Finite Group Databasebeta

← #11819065

Subgroups — #11819065

Order 1152.

1145 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×#63982C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
4C3×#4951C212yesmaximal
5#10591720C211yesmaximal, characteristic
6#10591692C212yesmaximal
7#10591396C211yesmaximal, characteristic, complemented
8#10591396C211yesmaximal, characteristic, complemented
9#10591343C212yesmaximal, complemented
10C4×#3724C211yesmaximal, characteristic, complemented
11#10591191C212yesmaximal, complemented
12#75547—32nomaximal
13C23×C3⋊Dic3C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C22×#627C2212yes—
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24#63982—24no—
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29#63919—24no—
30#63658C2211yescharacteristic
31#63658C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#888—32no—
39C2×#878—32no—
40C3×#388—32no—
41#4986—32no—
42#4951D312yes—
43#4947—32no—
44#4947—32no—
45#4942—32no—
46Dic3×C22⋊C4—32no—
47Dic3×C22⋊C4—61no—
48C4×Dic3⋊C4—32no—
49#4929—32no—
50#4660—32no—
51#4646—32no—
52#4646—32no—
53#4646—32no—
54C24×C32C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—22no—
58C22×C3⋊Dic3—22no—
59C22×C3⋊Dic3—22no—
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×#627—22no—
69C2×#627—24no—
70C2×#627—22no—
71C2×#627—22no—
72C2×#627—24no—
73C2×#627—42no—
74C32×C22⋊C4Q814yescomplemented
75#3757—22no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3—22no—
78C3×#217—24no—
79C3×#217—42no—
80C3×C4⋊Dic3—24no—
81C3×C4×Dic3—42no—
82#3724—22no—
83#3724—22no—
84#3724D414yes—
85Dic3⋊Dic3—24no—
86#2492—91noSylow
87C23×Dic3—32no—
88C23×Dic3—61no—
89C22×Dic6—32no—
90C22×Dic6—32no—
91C22×Dic6—32no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C22⋊C4C2×D312yes—
97C2×C3×C42—32no—
98C2×#217—32no—
99C2×#217—61no—
100C2×#217C2×D312yes—
101C2×#217C2×D312yes—
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3C2×D312yes—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3C2×D312yes—
113#888—68no—
114#878—68no—
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⋊#95—32no—
127C3⋊#95—61no—
128C3⋊#95—61no—
129C3⋊#95C2×D312yes—
130C3⋊#95C2×D312yes—
131C23×C32—21no—
132C23×C32—21no—
133C23×C32—21no—
134C23×C32—21no—
135C23×C32—21no—
136C23×C32—21no—
137C23×C32C2×Q812yes—
138C23×C32C2411yescharacteristic
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4C2×Q812yes—
144C2×C32×C4C2×Q812yes—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—44no—
154C2×C3⋊Dic3C2×D412yes—
155C2×C3⋊Dic3#4112yes—
156C2×C3⋊Dic3#4112yes—
157C2×C3⋊Dic3#4112yes—
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—22no—
169C2×C3×Dic3C2×D414yes—
170#627—48no—
171#627—44no—
172C2×C4⋊Q8—91no—
173C2×C22⋊Q8—91no—
174#400—92no—
175#393—92no—
176#391—91no—
177#391—91no—
178#391—92no—
179#388—32no—
180#380—91no—
181C4×C4⋊C4—91no—
182C4×C22⋊C4—91no—
183C24×C3—21no—
184C24×C3C22×D312yes—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—64no—
202C22×Dic3—64no—
203C22×Dic3—64no—
204C22×Dic3—64no—
205C22×Dic3—122no—
206C22×Dic3—122no—
207C22×Dic3C22×D312yes—
208C22×Dic3C22×D312yes—
209C22×Dic3C22×D312yes—
210C22×Dic3C22×D312yes—
211C2×Dic6—64no—
212C2×Dic6—64no—
213C2×Dic6—64no—
214C2×Dic6—64no—
215C2×Dic6—64no—
216C2×Dic6—64no—
217C2×Dic6—64no—
218C2×Dic6—122no—
219C2×Dic6—122no—
220C3×C4⋊C4—64no—
221C3×C22⋊C4—24no—
222C3×C22⋊C4—64no—
223C3×C22⋊C4—122no—
224C3×C22⋊C4Dic618yescomplemented
225C3×C42—122no—
226#217—24no—
227#217—42no—
228#217—64no—
229#217—64no—
230C4⋊Dic3—24no—
231C4⋊Dic3—64no—
232Dic3⋊C4—38no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235Dic3⋊C4—64no—
236C4×Dic3—42no—
237C4×Dic3—64no—
238C4×Dic3—64no—
239C4×Dic3—122no—
240C4×Dic3—122no—
241C22×C32—22no—
242C22×C32—22no—
243C22×C32—22no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32—41no—
247C22×C32—41no—
248C22×C32C22×D411yescharacteristic
249C22×C32C22×Q811yescharacteristic
250C22×C32C2×#4111yescharacteristic
251C22×C32C2×#4111yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32H(5,𝔽2)11yescharacteristic
254C22×C322−1+411yescharacteristic
255C32×C4—22no—
256C32×C4—22no—
257C3⋊Dic3—22no—
258C3⋊Dic3—41no—
259C3⋊Dic3—41no—
260C3⋊Dic3#12414yes—
261C3×Dic3—24no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C22×Q8—91no—
266C22×Q8—92no—
267C23×C4—91no—
268C4⋊Q8—184no—
269C22⋊Q8—184no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—92no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C22⋊C4—32no—
276C2×C22⋊C4—32no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4D3211yescharacteristic
279C2×C42—32no—
280C2×C42—91no—
281C2×C42—91no—
282#95—32no—
283#95—32no—
284#95—92no—
285#95—92no—
286#95—92no—
287#95—92no—
288#95—91no—
289#95—91no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—21no—
299C23×C3—22no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3C2×Dic614yes—
305C23×C3C23×D312yes—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—34no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
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×C4C2×Dic614yes—
329C2×C3×C4C2×Dic614yes—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—128no—
366C2×Dic3—128no—
367C2×Dic3D3×D414yes—
368Dic6—128no—
369Dic6—128no—
370Dic6—128no—
371C2×C32—42no—
372C2×C32C2×#12411yescharacteristic
373C2×C32#53311yescharacteristic
374C2×C32#54211yescharacteristic
375C2×C32#54611yescharacteristic
376C2×C32D4×Q811yescharacteristic
377C2×C32#55411yescharacteristic
378C2×C32#55611yescharacteristic
379C24C2×D3211yescharacteristic
380C2×Q8—184no—
381C2×Q8—182no—
382C2×Q8—184no—
383C2×Q8—182no—
384C2×Q8—182no—
385C2×Q8—362no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—182no—
395C22×C4—182no—
396C22×C4—182no—
397C22×C4C2×D3211yescharacteristic
398C22×C4C2×D3211yescharacteristic
399C4⋊C4—64no—
400C4⋊C4—94no—
401C4⋊C4—184no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C22⋊C4—64no—
405C22⋊C4—122no—
406C22⋊C4—182no—
407C22⋊C4#62714yescomplemented
408C42—122no—
409C42—182no—
410C42—182no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3C22×Dic612yes—
433C22×C3C2×D3×D412yes—
434C22×C3#100412yes—
435C22×C3D3×#4112yes—
436C22×C3D3×#4112yes—
437C22×C3D3×#4112yes—
438C22×C3#101012yes—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—64no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4—122no—
447Dic3—24no—
448Dic3—38no—
449Dic3—42no—
450Dic3—42no—
451Dic3—42no—
452Dic3—64no—
453Dic3—64no—
454Dic3—122no—
455Dic3—122no—
456Dic3—122no—
457Dic3—122no—
458Dic3—122no—
459C32#249211yescharacteristic, complemented, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23C2×#62712yes—
467C23C22×D3211yescharacteristic
468Q8—368no—
469Q8—364no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—34no—
475C2×C4—62no—
476C2×C4—62no—
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—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—364no—
499C2×C4C2×#62712yes—
500C2×C4C2×#62712yes—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—44no—
509C2×C3—44no—
510C2×C3#551712yes—
511C2×C3D4×Dic612yes—
512C2×C3#553912yes—
513C2×C3#561012yes—
514C2×C3#566212yes—
515C2×C3D3×#12412yes—
516C2×C3#570212yes—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22#6430611yescharacteristic
525C22#6430611yescharacteristic
526C22#6430911yescharacteristic
527C22D32×D411yescharacteristic
528C22#6431211yescharacteristic
529C22#6431311yescharacteristic
530C22C22×#62711yescharacteristic
531C4—22no—
532C4—22no—
533C4—64no—
534C4—94no—
535C4—122no—
536C4—122no—
537C4—122no—
538C4—182no—
539C4—361no—
540C4—361no—
541C3—21no—
542C3#7554712yescomplemented
543C2—42no—
544C2#1059422211yescharacteristic
545C2#1059425011yescharacteristic
546C2#1059427611yescharacteristic
547C2#1059428811yescharacteristic
548C2#1059505011yescharacteristic
549C2D4×#62711yescharacteristic
550C2#1059527411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63919C2semidirect
7. #10591396C2semidirect
8. #10591396C2semidirect
9. #10591343C2semidirect
10. C4×#3724C2semidirect
11. #10591191C2semidirect
74. C32×C22⋊C4Q8semidirect
224. C3×C22⋊C4Dic6semidirect
407. C22⋊C4#627semidirect
459. C32#2492semidirect
542. C3#75547semidirect

Maximal subgroups

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

subgroupindex
C2×#639822
C2×#639192
C22⋊C4×C3⋊Dic32
C3×#49512
#105917202
#105916922
#105913962
#105913432
C4×#37242
#105911912
#755473