Finite Group Databasebeta

← #11819108

Subgroups — #11819108

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×#63873C211yesmaximal, characteristic, complemented
2C2×#63865C211yesmaximal, characteristic
3#10592365C211yesmaximal, characteristic
4C3×#4646C212yesmaximal, complemented
5#10591396C211yesmaximal, characteristic, complemented
6#10591396C211yesmaximal, characteristic, complemented
7#10591355C211yesmaximal, characteristic
8C4×#3724C211yesmaximal, characteristic, complemented
9#10591310C212yesmaximal
10#10591202C212yesmaximal
11#10591199C212yesmaximal, complemented
12#76517—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×Dic6C2212yes—
15C22×#627C2211yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2211yescharacteristic
23C2×#3724C2212yes—
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28#63873—24no—
29#63865—24no—
30C32×#95C2211yescharacteristic
31#63658C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#944—32no—
39C2×#896—32no—
40C3×#391—32no—
41#5231—32no—
42#4985—32no—
43#4940—32no—
44C4×Dic3⋊C4—32no—
45#4673—32no—
46#4669—32no—
47#4667—32no—
48#4666—32no—
49#4666—61no—
50#4658—32no—
51#4646—32no—
52#4646—32no—
53#4646D312yescomplemented
54C23×C3⋊D3C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×C3×Dic6—24no—
69C2×C3×Dic6—24no—
70C2×C3×Dic6—42no—
71C2×#627—22no—
72C2×#627—22no—
73C2×#627—22no—
74#3752—22no—
75#3752Q814yescomplemented
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3—22no—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3—42no—
80#3724—22no—
81#3724—22no—
82#3724—24no—
83#3724D414yes—
84#3722—24no—
85#3722—42no—
86#2492—91noSylow
87C22×C3×Q8—32no—
88C22×C4×D3—32no—
89C22×C4×D3—61no—
90C22×Dic6—32no—
91C22×Dic6C2×D312yes—
92C2×C3×C4⋊C4—32no—
93C2×C3×C42—32no—
94#944—68no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4C2×D312yes—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3C2×D312yes—
114#896—68no—
115C3×#95—21no—
116C3×#95—32no—
117C3×#95—32no—
118C3×#95—32no—
119C3×#95C2×D312yes—
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⋊#95C2×D312yes—
129C3⋊#95C2×D312yes—
130C3⋊#95C2×D312yes—
131C23×C32C2411yescharacteristic
132C22×C3⋊D3—21no—
133C22×C3⋊D3—21no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3C2×Q812yes—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4C2×Q812yes—
147C2×C32×C4#4112yes—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3C2×D412yes—
154C2×C3⋊Dic3C2×Q812yes—
155C2×C3⋊Dic3#4112yes—
156C2×C3⋊Dic3#4112yes—
157C4×C3⋊D3—44no—
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—
170C3×Dic6—48no—
171#627—44no—
172C2×C4⋊Q8—91no—
173C2×C22⋊Q8—91no—
174#400—92no—
175#393—92no—
176#391—32no—
177#391—91no—
178#391—91no—
179#388—92no—
180#380—91no—
181C4×C4⋊C4—91no—
182C4×C22⋊C4—91no—
183C23×D3—32no—
184C23×D3—61no—
185C2×C3×Q8—64no—
186C2×C3×Q8—64no—
187C2×C3×Q8—122no—
188C22×C3×C4—21no—
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×C4C22×D312yes—
196C22×C3×C4C22×D312yes—
197C22×C3×C4C22×D312yes—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—32no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3C22×D312yes—
205C22×Dic3C22×D312yes—
206C22×Dic3C22×D312yes—
207C22×Dic3C22×D312yes—
208C2×C4×D3—64no—
209C2×C4×D3—64no—
210C2×C4×D3—64no—
211C2×C4×D3—64no—
212C2×C4×D3—122no—
213C2×C4×D3—122no—
214C2×Dic6—24no—
215C2×Dic6—24no—
216C2×Dic6—42no—
217C2×Dic6—64no—
218C2×Dic6—64no—
219C2×Dic6—64no—
220C3×C4⋊C4—64no—
221C3×C42—122no—
222(C2×D3)⋊C4—38no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—64no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—122no—
229(C2×D3)⋊C4—122no—
230Dic3⋊C4—24no—
231Dic3⋊C4—38no—
232Dic3⋊C4—64no—
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×C32C22×D411yescharacteristic
242C22×C32C22×Q811yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32C2×#4111yescharacteristic
245C22×C32C2×#4111yescharacteristic
246C22×C32H(5,𝔽2)11yescharacteristic
247C22×C322−1+411yescharacteristic
248C2×C3⋊D3—22no—
249C2×C3⋊D3—22no—
250C2×C3⋊D3—22no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C2×C3⋊D3—41no—
255C32×C4—22no—
256C32×C4—22no—
257C32×C4—41no—
258C3⋊Dic3—22no—
259C3⋊Dic3—41no—
260C3⋊Dic3#12414yes—
261C3×Dic3—24no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C22×Q8—32no—
266C22×Q8—91no—
267C23×C4—91no—
268C4⋊Q8—184no—
269C22⋊Q8—184no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—92no—
274C2×C4⋊C4—91no—
275C2×C22⋊C4—91no—
276C2×C22⋊C4—92no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—92no—
279C2×C42—32no—
280C2×C42—91no—
281C2×C42—91no—
282#95—32no—
283#95—32no—
284#95—32no—
285#95—92no—
286#95—92no—
287#95—92no—
288#95—91no—
289#95D3211yescharacteristic
290C23×C3—21no—
291C23×C3C23×D312yes—
292C22×D3—34no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C3×Q8—128no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—34no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
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—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4#23514yes—
336C2×C3×C4D3×Q814yes—
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—22no—
347C2×Dic3—22no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3D3×D414yes—
367C4×D3—128no—
368C4×D3—128no—
369Dic6—48no—
370Dic6—128no—
371C2×C32C2×#12411yescharacteristic
372C2×C32#53311yescharacteristic
373C2×C32#54211yescharacteristic
374C2×C32#54611yescharacteristic
375C2×C32D4×Q811yescharacteristic
376C2×C32#55411yescharacteristic
377C2×C32#55611yescharacteristic
378C3⋊D3—42no—
379C24—91no—
380C2×Q8—64no—
381C2×Q8—64no—
382C2×Q8—122no—
383C2×Q8—182no—
384C2×Q8—182no—
385C2×Q8—182no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4—182no—
396C22×C4C2×D3211yescharacteristic
397C22×C4C2×D3211yescharacteristic
398C22×C4C2×D3211yescharacteristic
399C4⋊C4—64no—
400C4⋊C4—94no—
401C4⋊C4—184no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C22⋊C4—94no—
405C22⋊C4—184no—
406C22⋊C4—182no—
407C22⋊C4—362no—
408C42—122no—
409C42—182no—
410C42—182no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3C2×#23512yes—
419C22×C3C2×D3×D412yes—
420C22×C3#100412yes—
421C22×C3C2×D3×Q812yes—
422C22×C3#100712yes—
423C22×C3D3×#4112yes—
424C22×C3D3×#4112yes—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—64no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4—122no—
449Dic3—24no—
450Dic3—38no—
451Dic3—42no—
452Dic3—42no—
453Dic3—42no—
454Dic3—64no—
455Dic3—64no—
456Dic3—122no—
457Dic3—122no—
458Dic3—122no—
459C32#249211yescharacteristic, complemented, Sylow
460C23—92no—
461C23—181no—
462C23—181no—
463C23—181no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23C22×D3211yescharacteristic
468Q8—128no—
469Q8—364no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—34no—
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—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—364no—
499C2×C4#379712yes—
500C2×C4#379812yes—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3#549012yes—
509C2×C3#556812yes—
510C2×C3#557812yes—
511C2×C3#563612yes—
512C2×C3#564012yes—
513C2×C3D3×#12412yes—
514C2×C3#572712yes—
515D3—124no—
516D3—124no—
517C22—182no—
518C22—182no—
519C22—182no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22C2×#379711yescharacteristic
525C22C2×#379811yescharacteristic
526C22#6430611yescharacteristic
527C22D32×D411yescharacteristic
528C22#6431211yescharacteristic
529C22#6431311yescharacteristic
530C22#6431611yescharacteristic
531C4—22no—
532C4—22no—
533C4—41no—
534C4—64no—
535C4—94no—
536C4—122no—
537C4—122no—
538C4—122no—
539C4—182no—
540C4—361no—
541C3—21no—
542C3#7651712yescomplemented
543C2—362no—
544C2#1059388211yescharacteristic
545C2#1059416811yescharacteristic
546C2#1059418311yescharacteristic
547C2#1059428811yescharacteristic
548C2#1059435011yescharacteristic
549C2#1059437911yescharacteristic
550C2#1059456911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63873C2semidirect
4. C3×#4646C2semidirect
5. #10591396C2semidirect
6. #10591396C2semidirect
8. C4×#3724C2semidirect
11. #10591199C2semidirect
53. #4646D3semidirect
75. #3752Q8semidirect
459. C32#2492semidirect
542. C3#76517semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
C2×#638652
#105923652
C3×#46462
#105913962
#105913552
C4×#37242
#105913102
#105912022
#105911992
#765173