Finite Group Databasebeta

← #11802730

Subgroups — #11802730

Order 1152.

2205 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591711C214yesmaximal, complemented
5#10591325C214yesmaximal, complemented
6#10591320C212yesmaximal, complemented
7#10591213C212yesmaximal, complemented
8#82270—31nomaximal
9#82186—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#638C2212yes—
12C2×#3828—24no—
13C2×#3828—24no—
14C2×#3828C418yescomplemented
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×#634C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C2×C3×#217C2212yes—
20C3×#926—24no—
21C2×C3×C4⋊Dic3—24no—
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3722C2218yes—
27#63579C2218yes—
28C22×#235—31no—
29C22×#235—31no—
30C22×#235—61no—
31C2×C3×#117—31no—
32C22×C3×C4⋊C4—31no—
33C2×#926D311yescharacteristic, complemented
34C22×C4⋊Dic3D311yescharacteristic, complemented
35#5213—34no—
36#4988—32no—
37#4987—34no—
38#4987—34no—
39#4973—32no—
40#4958—34no—
41#4939—32no—
42#4929—32no—
43C24×C32C2311yescharacteristic
44C23×C3⋊D3C2312yes—
45C22×C32×C4C2×C414yes—
46C22×C32×C4D414yes—
47C22×C32×C4D414yes—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C2×#638—24no—
51C2×#638—24no—
52C2×#638C2×C418yes—
53C22×C3⋊Dic3C2312yes—
54#3828—232no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yescomplemented
58C2×C4×C3⋊D3—24no—
59C2×C4×C3⋊D3—24no—
60C2×C4×C3⋊D3C2×C418yescomplemented
61C2×#634—22no—
62C2×#634—22no—
63C2×#634C2×C414yescomplemented
64C22×C3×Dic3—24no—
65C22×C3×Dic3—44no—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2314yes—
68C3×#217—24no—
69C3×C4⋊Dic3—24no—
70C3×C4⋊Dic3—24no—
71C3×C4⋊Dic3—24no—
72C3×C4×Dic3—24no—
73#3722—48no—
74#2311—91noSylow
75C23×C3×C4—21no—
76C23×C3×C4—32no—
77C23×C3×C4C2×D311yescharacteristic
78C23×C3×C4C2×D311yescharacteristic
79C22×#67—32no—
80C22×#67—32no—
81C22×#67—62no—
82C23×Dic3C2×D312yes—
83C2×#235—38no—
84C2×#235—38no—
85C2×#235—68no—
86C2×#235—68no—
87C2×#235—68no—
88C2×#235—64no—
89C2×#235—64no—
90C2×#235—64no—
91C2×#235—64no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—62no—
98C22×Dic6—31no—
99C22×Dic6—31no—
100C22×Dic6—61no—
101C3×#117—64no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—64no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C42—32no—
108C2×#217C2×D312yes—
109C2×(C2×D3)⋊C4—38no—
110C2×(C2×D3)⋊C4—38no—
111#926—24no—
112C2×C4⋊Dic3—24no—
113C2×C4⋊Dic3C2×D312yes—
114C2×C4⋊Dic3C2×D312yes—
115C2×C4⋊Dic3C2×D312yes—
116C2×C4×Dic3C2×D312yes—
117C3⋊#95—38no—
118C3⋊#95—38no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32C22×C412yes—
122C23×C32C2×D412yes—
123C23×C32C2×D412yes—
124C23×C32C2411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—24no—
128C22×C3⋊D3—24no—
129C22×C3⋊D3C22×C414yes—
130C2×C32×C4C22⋊C4116yescomplemented
131C2×C32×C4C22×C412yes—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×D412yes—
137#638—216no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C22×C414yes—
141C4⋊(C3⋊D3)—28no—
142C4×C3⋊D3—216no—
143#634—28no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—28no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—48no—
150C22×#41—91no—
151C2×#117—31no—
152C22×C4⋊C4—31no—
153#391—92no—
154#390—92no—
155#386—94no—
156#380—94no—
157C24×C3—21no—
158C24×C3C22×D311yescharacteristic
159C24×C3C22×D311yescharacteristic
160C23×D3—32no—
161C23×D3—32no—
162C23×D3—62no—
163C22×C3×C4—24no—
164C22×C3×C4—24no—
165C22×C3×C4—24no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—34no—
169C22×C3×C4—34no—
170C22×C3×C4—64no—
171C22×C3×C4—124no—
172C22×C3×C4C4×D314yes—
173C22×C3×C4C4×D314yes—
174C22×C3×C4D1214yes—
175C22×C3×C4D1214yes—
176C22×C3×C4#6714yes—
177C22×C3×C4#6714yes—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—38no—
183C2×#67—38no—
184C2×#67—68no—
185C2×#67—68no—
186C2×#67—68no—
187C2×#67—64no—
188C2×#67—64no—
189C2×#67—64no—
190C2×#67—64no—
191C22×Dic3—24no—
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—44no—
195C22×Dic3—62no—
196C22×Dic3C22×D314yes—
197C22×Dic3C22×D314yes—
198#235—664no—
199#235—632no—
200#235—632no—
201C2×D12—34no—
202C2×D12—34no—
203C2×D12—64no—
204C2×D12—64no—
205C2×D12—64no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×C4×D3—38no—
211C2×C4×D3—38no—
212C2×C4×D3—68no—
213C2×C4×D3—68no—
214C2×C4×D3—68no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×Dic6—34no—
220C2×Dic6—34no—
221C2×Dic6—64no—
222C2×Dic6—64no—
223C2×Dic6—64no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C3×C4⋊C4—64no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4—64no—
231C3×C22⋊C4—64no—
232C3×C42—64no—
233#217—24no—
234(C2×D3)⋊C4—128no—
235(C2×D3)⋊C4—128no—
236C4⋊Dic3—24no—
237C4⋊Dic3—24no—
238C4⋊Dic3—24no—
239C4×Dic3—24no—
240C22×C32—24no—
241C22×C32—22no—
242C22×C32—22no—
243C22×C32—24no—
244C22×C32C2×C22⋊C414yes—
245C22×C32C23×C411yescharacteristic
246C22×C32C22×D411yescharacteristic
247C22×C32C22×D411yescharacteristic
248C22×C32H(5,𝔽2)12yes—
249C22×C322−1+412yes—
250C2×C3⋊D3—24no—
251C2×C3⋊D3—28no—
252C2×C3⋊D3—42no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—44no—
255C32×C4C2×C22⋊C414yes—
256C32×C4C2×C22⋊C414yes—
257C3⋊Dic3—24no—
258C3×Dic3—44no—
259C3×Dic3—44no—
260C2×#41—98no—
261C2×#41—184no—
262C2×#41—184no—
263C22×Q8—91no—
264C22×D4—92no—
265C22×D4—91no—
266C23×C4—32no—
267C23×C4—92no—
268C23×C4D3211yescharacteristic
269#117—64no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—64no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—98no—
276C2×C42—32no—
277#95—98no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—21no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3C2×C4×D312yes—
289C23×C3C2×C4×D312yes—
290C23×C3C2×D1212yes—
291C23×C3C2×D1212yes—
292C23×C3C2×#6712yes—
293C23×C3C2×#6712yes—
294C23×C3C23×D311yescharacteristic
295C23×C3C23×D311yescharacteristic
296C22×D3—34no—
297C22×D3—34no—
298C22×D3—64no—
299C22×D3—64no—
300C22×D3—64no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—64no—
304C22×D3—64no—
305C22×D3—64no—
306C22×D3—64no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—124no—
310C22×D3—124no—
311C2×C3×C4—216no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—64no—
319C2×C3×C4—64no—
320C2×C3×C4—64no—
321C2×C3×C4—64no—
322C2×C3×C4—68no—
323C2×C3×C4—128no—
324C2×C3×C4(C2×D3)⋊C4116yescomplemented
325C2×C3×C4(C2×D3)⋊C4116yescomplemented
326C2×C3×C4C2×C4×D312yes—
327C2×C3×C4C2×C4×D312yes—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×D1212yes—
331C2×C3×C4C2×D1212yes—
332C2×C3×C4C2×D1212yes—
333C2×C3×C4C2×D1212yes—
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C2×#6712yes—
337C2×C3×C4C2×#6712yes—
338#67—632no—
339#67—616no—
340#67—616no—
341C2×Dic3—28no—
342C2×Dic3—24no—
343C2×Dic3—24no—
344C2×Dic3—24no—
345C2×Dic3—24no—
346C2×Dic3—34no—
347C2×Dic3—34no—
348C2×Dic3—48no—
349C2×Dic3—64no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356D12—616no—
357D12—68no—
358D12—68no—
359C4×D3—632no—
360C4×D3—616no—
361C4×D3—616no—
362Dic6—616no—
363Dic6—68no—
364Dic6—68no—
365C2×C32—24no—
366C2×C32C22×C22⋊C411yescharacteristic
367C2×C32#52012yes—
368C2×C32#53511yescharacteristic
369C2×C32#53611yescharacteristic
370C2×C32#53712yes—
371C3⋊D3—44no—
372C24—92no—
373C24C2×D3211yescharacteristic
374#41—1832no—
375C2×Q8—94no—
376C2×Q8—182no—
377C2×Q8—182no—
378C2×D4—98no—
379C2×D4—94no—
380C2×D4—184no—
381C2×D4—184no—
382C2×D4—182no—
383C2×D4—182no—
384C22×C4—34no—
385C22×C4—34no—
386C22×C4—64no—
387C22×C4—92no—
388C22×C4—98no—
389C22×C4—124no—
390C22×C4—184no—
391C22×C4—184no—
392C22×C4#62414yes—
393C22×C4#62614yes—
394C22×C4#62614yes—
395C22×C4C2×D3211yescharacteristic
396C22×C4C2×D3211yescharacteristic
397C4⋊C4—64no—
398C4⋊C4—64no—
399C4⋊C4—64no—
400C22⋊C4—64no—
401C22⋊C4—368no—
402C42—64no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—24no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—24no—
417C22×C3—42no—
418C22×C3—44no—
419C22×C3—42no—
420C22×C3—44no—
421C22×C3C2×(C2×D3)⋊C414yes—
422C22×C3C2×(C2×D3)⋊C414yes—
423C22×C3C22×C4×D311yescharacteristic
424C22×C3C22×C4×D311yescharacteristic
425C22×C3C22×D1211yescharacteristic
426C22×C3C22×D1211yescharacteristic
427C22×C3#100412yes—
428C22×C3#100712yes—
429C22×C3#100912yes—
430C22×C3#101012yes—
431C22×C3C22×#6711yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—68no—
434C2×D3—68no—
435C2×D3—68no—
436C2×D3—64no—
437C2×D3—64no—
438C2×D3—128no—
439C2×D3—124no—
440C2×D3—124no—
441C2×D3—128no—
442C2×D3—124no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—124no—
451C3×C4—124no—
452C3×C4C2×(C2×D3)⋊C414yes—
453C3×C4C2×(C2×D3)⋊C414yes—
454C3×C4C2×(C2×D3)⋊C414yes—
455C3×C4C2×(C2×D3)⋊C414yes—
456Dic3—44no—
457Dic3—44no—
458Dic3—68no—
459Dic3—64no—
460Dic3—64no—
461C32#231111yescharacteristic, complemented, Sylow
462C23—22no—
463C23—22no—
464C23—94no—
465C23—184no—
466C23—184no—
467C23—182no—
468C23—182no—
469C23C2×#62412yes—
470C23C2×#62612yes—
471C23C2×#62612yes—
472C23C22×D3211yescharacteristic
473Q8—188no—
474D4—1816no—
475D4—188no—
476C2×C4—64no—
477C2×C4—64no—
478C2×C4—68no—
479C2×C4—64no—
480C2×C4—64no—
481C2×C4—94no—
482C2×C4—128no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—1816no—
486C2×C4#3722116yescomplemented
487C2×C4C2×#62412yes—
488C2×C4C2×#62412yes—
489C2×C4C2×#62612yes—
490C2×C4C2×#62612yes—
491C2×C4C2×#62612yes—
492C2×C4C2×#62612yes—
493C2×C3—24no—
494C2×C3—24no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—44no—
501C2×C3#550412yes—
502C2×C3#551012yes—
503C2×C3#552312yes—
504C2×C3#552511yescharacteristic
505C2×C3#552611yescharacteristic
506C2×C3C22×(C2×D3)⋊C411yescharacteristic
507C2×C3C22×(C2×D3)⋊C411yescharacteristic
508C2×C3#580511yescharacteristic
509C2×C3#581611yescharacteristic
510C2×C3#583312yes—
511D3—128no—
512D3—124no—
513D3—124no—
514C22—22no—
515C22—24no—
516C22—22no—
517C22—24no—
518C22—184no—
519C22—188no—
520C22—362no—
521C22—362no—
522C22—364no—
523C22C2×#372214yes—
524C22#6429712yes—
525C22#6430712yes—
526C22C22×#62411yescharacteristic
527C22C22×#62611yescharacteristic
528C22C22×#62611yescharacteristic
529C4—124no—
530C4—124no—
531C4—184no—
532C4C2×#372214yes—
533C4C2×#372214yes—
534C3—21no—
535C3#8218611yescharacteristic, complemented
536C3#8227011yescharacteristic, complemented
537C2—24no—
538C2—364no—
539C2#1059486611yescharacteristic
540C2#1059499012yes—
541C2#1059504211yescharacteristic
542C2#1059504312yes—
543C2C22×#372211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32#2311
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. #10591711C2semidirect
5. #10591325C2semidirect
6. #10591320C2semidirect
7. #10591213C2semidirect
14. C2×#3828C4semidirect
33. C2×#926D3semidirect
34. C22×C4⋊Dic3D3semidirect
57. C2×C4⋊(C3⋊D3)C2×C4semidirect
60. C2×C4×C3⋊D3C2×C4semidirect
63. C2×#634C2×C4semidirect
130. C2×C32×C4C22⋊C4semidirect
324. C2×C3×C4(C2×D3)⋊C4semidirect
325. C2×C3×C4(C2×D3)⋊C4semidirect
461. C32#2311semidirect
486. C2×C4#3722semidirect
535. C3#82186semidirect
536. C3#82270semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9262
C22×C3×C4⋊Dic32
#105917112
#105913252
#105913202
#105912132
#822703
#821863