Finite Group Databasebeta

← C2×#10593907 #11900782

Subgroups — C2×#10593907 #11900782

Order 1152.

3705 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C212yesmaximal, complemented
2C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#874C211yesmaximal, characteristic, complemented
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×#63916C214yesmaximal, complemented
6C2×#63898C214yesmaximal, complemented
7C2×#63863C212yesmaximal, complemented
8#10593907C2116yesmaximal, direct product factor
9C2×#5725—31nomaximal
10C2×#5716—31nomaximal
11C22×C4×C3⋊D3C2212yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2212yes—
14C22×C3×D12C2214yes—
15C22×C3×Dic6C2212yes—
16C22×#626C2214yes—
17C22×D3×Dic3C2214yes—
18C2×#3796—216no—
19C2×#3796C22116yescomplemented
20C2×C32×C42C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2212yes—
23C42×C3⋊D3C2218yescomplemented
24C2×C3×C4⋊Dic3C2214yes—
25C3×#874C2218yescomplemented
26C3×#869C2218yescomplemented
27C2×(C2×D3)⋊Dic3C2218yes—
28#63916C22132yescomplemented
29#63898C22132yescomplemented
30#63863C22116yescomplemented
31C22×#239—32no—
32C22×#237—32no—
33C2×C3×C4⋊Q8—31no—
34C2×C3×#127—31no—
35C2×#947—32no—
36C2×#938—34no—
37C2×#936—32no—
38C2×D4×Dic3—34no—
39#5725—316no—
40#5716—316no—
41C2×#895—34no—
42C2×#893—34no—
43C2×#874D311yescharacteristic, complemented
44C2×C42×D3—31no—
45C2×C42×D3—31no—
46C2×C42×D3—61no—
47C2×#869D311yescharacteristic, complemented
48C23×C3⋊D3C2311yescharacteristic
49C23×C3×D3C2314yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4×C3⋊D3—28no—
55C2×C4×C3⋊D3D418yescomplemented
56C2×C4×C3⋊D3C2318yes—
57C2×C4×C3⋊D3C2314yes—
58C22×C3×Dic3C2314yes—
59C2×C3×D12—28no—
60C2×C3×D12—216no—
61C2×C3×D12C2318yes—
62C2×C3×D12C23116yes—
63C2×C3×Dic6—28no—
64C2×C3×Dic6C2318yes—
65C2×#626—216no—
66C2×#626C23116yes—
67C2×D3×Dic3—216no—
68C2×D3×Dic3C23116yes—
69#3796—264no—
70C32×C42C2314yes—
71C4×C3⋊Dic3C2314yes—
72C4×C3⋊Dic3C2318yes—
73C3×C4⋊Dic3C23116yes—
74(C2×D3)⋊Dic3C23132yes—
75C2×#532—91noSylow
76C22×C3×Q8—32no—
77C22×C3×D4—32no—
78C22×C3×D4—34no—
79C22×#67—34no—
80C23×Dic3—34no—
81C2×#239—316no—
82C2×#239—616no—
83C2×#237—316no—
84C2×#237—616no—
85C22×D12—34no—
86C22×D12C2×D312yes—
87C22×D12C2×D314yes—
88C22×C4×D3—31no—
89C22×C4×D3—31no—
90C22×C4×D3—34no—
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—61no—
94C22×C4×D3—62no—
95C22×Dic6C2×D312yes—
96C3×C4⋊Q8—38no—
97C3×#127—38no—
98C2×C3×C4⋊C4—34no—
99C2×C3×C42—21no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#217—38no—
103#947—316no—
104#938—332no—
105#936—316no—
106D4×Dic3—332no—
107C2×(C2×D3)⋊C4—38no—
108C2×C4⋊Dic3C2×D314yes—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—62no—
114C2×C4×Dic3—61no—
115#895—332no—
116#893—332no—
117#874C2×D318yescomplemented
118C42×D3—38no—
119C42×D3—38no—
120C42×D3—68no—
121#869C2×D318yescomplemented
122C23×C32C2411yescharacteristic
123C22×C3⋊D3—24no—
124C22×C3⋊D3C2×D414yes—
125C22×C3⋊D3C2412yes—
126C22×C3×D3—28no—
127C22×C3×D3—216no—
128C22×C3×D3C2418yes—
129C2×C32×C4C2×D414yes—
130C2×C32×C4#4118yescomplemented
131C2×C32×C4C2412yes—
132C2×C32×C4C2414yes—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3C2×D414yes—
135C2×C3⋊Dic3C2414yes—
136C2×C3⋊Dic3C2412yes—
137C4×C3⋊D3—216no—
138C4×C3⋊D3C2×D4116yescomplemented
139C2×C3×Dic3—28no—
140C2×C3×Dic3C2418yes—
141C3×D12—216no—
142C3×D12—232no—
143C3×Dic6—216no—
144#626—232no—
145D3×Dic3—232no—
146C22×#41—92no—
147#532—916no—
148C2×C4⋊Q8—31no—
149C2×#127—31no—
150C2×#124—92no—
151C2×#121—94no—
152C2×C4×D4—94no—
153C22×C42—91no—
154C24×C3—34no—
155C23×D3—31no—
156C23×D3—31no—
157C23×D3—61no—
158C23×D3C22×D314yes—
159C2×C3×Q8—38no—
160C2×C3×Q8—68no—
161C2×C3×D4—316no—
162C2×C3×D4—38no—
163C2×C3×D4—68no—
164C2×C3×D4—616no—
165C22×C3×C4—22no—
166C22×C3×C4—21no—
167C22×C3×C4—34no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D312yes—
171C22×C3×C4C22×D312yes—
172C2×#67—316no—
173C2×#67—616no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—316no—
179C22×Dic3—61no—
180C22×Dic3—62no—
181C22×Dic3—616no—
182C22×Dic3C22×D314yes—
183#239—664no—
184#237—664no—
185C2×D12—28no—
186C2×D12—216no—
187C2×D12—316no—
188C2×D12—616no—
189C2×D12C22×D3116yes—
190C2×D12C22×D318yes—
191C2×C4×D3—38no—
192C2×C4×D3—38no—
193C2×C4×D3—34no—
194C2×C4×D3—34no—
195C2×C4×D3—316no—
196C2×C4×D3—38no—
197C2×C4×D3—38no—
198C2×C4×D3—64no—
199C2×C4×D3—68no—
200C2×C4×D3—68no—
201C2×C4×D3—616no—
202C2×C4×D3—616no—
203C2×C4×D3—68no—
204C2×C4×D3—68no—
205C2×Dic6—28no—
206C2×Dic6C22×D318yes—
207C3×C4⋊C4—316no—
208C3×C42—24no—
209C3×C42C22×D314yes—
210C3×C42C22×D314yes—
211#217—332no—
212(C2×D3)⋊C4—332no—
213C4⋊Dic3C22×D3116yes—
214C4×Dic3—38no—
215C4×Dic3—38no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C4×Dic3—68no—
219C4×Dic3—64no—
220C22×C32C22×D412yes—
221C22×C32C2×#4114yes—
222C22×C32C2511yescharacteristic
223C2×C3⋊D3—28no—
224C2×C3⋊D3—24no—
225C2×C3⋊D3C22×D414yes—
226C2×C3×D3—28no—
227C2×C3×D3—216no—
228C2×C3×D3—416no—
229C32×C4C22×D414yes—
230C32×C4C2×#4118yescomplemented
231C3⋊Dic3—24no—
232C3⋊Dic3C22×D414yes—
233C3×Dic3—28no—
234C2×#41—916no—
235C2×#41—1816no—
236C22×Q8—32no—
237C22×D4—34no—
238C22×D4—32no—
239C22×D4—94no—
240C23×C4—94no—
241C23×C4—91no—
242C23×C4—92no—
243C4⋊Q8—38no—
244#127—38no—
245#124—916no—
246#121—932no—
247C4×D4—932no—
248C2×C4⋊C4—34no—
249C2×C22⋊C4—98no—
250C2×C42—92no—
251C2×C42—91no—
252C2×C42—98no—
253C2×C42D3211yescharacteristic
254C23×C3—21no—
255C23×C3—38no—
256C23×C3—68no—
257C23×C3—616no—
258C23×C3C23×D311yescharacteristic
259C23×C3C23×D311yescharacteristic
260C22×D3—28no—
261C22×D3—216no—
262C22×D3—34no—
263C22×D3—34no—
264C22×D3—32no—
265C22×D3—32no—
266C22×D3—64no—
267C22×D3—62no—
268C22×D3—68no—
269C22×D3—64no—
270C22×D3—64no—
271C22×D3C23×D318yes—
272C3×Q8—616no—
273C3×D4—616no—
274C3×D4—632no—
275C2×C3×C4—24no—
276C2×C3×C4—22no—
277C2×C3×C4—28no—
278C2×C3×C4—24no—
279C2×C3×C4—38no—
280C2×C3×C4—68no—
281C2×C3×C4D3×D414yes—
282C2×C3×C4D3×D414yes—
283C2×C3×C4#23718yescomplemented
284C2×C3×C4#23918yescomplemented
285C2×C3×C4C23×D312yes—
286C2×C3×C4C23×D312yes—
287C2×C3×C4C23×D314yes—
288C2×C3×C4C23×D314yes—
289#67—632no—
290C2×Dic3—28no—
291C2×Dic3—34no—
292C2×Dic3—34no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—34no—
296C2×Dic3—34no—
297C2×Dic3—64no—
298C2×Dic3—62no—
299C2×Dic3—64no—
300C2×Dic3—632no—
301C2×Dic3—68no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304C2×Dic3C23×D318yes—
305D12—216no—
306D12—232no—
307D12—632no—
308C4×D3—316no—
309C4×D3—316no—
310C4×D3—616no—
311C4×D3—632no—
312C4×D3—632no—
313C4×D3—616no—
314C4×D3—616no—
315Dic6—216no—
316C2×C32#53214yescomplemented
317C2×C32C23×D411yescharacteristic
318C2×C32C22×#4112yes—
319C3⋊D3—24no—
320C3×D3—48no—
321C24—34no—
322C24—91no—
323#41—1864no—
324C2×Q8—38no—
325C2×Q8—68no—
326C2×D4—316no—
327C2×D4—38no—
328C2×D4—616no—
329C2×D4—68no—
330C2×D4—916no—
331C2×D4—1816no—
332C22×C4—34no—
333C22×C4—916no—
334C22×C4—91no—
335C22×C4—94no—
336C22×C4—98no—
337C22×C4—92no—
338C22×C4—98no—
339C22×C4—1816no—
340C22×C4—188no—
341C22×C4C2×D3212yes—
342C22×C4C2×D3211yescharacteristic
343C4⋊C4—316no—
344C22⋊C4—932no—
345C42—98no—
346C42—94no—
347C42C2×D3214yes—
348C22×C3—24no—
349C22×C3—22no—
350C22×C3—21no—
351C22×C3—68no—
352C22×C3—616no—
353C22×C3—1216no—
354C22×C3C2×D3×D412yes—
355C22×C3C2×D3×D412yes—
356C22×C3C2×#23714yes—
357C22×C3C2×#23914yes—
358C22×C3C24×D311yescharacteristic
359C22×C3C24×D311yescharacteristic
360C2×D3—28no—
361C2×D3—216no—
362C2×D3—34no—
363C2×D3—34no—
364C2×D3—416no—
365C2×D3—64no—
366C2×D3—68no—
367C2×D3—616no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—68no—
371C2×D3—68no—
372C3×C4—28no—
373C3×C4—24no—
374C3×C4—68no—
375C3×C4C2×D3×D414yes—
376C3×C4C2×D3×D414yes—
377C3×C4C2×#23718yescomplemented
378C3×C4C2×#23918yescomplemented
379Dic3—28no—
380Dic3—34no—
381Dic3—34no—
382Dic3—64no—
383Dic3—68no—
384Dic3—64no—
385Dic3—64no—
386C32C2×#53211yescharacteristic, complemented, Sylow
387C23—38no—
388C23—616no—
389C23—68no—
390C23—94no—
391C23—92no—
392C23—184no—
393C23C22×D3211yescharacteristic
394Q8—616no—
395D4—632no—
396D4—616no—
397D4—1832no—
398C2×C4—38no—
399C2×C4—68no—
400C2×C4—94no—
401C2×C4—92no—
402C2×C4—916no—
403C2×C4—94no—
404C2×C4—1832no—
405C2×C4—184no—
406C2×C4—1816no—
407C2×C4#379618yescomplemented
408C2×C4#380214yes—
409C2×C4C22×D3214yes—
410C2×C4C22×D3212yes—
411C2×C3—22no—
412C2×C3—21no—
413C2×C3—24no—
414C2×C3—128no—
415C2×C3#571614yescomplemented
416C2×C3#572514yescomplemented
417C2×C3C22×D3×D411yescharacteristic
418C2×C3C22×D3×D411yescharacteristic
419C2×C3C22×#23712yes—
420C2×C3C22×#23912yes—
421D3—48no—
422D3—68no—
423D3—64no—
424D3—64no—
425C22—616no—
426C22—68no—
427C22—94no—
428C22—1216no—
429C22—184no—
430C22—188no—
431C22C2×#379614yes—
432C22C2×#380212yes—
433C22C23×D3211yescharacteristic
434C4—68no—
435C4—94no—
436C4—184no—
437C4C2×#379618yescomplemented
438C4C2×#380214yes—
439C3—21no—
440C3C2×#571611yescharacteristic, complemented
441C3C2×#572511yescharacteristic, complemented
442C2—128no—
443C2—184no—
444C2#1059390714yesdirect product factor
445C2C22×#379612yes—
446C2C22×#380211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C2×C42×C3⋊D3C2semidirect
3. C2×C3×#874C2semidirect
4. C2×C3×#869C2semidirect
5. C2×#63916C2semidirect
6. C2×#63898C2semidirect
7. C2×#63863C2semidirect
8. #10593907C2direct (N × H)
19. C2×#3796C22semidirect
23. C42×C3⋊D3C22semidirect
25. C3×#874C22semidirect
26. C3×#869C22semidirect
28. #63916C22semidirect
29. #63898C22semidirect
30. #63863C22semidirect
43. C2×#874D3semidirect
47. C2×#869D3semidirect
55. C2×C4×C3⋊D3D4semidirect
117. #874C2×D3semidirect
121. #869C2×D3semidirect
130. C2×C32×C4#41semidirect
138. C4×C3⋊D3C2×D4semidirect
230. C32×C4C2×#41semidirect
283. C2×C3×C4#237semidirect
284. C2×C3×C4#239semidirect
316. C2×C32#532semidirect
377. C3×C4C2×#237semidirect
378. C3×C4C2×#239semidirect
386. C32C2×#532semidirect
407. C2×C4#3796semidirect
415. C2×C3#5716semidirect
416. C2×C3#5725semidirect
437. C4C2×#3796semidirect
440. C3C2×#5716semidirect
441. C3C2×#5725semidirect
444. C2#10593907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C42×C3⋊D32
C2×C3×#8742
C2×C3×#8692
C2×#639162
C2×#638982
C2×#638632
#105939072
C2×#57253
C2×#57163