Finite Group Databasebeta

← #11824513

Subgroups — #11824513

Order 1152.

1481 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic
3C2×#63888C214yesmaximal, complemented
4#10592687C211yesmaximal, characteristic
5C3×#4975C211yesmaximal, characteristic, complemented
6#10591359C211yesmaximal, characteristic, complemented
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#10591320C211yesmaximal, characteristic
9#10591203C214yesmaximal, complemented
10#83259—31nomaximal
11#74334—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2212yes—
14C22×#624C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752C2214yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#888—24no—
25C2×#3724C2214yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×#3722C2214yes—
28C2×#3722C2212yes—
29#63894—24no—
30#63888—216no—
31#63579C2212yes—
32C2×C3×C4⋊Q8—31no—
33C2×#946—34no—
34C2×#896—34no—
35C2×#893—31no—
36C2×#888D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C3×#384—31no—
39#4993—34no—
40#4993—34no—
41#4988—31no—
42#4988—31no—
43#4988—31no—
44#4988—61no—
45#4975—31no—
46#4975—31no—
47#4975D311yescharacteristic, complemented
48#4939—31no—
49C4×C4⋊Dic3—31no—
50C4×Dic3⋊C4—31no—
51C23×C3⋊D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)Q814yescomplemented
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2311yescharacteristic
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2311yescharacteristic
63C2×C3×Dic6—24no—
64C2×C3×Dic6—28no—
65C2×#624—28no—
66C2×#624—24no—
67C32×C4⋊C4—22no—
68#3752—28no—
69C4×C3⋊Dic3—22no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3—22no—
72C3×Dic3⋊C4—24no—
73C3×Dic3⋊C4—28no—
74C3×C4×Dic3—22no—
75C3×C4×Dic3D414yes—
76#3724—28no—
77Dic3⋊Dic3D418yescomplemented
78#3722—28no—
79#3722—24no—
80#2542—91noSylow
81C22×C3×Q8—32no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×Dic6C2×D312yes—
88C3×C4⋊Q8—64no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C4⋊C4—34no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×C3×C42—31no—
98#946—616no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—34no—
101C2×(C2×D3)⋊C4—34no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—34no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—64no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—34no—
111C2×Dic3⋊C4—34no—
112C2×Dic3⋊C4C2×D314yes—
113C2×Dic3⋊C4C2×D312yes—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3C2×D311yescharacteristic
118C2×C4×Dic3C2×D311yescharacteristic
119#896—616no—
120#893—64no—
121#888—24no—
122C4×D12—64no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—24no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—24no—
130C22×C3⋊D3C2×Q814yes—
131C2×C32×C4—24no—
132C2×C32×C4—22no—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×Q812yes—
135C2×C32×C4#4112yes—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3C2×D414yes—
139C4⋊(C3⋊D3)—28no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C2×D414yes—
148C2×C3×Dic3C2×D414yes—
149C2×C3×Dic3C2×D412yes—
150C2×C3×Dic3C2×D412yes—
151C3×Dic6—48no—
152#624—48no—
153C2×C4⋊Q8—31no—
154C2×C22⋊Q8—94no—
155C2×C4×D4—91no—
156#399—94no—
157#390—91no—
158#390—91no—
159#384—31no—
160#384—91no—
161C4×C4⋊C4—91no—
162C23×D3—32no—
163C23×D3—32no—
164C23×D3—62no—
165C2×C3×Q8—68no—
166C2×C3×Q8—64no—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—62no—
181C22×Dic3C22×D312yes—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D311yescharacteristic
185C22×Dic3C22×D311yescharacteristic
186C2×D12—34no—
187C2×D12—34no—
188C2×D12—64no—
189C2×D12—62no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—62no—
193C2×D12—122no—
194C2×D12—122no—
195C2×C4×D3—64no—
196C2×C4×D3—68no—
197C2×C4×D3—68no—
198C2×C4×D3—64no—
199C2×Dic6—28no—
200C2×Dic6—24no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—42no—
204C3×C4⋊C4—68no—
205C3×C4⋊C4—64no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4—62no—
208C3×C42—34no—
209C3×C42—62no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—68no—
212(C2×D3)⋊C4—68no—
213(C2×D3)⋊C4—68no—
214(C2×D3)⋊C4—68no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—128no—
217C4⋊Dic3—22no—
218C4⋊Dic3—22no—
219C4⋊Dic3—38no—
220Dic3⋊C4—28no—
221Dic3⋊C4—24no—
222Dic3⋊C4—38no—
223Dic3⋊C4—68no—
224Dic3⋊C4—68no—
225C4×Dic3—22no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C4×Dic3—122no—
229C4×Dic3#6714yes—
230C22×C32C22×D412yes—
231C22×C32C22×D411yescharacteristic
232C22×C32C22×Q811yescharacteristic
233C22×C32C2×#4111yescharacteristic
234C22×C322−1+412yes—
235C2×C3⋊D3—24no—
236C2×C3⋊D3—28no—
237C2×C3⋊D3—42no—
238C2×C3⋊D3—42no—
239C2×C3⋊D3—44no—
240C32×C4—42no—
241C32×C4C22⋊Q814yescomplemented
242C3⋊Dic3—24no—
243C3×Dic3—22no—
244C3×Dic3—24no—
245C3×Dic3—42no—
246C3×Dic3—42no—
247C3×Dic3#12714yes—
248C22×Q8—32no—
249C22×D4—91no—
250C23×C4—92no—
251C4⋊Q8—64no—
252C22⋊Q8—1816no—
253C4×D4—184no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—34no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—32no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—94no—
260C2×C4⋊C4D3211yescharacteristic
261C2×C22⋊C4—92no—
262C2×C22⋊C4—94no—
263C2×C22⋊C4—94no—
264C2×C42—31no—
265C2×C42—31no—
266C2×C42—91no—
267#95—92no—
268C23×C3—21no—
269C23×C3C23×D311yescharacteristic
270C23×C3C23×D311yescharacteristic
271C22×D3—34no—
272C22×D3—34no—
273C22×D3—64no—
274C22×D3—62no—
275C22×D3—64no—
276C22×D3—64no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—64no—
280C22×D3—64no—
281C22×D3—62no—
282C22×D3—124no—
283C22×D3—122no—
284C22×D3—122no—
285C22×D3—124no—
286C3×Q8—128no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—34no—
295C2×C3×C4—32no—
296C2×C3×C4—34no—
297C2×C3×C4—32no—
298C2×C3×C4—44no—
299C2×C3×C4—42no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—64no—
304C2×C3×C4—64no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D412yes—
309C2×C3×C4D3×Q812yes—
310C2×C3×C4D3×Q812yes—
311C2×C3×C4#23912yes—
312C2×C3×C4C2×#6712yes—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—24no—
317C2×Dic3—24no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—64no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3D3×D414yes—
330C2×Dic3D3×D414yes—
331C2×Dic3C2×#6712yes—
332C2×Dic3C2×#6712yes—
333D12—68no—
334D12—68no—
335D12—128no—
336C4×D3—128no—
337C4×D3—128no—
338Dic6—48no—
339C2×C32C2×C22⋊Q811yescharacteristic
340C2×C32C2×#12711yescharacteristic
341C2×C32#53611yescharacteristic
342C2×C32#54712yes—
343C2×C32D4×Q812yes—
344C3⋊D3—44no—
345C24—92no—
346C2×Q8—68no—
347C2×Q8—64no—
348C2×D4—94no—
349C2×D4—182no—
350C2×D4—182no—
351C22×C4—31no—
352C22×C4—31no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—92no—
357C22×C4—184no—
358C22×C4—188no—
359C22×C4C2×D3212yes—
360C22×C4C2×D3211yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—68no—
363C4⋊C4—64no—
364C4⋊C4—62no—
365C4⋊C4—62no—
366C4⋊C4—98no—
367C4⋊C4—188no—
368C22⋊C4—188no—
369C22⋊C4—184no—
370C22⋊C4—188no—
371C42—34no—
372C42—62no—
373C42—182no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3C2×#23511yescharacteristic
380C22×C3C2×D3×D412yes—
381C22×C3C2×D3×D412yes—
382C22×C3C2×D3×D411yescharacteristic
383C22×C3C2×D3×Q811yescharacteristic
384C22×C3C2×D3×Q811yescharacteristic
385C22×C3C2×#23911yescharacteristic
386C22×C3#100712yes—
387C22×C3#100712yes—
388C22×C3C22×#6711yescharacteristic
389C2×D3—68no—
390C2×D3—68no—
391C2×D3—64no—
392C2×D3—64no—
393C2×D3—124no—
394C2×D3—128no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—124no—
398C2×D3—124no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—242no—
402C2×D3—242no—
403C2×D3—244no—
404C3×C4—24no—
405C3×C4—34no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—62no—
409C3×C4—64no—
410C3×C4—82no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4#89614yescomplemented
414C3×C4#94614yescomplemented
415Dic3—24no—
416Dic3—22no—
417Dic3—42no—
418Dic3—42no—
419Dic3—64no—
420Dic3—64no—
421Dic3—124no—
422Dic3#94014yes—
423C32#254211yescharacteristic, complemented, Sylow
424C23—94no—
425C23—182no—
426C23—184no—
427C23—184no—
428C23—182no—
429C23C22×D3211yescharacteristic
430Q8—128no—
431D4—188no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—34no—
435C2×C4—32no—
436C2×C4—34no—
437C2×C4—32no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—64no—
442C2×C4—64no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—94no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—368no—
449C2×C4#379712yes—
450C2×C4#379912yes—
451C2×C4D3×#6712yes—
452C2×C3—21no—
453C2×C3—22no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—22no—
457C2×C3#550712yes—
458C2×C3C2×#89611yescharacteristic
459C2×C3D3×#12711yescharacteristic
460C2×C3#572411yescharacteristic
461C2×C3#572612yes—
462C2×C3#572712yes—
463C2×C3#572712yes—
464C2×C3C2×#94011yescharacteristic
465C2×C3C2×#94611yescharacteristic
466C2×C3#581611yescharacteristic
467D3—124no—
468D3—124no—
469D3—244no—
470C22—188no—
471C22—184no—
472C22—362no—
473C22—362no—
474C22—364no—
475C22C2×#379711yescharacteristic
476C22C2×#379911yescharacteristic
477C22D32×D412yes—
478C22#6431612yes—
479C22C2×D3×#6711yescharacteristic
480C4—34no—
481C4—42no—
482C4—62no—
483C4—64no—
484C4—122no—
485C4—122no—
486C4—184no—
487C4#6388814yescomplemented
488C3—21no—
489C3#7433411yescharacteristic, complemented
490C3#8325911yescharacteristic, complemented
491C2—364no—
492C2#1059437912yes—
493C2#1059451712yes—
494C2C2×#6388811yescharacteristic
495C2D3×#94011yescharacteristic
496C2#1059534011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#888C2semidirect
3. C2×#63888C2semidirect
5. C3×#4975C2semidirect
6. #10591359C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
9. #10591203C2semidirect
36. C2×#888D3semidirect
47. #4975D3semidirect
57. C2×C4⋊(C3⋊D3)Q8semidirect
77. Dic3⋊Dic3D4semidirect
241. C32×C4C22⋊Q8semidirect
413. C3×C4#896semidirect
414. C3×C4#946semidirect
423. C32#2542semidirect
487. C4#63888semidirect
489. C3#74334semidirect
490. C3#83259semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#638942
C2×#638882
#105926872
C3×#49752
#105913592
C4×Dic3⋊Dic32
#105913202
#105912032
#832593
#743343