Finite Group Databasebeta

← C2×#10594992 #11900096

Subgroups — C2×#10594992 #11900096

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C214yesmaximal, complemented
5#10594992C2116yesmaximal, direct product factor
6C2×Dic3×D12C212yesmaximal, complemented
7C2×D3×C4⋊Dic3C212yesmaximal, complemented
8C2×Dic3×Dic6C212yesmaximal, complemented
9C2×#63841C212yesmaximal, complemented
10C2×#5827—31nomaximal
11C2×#5523—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2212yes—
14C22×C3×#67C2212yes—
15C2×C3×#235C4116yescomplemented
16C2×C3×#235C2218yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×D3×Dic3C2214yes—
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×C4⋊(C3⋊Dic3)C2218yescomplemented
24C2×C3×#217C2212yes—
25C3×#926C2218yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29#67⋊Dic3C22132yescomplemented
30C2×Dic3⋊Dic3C2214yes—
31C2×(C2×D3)⋊Dic3C2214yes—
32C2×Dic32C2214yes—
33Dic3×D12C22116yescomplemented
34D3×C4⋊Dic3C22116yescomplemented
35Dic3×Dic6C22116yescomplemented
36#63841C22116yescomplemented
37C22×C3×#41—31no—
38C22×#235D311yescharacteristic
39C2×C3×#117—31no—
40#5827—316no—
41C2×Q8×Dic3—32no—
42C2×D4×Dic3—34no—
43C2×D4×Dic3—32no—
44C2×#926—32no—
45C2×#926D311yescharacteristic, complemented
46C22×C4⋊Dic3—31no—
47C22×C4⋊Dic3—31no—
48C22×C4⋊Dic3—32no—
49C22×C4⋊Dic3—61no—
50#5523—316no—
51C2×#892—32no—
52C2×D3×C4⋊C4—32no—
53C2×#67⋊C4—34no—
54C2×C4×D12—32no—
55C2×C4×Dic6—32no—
56C24×C32C2311yescharacteristic
57C23×C3×D3C2312yes—
58C22×C32×C4C2×C418yescomplemented
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2314yes—
62C22×C3⋊Dic3—44no—
63C22×C3⋊Dic3C2314yes—
64C22×C3⋊Dic3C2318yes—
65C2×C3×#67C2×C4116yescomplemented
66C2×C3×#67C2318yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C3×#235C2×C4164yescomplemented
71C2×C3×D12C2×C418yescomplemented
72C2×C3×D12C2314yes—
73C2×C3×C4×D3C2×C4116yescomplemented
74C2×C3×C4×D3C2318yes—
75C2×C3×Dic6C2×C418yescomplemented
76C2×C3×Dic6C2314yes—
77C2×D3×Dic3—48no—
78C2×D3×Dic3C23116yes—
79C4⋊(C3⋊Dic3)C2318yes—
80C4⋊(C3⋊Dic3)C2318yes—
81C3×#217C2318yes—
82C3×C4⋊Dic3C2314yes—
83C3×C4⋊Dic3C2314yes—
84C3×C4×Dic3C2318yes—
85Dic3⋊Dic3C23116yes—
86(C2×D3)⋊Dic3C23116yes—
87Dic32C23116yes—
88C2×#520—91noSylow
89C2×C3×#41—316no—
90C2×C3×#41—38no—
91C22×C3×Q8—31no—
92C22×C3×D4—32no—
93C22×C3×D4—31no—
94C23×C3×C4—21no—
95C23×C3×C4—32no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C22×#67C2×D312yes—
99C23×Dic3—32no—
100C23×Dic3—32no—
101C23×Dic3—34no—
102C23×Dic3—62no—
103C2×#235Dic3116yescomplemented
104C2×#235C2×D318yes—
105C22×D12C2×D311yescharacteristic
106C22×C4×D3—34no—
107C22×C4×D3C2×D312yes—
108C22×Dic6C2×D311yescharacteristic
109C3×#117—38no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—32no—
114C2×#217—34no—
115C2×#217C2×D312yes—
116Q8×Dic3—316no—
117D4×Dic3—332no—
118D4×Dic3—316no—
119C2×(C2×D3)⋊C4—34no—
120#926—316no—
121#926C2×D318yescomplemented
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—38no—
127C2×C4⋊Dic3—38no—
128C2×C4⋊Dic3—34no—
129C2×C4⋊Dic3—316no—
130C2×C4⋊Dic3—62no—
131C2×C4⋊Dic3—62no—
132C2×C4⋊Dic3—68no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—34no—
136C2×C4×Dic3—34no—
137C2×C4×Dic3—34no—
138C2×C4×Dic3C2×D312yes—
139#892—316no—
140D3×C4⋊C4—316no—
141#67⋊C4—332no—
142C4×D12—316no—
143C4×Dic6—316no—
144C23×C32—22no—
145C23×C32—22no—
146C23×C32C22×C414yes—
147C23×C32C2412yes—
148C23×C32C2411yescharacteristic
149C22×C3×D3—24no—
150C22×C3×D3—24no—
151C22×C3×D3C22×C418yes—
152C22×C3×D3C2414yes—
153C2×C32×C4C22×C414yes—
154C2×C32×C4C22×C414yes—
155C2×C32×C4C22×C4116yescomplemented
156C2×C32×C4C2412yes—
157C2×C32×C4C2412yes—
158C2×C3⋊Dic3—28no—
159C2×C3⋊Dic3—48no—
160C2×C3⋊Dic3C2418yes—
161C3×#67C22×C4132yescomplemented
162C2×C3×Dic3—24no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3C22×C418yes—
165C2×C3×Dic3C2414yes—
166C2×C3×Dic3C2414yes—
167C2×C3×Dic3C2414yes—
168C3×D12C22×C4116yescomplemented
169C3×C4×D3C22×C4132yescomplemented
170C3×Dic6C22×C4116yescomplemented
171D3×Dic3—416no—
172C22×#41—31no—
173#520—916no—
174C2×C4×Q8—92no—
175C2×C4×D4—92no—
176C2×C4×D4—94no—
177C2×#117—31no—
178C2×#117—92no—
179C22×C4⋊C4—92no—
180C22×C4⋊C4—91no—
181C24×C3—21no—
182C24×C3—32no—
183C24×C3C22×D311yescharacteristic
184C24×C3C22×D311yescharacteristic
185C23×D3C22×D312yes—
186C3×#41—364no—
187C2×C3×Q8—38no—
188C2×C3×Q8—34no—
189C2×C3×D4—316no—
190C2×C3×D4—38no—
191C2×C3×D4—38no—
192C2×C3×D4—34no—
193C22×C3×C4—28no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—24no—
197C22×C3×C4—32no—
198C22×C3×C4—316no—
199C22×C3×C4—38no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4C4×D318yescomplemented
203C22×C3×C4C2×Dic318yescomplemented
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D314yes—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D314yes—
210C2×#67C2×Dic3116yescomplemented
211C2×#67C22×D318yes—
212C22×Dic3—34no—
213C22×Dic3—34no—
214C22×Dic3—38no—
215C22×Dic3—38no—
216C22×Dic3—316no—
217C22×Dic3—64no—
218C22×Dic3—68no—
219C22×Dic3—128no—
220C22×Dic3—124no—
221C22×Dic3—124no—
222C22×Dic3—128no—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226#235C2×Dic3164yescomplemented
227C2×D12C2×Dic318yescomplemented
228C2×D12C22×D314yes—
229C2×C4×D3—316no—
230C2×C4×D3—128no—
231C2×C4×D3C2×Dic3116yescomplemented
232C2×C4×D3C22×D318yes—
233C2×Dic6C2×Dic318yescomplemented
234C2×Dic6C22×D314yes—
235C3×C4⋊C4—34no—
236C3×C4⋊C4—34no—
237C3×C22⋊C4—38no—
238C3×C42—38no—
239#217—316no—
240#217C22×D318yes—
241(C2×D3)⋊C4—316no—
242C4⋊Dic3—38no—
243C4⋊Dic3—38no—
244C4⋊Dic3—38no—
245C4⋊Dic3—38no—
246C4⋊Dic3—316no—
247C4⋊Dic3—68no—
248C4⋊Dic3—68no—
249C4⋊Dic3C22×D314yes—
250C4⋊Dic3C22×D314yes—
251Dic3⋊C4—316no—
252C4×Dic3—316no—
253C4×Dic3—316no—
254C4×Dic3C22×D318yes—
255C22×C32—28no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32C23×C414yes—
259C22×C32C23×C412yes—
260C22×C32H(5,𝔽2)12yes—
261C22×C322−1+412yes—
262C22×C32C2511yescharacteristic
263C2×C3×D3—216no—
264C2×C3×D3—24no—
265C2×C3×D3—24no—
266C2×C3×D3C23×C418yes—
267C32×C4C23×C414yes—
268C32×C4C23×C414yes—
269C3⋊Dic3—28no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C3×Dic3C23×C418yes—
273C2×#41—316no—
274C2×#41—38no—
275C22×Q8—31no—
276C22×D4—32no—
277C22×D4—31no—
278C23×C4—32no—
279C23×C4—94no—
280C23×C4—92no—
281C23×C4D3211yescharacteristic
282C4×Q8—916no—
283C4×D4—916no—
284C4×D4—932no—
285#117—38no—
286#117—916no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—916no—
290C2×C4⋊C4—94no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—98no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—94no—
296C2×C42—32no—
297C2×C42—94no—
298C23×C3—24no—
299C23×C3—24no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—24no—
307C23×C3—38no—
308C23×C3—34no—
309C23×C3—64no—
310C23×C3—64no—
311C23×C3C2×C4×D314yes—
312C23×C3C22×Dic314yes—
313C23×C3C23×D312yes—
314C23×C3C23×D312yes—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—24no—
318C22×D3—24no—
319C22×D3C22×Dic318yes—
320C22×D3C23×D314yes—
321C3×Q8—316no—
322C3×D4—332no—
323C3×D4—316no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—216no—
329C2×C3×C4—38no—
330C2×C3×C4—34no—
331C2×C3×C4—332no—
332C2×C3×C4—34no—
333C2×C3×C4—34no—
334C2×C3×C4—64no—
335C2×C3×C4—64no—
336C2×C3×C4C2×C4×D314yes—
337C2×C3×C4C2×C4×D314yes—
338C2×C3×C4C2×C4×D3116yescomplemented
339C2×C3×C4C22×Dic314yes—
340C2×C3×C4C22×Dic314yes—
341C2×C3×C4C22×Dic3116yescomplemented
342C2×C3×C4C23×D312yes—
343C2×C3×C4C23×D312yes—
344C2×C3×C4C23×D312yes—
345C2×C3×C4C23×D312yes—
346#67C22×Dic3132yescomplemented
347C2×Dic3—24no—
348C2×Dic3—24no—
349C2×Dic3—38no—
350C2×Dic3—38no—
351C2×Dic3—68no—
352C2×Dic3—68no—
353C2×Dic3—68no—
354C2×Dic3—128no—
355C2×Dic3—1216no—
356C2×Dic3—128no—
357C2×Dic3—128no—
358C2×Dic3—1216no—
359C2×Dic3C22×Dic318yes—
360C2×Dic3C23×D314yes—
361C2×Dic3C23×D314yes—
362C2×Dic3C23×D314yes—
363D12C22×Dic3116yescomplemented
364C4×D3—1216no—
365C4×D3C22×Dic3132yescomplemented
366Dic6C22×Dic3116yescomplemented
367C2×C32—24no—
368C2×C32#52014yescomplemented
369C2×C32C24×C411yescharacteristic
370C2×C32C2×H(5,𝔽2)11yescharacteristic
371C2×C32C2×2−1+411yescharacteristic
372C3×D3—28no—
373C24—32no—
374C24C2×D3211yescharacteristic
375#41—364no—
376C2×Q8—34no—
377C2×Q8—38no—
378C2×D4—38no—
379C2×D4—316no—
380C2×D4—34no—
381C2×D4—38no—
382C22×C4—32no—
383C22×C4—38no—
384C22×C4—316no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—916no—
388C22×C4—94no—
389C22×C4—98no—
390C22×C4—368no—
391C22×C4—364no—
392C22×C4D3×Dic318yescomplemented
393C22×C4C2×D3211yescharacteristic
394C22×C4C2×D3211yescharacteristic
395C22×C4C2×D3214yes—
396C4⋊C4—34no—
397C4⋊C4—34no—
398C4⋊C4—916no—
399C4⋊C4—98no—
400C4⋊C4—98no—
401C22⋊C4—38no—
402C22⋊C4—916no—
403C42—38no—
404C42—916no—
405C22×C3—24no—
406C22×C3—24no—
407C22×C3—216no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—28no—
413C22×C3—28no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—24no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—38no—
420C22×C3—64no—
421C22×C3—64no—
422C22×C3—616no—
423C22×C3C22×C4×D314yes—
424C22×C3C22×C4×D312yes—
425C22×C3#100912yes—
426C22×C3#100912yes—
427C22×C3#101012yes—
428C22×C3#101012yes—
429C22×C3C23×Dic314yes—
430C22×C3C23×Dic312yes—
431C22×C3C24×D311yescharacteristic
432C22×C3C24×D311yescharacteristic
433C2×D3—24no—
434C2×D3—24no—
435C2×D3—216no—
436C2×D3C23×Dic318yes—
437C3×C4—24no—
438C3×C4—24no—
439C3×C4—38no—
440C3×C4—64no—
441C3×C4—64no—
442C3×C4C22×C4×D314yes—
443C3×C4C22×C4×D314yes—
444C3×C4C23×Dic314yes—
445C3×C4C23×Dic314yes—
446Dic3—24no—
447Dic3—24no—
448Dic3—68no—
449Dic3—68no—
450Dic3—128no—
451Dic3C23×Dic318yes—
452C32C2×#52011yescharacteristic, complemented, Sylow
453C23—22no—
454C23—22no—
455C23—38no—
456C23—34no—
457C23—64no—
458C23—64no—
459C23C2×D3×Dic314yes—
460C23C22×D3212yes—
461C23C22×D3211yescharacteristic
462Q8—316no—
463D4—332no—
464D4—316no—
465C2×C4—38no—
466C2×C4—34no—
467C2×C4—332no—
468C2×C4—34no—
469C2×C4—34no—
470C2×C4—64no—
471C2×C4—64no—
472C2×C4—98no—
473C2×C4—188no—
474C2×C4—3616no—
475C2×C4—368no—
476C2×C4C2×D3×Dic314yes—
477C2×C4C2×D3×Dic314yes—
478C2×C4C2×D3×Dic3116yescomplemented
479C2×C4C22×D3212yes—
480C2×C4C22×D3212yes—
481C2×C3—28no—
482C2×C3—24no—
483C2×C3—24no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—24no—
488C2×C3—68no—
489C2×C3#552314yescomplemented
490C2×C3#582714yescomplemented
491C2×C3C23×C4×D311yescharacteristic
492C2×C3C2×#100911yescharacteristic
493C2×C3C2×#100911yescharacteristic
494C2×C3C2×#101011yescharacteristic
495C2×C3C2×#101011yescharacteristic
496C2×C3C24×Dic311yescharacteristic
497D3—28no—
498C22—22no—
499C22—22no—
500C22—28no—
501C22—38no—
502C22—64no—
503C22—64no—
504C22—616no—
505C22#6429812yes—
506C22#6430812yes—
507C22C22×D3×Dic314yes—
508C22C22×D3×Dic312yes—
509C22C23×D3211yescharacteristic
510C4—38no—
511C4—64no—
512C4—64no—
513C4—188no—
514C4C22×D3×Dic314yes—
515C4C22×D3×Dic314yes—
516C3—21no—
517C3C2×#552311yescharacteristic, complemented
518C3C2×#582711yescharacteristic, complemented
519C2—24no—
520C2—68no—
521C2#1059499214yesdirect product factor
522C2C2×#6429811yescharacteristic
523C2C2×#6430811yescharacteristic
524C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#235C2
cosocleC22×C32C25
hypercenterC23×C4D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊(C3⋊Dic3)C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. #10594992C2direct (N × H)
6. C2×Dic3×D12C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×Dic3×Dic6C2semidirect
9. C2×#63841C2semidirect
15. C2×C3×#235C4semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
25. C3×#926C22semidirect
29. #67⋊Dic3C22semidirect
33. Dic3×D12C22semidirect
34. D3×C4⋊Dic3C22semidirect
35. Dic3×Dic6C22semidirect
36. #63841C22semidirect
45. C2×#926D3semidirect
58. C22×C32×C4C2×C4semidirect
65. C2×C3×#67C2×C4semidirect
70. C3×#235C2×C4semidirect
71. C2×C3×D12C2×C4semidirect
73. C2×C3×C4×D3C2×C4semidirect
75. C2×C3×Dic6C2×C4semidirect
103. C2×#235Dic3semidirect
121. #926C2×D3semidirect
155. C2×C32×C4C22×C4semidirect
161. C3×#67C22×C4semidirect
168. C3×D12C22×C4semidirect
169. C3×C4×D3C22×C4semidirect
170. C3×Dic6C22×C4semidirect
202. C22×C3×C4C4×D3semidirect
203. C22×C3×C4C2×Dic3semidirect
210. C2×#67C2×Dic3semidirect
226. #235C2×Dic3semidirect
227. C2×D12C2×Dic3semidirect
231. C2×C4×D3C2×Dic3semidirect
233. C2×Dic6C2×Dic3semidirect
338. C2×C3×C4C2×C4×D3semidirect
341. C2×C3×C4C22×Dic3semidirect
346. #67C22×Dic3semidirect
363. D12C22×Dic3semidirect
365. C4×D3C22×Dic3semidirect
366. Dic6C22×Dic3semidirect
368. C2×C32#520semidirect
392. C22×C4D3×Dic3semidirect
452. C32C2×#520semidirect
478. C2×C4C2×D3×Dic3semidirect
489. C2×C3#5523semidirect
490. C2×C3#5827semidirect
517. C3C2×#5523semidirect
518. C3C2×#5827semidirect
521. C2#10594992direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×C4⋊(C3⋊Dic3)2
C2×C3×#9262
C2×#67⋊Dic32
#105949922
C2×Dic3×D122
C2×D3×C4⋊Dic32
C2×Dic3×Dic62
C2×#638412
C2×#58273
C2×#55233