Finite Group Databasebeta

← C2×#10595409 #11902626

Subgroups — C2×#10595409 #11902626

Order 1152.

3389 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
3C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10595409C2116yesmaximal, direct product factor
5C2×#63908C213yesmaximal, complemented
6C2×C4×#625C213yesmaximal, complemented
7C2×#63863C213yesmaximal, complemented
8C2×#63856C213yesmaximal, complemented
9C2×#5831—31nomaximal
10C2×#5817—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#239—28no—
13C2×C3×#239C2218yescomplemented
14C2×C3×D3×Q8—28no—
15C2×C3×D3×Q8C2218yescomplemented
16C22×C3×D12C2213yes—
17C22×C3×C4×D3C2213yes—
18C22×C3×C4×D3C2213yes—
19C22×C3×Dic6C2213yes—
20C22×#625C2213yes—
21Q8×C3⋊Dic3C2218yescomplemented
22C2×C4⋊(C3⋊Dic3)C2213yes—
23C2×C4×C3⋊Dic3C2213yes—
24C2×#3724C2213yes—
25C2×(C2×D3)⋊Dic3C2216yes—
26C2×(C2×D3)⋊Dic3C2213yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28#63908C22124yescomplemented
29C4×#625C22124yescomplemented
30#63863C22124yescomplemented
31#63856C22124yescomplemented
32C22×C3×#41—31no—
33C23×C3×Q8—31no—
34C22×#239D311yescharacteristic, complemented
35C22×D3×Q8D311yescharacteristic, complemented
36#5831—316no—
37#5817—316no—
38C2×#947—33no—
39C2×#946—33no—
40C2×Q8×Dic3—31no—
41C2×Q8×Dic3—31no—
42C2×Q8×Dic3—61no—
43C2×#938—33no—
44C2×#936—33no—
45C2×#930—33no—
46C2×C4×#67—33no—
47C2×C4×#67—33no—
48C2×#924—33no—
49C23×C3×D3C2313yes—
50C23×C3×D3C2311yescharacteristic
51C2×C32×Q8D418yescomplemented
52C2×C32×Q8C2314yes—
53C22×C32×C4C2313yes—
54C22×C3⋊Dic3C2313yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2313yes—
57C22×C3×Dic3C2311yescharacteristic
58C3×#239—232no—
59C3×D3×Q8—232no—
60C2×C3×D12—212no—
61C2×C3×D12C23112yes—
62C2×C3×C4×D3—212no—
63C2×C3×C4×D3—212no—
64C2×C3×C4×D3C23112yes—
65C2×C3×C4×D3C23112yes—
66C2×C3×Dic6—212no—
67C2×C3×Dic6C23112yes—
68C2×#625—212no—
69C2×#625C23112yes—
70C4⋊(C3⋊Dic3)C23112yes—
71C4×C3⋊Dic3C23112yes—
72#3724C23112yes—
73(C2×D3)⋊Dic3C23124yes—
74(C2×D3)⋊Dic3C23112yes—
75(C2×D3)⋊Dic3C2314yes—
76C2×#548—91noSylow
77C2×C3×#41—38no—
78C2×C3×#41—68no—
79C22×C3×Q8—21no—
80C22×C3×Q8—38no—
81C22×C3×Q8—33no—
82C22×C3×Q8—68no—
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×D4—33no—
86C23×C3×C4—33no—
87C23×C3×C4—33no—
88C22×#67—33no—
89C22×#67—33no—
90C2×#239—28no—
91C2×#239C2×D318yescomplemented
92C2×D3×Q8—28no—
93C2×D3×Q8C2×D318yescomplemented
94C22×D12C2×D313yes—
95C22×C4×D3C2×D313yes—
96C22×C4×D3C2×D313yes—
97C22×Dic6C2×D313yes—
98C2×#217—36no—
99C2×#217—31no—
100C2×#217—33no—
101#947—324no—
102#946—324no—
103Q8×Dic3—38no—
104Q8×Dic3—38no—
105Q8×Dic3—68no—
106#938—324no—
107#936—324no—
108#930—324no—
109C4×#67—324no—
110C4×#67—324no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—33no—
113C2×(C2×D3)⋊C4—36no—
114C2×C4⋊Dic3—33no—
115C2×C4⋊Dic3—33no—
116C2×C4⋊Dic3—63no—
117#924—324no—
118C2×Dic3⋊C4—33no—
119C2×Dic3⋊C4—33no—
120C2×C4×Dic3—33no—
121C2×C4×Dic3—33no—
122C2×C4×Dic3—63no—
123C23×C32C2411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—26no—
127C22×C3×D3—26no—
128C22×C3×D3—26no—
129C22×C3×D3#4114yescomplemented
130C22×C3×D3C2416yes—
131C22×C3×D3C2412yes—
132C32×Q8C2×D4116yescomplemented
133C2×C32×C4C2×D4112yes—
134C2×C32×C4C2416yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—26no—
137C2×C3⋊Dic3C2412yes—
138C2×C3⋊Dic3C2416yes—
139C2×C3×Dic3—26no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3C2416yes—
142C2×C3×Dic3C2412yes—
143C3×D12—224no—
144C3×C4×D3—224no—
145C3×C4×D3—224no—
146C3×Dic6—224no—
147#625—224no—
148C22×#41—31no—
149C23×Q8—31no—
150#548—916no—
151C2×#124—93no—
152C2×C22⋊Q8—93no—
153C2×#121—93no—
154C2×C4×Q8—91no—
155C2×C4×D4—93no—
156C24×C3—31no—
157C24×C3—33no—
158C23×D3C22×D313yes—
159C23×D3C22×D311yescharacteristic
160C3×#41—632no—
161C2×C3×Q8—28no—
162C2×C3×Q8—24no—
163C2×C3×Q8—312no—
164C2×C3×Q8—632no—
165C2×C3×Q8—612no—
166C2×C3×Q8#6718yescomplemented
167C2×C3×Q8#6718yescomplemented
168C2×C3×Q8C22×D314yes—
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—312no—
171C2×C3×D4—612no—
172C22×C3×C4—23no—
173C22×C3×C4—31no—
174C22×C3×C4—33no—
175C22×C3×C4—312no—
176C22×C3×C4—312no—
177C22×C3×C4—612no—
178C22×C3×C4—612no—
179C22×C3×C4C22×D313yes—
180C22×C3×C4C22×D313yes—
181C2×#67—312no—
182C2×#67—312no—
183C2×#67—612no—
184C2×#67—612no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—33no—
188C22×Dic3—33no—
189C22×Dic3—61no—
190C22×Dic3—63no—
191C22×Dic3C22×D311yescharacteristic
192C22×Dic3C22×D313yes—
193#239—232no—
194D3×Q8—232no—
195C2×D12—212no—
196C2×D12C22×D3112yes—
197C2×C4×D3—212no—
198C2×C4×D3—212no—
199C2×C4×D3C22×D3112yes—
200C2×C4×D3C22×D3112yes—
201C2×Dic6—212no—
202C2×Dic6C22×D3112yes—
203#217—324no—
204#217—34no—
205#217—312no—
206(C2×D3)⋊C4—34no—
207(C2×D3)⋊C4—312no—
208(C2×D3)⋊C4—324no—
209C4⋊Dic3—312no—
210C4⋊Dic3—312no—
211C4⋊Dic3—612no—
212Dic3⋊C4—312no—
213Dic3⋊C4—312no—
214C4×Dic3—312no—
215C4×Dic3—312no—
216C4×Dic3—612no—
217C22×C32C22×D412yes—
218C22×C32C2×#4112yes—
219C22×C322−1+412yes—
220C22×C32C2511yescharacteristic
221C2×C3×D3—28no—
222C2×C3×D3—22no—
223C2×C3×D3—22no—
224C2×C3×D3—26no—
225C2×C3×D3—26no—
226C2×C3×D3—26no—
227C2×C3×D3—412no—
228C2×C3×D3C2×#4114yescomplemented
229C32×C4C22×D4112yes—
230C3⋊Dic3—22no—
231C3⋊Dic3—26no—
232C3×Dic3—26no—
233C3×Dic3—22no—
234C2×#41—38no—
235C2×#41—68no—
236C22×Q8—38no—
237C22×Q8—33no—
238C22×Q8—68no—
239C22×Q8D3211yescharacteristic
240C22×D4—33no—
241C22×D4—93no—
242C23×C4—33no—
243C23×C4—33no—
244#124—924no—
245C22⋊Q8—924no—
246#121—924no—
247C4×Q8—98no—
248C4×D4—924no—
249C2×C4⋊C4—93no—
250C2×C4⋊C4—93no—
251C2×C22⋊C4—91no—
252C2×C22⋊C4—93no—
253C2×C22⋊C4—96no—
254C2×C42—93no—
255C23×C3—21no—
256C23×C3—34no—
257C23×C3—32no—
258C23×C3—36no—
259C23×C3—62no—
260C23×C3—62no—
261C23×C3—66no—
262C23×C3—66no—
263C23×C3—66no—
264C23×C3C23×D311yescharacteristic
265C23×C3C23×D311yescharacteristic
266C22×D3—22no—
267C22×D3—22no—
268C22×D3—26no—
269C22×D3—26no—
270C22×D3—26no—
271C22×D3#23914yescomplemented
272C22×D3C23×D316yes—
273C22×D3C23×D312yes—
274C3×Q8—216no—
275C3×Q8—624no—
276C3×Q8C2×#67116yescomplemented
277C3×Q8C2×#67116yescomplemented
278C3×D4—624no—
279C2×C3×C4—26no—
280C2×C3×C4—212no—
281C2×C3×C4—32no—
282C2×C3×C4—36no—
283C2×C3×C4—62no—
284C2×C3×C4—66no—
285C2×C3×C4—624no—
286C2×C3×C4—624no—
287C2×C3×C4C2×#67112yes—
288C2×C3×C4C2×#67112yes—
289C2×C3×C4C23×D316yes—
290C2×C3×C4C23×D316yes—
291#67—624no—
292#67—624no—
293C2×Dic3—26no—
294C2×Dic3—22no—
295C2×Dic3—32no—
296C2×Dic3—32no—
297C2×Dic3—36no—
298C2×Dic3—36no—
299C2×Dic3—62no—
300C2×Dic3—66no—
301C2×Dic3—64no—
302C2×Dic3—66no—
303C2×Dic3—62no—
304C2×Dic3—66no—
305C2×Dic3—62no—
306C2×Dic3—126no—
307C2×Dic3C23×D312yes—
308C2×Dic3C23×D316yes—
309D12—224no—
310C4×D3—224no—
311C4×D3—224no—
312Dic6—224no—
313C2×C32#54814yescomplemented
314C2×C32C23×D411yescharacteristic
315C2×C32C22×#4111yescharacteristic
316C2×C32C2×2−1+411yescharacteristic
317C3×D3—24no—
318C3×D3—46no—
319C24—31no—
320C24—33no—
321#41—632no—
322C2×Q8—312no—
323C2×Q8—632no—
324C2×Q8—612no—
325C2×Q8#62518yescomplemented
326C2×Q8C2×D3214yes—
327C2×D4—312no—
328C2×D4—612no—
329C2×D4—912no—
330C2×D4—1812no—
331C22×C4—33no—
332C22×C4—31no—
333C22×C4—312no—
334C22×C4—312no—
335C22×C4—612no—
336C22×C4—612no—
337C22×C4—91no—
338C22×C4—93no—
339C22×C4C2×D3213yes—
340C4⋊C4—912no—
341C4⋊C4—912no—
342C22⋊C4—94no—
343C22⋊C4—912no—
344C22⋊C4—924no—
345C42—912no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—34no—
351C22×C3—62no—
352C22×C3—62no—
353C22×C3—68no—
354C22×C3—66no—
355C22×C3—66no—
356C22×C3—66no—
357C22×C3—1212no—
358C22×C3C2×#23912yes—
359C22×C3#100712yes—
360C22×C3D3×#4112yes—
361C22×C3#101012yes—
362C22×C3C22×#6712yes—
363C22×C3C22×#6712yes—
364C22×C3C24×D311yescharacteristic
365C22×C3C24×D311yescharacteristic
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—28no—
369C2×D3—26no—
370C2×D3—26no—
371C2×D3—26no—
372C2×D3—412no—
373C2×D3C2×#23914yescomplemented
374C3×C4—212no—
375C3×C4—62no—
376C3×C4—66no—
377C3×C4C22×#67112yes—
378C3×C4C22×#67112yes—
379Dic3—26no—
380Dic3—22no—
381Dic3—64no—
382Dic3—66no—
383Dic3—62no—
384Dic3—66no—
385Dic3—62no—
386Dic3—126no—
387C32C2×#54811yescharacteristic, complemented, Sylow
388C23—34no—
389C23—32no—
390C23—36no—
391C23—62no—
392C23—62no—
393C23—66no—
394C23—66no—
395C23—66no—
396C23C22×D3211yescharacteristic
397Q8—624no—
398Q8C2×#625116yescomplemented
399D4—624no—
400D4—1824no—
401C2×C4—36no—
402C2×C4—32no—
403C2×C4—62no—
404C2×C4—66no—
405C2×C4—624no—
406C2×C4—624no—
407C2×C4—92no—
408C2×C4—96no—
409C2×C4—182no—
410C2×C4—186no—
411C2×C4C2×#625112yes—
412C2×C4C22×D3216yes—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—24no—
416C2×C3—21no—
417C2×C3—64no—
418C2×C3—126no—
419C2×C3#581714yescomplemented
420C2×C3#583114yescomplemented
421C2×C3C22×#23911yescharacteristic
422C2×C3C2×#100711yescharacteristic
423C2×C3C2×D3×#4111yescharacteristic
424C2×C3C2×#101011yescharacteristic
425C2×C3C23×#6711yescharacteristic
426C2×C3C23×#6711yescharacteristic
427D3—24no—
428D3—46no—
429C22—34no—
430C22—62no—
431C22—68no—
432C22—62no—
433C22—66no—
434C22—66no—
435C22—66no—
436C22—1212no—
437C22#6431512yes—
438C22D3×#23912yes—
439C22C22×#62512yes—
440C22C23×D3211yescharacteristic
441C4—62no—
442C4—66no—
443C4—182no—
444C4—186no—
445C4C22×#625112yes—
446C3—21no—
447C3C2×#581711yescharacteristic, complemented
448C3C2×#583111yescharacteristic, complemented
449C2—64no—
450C2—126no—
451C2#1059540914yesdirect product factor
452C2C2×#6431511yescharacteristic
453C2C2×D3×#23911yescharacteristic
454C2C23×#62511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×C3×D3×Q8C2semidirect
3. C2×Q8×C3⋊Dic3C2semidirect
4. #10595409C2direct (N × H)
5. C2×#63908C2semidirect
6. C2×C4×#625C2semidirect
7. C2×#63863C2semidirect
8. C2×#63856C2semidirect
13. C2×C3×#239C22semidirect
15. C2×C3×D3×Q8C22semidirect
21. Q8×C3⋊Dic3C22semidirect
28. #63908C22semidirect
29. C4×#625C22semidirect
30. #63863C22semidirect
31. #63856C22semidirect
34. C22×#239D3semidirect
35. C22×D3×Q8D3semidirect
51. C2×C32×Q8D4semidirect
91. C2×#239C2×D3semidirect
93. C2×D3×Q8C2×D3semidirect
129. C22×C3×D3#41semidirect
132. C32×Q8C2×D4semidirect
166. C2×C3×Q8#67semidirect
167. C2×C3×Q8#67semidirect
228. C2×C3×D3C2×#41semidirect
271. C22×D3#239semidirect
276. C3×Q8C2×#67semidirect
277. C3×Q8C2×#67semidirect
313. C2×C32#548semidirect
325. C2×Q8#625semidirect
373. C2×D3C2×#239semidirect
387. C32C2×#548semidirect
398. Q8C2×#625semidirect
419. C2×C3#5817semidirect
420. C2×C3#5831semidirect
447. C3C2×#5817semidirect
448. C3C2×#5831semidirect
451. C2#10595409direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×C3×D3×Q82
C2×Q8×C3⋊Dic32
#105954092
C2×#639082
C2×C4×#6252
C2×#638632
C2×#638562
C2×#58313
C2×#58173