Finite Group Databasebeta

← #11808720

Subgroups — #11808720

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic, complemented
3C3×#4982C212yesmaximal, complemented
4#10591397C211yesmaximal, characteristic, complemented
5#10591311C212yesmaximal
6#10591274C211yesmaximal, characteristic, complemented
7#10591260C212yesmaximal
8#10591241C212yesmaximal, complemented
9#10591218C211yesmaximal, characteristic, complemented
10#10591205C211yesmaximal, characteristic
11#10591203C211yesmaximal, characteristic
12#77739—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64101—24no—
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×#3724C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63838—24no—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2211yescharacteristic
37#63579C2211yescharacteristic
38C2×#892—32no—
39C2×#892—61no—
40C2×#887—32no—
41C3×#398—32no—
42#4994—32no—
43#4994—32no—
44#4993—32no—
45#4982D312yescomplemented
46Dic3×C4⋊C4—32no—
47Dic3×C4⋊C4—32no—
48#4673—32no—
49#4666—32no—
50#4666—32no—
51#4660—32no—
52#4656—32no—
53#4649—32no—
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⋊D3Q814yescomplemented
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×#627—22no—
69C2×#627—24no—
70C32×C4⋊C4—22no—
71#3752—22no—
72#3752—22no—
73C4⋊(C3⋊Dic3)—22no—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3D414yes—
76C3×C4⋊Dic3—24no—
77C3×Dic3⋊C4—24no—
78C3×Dic3⋊C4—24no—
79#3724—22no—
80Dic3⋊Dic3—24no—
81#3722—24no—
82#3722—24no—
83Dic32—24no—
84Dic32—24no—
85#2396—91noSylow
86C22×C4×D3—32no—
87C22×C4×D3—61no—
88C22×Dic6—32no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C4⋊C4—32no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4C2×D312yes—
94C2×(C2×D3)⋊C4—32no—
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—61no—
101C2×(C2×D3)⋊C4—61no—
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3C2×D312yes—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4C2×D312yes—
109C2×Dic3⋊C4C2×D312yes—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118#892—68no—
119#892—68no—
120#887—68no—
121C3×#95—32no—
122C3×#95—32no—
123C3×#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95C2×D312yes—
129C3⋊#95C2×D312yes—
130C3⋊#95C2×D312yes—
131C23×C32C2411yescharacteristic
132C22×C3⋊D3—21no—
133C22×C3⋊D3—21no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3C2×Q812yes—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×Q812yes—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3C2×D412yes—
148C2×C3⋊Dic3C2×D412yes—
149C2×C3⋊Dic3C2×Q812yes—
150C2×C3⋊Dic3#4112yes—
151C4×C3⋊D3—28no—
152C2×C3×Dic3—22no—
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#4114yes—
163C2×C3×Dic3#4114yes—
164#627—28no—
165C2×C4×Q8—91no—
166C2×#117—91no—
167#400—91no—
168#399—91no—
169#398—32no—
170#396—92no—
171#395—91no—
172#393—91no—
173C4×C4⋊C4—92no—
174C4×C4⋊C4—91no—
175C4×C22⋊C4—92no—
176C23×D3—32no—
177C23×D3—61no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4C22×D312yes—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C2×C4×D3—38no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×Dic6—64no—
205C2×Dic6—64no—
206C2×Dic6—64no—
207C3×C4⋊C4—24no—
208C3×C4⋊C4—24no—
209C3×C4⋊C4—64no—
210C3×C4⋊C4—64no—
211C3×C4⋊C4—64no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—64no—
220C4⋊Dic3—24no—
221C4⋊Dic3—64no—
222C4⋊Dic3—64no—
223C4⋊Dic3—64no—
224Dic3⋊C4—24no—
225Dic3⋊C4—24no—
226Dic3⋊C4—64no—
227Dic3⋊C4—64no—
228C4×Dic3—38no—
229C4×Dic3—64no—
230C4×Dic3—64no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3—64no—
234C4×Dic3—64no—
235C4×Dic3—64no—
236C22×C32C22×D411yescharacteristic
237C22×C32C22×Q811yescharacteristic
238C22×C32C2×#4112yes—
239C22×C32C2×#4112yes—
240C22×C32C2×#4111yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3—24no—
243C2×C3⋊D3—41no—
244C2×C3⋊D3—42no—
245C2×C3⋊D3—41no—
246C32×C4—22no—
247C32×C4—22no—
248C32×C4—41no—
249C3⋊Dic3—22no—
250C3⋊Dic3—41no—
251C3⋊Dic3C22⋊Q814yes—
252C3×Dic3—24no—
253C3×Dic3—24no—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C22×Q8—91no—
257C23×C4—91no—
258C4×Q8—184no—
259#117—184no—
260C2×C4⋊C4—32no—
261C2×C4⋊C4—32no—
262C2×C4⋊C4—32no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—92no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4D3211yescharacteristic
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—91no—
270C2×C22⋊C4—91no—
271C2×C42—91no—
272C2×C42—92no—
273C2×C42—92no—
274C2×C42—91no—
275#95—32no—
276#95—32no—
277#95—32no—
278#95—91no—
279#95—91no—
280#95—92no—
281C23×C3—21no—
282C23×C3C23×D312yes—
283C22×D3—34no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—122no—
294C22×D3—122no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—34no—
308C2×C3×C4—34no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4D3×D414yes—
322C2×C3×C4D3×Q814yes—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—34no—
334C2×Dic3—34no—
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3#23714yes—
350C2×Dic3#23914yes—
351C4×D3—616no—
352C4×D3—616no—
353Dic6—616no—
354C2×C32C2×C22⋊Q811yescharacteristic
355C2×C32#52511yescharacteristic
356C2×C32#52912yes—
357C2×C32#53211yescharacteristic
358C2×C32#53312yes—
359C3⋊D3—42no—
360C24—91no—
361C2×Q8—184no—
362C2×Q8—182no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—32no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—94no—
370C22×C4—91no—
371C22×C4—182no—
372C22×C4—182no—
373C22×C4C2×D3211yescharacteristic
374C22×C4C2×D3211yescharacteristic
375C22×C4C2×D3211yescharacteristic
376C4⋊C4—22no—
377C4⋊C4—64no—
378C4⋊C4—64no—
379C4⋊C4—64no—
380C4⋊C4—182no—
381C4⋊C4—184no—
382C4⋊C4—182no—
383C22⋊C4—182no—
384C22⋊C4—184no—
385C22⋊C4—184no—
386C22⋊C4—182no—
387C42—94no—
388C42—182no—
389C42—184no—
390C42—184no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3C2×D3×D412yes—
397C22×C3C2×#23712yes—
398C22×C3C2×D3×Q812yes—
399C22×C3C2×#23912yes—
400C22×C3D3×#4112yes—
401C22×C3D3×#4112yes—
402C22×C3D3×#4112yes—
403C2×D3—64no—
404C2×D3—64no—
405C2×D3—64no—
406C2×D3—64no—
407C2×D3—124no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—124no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C3×C4—24no—
416C3×C4—24no—
417C3×C4—24no—
418C3×C4—42no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—64no—
422C3×C4—64no—
423C3×C4—122no—
424C3×C4—122no—
425Dic3—24no—
426Dic3—24no—
427Dic3—38no—
428Dic3—42no—
429Dic3—42no—
430Dic3—64no—
431Dic3—64no—
432Dic3—122no—
433Dic3—122no—
434Dic3—122no—
435C32#239611yescharacteristic, complemented, Sylow
436C23—92no—
437C23—181no—
438C23—182no—
439C23—182no—
440C23—181no—
441C23C22×D3211yescharacteristic
442Q8—188no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—34no—
449C2×C4—34no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—92no—
461C2×C4—92no—
462C2×C4—92no—
463C2×C4—92no—
464C2×C4—188no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4—181no—
468C2×C4#379712yes—
469C2×C4#381112yes—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3#559612yes—
476C2×C3D3×C22⋊Q812yes—
477C2×C3#562712yes—
478C2×C3#564912yes—
479C2×C3#568812yes—
480C2×C3#569112yes—
481C2×C3#572812yes—
482D3—124no—
483D3—124no—
484C22—182no—
485C22—184no—
486C22—361no—
487C22—361no—
488C22—362no—
489C22C2×#379711yescharacteristic
490C22#6430611yescharacteristic
491C22D3×#23712yes—
492C22D3×#23912yes—
493C22C2×#381111yescharacteristic
494C4—22no—
495C4—22no—
496C4—41no—
497C4—64no—
498C4—64no—
499C4—94no—
500C4—122no—
501C4—122no—
502C4—182no—
503C4—361no—
504C3—21no—
505C3#7773912yescomplemented
506C2—362no—
507C2#1059444112yes—
508C2#1059444812yes—
509C2#1059492511yescharacteristic
510C2#1059516511yescharacteristic
511C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63838C2semidirect
3. C3×#4982C2semidirect
4. #10591397C2semidirect
6. #10591274C2semidirect
8. #10591241C2semidirect
9. #10591218C2semidirect
45. #4982D3semidirect
63. C2×C4×C3⋊D3Q8semidirect
435. C32#2396semidirect
505. C3#77739semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638382
C3×#49822
#105913972
#105913112
#105912742
#105912602
#105912412
#105912182
#105912052
#105912032
#777393