Finite Group Databasebeta

← #11808809

Subgroups — #11808809

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic, complemented
3C3×C4×#217C212yesmaximal, complemented
4#10591712C212yesmaximal
5#10591694C211yesmaximal, characteristic, complemented
6#10591692C211yesmaximal, characteristic, complemented
7C4×#3722C212yesmaximal, complemented
8#10591222C211yesmaximal, characteristic, complemented
9#10591216C211yesmaximal, characteristic, complemented
10#10591210C212yesmaximal, complemented
11#10591205C211yesmaximal, characteristic, complemented
12#73481—32nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#627C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C4×#638—24no—
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C4×#627—24no—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2211yescharacteristic
36#63579C2211yescharacteristic
37#63579C2212yes—
38C2×C4×#67—32no—
39C2×C4×#67—61no—
40C2×C4×Dic6—32no—
41C3×C4×C22⋊C4—32no—
42C4×#217D312yescomplemented
43#4961—32no—
44#4959—32no—
45#4952—32no—
46#4947—32no—
47C4×(C2×D3)⋊C4—32no—
48C4×(C2×D3)⋊C4—32no—
49#4932—32no—
50#4675—32no—
51#4673—32no—
52#4660—32no—
53#4658—32no—
54C24×C32C2311yescharacteristic
55C23×C3⋊D3C2311yescharacteristic
56C22×C32×C4—22no—
57C22×C32×C4—24no—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61C2×#638—22no—
62C2×#638—22no—
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—24no—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×#627—22no—
73C2×#627—24no—
74#3757—22no—
75#3752—22no—
76#3750—22no—
77C4×C3⋊Dic3D414yes—
78C3×#217—24no—
79C3×#217—24no—
80C3×C4×Dic3—24no—
81C3×C4×Dic3—24no—
82#3724—22no—
83Dic3⋊Dic3—24no—
84#3722—24no—
85#3722—24no—
86#2398—91noSylow
87C23×C3×C4—21no—
88C23×C3×C4C2×D312yes—
89C22×#67—32no—
90C22×#67—61no—
91C22×C4×D3—32no—
92C22×C4×D3—61no—
93C22×Dic6—32no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C42—32no—
97C2×C3×C42—32no—
98C2×#217—32no—
99C2×#217—61no—
100C2×#217C2×D312yes—
101C2×#217C2×D312yes—
102C4×#67—68no—
103C4×#67—68no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—61no—
110C2×C4⋊Dic3—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—61no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3C2×D312yes—
118C2×C4×Dic3C2×D312yes—
119C4×Dic6—68no—
120C3×#95—32no—
121C3×#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95C2×D312yes—
131C3⋊#95C2×D312yes—
132C23×C32—21no—
133C23×C32—21no—
134C23×C32—22no—
135C23×C32—22no—
136C23×C32#4112yes—
137C23×C32C2411yescharacteristic
138C22×C3⋊D3—21no—
139C22×C3⋊D3—21no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3#4112yes—
143C2×C32×C4—21no—
144C2×C32×C4—22no—
145C2×C32×C4—44no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4114yes—
148#638—28no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3C2×D412yes—
155C2×C3⋊Dic3C2×D412yes—
156C4×C3⋊D3—44no—
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—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3#4114yes—
169#627—28no—
170C2×C4×Q8—91no—
171C2×C4×D4—91no—
172#400—92no—
173#397—91no—
174#397—91no—
175#394—92no—
176#393—91no—
177#393—91no—
178C4×C22⋊C4—32no—
179C4×C22⋊C4—92no—
180#376—91no—
181C24×C3—21no—
182C24×C3C22×D312yes—
183C23×D3—32no—
184C23×D3—61no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—24no—
188C22×C3×C4—24no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—32no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—44no—
196C22×C3×C4C22×D312yes—
197C22×C3×C4C22×D312yes—
198C2×#67—64no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—64no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D312yes—
213C22×Dic3C22×D312yes—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—124no—
219C2×Dic6—64no—
220C2×Dic6—64no—
221C2×Dic6—64no—
222C3×C22⋊C4—64no—
223C3×C22⋊C4—64no—
224C3×C42—64no—
225C3×C42—64no—
226#217—24no—
227#217—24no—
228#217—64no—
229#217—64no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236C4⋊Dic3—64no—
237Dic3⋊C4—64no—
238Dic3⋊C4—64no—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241C4×Dic3—24no—
242C4×Dic3—24no—
243C4×Dic3—38no—
244C4×Dic3—64no—
245C22×C32—22no—
246C22×C32—24no—
247C22×C32—41no—
248C22×C32—41no—
249C22×C32—42no—
250C22×C32C22×D411yescharacteristic
251C22×C32C2×#4111yescharacteristic
252C22×C32C2×#4112yes—
253C22×C32C2×#4112yes—
254C22×C32C2×#4111yescharacteristic
255C2×C3⋊D3—22no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—41no—
259C2×C3⋊D3—42no—
260C32×C4—41no—
261C32×C4#12414yes—
262C3⋊Dic3—22no—
263C3⋊Dic3—22no—
264C3⋊Dic3—41no—
265C3×Dic3—24no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—91no—
270C22×D4—91no—
271C23×C4—91no—
272C23×C4D3211yescharacteristic
273C4×Q8—184no—
274C4×D4—184no—
275C2×C4⋊C4—92no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C22⋊C4—32no—
279C2×C22⋊C4—32no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—91no—
284C2×C42—32no—
285C2×C42—32no—
286C2×C42—91no—
287#95—32no—
288#95—32no—
289#95—91no—
290#95—91no—
291#95—92no—
292#95—92no—
293#95—92no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—22no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3#23514yes—
307C23×C3C23×D312yes—
308C22×D3—34no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—122no—
319C22×D3—122no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—34no—
327C2×C3×C4—42no—
328C2×C3×C4—48no—
329C2×C3×C4—48no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4#23514yes—
342C2×C3×C4D3×D414yes—
343C2×C3×C4#23714yes—
344#67—616no—
345#67—616no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3#23514yes—
374C4×D3—128no—
375C4×D3—128no—
376Dic6—616no—
377C2×C32—42no—
378C2×C32#52511yescharacteristic
379C2×C32#52511yescharacteristic
380C2×C32C2×#12411yescharacteristic
381C2×C32#52912yes—
382C2×C32#52912yes—
383C3⋊D3—42no—
384C24—91no—
385C24C2×D3211yescharacteristic
386C2×Q8—184no—
387C2×Q8—182no—
388C2×D4—182no—
389C2×D4—182no—
390C2×D4—182no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—184no—
401C22×C4—182no—
402C22×C4C2×D3211yescharacteristic
403C22×C4C2×D3211yescharacteristic
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—184no—
407C22⋊C4—64no—
408C22⋊C4—64no—
409C22⋊C4—182no—
410C22⋊C4—184no—
411C22⋊C4—184no—
412C22⋊C4—182no—
413C42—64no—
414C42—64no—
415C42—94no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—21no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—44no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3C2×#23512yes—
434C22×C3C2×#23512yes—
435C22×C3C2×#23512yes—
436C22×C3C2×D3×D412yes—
437C22×C3C2×#23712yes—
438C22×C3D3×#4112yes—
439C22×C3D3×#4112yes—
440C2×D3—64no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—124no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—124no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C3×C4—24no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—64no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4—122no—
459C3×C4#88518yes—
460Dic3—24no—
461Dic3—42no—
462Dic3—42no—
463Dic3—42no—
464Dic3—64no—
465Dic3—64no—
466Dic3—64no—
467Dic3—122no—
468Dic3—122no—
469Dic3—122no—
470C32#239811yescharacteristic, complemented, Sylow
471C23—22no—
472C23—21no—
473C23—22no—
474C23—21no—
475C23—92no—
476C23—181no—
477C23—182no—
478C23—182no—
479C23—181no—
480C23#379812yes—
481C23C22×D3211yescharacteristic
482Q8—188no—
483D4—188no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—34no—
487C2×C4—44no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—181no—
502C2×C4—182no—
503C2×C4—181no—
504C2×C4—182no—
505C2×C4—181no—
506C2×C4—364no—
507C2×C4#380414yes—
508C2×C4#381112yes—
509C2×C3—21no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—44no—
515C2×C3—44no—
516C2×C3#547912yes—
517C2×C3C2×#88512yes—
518C2×C3#552812yes—
519C2×C3#553812yes—
520C2×C3#554712yes—
521C2×C3#554712yes—
522C2×C3#555712yes—
523D3—124no—
524D3—124no—
525C22—24no—
526C22—22no—
527C22—41no—
528C22—42no—
529C22—41no—
530C22—184no—
531C22—182no—
532C22—361no—
533C22—362no—
534C22—361no—
535C22C2×#379811yescharacteristic
536C22D3×#23512yes—
537C22#6430611yescharacteristic
538C22C2×#380412yes—
539C22C2×#381111yescharacteristic
540C4—41no—
541C4—64no—
542C4—122no—
543C4—122no—
544C4—122no—
545C4—182no—
546C4—182no—
547C4—361no—
548C4#6395314yes—
549C3—21no—
550C3#7348112yescomplemented
551C2—42no—
552C2—362no—
553C2#1059483612yes—
554C2#1059483912yes—
555C2#1059501611yescharacteristic
556C2#1059507611yescharacteristic
557C2C2×#6395311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#627C2semidirect
3. C3×C4×#217C2semidirect
5. #10591694C2semidirect
6. #10591692C2semidirect
7. C4×#3722C2semidirect
8. #10591222C2semidirect
9. #10591216C2semidirect
10. #10591210C2semidirect
11. #10591205C2semidirect
42. C4×#217D3semidirect
470. C32#2398semidirect
550. C3#73481semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C4×#6272
C3×C4×#2172
#105917122
#105916942
#105916922
C4×#37222
#105912222
#105912162
#105912102
#105912052
#734813