Finite Group Databasebeta

← #11808482

Subgroups — #11808482

Order 1152.

2153 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63974C212yesmaximal
3C2×#63900C211yesmaximal, characteristic, complemented
4C2×#63883C212yesmaximal, complemented
5C3×#4949C212yesmaximal, complemented
6#10591715C212yesmaximal, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591350C212yesmaximal, complemented
9#10591203C212yesmaximal, complemented
10D3×#399—32nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#624C2212yes—
15C22×#624C2212yes—
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C22⋊C4×C3⋊D3—24no—
21C2×C3×#217C2214yes—
22C2×C3×C4⋊Dic3C2212yescomplemented
23C2×C3×Dic3⋊C4C2214yescomplemented
24#63974—28no—
25C2×#3724C2212yescomplemented
26C2×Dic3⋊Dic3C2214yescomplemented
27C2×#3722C2214yes—
28#63900—24no—
29#63883—28no—
30C3×C3⋊#95C2212yescomplemented
31#63579C2212yescomplemented
32C2×D3×C4⋊C4—32no—
33C2×D3×C4⋊C4—34no—
34C2×D3×C22⋊C4—32no—
35C2×D3×C22⋊C4—34no—
36C2×D3×C22⋊C4—61no—
37C3×#399—32no—
38#4993—34no—
39#4993—32no—
40#4949—34no—
41#4949D312yescomplemented
42#4677—32no—
43D3×#95—32no—
44C24×C32C2311yescharacteristic
45C23×C3⋊D3—22no—
46C23×C3⋊D3—24no—
47C23×C3⋊D3—22no—
48C23×C3⋊D3—24no—
49C23×C3⋊D3Q814yes—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—24no—
59C2×C4×C3⋊D3D414yes—
60C22×C3×Dic3C2314yes—
61C22×C3×Dic3C2314yes—
62C2×#624—24no—
63C2×#624—24no—
64C2×#624—24no—
65C2×#624—24no—
66C2×#624—24no—
67C2×#624D418yes—
68C32×C22⋊C4—22no—
69#3757—22no—
70#3752—22no—
71#3752—22no—
72C3×#217—28no—
73C3×C4⋊Dic3—24no—
74C3×Dic3⋊C4—28no—
75#3724—24no—
76Dic3⋊Dic3—28no—
77#3722—28no—
78C2×#399—91noSylow
79C24×D3—32no—
80C24×D3—61no—
81C22×C4×D3—32no—
82C22×C4×D3—34no—
83C22×C4×D3—32no—
84C22×C4×D3—34no—
85C22×C4×D3—61no—
86C22×C4×D3—61no—
87C2×C3×C4⋊C4—34no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C22⋊C4—21no—
90C2×C3×C22⋊C4—34no—
91C2×C3×C22⋊C4C2×D312yes—
92C2×#217—32no—
93C2×#217—61no—
94C2×#217C2×D314yes—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—34no—
98C2×(C2×D3)⋊C4—34no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3—34no—
102C2×C4⋊Dic3C2×D312yescomplemented
103C2×Dic3⋊C4—34no—
104C2×Dic3⋊C4—34no—
105C2×Dic3⋊C4C2×D314yescomplemented
106D3×C4⋊C4—616no—
107D3×C4⋊C4—68no—
108D3×C22⋊C4—616no—
109D3×C22⋊C4—68no—
110D3×C22⋊C4—68no—
111C3×#95—32no—
112C3⋊#95—34no—
113C3⋊#95C2×D312yescomplemented
114C23×C32—21no—
115C23×C32—21no—
116C23×C32—22no—
117C23×C32—22no—
118C23×C32C2×Q812yes—
119C23×C32C2411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—28no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—216no—
126C22×C3⋊D3—48no—
127C22×C3⋊D3—44no—
128C22×C3⋊D3—44no—
129C22×C3⋊D3C2×D414yes—
130C22×C3⋊D3C2×D412yes—
131C22×C3⋊D3C2×Q812yes—
132C22×C3⋊D3C2×Q812yes—
133C22×C3⋊D3#4112yes—
134C22×C3⋊D3#4114yes—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C2×D412yes—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C2×D412yes—
143C4×C3⋊D3—28no—
144C4×C3⋊D3—44no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3C2×D418yes—
151#624—216no—
152#624—48no—
153C22×C4⋊C4—92no—
154C22×C4⋊C4—91no—
155C22×C22⋊C4—92no—
156C22×C22⋊C4—91no—
157#399—32no—
158#399—92no—
159#399—92no—
160#399—92no—
161C2×#95—91no—
162C24×C3—21no—
163C24×C3C22×D312yes—
164C23×D3—32no—
165C23×D3—38no—
166C23×D3—32no—
167C23×D3—61no—
168C23×D3—64no—
169C23×D3—61no—
170C23×D3—64no—
171C23×D3—68no—
172C23×D3—64no—
173C23×D3—68no—
174C23×D3—64no—
175C23×D3—64no—
176C23×D3—124no—
177C23×D3—124no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—34no—
181C22×C3×C4—34no—
182C22×C3×C4C22×D312yes—
183C22×C3×C4C22×D312yes—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3C22×D314yes—
189C22×Dic3C22×D314yes—
190C2×C4×D3—38no—
191C2×C4×D3—316no—
192C2×C4×D3—64no—
193C2×C4×D3—68no—
194C2×C4×D3—68no—
195C2×C4×D3—68no—
196C2×C4×D3—68no—
197C2×C4×D3—68no—
198C2×C4×D3—68no—
199C2×C4×D3—64no—
200C2×C4×D3—68no—
201C2×C4×D3—64no—
202C2×C4×D3—124no—
203C2×C4×D3—124no—
204C3×C4⋊C4—68no—
205C3×C4⋊C4—64no—
206C3×C22⋊C4—24no—
207C3×C22⋊C4—24no—
208C3×C22⋊C4—68no—
209#217—28no—
210#217—64no—
211#217—64no—
212(C2×D3)⋊C4—68no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—68no—
218C4⋊Dic3—24no—
219C4⋊Dic3—68no—
220Dic3⋊C4—28no—
221Dic3⋊C4—68no—
222Dic3⋊C4—68no—
223C22×C32—22no—
224C22×C32—24no—
225C22×C32—42no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32C22×D412yes—
229C22×C32C22×D411yescharacteristic
230C22×C32C22×Q811yescharacteristic
231C22×C32C2×#4111yescharacteristic
232C22×C32C2×#4112yes—
233C2×C3⋊D3—22no—
234C2×C3⋊D3—24no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—416no—
239C2×C3⋊D3C22⋊Q814yes—
240C2×C3⋊D3C22⋊Q818yes—
241C2×C3⋊D3#12318yes—
242C2×C3⋊D3#12314yes—
243C2×C3⋊D3#12714yes—
244C32×C4—22no—
245C32×C4—41no—
246C3⋊Dic3—22no—
247C3⋊Dic3—41no—
248C3×Dic3—28no—
249C3×Dic3—44no—
250C25—91no—
251C23×C4—92no—
252C23×C4—92no—
253C23×C4—91no—
254C23×C4—91no—
255C2×C4⋊C4—34no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—92no—
258C2×C4⋊C4—94no—
259C2×C4⋊C4—188no—
260C2×C4⋊C4—184no—
261C2×C22⋊C4—34no—
262C2×C22⋊C4—94no—
263C2×C22⋊C4—91no—
264C2×C22⋊C4—91no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—184no—
267C2×C22⋊C4—188no—
268C2×C22⋊C4D3211yescharacteristic
269#95—32no—
270#95—92no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—24no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—24no—
277C23×C3—21no—
278C23×C3—22no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3D3×Q814yes—
282C23×C3C23×D312yes—
283C22×D3—38no—
284C22×D3—34no—
285C22×D3—34no—
286C22×D3—34no—
287C22×D3—38no—
288C22×D3—34no—
289C22×D3—62no—
290C22×D3—64no—
291C22×D3—62no—
292C22×D3—64no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—616no—
296C22×D3—632no—
297C22×D3—62no—
298C22×D3—616no—
299C22×D3—62no—
300C22×D3—64no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—64no—
304C22×D3—1216no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—128no—
308C22×D3—1216no—
309C22×D3—128no—
310C22×D3—128no—
311C22×D3—128no—
312C22×D3—1216no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—38no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—64no—
322C2×C3×C4—64no—
323C2×C3×C4—64no—
324C2×C3×C4—64no—
325C2×C3×C4—64no—
326C2×C3×C4D3×D414yes—
327C2×Dic3—24no—
328C2×Dic3—24no—
329C2×Dic3—24no—
330C2×Dic3—24no—
331C2×Dic3—24no—
332C2×Dic3—34no—
333C2×Dic3—62no—
334C2×Dic3—64no—
335C2×Dic3—62no—
336C2×Dic3—64no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3D3×D418yes—
341C4×D3—632no—
342C4×D3—616no—
343C4×D3—128no—
344C4×D3—1216no—
345C4×D3—128no—
346C4×D3—128no—
347C2×C32—42no—
348C2×C32C2×C22⋊Q812yes—
349C2×C32C2×C22⋊Q811yescharacteristic
350C2×C32C2×#12312yes—
351C2×C32C2×#12311yescharacteristic
352C2×C32C2×#12711yescharacteristic
353C3⋊D3—42no—
354C3⋊D3#39918yescomplemented
355C24—91no—
356C24—91no—
357C24—94no—
358C24—182no—
359C24—184no—
360C24—182no—
361C24—184no—
362C24C2×D3211yescharacteristic
363C22×C4—34no—
364C22×C4—34no—
365C22×C4—98no—
366C22×C4—91no—
367C22×C4—94no—
368C22×C4—91no—
369C22×C4—184no—
370C22×C4—182no—
371C22×C4—184no—
372C22×C4—184no—
373C22×C4—184no—
374C22×C4—184no—
375C22×C4—184no—
376C22×C4—184no—
377C22×C4C2×D3211yescharacteristic
378C22×C4C2×D3211yescharacteristic
379C4⋊C4—68no—
380C4⋊C4—64no—
381C4⋊C4—188no—
382C4⋊C4—184no—
383C22⋊C4—22no—
384C22⋊C4—68no—
385C22⋊C4—182no—
386C22⋊C4—188no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C22×C3—24no—
390C22×C3—28no—
391C22×C3—24no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—44no—
398C22×C3—42no—
399C22×C3—44no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—44no—
403C22×C3—42no—
404C22×C3C2×D3×D414yes—
405C22×C3C2×D3×D412yes—
406C22×C3C2×D3×Q812yes—
407C22×C3D3×#4112yes—
408C22×C3D3×#4114yes—
409C2×D3—38no—
410C2×D3—316no—
411C2×D3—38no—
412C2×D3—316no—
413C2×D3—38no—
414C2×D3—64no—
415C2×D3—64no—
416C2×D3—64no—
417C2×D3—68no—
418C2×D3—68no—
419C2×D3—64no—
420C2×D3—68no—
421C2×D3—64no—
422C2×D3—124no—
423C2×D3—1232no—
424C2×D3—1232no—
425C2×D3—122no—
426C2×D3—124no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—124no—
430C2×D3—122no—
431C3×C4—24no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—68no—
436C3×C4—124no—
437Dic3—28no—
438Dic3—44no—
439Dic3—64no—
440Dic3—122no—
441Dic3—122no—
442Dic3—122no—
443C32C2×#39911yescharacteristic, complemented, Sylow
444C23—21no—
445C23—22no—
446C23—22no—
447C23—21no—
448C23—92no—
449C23—92no—
450C23—94no—
451C23—94no—
452C23—92no—
453C23—92no—
454C23—188no—
455C23—1816no—
456C23—181no—
457C23—182no—
458C23—182no—
459C23—181no—
460C23—364no—
461C23—368no—
462C23—364no—
463C23#379712yes—
464C23C22×D3211yescharacteristic
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—38no—
469C2×C4—64no—
470C2×C4—64no—
471C2×C4—64no—
472C2×C4—64no—
473C2×C4—64no—
474C2×C4—92no—
475C2×C4—188no—
476C2×C4—1816no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—181no—
480C2×C4—364no—
481C2×C4—368no—
482C2×C4#381112yes—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—44no—
489C2×C3—44no—
490C2×C3D3×C22⋊Q814yes—
491C2×C3D3×C22⋊Q812yes—
492C2×C3D3×#12312yes—
493C2×C3D3×#12314yes—
494C2×C3D3×#12712yes—
495D3—316no—
496D3—68no—
497D3—124no—
498D3—124no—
499C22—24no—
500C22—22no—
501C22—41no—
502C22—42no—
503C22—41no—
504C22—98no—
505C22—94no—
506C22—94no—
507C22—98no—
508C22—94no—
509C22—184no—
510C22—182no—
511C22—3616no—
512C22—361no—
513C22—362no—
514C22—361no—
515C22C2×#379711yescharacteristic
516C22#6430611yescharacteristic
517C22D32×D412yes—
518C22#6431212yes—
519C22C2×#381111yescharacteristic
520C4—22no—
521C4—41no—
522C4—68no—
523C4—124no—
524C4—182no—
525C4—361no—
526C3—21no—
527C3D3×#39912yescomplemented
528C2—42no—
529C2—98no—
530C2—362no—
531C2#1059406712yes—
532C2#1059426012yes—
533C2#1059492511yescharacteristic
534C2#1059516911yescharacteristic
535C2#1059530011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C3⋊D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63900C2semidirect
4. C2×#63883C2semidirect
5. C3×#4949C2semidirect
6. #10591715C2semidirect
7. #10591370C2semidirect
8. #10591350C2semidirect
9. #10591203C2semidirect
22. C2×C3×C4⋊Dic3C22semidirect
23. C2×C3×Dic3⋊C4C22semidirect
25. C2×#3724C22semidirect
26. C2×Dic3⋊Dic3C22semidirect
30. C3×C3⋊#95C22semidirect
31. #63579C22semidirect
41. #4949D3semidirect
102. C2×C4⋊Dic3C2×D3semidirect
105. C2×Dic3⋊C4C2×D3semidirect
113. C3⋊#95C2×D3semidirect
354. C3⋊D3#399semidirect
443. C32C2×#399semidirect
527. C3D3×#399semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639742
C2×#639002
C2×#638832
C3×#49492
#105917152
#105913702
#105913502
#105912032
D3×#3993