C2×C3×C4⋊C4—68no—
69C2×(C2×D3)⋊C4—38no—
70C2×(C2×D3)⋊C4—38no—
71C2×(C2×D3)⋊C4—38no—
72C2×(C2×D3)⋊C4—64no—
73C2×(C2×D3)⋊C4—68no—
74C2×(C2×D3)⋊C4—68no—
75C2×(C2×D3)⋊C4—68no—
76C2×(C2×D3)⋊C4—68no—
77C2×Dic3⋊C4—28no—
78C2×Dic3⋊C4—38no—
79C2×Dic3⋊C4—68no—
80C2×Dic3⋊C4C2×D318yescomplemented
81C3⋊#95—38no—
82C23×C32C2×D412yes—
83C23×C32C2×D414yes—
84C23×C32C2×Q812yes—
85C23×C32#4112yes—
86C23×C32#4114yes—
87C23×C32C2411yescharacteristic
88C22×C3⋊D3—28no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3—216no—
92C22×C3⋊D3—24no—
93C22×C3⋊D3—24no—
94C22×C3⋊D3—44no—
95C22×C3⋊D3—48no—
96C22×C3⋊D3—44no—
97C22×C3⋊D3C2×Q814yes—
98C2×C32×C4—22no—
99C2×C32×C4—24no—
100C2×C32×C4—44no—
101C2×C3⋊Dic3—28no—
102C2×C3⋊Dic3—24no—
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—32no—
113C22×C4⋊C4—91no—
114C22×C22⋊C4—92no—
115C22×C22⋊C4—91no—
116#399—98no—
117C2×#95—91no—
118C24×C3—21no—
119C24×C3C22×D312yes—
120C23×D3—38no—
121C23×D3—34no—
122C23×D3—64no—
123C23×D3—62no—
124C23×D3—64no—
125C23×D3—64no—
126C23×D3—64no—
127C23×D3—64no—
128C23×D3—64no—
129C23×D3—64no—
130C23×D3—64no—
131C23×D3—64no—
132C23×D3—124no—
133C23×D3—124no—
134C22×C3×C4—24no—
135C22×C3×C4—24no—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—22no—
139C22×C3×C4—38no—
140C22×C3×C4—34no—
141C22×C3×C4—34no—
142C22×C3×C4—44no—
143C22×C3×C4—64no—
144C22×C3×C4—64no—
145C22×C3×C4—64no—
146C22×C3×C4—64no—
147C22×C3×C4—64no—
148C22×C3×C4C22×D314yes—
149C22×Dic3—24no—
150C22×Dic3—24no—
151C22×Dic3—24no—
152C22×Dic3—24no—
153C22×Dic3—24no—
154C22×Dic3—38no—
155C22×Dic3—34no—
156C22×Dic3—64no—
157C22×Dic3—62no—
158C22×Dic3—64no—
159C22×Dic3—64no—
160C22×Dic3—124no—
161C22×Dic3#6718yes—
162C22×Dic3C22×D314yes—
163C22×Dic3C22×D314yes—
164C3×C4⋊C4—616no—
165(C2×D3)⋊C4—616no—
166(C2×D3)⋊C4—616no—
167(C2×D3)⋊C4—616no—
168(C2×D3)⋊C4—616no—
169Dic3⋊C4—216no—
170Dic3⋊C4—616no—
171C22×C32C22⋊Q814yes—
172C22×C32C22⋊Q818yes—
173C22×C32#12314yes—
174C22×C32#12318yes—
175C22×C32#12714yes—
176C22×C32C22×D411yescharacteristic
177C22×C32C22×D412yes—
178C22×C32C22×Q811yescharacteristic
179C22×C32C2×#4111yescharacteristic
180C22×C32C2×#4112yes—
181C2×C3⋊D3—24no—
182C2×C3⋊D3—28no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—44no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—416no—
187C32×C4—42no—
188C3⋊Dic3—24no—
189C3×Dic3—28no—
190C3×Dic3—44no—
191C25—91no—
192C23×C4—32no—
193C23×C4—32no—
194C23×C4—91no—
195C23×C4D3211yescharacteristic
196C2×C4⋊C4—38no—
197C2×C4⋊C4—68no—
198C2×C4⋊C4—94no—
199C2×C4⋊C4—184no—
200C2×C22⋊C4—98no—
201C2×C22⋊C4—94no—
202C2×C22⋊C4—184no—
203C2×C22⋊C4—188no—
204#95—94no—
205C23×C3—21no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—22no—
211C23×C3#23514yes—
212C23×C3#23514yes—
213C23×C3D3×D414yes—
214C23×C3D3×D414yes—
215C23×C3D3×Q814yes—
216C23×C3#23914yes—
217C23×C3C2×#6714yes—
218C23×C3C23×D312yes—
219C22×D3—38no—
220C22×D3—64no—
221C22×D3—64no—
222C22×D3—64no—
223C22×D3—616no—
224C22×D3—616no—
225C22×D3—616no—
226C22×D3—616no—
227C22×D3—64no—
228C22×D3—64no—
229C22×D3—64no—
230C22×D3—64no—
231C22×D3—64no—
232C22×D3—64no—
233C22×D3—124no—
234C22×D3—124no—
235C22×D3—1216no—
236C22×D3—1216no—
237C22×D3—128no—
238C22×D3—128no—
239C22×D3—128no—
240C22×D3—128no—
241C22×D3—128no—
242C22×D3—128no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—38no—
248C2×C3×C4—44no—
249C2×C3×C4—48no—
250C2×C3×C4—48no—
251C2×C3×C4—616no—
252C2×C3×C4—64no—
253C2×C3×C4—64no—
254C2×C3×C4—64no—
255C2×C3×C4—64no—
256C2×C3×C4—64no—
257C2×C3×C4—128no—
258C2×Dic3—216no—
259C2×Dic3—24no—
260C2×Dic3—24no—
261C2×Dic3—24no—
262C2×Dic3—24no—
263C2×Dic3—24no—
264C2×Dic3—38no—
265C2×Dic3—48no—
266C2×Dic3—64no—
267C2×Dic3—616no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—124no—
271C2×Dic3—128no—
272C2×Dic3C2×#6718yes—
273C2×C32#39918yescomplemented
274C2×C32C2×C22⋊Q811yescharacteristic
275C2×C32C2×C22⋊Q812yes—
276C2×C32C2×#12311yescharacteristic
277C2×C32C2×#12312yes—
278C2×C32C2×#12711yescharacteristic
279C3⋊D3—44no—
280C24—92no—
281C24—94no—
282C24—182no—
283C24—184no—
284C24—184no—
285C24—182no—
286C24C2×D3211yescharacteristic
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—34no—
290C22×C4—38no—
291C22×C4—34no—
292C22×C4—64no—
293C22×C4—64no—
294C22×C4—64no—
295C22×C4—64no—
296C22×C4—64no—
297C22×C4—92no—
298C22×C4—94no—
299C22×C4—184no—
300C22×C4C2×D3212yes—
301C4⋊C4—616no—
302C4⋊C4—188no—
303C22⋊C4—188no—
304C22⋊C4—1816no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—28no—
311C22×C3—24no—
312C22×C3—28no—
313C22×C3—24no—
314C22×C3—24no—
315C22×C3#89418yes—
316C22×C3#89418yes—
317C22×C3#89618yes—
318C22×C3#89618yes—
319C22×C3#92918yes—
320C22×C3#94018yes—
321C22×C3#94618yes—
322C22×C3C2×#23512yes—
323C22×C3C2×#23512yes—
324C22×C3C2×D3×D412yes—
325C22×C3C2×D3×D412yes—
326C22×C3C2×D3×Q812yes—
327C22×C3C2×#23912yes—
328C22×C3C22×#6712yes—
329C2×D3—68no—
330C2×D3—68no—
331C2×D3—68no—
332C2×D3—68no—
333C2×D3—128no—
334C2×D3—128no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—1232no—
338C2×D3—1232no—
339C2×D3—124no—
340C2×D3—124no—
341C2×D3—124no—
342C2×D3—124no—
343C3×C4—44no—
344C3×C4—44no—
345C3×C4—68no—
346C3×C4—124no—
347Dic3—28no—
348Dic3—44no—
349Dic3—68no—
350Dic3—124no—
351C32C2×#39911yescharacteristic, complemented, Sylow
352C23—94no—
353C23—182no—
354C23—184no—
355C23—184no—
356C23—182no—
357C23—188no—
358C23—1816no—
359C23—368no—
360C23—364no—
361C23—364no—
362C23#379712yes—
363C23#379812yes—
364C23#379914yes—
365C23D3×#6714yes—
366C23#381112yes—
367C23C22×D3211yescharacteristic
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—38no—
371C2×C4—44no—
372C2×C4—64no—
373C2×C4—64no—
374C2×C4—616no—
375C2×C4—64no—
376C2×C4—64no—
377C2×C4—64no—
378C2×C4—94no—
379C2×C4—128no—
380C2×C4—184no—
381C2×C4—188no—
382C2×C3—22no—
383C2×C3—21no—
384C2×C3—22no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—28no—
388C2×C3#4993116yescomplemented
389C2×C3C2×#89412yes—
390C2×C3C2×#89412yes—
391C2×C3C2×#89612yes—
392C2×C3C2×#89612yes—
393C2×C3C2×#92912yes—
394C2×C3C2×#94012yes—
395C2×C3C2×#94612yes—
396D3—128no—
397D3—128no—
398C22—184no—
399C22—188no—
400C22—364no—
401C22—362no—
402C22—362no—
403C22—3616no—
404C22#6385018yes—
405C22#6386514yes—
406C22#6388818yes—
407C22#6389714yes—
408C22#6397914yes—
409C22C2×#379711yescharacteristic
410C22C2×#379811yescharacteristic
411C22C2×#379912yes—
412C22C2×D3×#6712yes—
413C22C2×#381111yescharacteristic
414C4—42no—
415C4—68no—
416C4—124no—
417C4—184no—
418C3—21no—
419C3C2×#499312yescomplemented
420C2—364no—
421C2#1059120318yesdirect product factor
422C2C2×#6385012yes—
423C2C2×#6386511yescharacteristic
424C2C2×#6388812yes—
425C2C2×#6389711yescharacteristic
426C2C2×#6397911yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
3. C22×#3724C2semidirect
5. C2×#63579C2semidirect
6. #10591203C2direct (N × H)
16. C2×C3×Dic3⋊C4C22semidirect
18. C2×#3724C22semidirect
21. #63579C22semidirect
28. C22×Dic3⋊C4D3semidirect
80. C2×Dic3⋊C4C2×D3semidirect
273. C2×C32#399semidirect
351. C32C2×#399semidirect
388. C2×C3#4993semidirect
419. C3C2×#4993semidirect
421. C2#10591203direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37522
C22×C3×Dic3⋊C42
C22×#37242
C22×#37222
C2×#635792
#105912032
C2×#49933