Finite Group Databasebeta

← #11895260

Subgroups — #11895260

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593956C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic, complemented
3C8×#634C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590868C212yesmaximal, complemented
7#10590821C212yesmaximal, complemented
8#10590751C212yesmaximal
9#10590742C212yesmaximal, complemented
10#10590363C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#81621—31nomaximal
13#79568—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×D24C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63898C2212yes—
21D3×C4⋊Dic3—21no—
22#63887—22no—
23#63872C2212yes—
24#63863C2212yes—
25#63858—22no—
26#63857—21no—
27#63857—21no—
28#63843C2212yes—
29#63841—21no—
30C2×#3715C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×#816C2212yes—
39C3×#816C2212yes—
40#63574C2212yes—
41#63565C2212yes—
42#63562C2212yes—
43#5732—31no—
44#5730—31no—
45#5543—31no—
46#5542—31no—
47C3×#487—31no—
48C3×C4×D8—31no—
49#5153—32no—
50#5084—31no—
51#5083—31no—
52#5019—31no—
53#5008—31no—
54#4877—32no—
55#4819—32no—
56#4800—32no—
57#4796—32no—
58#4788—32no—
59#4768—32no—
60#4758—32no—
61C4×D24D311yescharacteristic
62#4681D311yescharacteristic, complemented
63C8×Dic6—31no—
64C8×Dic6—31no—
65C8×Dic6—61no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2312yes—
73C2×D3×Dic3—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)D411yescharacteristic
78#3750D412yes—
79C4×C3⋊Dic3C2312yes—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×D24—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3715—24no—
98#3360—91noSylow
99C2×C3×D8—31no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—31no—
102C3×C4×D4—31no—
103C3×C4×D4—31no—
104#947—32no—
105#946—62no—
106Q8×Dic3—32no—
107C2×#215—32no—
108#936—32no—
109D4×Dic3—32no—
110C2×#214—32no—
111#926—61no—
112C2×C4⋊Dic3—61no—
113#924—61no—
114#924—61no—
115C2×D24C2×D311yescharacteristic
116#898—62no—
117#897—61no—
118#897—61no—
119#893—32no—
120#892—61no—
121D3×C4⋊C4—61no—
122#890—32no—
123#890—32no—
124#887—32no—
125#879—62no—
126#878—62no—
127C4×D12C2×D311yescharacteristic
128C4×D12C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130#869C2×D311yescharacteristic
131C4×Dic6—31no—
132C4×Dic6—31no—
133C4×Dic6—61no—
134C3×#107—31no—
135C3×#103—32no—
136C3×#103—32no—
137C3×#102—31no—
138C3×#102—31no—
139C3×C4×C8—21no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#835—32no—
143#832—32no—
144#821C2×D311yescharacteristic
145#821C2×D311yescharacteristic
146#818C2×D311yescharacteristic
147#816C2×D312yes—
148#816C2×D312yes—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—62no—
152C8×Dic3—32no—
153C8×Dic3—32no—
154C8×Dic3—62no—
155#810—32no—
156#809—32no—
157#808—32no—
158#808—32no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—61no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×D412yes—
169#634—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C3×D12—21no—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12#4112yes—
178C3×C4×D3—42no—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—81no—
183D3×Dic3—82no—
184C32×C8—21no—
185C32×C8—21no—
186C3⋊(C3⋊C8)—22no—
187#556—91no—
188#554—91no—
189#488—92no—
190#487—31no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—91no—
195C8×Q8—91no—
196C4×SD16—92no—
197C4×D8—31no—
198C2×C3×Q8—32no—
199C2×C3×Q8—61no—
200C2×C3×D4—31no—
201C2×C3×D4—31no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×Dic3—62no—
205C2×D12C22×D311yescharacteristic
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—21no—
209C2×C4×D3—62no—
210C2×Dic6—21no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6C22×D312yes—
215C3×D8—62no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C22⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234#217—62no—
235#217—62no—
236#215—64no—
237#214—64no—
238(C2×D3)⋊C4—21no—
239(C2×D3)⋊C4—21no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3C22×D311yescharacteristic
253C4⋊Dic3C22×D312yes—
254C4⋊Dic3C22×D311yescharacteristic
255Dic3⋊C4—32no—
256Dic3⋊C4—32no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269D24—22no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—22no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C32×C4—21no—
278C32×C4#13512yes—
279C32×C4C2×#4111yescharacteristic
280C32×C42−1+411yescharacteristic
281C3⋊Dic3—22no—
282C3⋊Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C3×Dic3—42no—
287C2×SD16—92no—
288C2×D8—31no—
289C4⋊Q8—31no—
290C4⋊Q8—31no—
291#126—182no—
292#125—92no—
293#124—92no—
294C22⋊Q8—182no—
295C22⋊Q8—181no—
296C22⋊Q8—181no—
297C4×Q8—91no—
298C4×Q8—92no—
299C4×D4—31no—
300C4×D4—31no—
301C4×D4—92no—
302#117—181no—
303C2×C4⋊C4—181no—
304#107—31no—
305#106—92no—
306C4⋊C8—92no—
307C4⋊C8—91no—
308#103—32no—
309#103—32no—
310#103—92no—
311#102—31no—
312#102—31no—
313#102—92no—
314C4×C8—92no—
315C4×C8D3211yescharacteristic
316C23×C3—61no—
317C23×C3—61no—
318C22×D3—21no—
319C22×D3—21no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—241no—
323C3×D4—32no—
324C3×D4—61no—
325C3×D4—61no—
326C3×D4—61no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—61no—
331C2×C3×C4—62no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—122no—
335C2×C3×C4—122no—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—22no—
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—242no—
353D12—21no—
354D12—21no—
355D12—21no—
356D12#23512yes—
357C4×D3—42no—
358C4×D3—42no—
359C4×D3—242no—
360Dic6—22no—
361Dic6—22no—
362Dic6—64no—
363Dic6—62no—
364Dic6—62no—
365Dic6—81no—
366C3×C8—22no—
367C3×C8—21no—
368C3×C8—21no—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—41no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32#54811yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C2×C32#57711yescharacteristic
378C3×D3—42no—
379C3×D3—81no—
380C2×Q8—32no—
381C2×Q8—61no—
382C2×Q8—91no—
383C2×D4—31no—
384C2×D4—31no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—182no—
388SD16—184no—
389D8—62no—
390C2×C8—92no—
391C2×C8C2×D3211yescharacteristic
392C2×C8C2×D3211yescharacteristic
393C4⋊C4—31no—
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—61no—
399C4⋊C4—91no—
400C4⋊C4—92no—
401C4⋊C4—182no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—182no—
407C22⋊C4—182no—
408C22⋊C4—182no—
409C42—92no—
410C42—182no—
411C42C2×D3211yescharacteristic
412C22×C3—21no—
413C22×C3—62no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—121no—
434C3×C4—121no—
435C3×C4—122no—
436C3×C4—122no—
437C3×C4#91212yes—
438C3×C4#91912yes—
439C3×C4C2×#23511yescharacteristic
440C3×C4D3×#4111yescharacteristic
441C3×C4#101011yescharacteristic
442C3×C4#101011yescharacteristic
443Dic3—42no—
444Dic3—41no—
445Dic3—41no—
446Dic3—42no—
447Dic3—64no—
448Dic3—62no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—122no—
453C32#336011yescharacteristic, complemented, Sylow
454C23—61no—
455C23—61no—
456Q8—62no—
457Q8—62no—
458Q8—182no—
459Q8—241no—
460D4—32no—
461D4—61no—
462D4—61no—
463D4—61no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—62no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—122no—
471C2×C4—122no—
472C2×C4—722no—
473C2×C4#380211yescharacteristic
474C2×C4#380211yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—21no—
477C8—21no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3—241no—
484C2×C3#555211yescharacteristic
485C2×C3#567711yescharacteristic
486C2×C3C2×#91211yescharacteristic
487C2×C3#576211yescharacteristic
488C2×C3C2×#91911yescharacteristic
489C2×C3#577011yescharacteristic
490D3—42no—
491D3—81no—
492C22—62no—
493C22—121no—
494C22—121no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22C2×#380211yescharacteristic
499C4—21no—
500C4—122no—
501C4—122no—
502C4—121no—
503C4—121no—
504C4—182no—
505C4—182no—
506C4#6381012yes—
507C4#6429811yescharacteristic
508C4D3×#23511yescharacteristic
509C3—21no—
510C3#7956811yescharacteristic, complemented
511C3#8162111yescharacteristic, complemented
512C2—122no—
513C2—241no—
514C2#1059390511yescharacteristic
515C2#1059468611yescharacteristic
516C2C2×#6381011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC4×C8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593956C2semidirect
2. #10593863C2semidirect
3. C8×#634C2semidirect
5. C3×#4681C2semidirect
6. #10590868C2semidirect
7. #10590821C2semidirect
9. #10590742C2semidirect
10. #10590363C2semidirect
11. #10590266C2semidirect
62. #4681D3semidirect
453. C32#3360semidirect
510. C3#79568semidirect
511. C3#81621semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105938632
C8×#6342
C3×C4×D242
C3×#46812
#105908682
#105908212
#105907512
#105907422
#105903632
#105902662
#816213
#795683