Finite Group Databasebeta

← #11803045

Subgroups — #11803045

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C3×#5220C212yesmaximal
3#10591720C211yesmaximal, characteristic, complemented
4#10591705C211yesmaximal, characteristic, complemented
5#10591703C212yesmaximal, complemented
6#10591697C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#10591693C212yesmaximal, complemented
9#10591360C211yesmaximal, characteristic, complemented
10#10591271C212yesmaximal, complemented
11#10591229C211yesmaximal, characteristic, complemented
12#74663—32nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C2×#3757C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19D4×C3⋊Dic3C418yescomplemented
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×#3724C2212yes—
26C2×#3724C2212yes—
27C2×Dic32C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2211yescharacteristic
33#63579C2211yescharacteristic
34#63579C2212yes—
35#63579C2211yescharacteristic
36#63579C2211yescharacteristic
37C2×D4×Dic3—32no—
38C2×D4×Dic3—61no—
39C3×#386—32no—
40#5220D312yes—
41#5210—32no—
42C2×C3⋊#95—32no—
43#4946—32no—
44#4945—32no—
45#4944—32no—
46#4943—32no—
47#4942—32no—
48Dic3×C22⋊C4—32no—
49#4654—32no—
50#4653—32no—
51#4651—32no—
52#4650—32no—
53C24×C32C2311yescharacteristic
54C24×C32C2311yescharacteristic
55C2×C32×D4—24no—
56C2×C32×D4C2×C414yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—42no—
59C22×C3⋊Dic3—42no—
60C22×C3⋊Dic3C2×C414yes—
61C22×C3⋊Dic3C2×C414yescomplemented
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3×Dic3—24no—
67C22×C3×Dic3—42no—
68C22×C3×Dic3—42no—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73#3757C2×C414yes—
74#3757C2×C414yescomplemented
75C4⋊(C3⋊Dic3)C2×C414yescomplemented
76C4×C3⋊Dic3C2×C414yescomplemented
77C3×#217—24no—
78C3×#217—42no—
79C3×#217—42no—
80#3724—42no—
81#3724—42no—
82Dic32—42no—
83#2318—91noSylow
84C22×C3×D4—21no—
85C22×C3×D4C2×D312yes—
86C23×C3×C4—32no—
87C23×Dic3—32no—
88C23×Dic3—32no—
89C23×Dic3—61no—
90C23×Dic3—61no—
91C23×Dic3C2×D312yes—
92C2×C3×C22⋊C4—32no—
93C2×C3×C22⋊C4—32no—
94C2×C3×C22⋊C4—32no—
95C2×#217—32no—
96C2×#217—32no—
97C2×#217—61no—
98C2×#217—61no—
99C2×#217C2×D312yes—
100C2×#217C2×D312yes—
101C2×#217C2×D312yes—
102D4×Dic3—316no—
103D4×Dic3—68no—
104C2×C4⋊Dic3—32no—
105C2×C4⋊Dic3—61no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—61no—
114C3×#95—32no—
115C3×#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C23×C32—22no—
129C23×C32—21no—
130C23×C32—22no—
131C23×C32—21no—
132C23×C32—21no—
133C23×C32—22no—
134C23×C32—21no—
135C23×C32C22×C412yes—
136C23×C32C22×C412yes—
137C23×C32#4114yes—
138C23×C32C2411yescharacteristic
139C32×D4—28no—
140C2×C32×C4—22no—
141C2×C32×C4C22×C412yes—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—44no—
148C2×C3⋊Dic3—44no—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3C22×C412yes—
151C2×C3⋊Dic3C22×C412yes—
152C2×C3⋊Dic3C22×C412yes—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—48no—
166C2×C4×D4—91no—
167#388—92no—
168#387—92no—
169#386—32no—
170#385—92no—
171#383—91no—
172#382—91no—
173#381—91no—
174#380—91no—
175C4×C22⋊C4—91no—
176C2×#95—91no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3C22×D312yes—
180C24×C3C22×D312yes—
181C2×C3×D4—28no—
182C2×C3×D4—24no—
183C2×C3×D4—24no—
184C2×C3×D4—24no—
185C2×C3×D4C4×D318yes—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—64no—
192C22×C3×C4—122no—
193C22×C3×C4—122no—
194C22×C3×C4C22×D312yes—
195C22×Dic3—24no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—38no—
201C22×Dic3—38no—
202C22×Dic3—42no—
203C22×Dic3—42no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—64no—
209C22×Dic3—64no—
210C22×Dic3—122no—
211C22×Dic3—122no—
212C22×Dic3—122no—
213C22×Dic3—122no—
214C22×Dic3—124no—
215C22×Dic3—124no—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C3×C22⋊C4—64no—
221C3×C22⋊C4—122no—
222C3×C22⋊C4—122no—
223#217—24no—
224#217—38no—
225#217—38no—
226#217—42no—
227#217—42no—
228#217—64no—
229#217—64no—
230C4⋊Dic3—38no—
231C4⋊Dic3—64no—
232Dic3⋊C4—122no—
233Dic3⋊C4—122no—
234Dic3⋊C4—122no—
235Dic3⋊C4—122no—
236C4×Dic3—38no—
237C4×Dic3—64no—
238C4×Dic3—122no—
239C4×Dic3—122no—
240C22×C32—22no—
241C22×C32—22no—
242C22×C32—22no—
243C22×C32—24no—
244C22×C32—24no—
245C22×C32—22no—
246C22×C32—22no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32#11714yes—
250C22×C32C23×C411yescharacteristic
251C22×C32C2×#4112yes—
252C22×C32H(5,𝔽2)11yescharacteristic
253C22×C32H(5,𝔽2)12yes—
254C22×C322−1+411yescharacteristic
255C32×C4—22no—
256C3⋊Dic3—22no—
257C3⋊Dic3—22no—
258C3⋊Dic3—22no—
259C3⋊Dic3—22no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C22×D4D3211yescharacteristic
265C23×C4—32no—
266C23×C4—91no—
267C23×C4—91no—
268C4×D4—98no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—92no—
271C2×C4⋊C4—92no—
272C2×C22⋊C4—32no—
273C2×C22⋊C4—32no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C42—91no—
278C2×C42—92no—
279#95—32no—
280#95—32no—
281#95—91no—
282#95—91no—
283#95—92no—
284#95—91no—
285#95—91no—
286#95—92no—
287#95—92no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—24no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—24no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3C2×C4×D314yes—
310C23×C3C2×C4×D314yes—
311C23×C3#23714yes—
312C23×C3#23714yes—
313C23×C3C23×D312yes—
314C3×D4—216no—
315C3×D4—216no—
316C2×C3×C4—24no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—128no—
333C2×C3×C4C2×C4×D314yes—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—34no—
347C2×Dic3—34no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—48no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—64no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—128no—
369C2×Dic3—128no—
370C2×Dic3—128no—
371C2×Dic3—128no—
372C2×C32—24no—
373C2×C32—42no—
374C2×C32C2×#11711yescharacteristic
375C2×C32#51811yescharacteristic
376C2×C32#52011yescharacteristic
377C2×C32#53812yes—
378C2×C32#53912yes—
379C24C2×D3211yescharacteristic
380C24C2×D3211yescharacteristic
381C2×D4—24no—
382C2×D4#62414yes—
383C22×C4—32no—
384C22×C4—32no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—64no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—94no—
393C22×C4—94no—
394C22×C4—122no—
395C22×C4—122no—
396C22×C4—362no—
397C22×C4—362no—
398C22×C4C2×D3211yescharacteristic
399C4⋊C4—94no—
400C4⋊C4—362no—
401C4⋊C4—362no—
402C22⋊C4—64no—
403C22⋊C4—94no—
404C22⋊C4—94no—
405C22⋊C4—122no—
406C22⋊C4—122no—
407C42—94no—
408C42—362no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3—24no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—24no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3—42no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3#87718yes—
438C22×C3C22×C4×D312yes—
439C22×C3C2×#23712yes—
440C22×C3C2×#23712yes—
441C22×C3#100412yes—
442C22×C3#100412yes—
443C22×C3#100912yes—
444C22×C3#101012yes—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4—122no—
450C3×C4—122no—
451Dic3—42no—
452Dic3—42no—
453Dic3—42no—
454Dic3—42no—
455Dic3—64no—
456Dic3—64no—
457Dic3—64no—
458Dic3—64no—
459Dic3—64no—
460Dic3—122no—
461Dic3—122no—
462Dic3—122no—
463C32#231811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—21no—
466C23—22no—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—22no—
471C23#380514yes—
472C23C2×#62412yes—
473C23C2×#62412yes—
474C23C22×D3211yescharacteristic
475D4—28no—
476C2×C4—22no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—128no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—364no—
500C2×C4—364no—
501C2×C4C2×#62412yes—
502C2×C3—28no—
503C2×C3—21no—
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—22no—
508C2×C3—44no—
509C2×C3—44no—
510C2×C3—44no—
511C2×C3C2×#87712yes—
512C2×C3#554512yes—
513C2×C3#554612yes—
514C2×C3#559312yes—
515C2×C3#560212yes—
516C2×C3#561712yes—
517C2×C3#566512yes—
518C22—22no—
519C22—24no—
520C22—22no—
521C22—24no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—42no—
526C22—42no—
527C22#6395714yes—
528C22#6430911yescharacteristic
529C22#6431311yescharacteristic
530C22#6431412yes—
531C22C2×#380512yes—
532C22C22×#62411yescharacteristic
533C4—22no—
534C4—122no—
535C4—122no—
536C4—122no—
537C4—122no—
538C4—182no—
539C4—182no—
540C4—182no—
541C4—182no—
542C3—21no—
543C3#7466312yescomplemented
544C2—24no—
545C2—42no—
546C2#1059521911yescharacteristic
547C2#1059522012yes—
548C2#1059522311yescharacteristic
549C2#1059526712yes—
550C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591720C2semidirect
4. #10591705C2semidirect
5. #10591703C2semidirect
6. #10591697C2semidirect
7. C2×#63579C2semidirect
8. #10591693C2semidirect
9. #10591360C2semidirect
10. #10591271C2semidirect
11. #10591229C2semidirect
19. D4×C3⋊Dic3C4semidirect
61. C22×C3⋊Dic3C2×C4semidirect
74. #3757C2×C4semidirect
75. C4⋊(C3⋊Dic3)C2×C4semidirect
76. C4×C3⋊Dic3C2×C4semidirect
463. C32#2318semidirect
543. C3#74663semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C3×#52202
#105917202
#105917052
#105917032
#105916972
C2×#635792
#105916932
#105913602
#105912712
#105912292
#746633