Finite Group Databasebeta

← C2×#10595410 #11902730

Subgroups — C2×#10595410 #11902730

Order 1152.

3917 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595410C2116yesmaximal, direct product factor
5C2×#63916C213yesmaximal, complemented
6C2×#63911C213yesmaximal, complemented
7C2×#63909C213yesmaximal, complemented
8C2×C4×#626C213yesmaximal, complemented
9C2×#5834—31nomaximal
10C2×#5577—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×#3832—28no—
13C2×#3832C2218yescomplemented
14C22×C4⋊(C3⋊D3)C2213yes—
15C22×C4×C3⋊D3C2213yes—
16C2×C3×#239—28no—
17C2×C3×#239C2218yescomplemented
18C22×C3×D12C2213yes—
19C22×C3×C4×D3C2213yes—
20C22×#626C2213yes—
21C22×#626C2216yes—
22C3×Q8×Dic3C2218yescomplemented
23C2×C3×C4⋊Dic3C2213yes—
24C2×C3×C4×Dic3C2213yes—
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×#3722C2213yes—
27C2×(C2×D3)⋊Dic3C2213yes—
28#63916C22124yescomplemented
29#63911C22124yescomplemented
30#63909C22124yescomplemented
31C4×#626C22124yescomplemented
32C22×C3×#41—31no—
33C22×#239—31no—
34C22×#239—31no—
35C22×#239—61no—
36C22×#239D311yescharacteristic, complemented
37C2×C3×C4×Q8—31no—
38#5834—316no—
39C2×Q8×Dic3D311yescharacteristic, complemented
40C2×#940—33no—
41C2×#938—33no—
42C2×#930—33no—
43C2×C4×#67—33no—
44#5577—316no—
45C2×#895—33no—
46C2×#895—33no—
47C2×#874—33no—
48C2×C4×D12—33no—
49C23×C3⋊D3C2313yes—
50C23×C3×D3C2313yes—
51C2×C32×Q8D418yescomplemented
52C2×C32×Q8C2314yes—
53C22×C32×C4C2313yes—
54C22×C3⋊Dic3C2311yescharacteristic
55#3832—232no—
56C2×C4⋊(C3⋊D3)—212no—
57C2×C4⋊(C3⋊D3)C23112yes—
58C2×C4×C3⋊D3—212no—
59C2×C4×C3⋊D3C23112yes—
60C22×C3×Dic3C2313yes—
61C22×C3×Dic3C2311yescharacteristic
62C22×C3×Dic3C2311yescharacteristic
63C3×#239—232no—
64C2×C3×D12—212no—
65C2×C3×D12C23112yes—
66C2×C3×C4×D3—212no—
67C2×C3×C4×D3C23112yes—
68C2×#626—212no—
69C2×#626—412no—
70C2×#626C23112yes—
71C2×#626C23124yes—
72C3×C4⋊Dic3C23112yes—
73C3×C4×Dic3C23112yes—
74Dic3⋊Dic3C2314yes—
75#3722C23112yes—
76(C2×D3)⋊Dic3C23112yes—
77C2×#550—91noSylow
78C2×C3×#41—38no—
79C2×C3×#41—68no—
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×D4—33no—
84C23×C3×C4—33no—
85C22×#67—33no—
86C22×#67—36no—
87C2×#239—28no—
88C2×#239—38no—
89C2×#239—38no—
90C2×#239—68no—
91C2×#239—616no—
92C2×#239—68no—
93C2×#239—68no—
94C2×#239C2×D318yescomplemented
95C22×D12—33no—
96C22×D12—33no—
97C22×D12—33no—
98C22×D12—36no—
99C22×D12—63no—
100C22×D12C2×D313yes—
101C22×C4×D3—33no—
102C22×C4×D3—33no—
103C22×C4×D3—63no—
104C22×C4×D3C2×D313yes—
105C3×C4×Q8—38no—
106C2×C3×C4⋊C4—33no—
107C2×C3×C42—33no—
108C2×#217—33no—
109Q8×Dic3C2×D318yescomplemented
110#940—324no—
111#938—324no—
112#930—324no—
113C4×#67—324no—
114C2×(C2×D3)⋊C4—33no—
115C2×(C2×D3)⋊C4—33no—
116C2×(C2×D3)⋊C4—33no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3C2×D313yes—
119C2×Dic3⋊C4—31no—
120C2×C4×Dic3C2×D313yes—
121#895—324no—
122#895—324no—
123#874—324no—
124C4×D12—324no—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—26no—
127C22×C3⋊D3—26no—
128C22×C3⋊D3—26no—
129C22×C3⋊D3C2416yes—
130C22×C3×D3—26no—
131C22×C3×D3—26no—
132C22×C3×D3—26no—
133C22×C3×D3C2416yes—
134C32×Q8C2×D4116yescomplemented
135C2×C32×C4C2×D4112yes—
136C2×C32×C4C2416yes—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3C2412yes—
139C4⋊(C3⋊D3)—224no—
140C4×C3⋊D3—224no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—26no—
143C2×C3×Dic3#4114yescomplemented
144C2×C3×Dic3C2416yes—
145C2×C3×Dic3C2412yes—
146C2×C3×Dic3C2412yes—
147C3×D12—224no—
148C3×C4×D3—224no—
149#626—224no—
150#626—424no—
151C22×#41—31no—
152C22×#41—91no—
153#550—916no—
154C2×#127—93no—
155C2×#121—93no—
156C2×#121—93no—
157C2×C4×Q8—31no—
158C2×C4×D4—93no—
159C24×C3—33no—
160C23×D3—33no—
161C23×D3—33no—
162C23×D3—63no—
163C23×D3C22×D313yes—
164C3×#41—632no—
165C2×C3×Q8—28no—
166C2×C3×Q8—24no—
167C2×C3×Q8D1218yescomplemented
168C2×C3×Q8#6718yescomplemented
169C2×C3×Q8C22×D314yes—
170C2×C3×Q8C22×D314yes—
171C2×C3×D4—312no—
172C2×C3×D4—612no—
173C22×C3×C4—23no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—33no—
177C22×C3×C4—312no—
178C22×C3×C4—612no—
179C22×C3×C4C22×D313yes—
180C22×C3×C4C22×D313yes—
181C2×#67—312no—
182C2×#67—324no—
183C2×#67—612no—
184C2×#67—1212no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—61no—
188C22×Dic3C22×D313yes—
189C22×Dic3C22×D311yescharacteristic
190C22×Dic3C22×D311yescharacteristic
191#239—232no—
192#239—664no—
193#239—632no—
194#239—632no—
195C2×D12—212no—
196C2×D12—312no—
197C2×D12—312no—
198C2×D12—312no—
199C2×D12—324no—
200C2×D12—612no—
201C2×D12—624no—
202C2×D12—612no—
203C2×D12—612no—
204C2×D12—612no—
205C2×D12—1212no—
206C2×D12C22×D3112yes—
207C2×C4×D3—212no—
208C2×C4×D3—312no—
209C2×C4×D3—312no—
210C2×C4×D3—612no—
211C2×C4×D3—624no—
212C2×C4×D3—612no—
213C2×C4×D3—612no—
214C2×C4×D3C22×D3112yes—
215C3×C4⋊C4—312no—
216C3×C42—312no—
217#217—312no—
218(C2×D3)⋊C4—312no—
219(C2×D3)⋊C4—312no—
220(C2×D3)⋊C4—312no—
221C4⋊Dic3—34no—
222C4⋊Dic3C22×D3112yes—
223Dic3⋊C4—34no—
224C4×Dic3C22×D3112yes—
225C22×C32C22×D412yes—
226C22×C32C2×#4112yes—
227C22×C32H(5,𝔽2)12yes—
228C22×C32C2511yescharacteristic
229C2×C3⋊D3—26no—
230C2×C3⋊D3—26no—
231C2×C3⋊D3—26no—
232C2×C3⋊D3—412no—
233C2×C3×D3—26no—
234C2×C3×D3—26no—
235C2×C3×D3—26no—
236C2×C3×D3—412no—
237C32×C4C22×D4112yes—
238C3⋊Dic3—22no—
239C3×Dic3—22no—
240C3×Dic3—26no—
241C3×Dic3C2×#4114yescomplemented
242C2×#41—38no—
243C2×#41—68no—
244C2×#41—98no—
245C2×#41—188no—
246C22×Q8D3211yescharacteristic
247C22×D4—33no—
248C22×D4—93no—
249C22×D4—96no—
250C22×D4—93no—
251C23×C4—33no—
252C23×C4—93no—
253#127—924no—
254#121—924no—
255#121—924no—
256C4×Q8—38no—
257C4×D4—924no—
258C2×C4⋊C4—33no—
259C2×C4⋊C4—91no—
260C2×C22⋊C4—93no—
261C2×C22⋊C4—93no—
262C2×C42—33no—
263C23×C3—21no—
264C23×C3—36no—
265C23×C3—66no—
266C23×C3—66no—
267C23×C3—66no—
268C23×C3C23×D311yescharacteristic
269C23×C3C23×D311yescharacteristic
270C22×D3—26no—
271C22×D3—26no—
272C22×D3—26no—
273C22×D3—36no—
274C22×D3—36no—
275C22×D3—66no—
276C22×D3—612no—
277C22×D3—66no—
278C22×D3—66no—
279C22×D3—66no—
280C22×D3—66no—
281C22×D3—66no—
282C22×D3—66no—
283C22×D3—126no—
284C22×D3—126no—
285C22×D3C23×D316yes—
286C3×Q8—216no—
287C3×Q8C2×D12116yescomplemented
288C3×Q8C2×#67116yescomplemented
289C3×D4—624no—
290C2×C3×C4—26no—
291C2×C3×C4—212no—
292C2×C3×C4—34no—
293C2×C3×C4—32no—
294C2×C3×C4—32no—
295C2×C3×C4—36no—
296C2×C3×C4—62no—
297C2×C3×C4—66no—
298C2×C3×C4—624no—
299C2×C3×C4C2×D12112yes—
300C2×C3×C4C2×#67112yes—
301C2×C3×C4C23×D316yes—
302C2×C3×C4C23×D316yes—
303#67—624no—
304#67—1224no—
305C2×Dic3—26no—
306C2×Dic3—22no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—62no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3#23914yescomplemented
314C2×Dic3C23×D316yes—
315C2×Dic3C23×D312yes—
316C2×Dic3C23×D312yes—
317D12—224no—
318D12—648no—
319D12—624no—
320D12—624no—
321D12—624no—
322D12—1224no—
323C4×D3—224no—
324C4×D3—648no—
325C4×D3—624no—
326C4×D3—624no—
327C2×C32#55014yescomplemented
328C2×C32C23×D411yescharacteristic
329C2×C32C22×#4111yescharacteristic
330C2×C32C2×H(5,𝔽2)11yescharacteristic
331C3⋊D3—46no—
332C3×D3—46no—
333C24—33no—
334C24—93no—
335#41—632no—
336#41—1832no—
337C2×Q8#62618yescomplemented
338C2×Q8C2×D3214yes—
339C2×D4—312no—
340C2×D4—612no—
341C2×D4—912no—
342C2×D4—924no—
343C2×D4—912no—
344C2×D4—1812no—
345C2×D4—1812no—
346C2×D4—3612no—
347C22×C4—31no—
348C22×C4—33no—
349C22×C4—31no—
350C22×C4—312no—
351C22×C4—612no—
352C22×C4—91no—
353C22×C4—912no—
354C22×C4—1812no—
355C22×C4C2×D3213yes—
356C4⋊C4—312no—
357C4⋊C4—94no—
358C22⋊C4—912no—
359C22⋊C4—912no—
360C42—312no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—66no—
366C22×C3—66no—
367C22×C3—66no—
368C22×C3—1212no—
369C22×C3C22×D1212yes—
370C22×C3C2×#23912yes—
371C22×C3D3×#4112yes—
372C22×C3#100912yes—
373C22×C3#100912yes—
374C22×C3C22×#6712yes—
375C22×C3C24×D311yescharacteristic
376C22×C3C24×D311yescharacteristic
377C2×D3—26no—
378C2×D3—26no—
379C2×D3—26no—
380C2×D3—412no—
381C2×D3—612no—
382C2×D3—66no—
383C2×D3—66no—
384C2×D3—66no—
385C2×D3—66no—
386C2×D3—66no—
387C2×D3—66no—
388C2×D3—126no—
389C2×D3—126no—
390C2×D3—1224no—
391C2×D3—1212no—
392C2×D3—1212no—
393C3×C4—212no—
394C3×C4—34no—
395C3×C4—62no—
396C3×C4—66no—
397C3×C4C22×D12112yes—
398C3×C4C22×#67112yes—
399Dic3—26no—
400Dic3—22no—
401Dic3—64no—
402Dic3—62no—
403Dic3—62no—
404Dic3C2×#23914yescomplemented
405C32C2×#55011yescharacteristic, complemented, Sylow
406C23—36no—
407C23—66no—
408C23—66no—
409C23—66no—
410C23—96no—
411C23—186no—
412C23—186no—
413C23—186no—
414C23C22×D3211yescharacteristic
415Q8C2×#626116yescomplemented
416D4—624no—
417D4—1824no—
418D4—1824no—
419D4—3624no—
420C2×C4—34no—
421C2×C4—32no—
422C2×C4—36no—
423C2×C4—32no—
424C2×C4—66no—
425C2×C4—62no—
426C2×C4—624no—
427C2×C4—92no—
428C2×C4—182no—
429C2×C4—1824no—
430C2×C4C2×#626112yes—
431C2×C4C22×D3216yes—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—24no—
435C2×C3—21no—
436C2×C3—126no—
437C2×C3#557714yescomplemented
438C2×C3#583414yescomplemented
439C2×C3C23×D1211yescharacteristic
440C2×C3C22×#23911yescharacteristic
441C2×C3C2×D3×#4111yescharacteristic
442C2×C3C2×#100911yescharacteristic
443C2×C3C2×#100911yescharacteristic
444C2×C3C23×#6711yescharacteristic
445D3—46no—
446D3—1212no—
447D3—126no—
448D3—126no—
449C22—66no—
450C22—66no—
451C22—66no—
452C22—1212no—
453C22—186no—
454C22—186no—
455C22—186no—
456C22—3612no—
457C22D3×#23912yes—
458C22#6432012yes—
459C22C22×#62612yes—
460C22C23×D3211yescharacteristic
461C4—34no—
462C4—66no—
463C4—62no—
464C4—182no—
465C4C22×#626112yes—
466C3—21no—
467C3C2×#557711yescharacteristic, complemented
468C3C2×#583411yescharacteristic, complemented
469C2—126no—
470C2—366no—
471C2#1059541014yesdirect product factor
472C2C2×D3×#23911yescharacteristic
473C2C2×#6432011yescharacteristic
474C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C22×C3×#239C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595410C2direct (N × H)
5. C2×#63916C2semidirect
6. C2×#63911C2semidirect
7. C2×#63909C2semidirect
8. C2×C4×#626C2semidirect
13. C2×#3832C22semidirect
17. C2×C3×#239C22semidirect
22. C3×Q8×Dic3C22semidirect
28. #63916C22semidirect
29. #63911C22semidirect
30. #63909C22semidirect
31. C4×#626C22semidirect
36. C22×#239D3semidirect
39. C2×Q8×Dic3D3semidirect
51. C2×C32×Q8D4semidirect
94. C2×#239C2×D3semidirect
109. Q8×Dic3C2×D3semidirect
134. C32×Q8C2×D4semidirect
143. C2×C3×Dic3#41semidirect
167. C2×C3×Q8D12semidirect
168. C2×C3×Q8#67semidirect
241. C3×Dic3C2×#41semidirect
287. C3×Q8C2×D12semidirect
288. C3×Q8C2×#67semidirect
313. C2×Dic3#239semidirect
327. C2×C32#550semidirect
337. C2×Q8#626semidirect
404. Dic3C2×#239semidirect
405. C32C2×#550semidirect
415. Q8C2×#626semidirect
437. C2×C3#5577semidirect
438. C2×C3#5834semidirect
467. C3C2×#5577semidirect
468. C3C2×#5834semidirect
471. C2#10595410direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×C3×#2392
C2×C3×Q8×Dic32
#105954102
C2×#639162
C2×#639112
C2×#639092
C2×C4×#6262
C2×#58343
C2×#55773