Finite Group Databasebeta

← C2×#10595441 #11918503

Subgroups — C2×#10595441 #11918503

Order 1152.

3053 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×#64157C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10595441C2116yesmaximal, direct product factor
5C22×#3711C213yesmaximal, complemented
6C2×#63815C213yesmaximal, complemented
7C2×#63814C213yesmaximal, complemented
8C2×D3×#208C213yesmaximal, complemented
9C2×#5819—31nomaximal
10C2×#5750—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C3×D3×#41C418yes—
13C3×D3×#41C2218yes—
14C2×C3×#239C411yescharacteristic
15C2×C3×D3×Q8C411yescharacteristic
16C2×C3×#237C413yes—
17C2×C3×D3×D4C413yes—
18C2×C3×#235C2213yes—
19C22×C3×C4×D3C2213yes—
20#64157C2218yescomplemented
21C2×#3748C2213yescomplemented
22C22×C3⋊(C3⋊C8)C2213yescomplemented
23C3×#948C2218yescomplemented
24C2×C3×#208C2213yescomplemented
25C22×C3×C3⋊C8C2213yescomplemented
26C2×#3711C2213yes—
27C2×#3711C2211yescharacteristic
28C2×#3711C22124yescomplemented
29C2×#3711C2213yescomplemented
30C2×#3711C2213yescomplemented
31#63815C22124yescomplemented
32#63814C22124yescomplemented
33D3×#208C22124yescomplemented
34C2×D3×C3⋊C8C2216yescomplemented
35C22×C3×#41—31no—
36C2×D3×#41D311yescharacteristic
37C2×C3×#131—31no—
38#5819—316no—
39C2×#948—31no—
40C2×#948—31no—
41C2×#948—33no—
42C2×#948—33no—
43C2×#948—61no—
44C2×#948D311yescharacteristic, complemented
45C22×#208—33no—
46C22×#208—33no—
47#5750—316no—
48C2×#907—33no—
49C2×D3×M16—33no—
50C2×#901—33no—
51C22×ΓL(1,𝔽25)—33no—
52C23×C3×D3C2×C413yes—
53C32×#41C2×C414yes—
54C32×#41C2314yes—
55C2×C32×Q8C2×C411yescharacteristic
56C2×C32×D4C2×C413yes—
57C22×C32×C4C2313yes—
58C2×C3×#67C2×C416yes—
59C22×C3×Dic3C2×C413yes—
60C3×#239C2×C418yes—
61C3×D3×Q8C2×C418yes—
62C3×#237C2×C4124yes—
63C3×D3×D4C2×C4124yes—
64C3×#235C2×C4112yes—
65C3×#235C23112yes—
66C2×C3×D12C2×C413yes—
67C2×C3×C4×D3C2×C413yes—
68C2×C3×C4×D3C2×C413yes—
69C2×C3×C4×D3C2×C4112yes—
70C2×C3×C4×D3C2313yes—
71C2×C3×C4×D3C23112yes—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2×C413yes—
74#3748C23112yescomplemented
75C2×C3⋊(C3⋊C8)C2313yes—
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C23112yescomplemented
78C3×#208C23112yescomplemented
79C2×C3×C3⋊C8C2311yescharacteristic
80C2×C3×C3⋊C8C2313yes—
81C2×C3×C3⋊C8C23112yescomplemented
82#3711C23112yes—
83#3711C2314yes—
84#3711C23112yescomplemented
85#3711C23112yescomplemented
86D3×C3⋊C8C23124yescomplemented
87C2×#568—91noSylow
88C2×C3×#41—21no—
89C2×C3×#41—38no—
90C2×C3×#41—38no—
91C2×C3×#41—31no—
92C2×C3×#41—33no—
93C2×C3×#41—33no—
94C2×C3×#41C2×D311yescharacteristic
95C2×C3×#41C2×D311yescharacteristic
96C22×C3×Q8—31no—
97C22×C3×D4—33no—
98C23×C3×C4—33no—
99D3×#41Dic318yes—
100D3×#41C2×D318yes—
101C2×#239Dic311yescharacteristic
102C2×D3×Q8Dic311yescharacteristic
103C2×#237Dic313yes—
104C2×D3×D4Dic313yes—
105C2×#235C2×D313yes—
106C22×C4×D3C2×D313yes—
107C3×#131—38no—
108C2×C3×M16—33no—
109C22×C3×C8—33no—
110#948—38no—
111#948—38no—
112#948—324no—
113#948—324no—
114#948—68no—
115#948C2×D318yescomplemented
116C2×#208—33no—
117C2×#208—33no—
118C2×#208—324no—
119C2×#208—33no—
120C2×#208—31no—
121C2×#208—33no—
122C2×#208—33no—
123C2×#208—324no—
124C2×#208—63no—
125C2×#208C2×D313yescomplemented
126C22×C3⋊C8—33no—
127C22×C3⋊C8—33no—
128C22×C3⋊C8—36no—
129C22×C3⋊C8—63no—
130C22×C3⋊C8C2×D313yescomplemented
131#907—324no—
132D3×M16—324no—
133#901—324no—
134C2×ΓL(1,𝔽25)—31no—
135C2×ΓL(1,𝔽25)—33no—
136C2×ΓL(1,𝔽25)—33no—
137C2×ΓL(1,𝔽25)—33no—
138C2×ΓL(1,𝔽25)—324no—
139C2×D3×C8—36no—
140C23×C32C22×C413yes—
141C22×C3×D3—46no—
142C22×C3×D3C22×C411yescharacteristic
143C22×C3×D3C22×C413yes—
144C22×C3×D3C22×C4112yes—
145C32×Q8C22×C414yes—
146C32×D4C22×C4112yes—
147C2×C32×C4C22×C413yes—
148C2×C32×C4C22×C416yes—
149C2×C32×C4C2411yescharacteristic
150C2×C32×C4C2416yes—
151C3×#67C22×C4124yes—
152C2×C3×Dic3C22×C413yes—
153C2×C3×Dic3C22×C411yescharacteristic
154C2×C3×Dic3C22×C4112yes—
155C3×D12C22×C4112yes—
156C3×C4×D3C22×C412yes—
157C3×C4×D3C22×C416yes—
158C3×C4×D3C22×C4112yes—
159C3×C4×D3C22×C4112yes—
160C3×C4×D3C2416yes—
161C3×C4×D3C2412yes—
162C3×Dic6C22×C4112yes—
163C3⋊(C3⋊C8)C2416yes—
164C3⋊(C3⋊C8)C2412yes—
165C3×C3⋊C8C2416yes—
166C3×C3⋊C8C2412yes—
167C22×#41—31no—
168#568—916no—
169C2×#131—31no—
170C2×#131—93no—
171C2×#131—93no—
172C2×#131—91no—
173C22×M16—93no—
174C22×M16—93no—
175C24×C3—33no—
176C23×D3C2×Dic313yes—
177C3×#41—24no—
178C3×#41—24no—
179C3×#41—38no—
180C3×#41—324no—
181C3×#41—312no—
182C3×#41—312no—
183C3×#41C4×D314yes—
184C3×#41C2×Dic314yes—
185C3×#41C22×D314yes—
186C3×#41C22×D314yes—
187C2×C3×Q8—21no—
188C2×C3×Q8—38no—
189C2×C3×Q8—33no—
190C2×C3×Q8C4×D311yescharacteristic
191C2×C3×Q8C2×Dic311yescharacteristic
192C2×C3×D4—23no—
193C2×C3×D4—36no—
194C2×C3×D4—324no—
195C2×C3×D4—33no—
196C2×C3×D4C4×D313yes—
197C2×C3×D4C2×Dic313yes—
198C22×C3×C4—23no—
199C22×C3×C4—33no—
200C22×C3×C4—33no—
201C22×C3×C4—33no—
202C22×C3×C4—312no—
203C22×C3×C4—33no—
204C22×C3×C4—31no—
205C22×C3×C4—312no—
206C22×C3×C4C22×D313yes—
207C22×C3×C4C22×D313yes—
208C2×#67C2×Dic316yes—
209C22×Dic3C2×Dic313yes—
210#239C2×Dic318yes—
211D3×Q8C2×Dic318yes—
212#237C2×Dic3124yes—
213D3×D4C2×Dic3124yes—
214#235C2×Dic3112yes—
215#235C22×D3112yes—
216C2×D12C2×Dic313yes—
217C2×C4×D3C2×Dic313yes—
218C2×C4×D3C2×Dic313yes—
219C2×C4×D3C2×Dic3112yes—
220C2×C4×D3C22×D313yes—
221C2×C4×D3C22×D311yescharacteristic
222C2×C4×D3C22×D3112yes—
223C2×Dic6C2×Dic313yes—
224C3×M16—312no—
225C2×C3×C8—33no—
226C2×C3×C8—31no—
227C2×C3×C8—312no—
228#208—312no—
229#208—312no—
230#208—312no—
231#208—34no—
232#208—312no—
233#208—312no—
234#208—612no—
235#208C22×D3112yescomplemented
236C2×C3⋊C8—33no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—312no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—33no—
241C2×C3⋊C8—312no—
242C2×C3⋊C8—324no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—63no—
245C2×C3⋊C8—612no—
246C2×C3⋊C8C22×D313yes—
247C2×C3⋊C8C22×D311yescharacteristic
248C2×C3⋊C8C22×D3112yescomplemented
249ΓL(1,𝔽25)—34no—
250ΓL(1,𝔽25)—312no—
251ΓL(1,𝔽25)—312no—
252ΓL(1,𝔽25)—312no—
253D3×C8—324no—
254C22×C32—26no—
255C22×C32C23×C416yes—
256C22×C32C23×C411yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—26no—
259C2×C3×D3—412no—
260C2×C3×D3C23×C412yes—
261C2×C3×D3C23×C416yes—
262C32×C4C23×C416yes—
263C32×C4C23×C411yescharacteristic
264C32×C4C2511yescharacteristic
265C3×Dic3C23×C416yes—
266C3×Dic3C23×C412yes—
267C2×#41—38no—
268C2×#41—38no—
269C2×#41—31no—
270C2×#41—33no—
271C2×#41—33no—
272C2×#41D3211yescharacteristic
273C22×Q8—31no—
274C22×D4—33no—
275C23×C4—33no—
276#131—38no—
277#131—924no—
278#131—924no—
279#131—98no—
280C2×M16—33no—
281C2×M16—91no—
282C2×M16—93no—
283C2×M16—93no—
284C2×M16—93no—
285C2×M16—924no—
286C2×M16—924no—
287C2×M16—93no—
288C22×C8—33no—
289C22×C8—96no—
290C22×C8—93no—
291C23×C3—23no—
292C23×C3—31no—
293C23×C3—33no—
294C23×C3—312no—
295C23×C3—126no—
296C23×C3C2×C4×D313yes—
297C23×C3C22×Dic313yes—
298C22×D3—46no—
299C22×D3C22×Dic311yescharacteristic
300C22×D3C22×Dic313yes—
301C22×D3C22×Dic3112yes—
302C3×Q8—24no—
303C3×Q8—312no—
304C3×Q8C2×C4×D314yes—
305C3×Q8C22×Dic314yes—
306C3×D4—212no—
307C3×D4—324no—
308C3×D4—312no—
309C3×D4C2×C4×D3112yes—
310C3×D4C22×Dic3112yes—
311C2×C3×C4—26no—
312C2×C3×C4—21no—
313C2×C3×C4—23no—
314C2×C3×C4—26no—
315C2×C3×C4—31no—
316C2×C3×C4—33no—
317C2×C3×C4—312no—
318C2×C3×C4—32no—
319C2×C3×C4—312no—
320C2×C3×C4—312no—
321C2×C3×C4—36no—
322C2×C3×C4—36no—
323C2×C3×C4—32no—
324C2×C3×C4C2×C4×D313yes—
325C2×C3×C4C2×C4×D316yes—
326C2×C3×C4C22×Dic313yes—
327C2×C3×C4C22×Dic316yes—
328C2×C3×C4C23×D316yes—
329C2×C3×C4C23×D316yes—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67C22×Dic3124yes—
333C2×Dic3C22×Dic313yes—
334C2×Dic3C22×Dic311yescharacteristic
335C2×Dic3C22×Dic3112yes—
336D12C22×Dic3112yes—
337C4×D3C22×Dic312yes—
338C4×D3C22×Dic316yes—
339C4×D3C22×Dic3112yes—
340C4×D3C22×Dic3112yes—
341C4×D3C23×D316yes—
342C4×D3C23×D312yes—
343Dic6C22×Dic3112yes—
344C3×C8—36no—
345C3×C8—32no—
346C3⋊C8—36no—
347C3⋊C8—32no—
348C3⋊C8—36no—
349C3⋊C8—32no—
350C3⋊C8—62no—
351C3⋊C8—66no—
352C3⋊C8C23×D316yes—
353C3⋊C8C23×D312yes—
354C2×C32—26no—
355C2×C32#56812yescomplemented
356C2×C32C24×C411yescharacteristic
357C3×D3—22no—
358C3×D3—26no—
359C24—33no—
360#41—38no—
361#41—324no—
362#41—312no—
363#41—312no—
364#41D3×Dic314yes—
365#41C2×D3214yes—
366C2×Q8—38no—
367C2×Q8—33no—
368C2×Q8D3×Dic311yescharacteristic
369C2×D4—36no—
370C2×D4—324no—
371C2×D4—33no—
372C2×D4D3×Dic313yes—
373C22×C4—33no—
374C22×C4—312no—
375C22×C4—33no—
376C22×C4—31no—
377C22×C4—33no—
378C22×C4—33no—
379C22×C4—312no—
380C22×C4C2×D3213yes—
381M16—312no—
382M16—94no—
383M16—912no—
384M16—912no—
385M16—912no—
386M16—912no—
387C2×C8—312no—
388C2×C8—31no—
389C2×C8—33no—
390C2×C8—924no—
391C2×C8—912no—
392C2×C8—93no—
393C2×C8—91no—
394C22×C3—26no—
395C22×C3—26no—
396C22×C3—21no—
397C22×C3—26no—
398C22×C3—32no—
399C22×C3—36no—
400C22×C3—46no—
401C22×C3—62no—
402C22×C3—66no—
403C22×C3—1212no—
404C22×C3C22×C4×D316yes—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C23×Dic316yes—
407C22×C3C23×Dic311yescharacteristic
408C2×D3—22no—
409C2×D3—26no—
410C2×D3—412no—
411C2×D3C23×Dic312yes—
412C2×D3C23×Dic316yes—
413C3×C4—21no—
414C3×C4—26no—
415C3×C4—21no—
416C3×C4—32no—
417C3×C4—36no—
418C3×C4C22×C4×D311yescharacteristic
419C3×C4C22×C4×D316yes—
420C3×C4C23×Dic316yes—
421C3×C4C23×Dic311yescharacteristic
422C3×C4C24×D311yescharacteristic
423C3×C4C24×D311yescharacteristic
424Dic3C23×Dic316yes—
425Dic3C23×Dic312yes—
426C32C2×#56811yescharacteristic, complemented, Sylow
427C23—31no—
428C23—33no—
429C23—312no—
430C23—126no—
431C23C2×D3×Dic313yes—
432Q8—312no—
433Q8C2×D3×Dic314yes—
434D4—324no—
435D4—312no—
436D4C2×D3×Dic3112yes—
437C2×C4—31no—
438C2×C4—33no—
439C2×C4—312no—
440C2×C4—32no—
441C2×C4—312no—
442C2×C4—312no—
443C2×C4—36no—
444C2×C4—36no—
445C2×C4—32no—
446C2×C4C2×D3×Dic313yes—
447C2×C4C2×D3×Dic316yes—
448C2×C4C22×D3216yes—
449C2×C4C22×D3211yescharacteristic
450C8—32no—
451C8—36no—
452C8—96no—
453C8—92no—
454C2×C3—26no—
455C2×C3—26no—
456C2×C3—21no—
457C2×C3—22no—
458C2×C3—46no—
459C2×C3—62no—
460C2×C3—66no—
461C2×C3#575012yescomplemented
462C2×C3#581912yescomplemented
463C2×C3C23×C4×D311yescharacteristic
464C2×C3C24×Dic311yescharacteristic
465D3—22no—
466D3—26no—
467C22—26no—
468C22—32no—
469C22—36no—
470C22—62no—
471C22—66no—
472C22—1212no—
473C22C22×D3×Dic316yes—
474C22C22×D3×Dic311yescharacteristic
475C4—32no—
476C4—36no—
477C4C22×D3×Dic311yescharacteristic
478C4C22×D3×Dic316yes—
479C4C23×D3211yescharacteristic
480C3—21no—
481C3C2×#575011yescharacteristic, complemented
482C3C2×#581911yescharacteristic, complemented
483C2—26no—
484C2—62no—
485C2—66no—
486C2#1059544112yesdirect product factor
487C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C23×C4
prime radicalC2×C3×D3×#41C2
cosocleC32×C4C25
hypercenterC2×#41D32
hypocenterC32C2×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64157C2semidirect
3. C2×C3×#948C2semidirect
4. #10595441C2direct (N × H)
5. C22×#3711C2semidirect
6. C2×#63815C2semidirect
7. C2×#63814C2semidirect
8. C2×D3×#208C2semidirect
20. #64157C22semidirect
21. C2×#3748C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
23. C3×#948C22semidirect
24. C2×C3×#208C22semidirect
25. C22×C3×C3⋊C8C22semidirect
28. C2×#3711C22semidirect
29. C2×#3711C22semidirect
30. C2×#3711C22semidirect
31. #63815C22semidirect
32. #63814C22semidirect
33. D3×#208C22semidirect
34. C2×D3×C3⋊C8C22semidirect
44. C2×#948D3semidirect
74. #3748C23semidirect
77. C2×C3⋊(C3⋊C8)C23semidirect
78. C3×#208C23semidirect
81. C2×C3×C3⋊C8C23semidirect
84. #3711C23semidirect
85. #3711C23semidirect
86. D3×C3⋊C8C23semidirect
115. #948C2×D3semidirect
125. C2×#208C2×D3semidirect
130. C22×C3⋊C8C2×D3semidirect
235. #208C22×D3semidirect
248. C2×C3⋊C8C22×D3semidirect
355. C2×C32#568semidirect
426. C32C2×#568semidirect
461. C2×C3#5750semidirect
462. C2×C3#5819semidirect
481. C3C2×#5750semidirect
482. C3C2×#5819semidirect
486. C2#10595441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×#641572
C2×C3×#9482
#105954412
C22×#37112
C2×#638152
C2×#638142
C2×D3×#2082
C2×#58193
C2×#57503