Finite Group Databasebeta

← C2×#10595414 #11902625

Subgroups — C2×#10595414 #11902625

Order 1152.

3665 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595414C2116yesmaximal, direct product factor
5C2×#63916C213yesmaximal, complemented
6C2×C4×#626C213yesmaximal, complemented
7C2×#63860C213yesmaximal, complemented
8C2×#63857C213yesmaximal, complemented
9C2×#5831—31nomaximal
10C2×#5576—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×Q8×C3⋊D3—28no—
13C2×Q8×C3⋊D3C2218yescomplemented
14C22×C4×C3⋊D3C2213yes—
15C22×#634C2213yes—
16C2×C3×#239—28no—
17C2×C3×#239C2218yescomplemented
18C22×C3×D12C2213yes—
19C22×C3×C4×D3C2213yes—
20C22×#626C2213yes—
21C3×Q8×Dic3C2218yescomplemented
22C2×C3×C4⋊Dic3C2213yes—
23C2×C3×C4×Dic3C2213yes—
24C2×Dic3⋊Dic3C2213yes—
25C2×#3722C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2216yes—
27C2×(C2×D3)⋊Dic3C2213yes—
28#63916C22124yescomplemented
29C4×#626C22124yescomplemented
30#63860C22124yescomplemented
31#63857C22124yescomplemented
32C22×C3×#41—31no—
33C22×#239D311yescharacteristic, complemented
34C22×D3×Q8—31no—
35C22×D3×Q8—31no—
36C22×D3×Q8—61no—
37C2×C3×C4×Q8—31no—
38#5831—316no—
39C2×Q8×Dic3D311yescharacteristic, complemented
40C2×#938—33no—
41C2×#936—33no—
42C2×C4×#67—33no—
43C2×#924—33no—
44#5576—316no—
45C2×#897—33no—
46C2×#895—33no—
47C2×#875—33no—
48C2×C4×D12—33no—
49C23×C3⋊D3C2311yescharacteristic
50C23×C3×D3C2313yes—
51C2×C32×Q8D418yescomplemented
52C2×C32×Q8C2314yes—
53C22×C32×C4C2313yes—
54C22×C3⋊Dic3C2313yes—
55Q8×C3⋊D3—232no—
56C2×C4×C3⋊D3—212no—
57C2×C4×C3⋊D3C23112yes—
58C2×#634—212no—
59C2×#634C23112yes—
60C22×C3×Dic3C2311yescharacteristic
61C22×C3×Dic3C2313yes—
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×#626C23112yes—
70C3×C4⋊Dic3C23112yes—
71C3×C4×Dic3C23112yes—
72Dic3⋊Dic3C23112yes—
73#3722C2314yes—
74(C2×D3)⋊Dic3C23124yes—
75(C2×D3)⋊Dic3C23112yes—
76C2×#548—91noSylow
77C2×C3×#41—38no—
78C2×C3×#41—68no—
79C22×C3×Q8—21no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×D4—33no—
83C23×C3×C4—33no—
84C22×#67—33no—
85C2×#239—28no—
86C2×#239C2×D318yescomplemented
87C2×D3×Q8—38no—
88C2×D3×Q8—38no—
89C2×D3×Q8—68no—
90C2×D3×Q8—616no—
91C2×D3×Q8—68no—
92C2×D3×Q8—68no—
93C22×D12—33no—
94C22×D12C2×D313yes—
95C22×C4×D3—33no—
96C22×C4×D3—33no—
97C22×C4×D3—63no—
98C22×C4×D3C2×D313yes—
99C22×Dic6—33no—
100C22×Dic6—33no—
101C22×Dic6—63no—
102C3×C4×Q8—38no—
103C2×C3×C4⋊C4—33no—
104C2×C3×C42—33no—
105C2×#217—36no—
106C2×#217—33no—
107Q8×Dic3C2×D318yescomplemented
108#938—324no—
109#936—324no—
110C4×#67—324no—
111C2×(C2×D3)⋊C4—33no—
112C2×(C2×D3)⋊C4—36no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×C4⋊Dic3—33no—
116C2×C4⋊Dic3C2×D313yes—
117#924—324no—
118C2×Dic3⋊C4—33no—
119C2×C4×Dic3C2×D313yes—
120#897—324no—
121#895—324no—
122#875—324no—
123C4×D12—324no—
124C23×C32C2411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3#4114yescomplemented
128C22×C3⋊D3C2412yes—
129C22×C3×D3—26no—
130C22×C3×D3—26no—
131C22×C3×D3—26no—
132C22×C3×D3C2416yes—
133C32×Q8C2×D4116yescomplemented
134C2×C32×C4C2×D4112yes—
135C2×C32×C4C2416yes—
136C2×C3⋊Dic3—26no—
137C2×C3⋊Dic3C2416yes—
138C4×C3⋊D3—224no—
139#634—224no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—26no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3C2412yes—
144C2×C3×Dic3C2416yes—
145C2×C3×Dic3C2412yes—
146C3×D12—224no—
147C3×C4×D3—224no—
148#626—224no—
149C22×#41—31no—
150C23×Q8—91no—
151#548—916no—
152C2×#124—93no—
153C2×C22⋊Q8—93no—
154C2×#121—93no—
155C2×C4×Q8—31no—
156C2×C4×D4—93no—
157C24×C3—33no—
158C23×D3—31no—
159C23×D3—31no—
160C23×D3—61no—
161C23×D3C22×D313yes—
162C3×#41—632no—
163C2×C3×Q8—28no—
164C2×C3×Q8—24no—
165C2×C3×Q8D1218yescomplemented
166C2×C3×Q8#6718yescomplemented
167C2×C3×Q8C22×D314yes—
168C2×C3×Q8C22×D314yes—
169C2×C3×D4—312no—
170C2×C3×D4—612no—
171C22×C3×C4—23no—
172C22×C3×C4—31no—
173C22×C3×C4—33no—
174C22×C3×C4—31no—
175C22×C3×C4—312no—
176C22×C3×C4—612no—
177C22×C3×C4C22×D313yes—
178C22×C3×C4C22×D313yes—
179C2×#67—312no—
180C2×#67—612no—
181C22×Dic3—33no—
182C22×Dic3—33no—
183C22×Dic3—63no—
184C22×Dic3C22×D311yescharacteristic
185C22×Dic3C22×D313yes—
186C22×Dic3C22×D311yescharacteristic
187#239—232no—
188D3×Q8—664no—
189D3×Q8—632no—
190D3×Q8—632no—
191C2×D12—212no—
192C2×D12—312no—
193C2×D12—612no—
194C2×D12C22×D3112yes—
195C2×C4×D3—212no—
196C2×C4×D3—312no—
197C2×C4×D3—312no—
198C2×C4×D3—612no—
199C2×C4×D3—624no—
200C2×C4×D3—612no—
201C2×C4×D3—612no—
202C2×C4×D3C22×D3112yes—
203C2×Dic6—312no—
204C2×Dic6—312no—
205C2×Dic6—612no—
206C2×Dic6—624no—
207C2×Dic6—612no—
208C2×Dic6—612no—
209C3×C4⋊C4—312no—
210C3×C42—312no—
211#217—324no—
212#217—312no—
213(C2×D3)⋊C4—312no—
214(C2×D3)⋊C4—324no—
215(C2×D3)⋊C4—34no—
216(C2×D3)⋊C4—34no—
217C4⋊Dic3—312no—
218C4⋊Dic3C22×D3112yes—
219Dic3⋊C4—312no—
220C4×Dic3C22×D3112yes—
221C22×C32C22×D412yes—
222C22×C32C2×#4112yes—
223C22×C322−1+412yes—
224C22×C32C2511yescharacteristic
225C2×C3⋊D3—28no—
226C2×C3⋊D3—22no—
227C2×C3⋊D3—22no—
228C2×C3⋊D3C2×#4114yescomplemented
229C2×C3×D3—26no—
230C2×C3×D3—26no—
231C2×C3×D3—26no—
232C2×C3×D3—412no—
233C32×C4C22×D4112yes—
234C3⋊Dic3—26no—
235C3×Dic3—22no—
236C3×Dic3—26no—
237C3×Dic3—22no—
238C2×#41—38no—
239C2×#41—68no—
240C22×Q8—98no—
241C22×Q8—93no—
242C22×Q8—188no—
243C22×Q8D3211yescharacteristic
244C22×D4—33no—
245C22×D4—93no—
246C23×C4—33no—
247C23×C4—93no—
248#124—924no—
249C22⋊Q8—924no—
250#121—924no—
251C4×Q8—38no—
252C4×D4—924no—
253C2×C4⋊C4—33no—
254C2×C4⋊C4—93no—
255C2×C22⋊C4—91no—
256C2×C22⋊C4—93no—
257C2×C22⋊C4—96no—
258C2×C42—33no—
259C23×C3—21no—
260C23×C3—36no—
261C23×C3—66no—
262C23×C3—66no—
263C23×C3—66no—
264C23×C3C23×D311yescharacteristic
265C23×C3C23×D311yescharacteristic
266C22×D3—26no—
267C22×D3—26no—
268C22×D3—26no—
269C22×D3—34no—
270C22×D3—34no—
271C22×D3—32no—
272C22×D3—32no—
273C22×D3—64no—
274C22×D3—62no—
275C22×D3—64no—
276C22×D3—64no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3C23×D316yes—
282C3×Q8—216no—
283C3×Q8C2×D12116yescomplemented
284C3×Q8C2×#67116yescomplemented
285C3×D4—624no—
286C2×C3×C4—26no—
287C2×C3×C4—212no—
288C2×C3×C4—32no—
289C2×C3×C4—36no—
290C2×C3×C4—32no—
291C2×C3×C4—62no—
292C2×C3×C4—66no—
293C2×C3×C4—62no—
294C2×C3×C4—624no—
295C2×C3×C4C2×D12112yes—
296C2×C3×C4C2×#67112yes—
297C2×C3×C4C23×D316yes—
298C2×C3×C4C23×D316yes—
299#67—624no—
300C2×Dic3—22no—
301C2×Dic3—26no—
302C2×Dic3—22no—
303C2×Dic3—36no—
304C2×Dic3—36no—
305C2×Dic3—66no—
306C2×Dic3—612no—
307C2×Dic3—66no—
308C2×Dic3—66no—
309C2×Dic3C23×D312yes—
310C2×Dic3C23×D316yes—
311C2×Dic3C23×D312yes—
312D12—224no—
313D12—624no—
314C4×D3—224no—
315C4×D3—648no—
316C4×D3—624no—
317C4×D3—624no—
318Dic6—648no—
319Dic6—624no—
320Dic6—624no—
321C2×C32#54814yescomplemented
322C2×C32C23×D411yescharacteristic
323C2×C32C22×#4111yescharacteristic
324C2×C32C2×2−1+411yescharacteristic
325C3⋊D3—24no—
326C3×D3—46no—
327C24—33no—
328C24—91no—
329#41—632no—
330C2×Q8—912no—
331C2×Q8—1832no—
332C2×Q8—1812no—
333C2×Q8#62618yescomplemented
334C2×Q8C2×D3214yes—
335C2×D4—312no—
336C2×D4—612no—
337C2×D4—912no—
338C2×D4—1812no—
339C22×C4—31no—
340C22×C4—33no—
341C22×C4—31no—
342C22×C4—312no—
343C22×C4—612no—
344C22×C4—93no—
345C22×C4—912no—
346C22×C4—1812no—
347C22×C4C2×D3213yes—
348C4⋊C4—312no—
349C4⋊C4—912no—
350C22⋊C4—94no—
351C22⋊C4—912no—
352C22⋊C4—924no—
353C42—312no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—66no—
359C22×C3—66no—
360C22×C3—66no—
361C22×C3—1212no—
362C22×C3C22×D1212yes—
363C22×C3#100712yes—
364C22×C3D3×#4112yes—
365C22×C3D3×#4112yes—
366C22×C3#101012yes—
367C22×C3C22×#6712yes—
368C22×C3C24×D311yescharacteristic
369C22×C3C24×D311yescharacteristic
370C2×D3—26no—
371C2×D3—26no—
372C2×D3—26no—
373C2×D3—34no—
374C2×D3—34no—
375C2×D3—412no—
376C2×D3—64no—
377C2×D3—64no—
378C2×D3—64no—
379C2×D3—616no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—68no—
385C2×D3—68no—
386C3×C4—212no—
387C3×C4—62no—
388C3×C4—66no—
389C3×C4—62no—
390C3×C4C22×D12112yes—
391C3×C4C22×#67112yes—
392Dic3—22no—
393Dic3—26no—
394Dic3—22no—
395Dic3—612no—
396Dic3—66no—
397Dic3—66no—
398C32C2×#54811yescharacteristic, complemented, Sylow
399C23—36no—
400C23—66no—
401C23—66no—
402C23—66no—
403C23—94no—
404C23—92no—
405C23—182no—
406C23—182no—
407C23C22×D3211yescharacteristic
408Q8—1824no—
409Q8C2×#626116yescomplemented
410D4—624no—
411D4—1824no—
412C2×C4—32no—
413C2×C4—36no—
414C2×C4—32no—
415C2×C4—62no—
416C2×C4—66no—
417C2×C4—62no—
418C2×C4—624no—
419C2×C4—96no—
420C2×C4—186no—
421C2×C4—1824no—
422C2×C4C2×#626112yes—
423C2×C4C22×D3216yes—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—24no—
427C2×C3—21no—
428C2×C3—126no—
429C2×C3#557614yescomplemented
430C2×C3#583114yescomplemented
431C2×C3C23×D1211yescharacteristic
432C2×C3C2×#100711yescharacteristic
433C2×C3C2×D3×#4111yescharacteristic
434C2×C3C2×D3×#4111yescharacteristic
435C2×C3C2×#101011yescharacteristic
436C2×C3C23×#6711yescharacteristic
437D3—46no—
438D3—68no—
439D3—64no—
440D3—64no—
441C22—66no—
442C22—66no—
443C22—66no—
444C22—94no—
445C22—1212no—
446C22—182no—
447C22—188no—
448C22—182no—
449C22#6431512yes—
450C22#6431912yes—
451C22C22×#62612yes—
452C22C23×D3211yescharacteristic
453C4—62no—
454C4—66no—
455C4—62no—
456C4—186no—
457C4C22×#626112yes—
458C3—21no—
459C3C2×#557611yescharacteristic, complemented
460C3C2×#583111yescharacteristic, complemented
461C2—126no—
462C2—184no—
463C2#1059541414yesdirect product factor
464C2C2×#6431511yescharacteristic
465C2C2×#6431911yescharacteristic
466C2C23×#62611yescharacteristic
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×Q8×C3⋊D3C2semidirect
2. C22×C3×#239C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595414C2direct (N × H)
5. C2×#63916C2semidirect
6. C2×C4×#626C2semidirect
7. C2×#63860C2semidirect
8. C2×#63857C2semidirect
13. C2×Q8×C3⋊D3C22semidirect
17. C2×C3×#239C22semidirect
21. C3×Q8×Dic3C22semidirect
28. #63916C22semidirect
29. C4×#626C22semidirect
30. #63860C22semidirect
31. #63857C22semidirect
33. C22×#239D3semidirect
39. C2×Q8×Dic3D3semidirect
51. C2×C32×Q8D4semidirect
86. C2×#239C2×D3semidirect
107. Q8×Dic3C2×D3semidirect
127. C22×C3⋊D3#41semidirect
133. C32×Q8C2×D4semidirect
165. C2×C3×Q8D12semidirect
166. C2×C3×Q8#67semidirect
228. C2×C3⋊D3C2×#41semidirect
283. C3×Q8C2×D12semidirect
284. C3×Q8C2×#67semidirect
321. C2×C32#548semidirect
333. C2×Q8#626semidirect
398. C32C2×#548semidirect
409. Q8C2×#626semidirect
429. C2×C3#5576semidirect
430. C2×C3#5831semidirect
459. C3C2×#5576semidirect
460. C3C2×#5831semidirect
463. C2#10595414direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C22×C3×#2392
C2×C3×Q8×Dic32
#105954142
C2×#639162
C2×C4×#6262
C2×#638602
C2×#638572
C2×#58313
C2×#55763