Finite Group Databasebeta

← #11802811

Subgroups — #11802811

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C3×#4980C212yesmaximal, complemented
3#10591355C211yesmaximal, characteristic
4#10591325C211yesmaximal, characteristic
5C4×#3722C211yesmaximal, characteristic
6#10591271C212yesmaximal, complemented
7#10591263C212yesmaximal, complemented
8#10591260C211yesmaximal, characteristic
9#10591219C211yesmaximal, characteristic
10#10591219C211yesmaximal, characteristic
11#10591197C212yesmaximal, complemented
12#75296—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C4⋊C4×C3⋊D3C418yescomplemented
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2212yes—
24C2×#3722C2211yescharacteristic
25C2×#3722C2211yescharacteristic
26C2×#3722C2211yescharacteristic
27C2×#3722C2211yescharacteristic
28C2×Dic32C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×D3×C4⋊C4—32no—
38C2×D3×C4⋊C4—61no—
39C3×#387—32no—
40#4987—32no—
41#4980D312yescomplemented
42#4978—32no—
43C4×(C2×D3)⋊C4—32no—
44#4933—32no—
45#4667—32no—
46#4666—32no—
47#4664—32no—
48#4664—32no—
49#4655—32no—
50#4654—32no—
51#4653—32no—
52#4652—32no—
53C23×C3⋊D3C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—42no—
63C2×C4×C3⋊D3—42no—
64C2×C4×C3⋊D3C2×C414yes—
65C2×C4×C3⋊D3C2×C414yes—
66C2×C4×C3⋊D3C2×C414yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C32×C4⋊C4C2×C414yes—
72C4⋊(C3⋊Dic3)C2×C414yes—
73#3750C2×C414yes—
74#3750C2×C414yes—
75C3×C4⋊Dic3—42no—
76C3×C4×Dic3—42no—
77#3724—42no—
78#3722—22no—
79#3722—22no—
80#3722—22no—
81#3722—22no—
82Dic32—42no—
83#2313—91noSylow
84C22×C4×D3—32no—
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—61no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—32no—
92C2×C3×C4⋊C4C2×D312yes—
93C2×C3×C42—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D312yes—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3C2×D312yes—
110D3×C4⋊C4—316no—
111D3×C4⋊C4—68no—
112C3×#95—32no—
113C3×#95—32no—
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⋊#95C2×D312yes—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3C22×C412yes—
132C22×C3⋊D3#4112yes—
133C22×C3⋊D3#4112yes—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C22×C412yes—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3C22×C412yes—
146C2×C3⋊Dic3C22×C412yes—
147C2×C3⋊Dic3C22×C412yes—
148C4×C3⋊D3—28no—
149C4×C3⋊D3—44no—
150C4×C3⋊D3—44no—
151C2×C3×Dic3—22no—
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—22no—
163C22×C4⋊C4—91no—
164#387—32no—
165#387—92no—
166#387—92no—
167#387—92no—
168#381—91no—
169#381—91no—
170#380—91no—
171#380—91no—
172C4×C22⋊C4—91no—
173C4×C22⋊C4—91no—
174C23×D3—32no—
175C23×D3—61no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D312yes—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C2×C4×D3—38no—
197C2×C4×D3—38no—
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×C4×D3—64no—
205C2×C4×D3—64no—
206C2×C4×D3—122no—
207C2×C4×D3—122no—
208C2×C4×D3—122no—
209C2×C4×D3—122no—
210C2×C4×D3—124no—
211C2×C4×D3—124no—
212C3×C4⋊C4—24no—
213C3×C4⋊C4—122no—
214C3×C4⋊C4C4×D318yes—
215C3×C42—122no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—64no—
220C4⋊Dic3—38no—
221C4⋊Dic3—42no—
222C4⋊Dic3—64no—
223Dic3⋊C4—38no—
224Dic3⋊C4—38no—
225Dic3⋊C4—64no—
226Dic3⋊C4—64no—
227Dic3⋊C4—122no—
228Dic3⋊C4—122no—
229C4×Dic3—42no—
230C4×Dic3—122no—
231C4×Dic3—122no—
232C22×C32C23×C411yescharacteristic
233C22×C32C2×#4111yescharacteristic
234C22×C32C2×#4111yescharacteristic
235C22×C32H(5,𝔽2)12yes—
236C22×C322−1+412yes—
237C2×C3⋊D3—22no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—24no—
240C2×C3⋊D3—24no—
241C2×C3⋊D3#11714yes—
242C32×C4—22no—
243C32×C4—22no—
244C32×C4—22no—
245C3⋊Dic3—22no—
246C3⋊Dic3—22no—
247C3⋊Dic3—22no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C23×C4—91no—
253C23×C4—91no—
254C23×C4—91no—
255C2×C4⋊C4—32no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—98no—
260C2×C4⋊C4—92no—
261C2×C4⋊C4D3211yescharacteristic
262C2×C22⋊C4—91no—
263C2×C22⋊C4—91no—
264C2×C22⋊C4—91no—
265C2×C22⋊C4—91no—
266C2×C42—32no—
267C2×C42—92no—
268#95—32no—
269#95—32no—
270#95—32no—
271#95—32no—
272#95—92no—
273#95—92no—
274#95—92no—
275#95—92no—
276C23×C3—21no—
277C23×C3C23×D312yes—
278C22×D3—34no—
279C22×D3—34no—
280C22×D3—34no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—64no—
285C22×D3—64no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
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—42no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4C2×C4×D314yes—
316C2×C3×C4C2×C4×D314yes—
317C2×C3×C4C2×C4×D314yes—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—34no—
331C2×Dic3—34no—
332C2×Dic3—34no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C4×D3—616no—
347C4×D3—616no—
348C4×D3—128no—
349C4×D3—128no—
350C4×D3—128no—
351C4×D3—128no—
352C2×C32C2×#11711yescharacteristic
353C2×C32#51811yescharacteristic
354C2×C32#51911yescharacteristic
355C2×C32#53912yes—
356C2×C32#53912yes—
357C3⋊D3—24no—
358C24—91no—
359C22×C4—32no—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—94no—
367C22×C4—94no—
368C22×C4—94no—
369C22×C4—182no—
370C22×C4—182no—
371C22×C4—362no—
372C22×C4—362no—
373C22×C4C2×D3211yescharacteristic
374C22×C4C2×D3211yescharacteristic
375C22×C4C2×D3211yescharacteristic
376C4⋊C4—94no—
377C4⋊C4—94no—
378C4⋊C4—94no—
379C4⋊C4—122no—
380C4⋊C4—362no—
381C4⋊C4#62414yes—
382C22⋊C4—182no—
383C22⋊C4—182no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C42—122no—
387C42—362no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3C22×C4×D312yes—
394C22×C3#100412yes—
395C22×C3#100712yes—
396C22×C3D3×#4112yes—
397C22×C3D3×#4112yes—
398C22×C3#100912yes—
399C22×C3#101012yes—
400C2×D3—38no—
401C2×D3—64no—
402C2×D3—64no—
403C2×D3—64no—
404C2×D3—68no—
405C2×D3—68no—
406C2×D3—64no—
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—64no—
410C2×D3—64no—
411C2×D3—64no—
412C3×C4—24no—
413C3×C4—24no—
414C3×C4—24no—
415C3×C4—24no—
416C3×C4—42no—
417C3×C4—42no—
418C3×C4—122no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4—122no—
422Dic3—42no—
423Dic3—42no—
424Dic3—42no—
425Dic3—42no—
426Dic3—64no—
427Dic3—64no—
428Dic3—64no—
429Dic3—64no—
430Dic3—122no—
431Dic3—122no—
432C32#231311yescharacteristic, complemented, Sylow
433C23—92no—
434C23—92no—
435C23—92no—
436C23—182no—
437C23—182no—
438C23C22×D3211yescharacteristic
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—92no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—188no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—182no—
462C2×C4—182no—
463C2×C4—364no—
464C2×C4—364no—
465C2×C4C2×#62412yes—
466C2×C4C2×#62412yes—
467C2×C4C2×#62412yes—
468C2×C3—21no—
469C2×C3—22no—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3D3×#11712yes—
474C2×C3#554512yes—
475C2×C3#557212yes—
476C2×C3#563812yes—
477C2×C3#566012yes—
478C2×C3#569212yes—
479C2×C3#570712yes—
480D3—68no—
481D3—68no—
482C22—94no—
483C22—182no—
484C22—184no—
485C22—184no—
486C22—182no—
487C22#6430611yescharacteristic
488C22#6430611yescharacteristic
489C22#6431412yes—
490C22#6431512yes—
491C22C22×#62411yescharacteristic
492C4—22no—
493C4—22no—
494C4—22no—
495C4—122no—
496C4—122no—
497C4—122no—
498C4—122no—
499C4—182no—
500C4—182no—
501C4—182no—
502C3—21no—
503C3#7529612yescomplemented
504C2—184no—
505C2#1059457212yes—
506C2#1059457312yes—
507C2#1059496911yescharacteristic
508C2#1059522311yescharacteristic
509C2#1059533911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4980C2semidirect
6. #10591271C2semidirect
7. #10591263C2semidirect
11. #10591197C2semidirect
20. C4⋊C4×C3⋊D3C4semidirect
41. #4980D3semidirect
432. C32#2313semidirect
503. C3#75296semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C3×#49802
#105913552
#105913252
C4×#37222
#105912712
#105912632
#105912602
#105912192
#105911972
#752963