Finite Group Databasebeta

← #11860273

Subgroups — #11860273

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64120C211yesmaximal, characteristic
2C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C4×#3830C211yesmaximal, characteristic, complemented
4C32×#442C211yesmaximal, characteristic, complemented
5D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592717C211yesmaximal, characteristic, complemented
7#10592713C211yesmaximal, characteristic, complemented
8#10592560C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592470C211yesmaximal, characteristic, complemented
11#10592469C211yesmaximal, characteristic, complemented
12#10592457C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592406C211yesmaximal, characteristic, complemented
16#79865—34nomaximal
17C2×#3830C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C2×C32×D8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C4×#638—21no—
28C4×#638—21no—
29C2×C4×C3⋊Dic3—21no—
30#64120C418yescomplemented
31C2×#3744C2211yescharacteristic
32C2×#3743C2211yescharacteristic
33C2×#3743C2211yescharacteristic
34#64102C2211yescharacteristic
35#64101C2211yescharacteristic
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64096C2211yescharacteristic, complemented
38#64090—21no—
39#64090—21no—
40C22⋊C4×C3⋊D3—21no—
41#64086—21no—
42C4×C4⋊(C3⋊D3)C2211yescharacteristic
43C42×C3⋊D3C2211yescharacteristic
44C4×#634C2211yescharacteristic, complemented
45C32×#106C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic, complemented
48C32×#97C2211yescharacteristic, complemented
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic, complemented
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54C8×C3⋊Dic3C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#63630C2211yescharacteristic, complemented
61C2×#911—34no—
62C4×D3×D4—34no—
63C4×#237—34no—
64C3×#442D314yescomplemented
65Dic3×D8—34no—
66#5018—34no—
67#5014—34no—
68#4861—34no—
69#4852—34no—
70#4771—34no—
71#4770—34no—
72#4758—34no—
73#4756—34no—
74#4710—34no—
75#4707—34no—
76C23×C3⋊D3—21no—
77C2×C32×D4C2311yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C2×#638—21no—
82C2×#638—21no—
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—21no—
85C22×C3⋊Dic3—21no—
86#3830—22no—
87#3830C2×C414yescomplemented
88D4×C3⋊D3—22no—
89D4×C3⋊D3C2×C414yescomplemented
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—44no—
95C2×C4×C3⋊D3D411yescharacteristic
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C32×D8C2×C414yescomplemented
100C2×C32×C8C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C22⋊C4—21no—
105C32×C22⋊C4—21no—
106C32×C42C2311yescharacteristic
107#3757—21no—
108#3757—21no—
109#3754C2×C414yescomplemented
110#3753C2×C414yescomplemented
111#3752—21no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3D411yescharacteristic
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3744C2×C414yescomplemented
128#3743—22no—
129#3743C2×C414yescomplemented
130C4×AGL(1,ℤ/8)—91noSylow
131C2×#237—34no—
132C2×D3×D4—34no—
133C22×C4×D3—64no—
134C2×C3×D8C2×D314yes—
135C3×C4×D4C2×D314yes—
136C3×C4×D4C2×D314yescomplemented
137D4×Dic3—34no—
138D4×Dic3—34no—
139C2×#214—34no—
140C2×#213—34no—
141C4×#67—64no—
142C4×#67—64no—
143C2×C4×Dic3—64no—
144#911—332no—
145C2×#204—34no—
146C2×ΓL(1,𝔽25)—34no—
147C2×ΓL(1,𝔽25)—34no—
148#893—34no—
149#892—34no—
150D3×C4⋊C4—34no—
151#887—34no—
152#67⋊C4—64no—
153#67⋊C4—64no—
154D3×C22⋊C4—64no—
155#877—64no—
156C4×D12—34no—
157C42×D3—34no—
158C4×Dic6—34no—
159C3×#106C2×D314yescomplemented
160C3×#102C2×D314yes—
161C3×#102C2×D314yescomplemented
162C3×#97C2×D314yescomplemented
163#832—34no—
164#832—34no—
165#821—34no—
166#818—34no—
167#816—34no—
168C8×Dic3—34no—
169C8×Dic3—34no—
170#810—34no—
171#809—34no—
172#808—34no—
173#807—34no—
174#803—34no—
175C23×C32—21no—
176C23×C32—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—24no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—42no—
181C22×C3⋊D3C2×D411yescharacteristic
182C32×D4—21no—
183C32×D4—21no—
184C32×D4C22×C412yes—
185C32×D4C22×C412yescomplemented
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—42no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193#638—24no—
194#638—24no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—42no—
200C2×C3⋊Dic3—42no—
201C2×C3⋊Dic3C2×D411yescharacteristic
202C2×C3⋊Dic3C2×D411yescharacteristic
203C2×C3⋊Dic3C2×D411yescharacteristic
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)C22×C412yes—
206C4×C3⋊D3—22no—
207C4×C3⋊D3—41no—
208C4×C3⋊D3—42no—
209C4×C3⋊D3—42no—
210C4×C3⋊D3—42no—
211C4×C3⋊D3C22×C412yes—
212C4×C3⋊D3#4112yes—
213#634—21no—
214#634C22×C412yescomplemented
215C32×C8—21no—
216C32×C8C22×C412yescomplemented
217C3⋊(C3⋊C8)—21no—
218C3⋊(C3⋊C8)C22×C412yescomplemented
219C2×AGL(1,ℤ/8)—91no—
220C4×#41—91no—
221C2×C4×D4—91no—
222#442—91no—
223#442C3⋊D311yescharacteristic, complemented
224#440—91no—
225#440—91no—
226C4×SD16—91no—
227C4×SD16—91no—
228C4×D8—91no—
229C4×D8—91no—
230#428—91no—
231#418—91no—
232#417—91no—
233C4×M16—91no—
234C23×D3—64no—
235C2×C3×D4C22×D314yes—
236C2×C3×D4C22×D314yes—
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C2×#67—64no—
240C2×#67—64no—
241C22×Dic3—64no—
242C22×Dic3—64no—
243C22×Dic3—64no—
244#237—316no—
245#237—68no—
246D3×D4—316no—
247D3×D4—68no—
248C2×D12—34no—
249C2×C4×D3—34no—
250C2×C4×D3—34no—
251C2×C4×D3—34no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—64no—
255C2×C4×D3—1216no—
256C2×Dic6—34no—
257C3×D8C4×D3116yescomplemented
258C2×C3×C8C22×D314yes—
259C2×C3×C8C22×D314yes—
260C3×C4⋊C4C22×D314yes—
261C3×C4⋊C4C22×D314yes—
262C3×C22⋊C4—24no—
263C3×C22⋊C4—24no—
264C3×C42C22×D314yes—
265#217—64no—
266#217—64no—
267#214—316no—
268#213—316no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272C4⋊Dic3—34no—
273C4⋊Dic3—34no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277C4×Dic3—34no—
278C4×Dic3—34no—
279C4×Dic3—34no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C2×C3⋊C8—34no—
284C2×C3⋊C8—34no—
285#204—316no—
286ΓL(1,𝔽25)—316no—
287ΓL(1,𝔽25)—68no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32C22×D411yescharacteristic
295C2×C3⋊D3—21no—
296C2×C3⋊D3—21no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—48no—
299C2×C3⋊D3—41no—
300C2×C3⋊D3—41no—
301C2×C3⋊D3C4×D412yes—
302C32×C4—21no—
303C32×C4—21no—
304C32×C4—41no—
305C32×C4—41no—
306C32×C4C23×C411yescharacteristic
307C32×C4C2×#4111yescharacteristic
308C3⋊Dic3—22no—
309C3⋊Dic3—21no—
310C3⋊Dic3—41no—
311C3⋊Dic3—41no—
312C3⋊Dic3C4×D412yes—
313C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
314C2×#41—91no—
315C22×D4—91no—
316C23×C4—181no—
317AGL(1,ℤ/8)—98no—
318C2×SD16—91no—
319C2×SD16—91no—
320C2×D8—91no—
321C2×D8C2×C3⋊D311yescharacteristic
322C2×M16—91no—
323C2×M16—91no—
324C4×Q8—91no—
325C4×Q8—91no—
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—181no—
331C4×D4—181no—
332C4×D4—181no—
333C4×D4—181no—
334C4×D4C2×C3⋊D311yescharacteristic
335C4×D4C2×C3⋊D311yescharacteristic, complemented
336#117—91no—
337#117—181no—
338C2×C4⋊C4—91no—
339C2×C22⋊C4—181no—
340C2×C42—91no—
341C2×C42—181no—
342#107—91no—
343#107—91no—
344#106—91no—
345#106C2×C3⋊D311yescharacteristic, complemented
346#103—91no—
347#103—91no—
348#102—91no—
349#102—91no—
350#102—91no—
351#102—91no—
352#102C2×C3⋊D311yescharacteristic
353#102C2×C3⋊D311yescharacteristic, complemented
354#97—91no—
355#97C2×C3⋊D311yescharacteristic, complemented
356C4×C8—91no—
357C4×C8—91no—
358C23×C3—24no—
359C23×C3—24no—
360C22×D3—34no—
361C22×D3—616no—
362C22×D3—64no—
363C22×D3—128no—
364C22×D3—128no—
365C3×D4—24no—
366C3×D4—24no—
367C3×D4C2×C4×D318yes—
368C3×D4C2×C4×D318yescomplemented
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—48no—
372C2×C3×C4—48no—
373C2×C3×C4D3×D414yes—
374C2×C3×C4D3×D414yes—
375C2×C3×C4C23×D314yes—
376#67—616no—
377#67—616no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—616no—
382C2×Dic3—64no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—128no—
386C2×Dic3—128no—
387D12—38no—
388D12—64no—
389C4×D3—38no—
390C4×D3—38no—
391C4×D3—68no—
392C4×D3—128no—
393C4×D3—124no—
394C4×D3—128no—
395C4×D3—128no—
396Dic6—38no—
397Dic6—64no—
398C3×C8—24no—
399C3×C8C2×C4×D318yescomplemented
400C3⋊C8—38no—
401C3⋊C8—64no—
402C2×C32—42no—
403C2×C32—42no—
404C2×C32C2×C4×D411yescharacteristic
405C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C32#57511yescharacteristic
407C3⋊D3—22no—
408C3⋊D3—42no—
409C24—181no—
410#41—94no—
411#41—182no—
412C2×Q8—91no—
413C2×D4—94no—
414C2×D4—91no—
415C2×D4—182no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4C22×C3⋊D311yescharacteristic
419C2×D4C22×C3⋊D311yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4—181no—
429C22×C4—181no—
430C22×C4—181no—
431C22×C4—364no—
432SD16—94no—
433SD16—94no—
434D8—94no—
435D8C4×C3⋊D314yescomplemented
436M16—94no—
437M16—182no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8C22×C3⋊D311yescharacteristic
441C2×C8C22×C3⋊D311yescharacteristic
442C4⋊C4—91no—
443C4⋊C4—91no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C4⋊C4C22×C3⋊D311yescharacteristic
448C4⋊C4C22×C3⋊D311yescharacteristic
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C42—91no—
457C42—91no—
458C42—91no—
459C42—181no—
460C42—181no—
461C42—181no—
462C42C22×C3⋊D311yescharacteristic
463C22×C3—28no—
464C22×C3—28no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—44no—
468C22×C3—44no—
469C22×C3C2×D3×D414yes—
470C2×D3—38no—
471C2×D3—64no—
472C2×D3—64no—
473C2×D3—68no—
474C2×D3—1232no—
475C2×D3—124no—
476C2×D3—124no—
477C3×C4—24no—
478C3×C4—24no—
479C3×C4—44no—
480C3×C4—44no—
481C3×C4C22×C4×D314yes—
482C3×C4D3×#4114yes—
483Dic3—38no—
484Dic3—38no—
485Dic3—64no—
486Dic3—68no—
487Dic3—124no—
488Dic3—124no—
489C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
490C23—21no—
491C23—21no—
492C23—91no—
493C23—184no—
494C23—181no—
495C23—362no—
496C23—362no—
497Q8—92no—
498Q8—181no—
499D4—21no—
500D4—21no—
501D4—92no—
502D4—184no—
503D4—184no—
504D4—181no—
505D4C2×C4×C3⋊D312yes—
506D4C2×C4×C3⋊D312yescomplemented
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—91no—
512C2×C4—91no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—91no—
516C2×C4—182no—
517C2×C4—184no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—361no—
522C2×C4—362no—
523C2×C4—362no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4—362no—
527C2×C4D4×C3⋊D311yescharacteristic
528C2×C4D4×C3⋊D311yescharacteristic
529C2×C4C23×C3⋊D311yescharacteristic
530C8—21no—
531C8—92no—
532C8—181no—
533C8C2×C4×C3⋊D312yescomplemented
534C2×C3—48no—
535C2×C3—48no—
536C2×C3C4×D3×D414yes—
537C2×C3D3×AGL(1,ℤ/8)14yes—
538C2×C3#577314yes—
539D3—68no—
540D3—128no—
541C22—22no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—92no—
548C22—181no—
549C22—181no—
550C22—182no—
551C22—368no—
552C22—361no—
553C22—361no—
554C22C2×D4×C3⋊D311yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—92no—
560C4—92no—
561C4—181no—
562C4—182no—
563C4—361no—
564C4—361no—
565C4C22×C4×C3⋊D311yescharacteristic
566C4#41×C3⋊D311yescharacteristic
567C3#7986514yescomplemented
568C2—42no—
569C2—42no—
570C2—182no—
571C2—362no—
572C2C4×D4×C3⋊D311yescharacteristic
573C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
574C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#442C2
socleC22×C32C22×D4
prime radicalC2×#64120C2
cosocleC2×C32×C4C24
hypercenter#442C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×C3⋊D3C2semidirect
3. C4×#3830C2semidirect
4. C32×#442C2semidirect
5. D8×C3⋊Dic3C2semidirect
6. #10592717C2semidirect
7. #10592713C2semidirect
8. #10592560C2semidirect
9. #10592551C2semidirect
10. #10592470C2semidirect
11. #10592469C2semidirect
12. #10592457C2semidirect
13. #10592455C2semidirect
14. #10592409C2semidirect
15. #10592406C2semidirect
22. C32×C4×D4C22semidirect
24. D4×C3⋊Dic3C22semidirect
30. #64120C4semidirect
37. #64096C22semidirect
44. C4×#634C22semidirect
45. C32×#106C22semidirect
47. C32×#102C22semidirect
48. C32×#97C22semidirect
50. #63659C22semidirect
52. #63645C22semidirect
53. #63643C22semidirect
54. C8×C3⋊Dic3C22semidirect
55. C8×C3⋊Dic3C22semidirect
56. #63637C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
60. #63630C22semidirect
64. C3×#442D3semidirect
87. #3830C2×C4semidirect
89. D4×C3⋊D3C2×C4semidirect
99. C32×D8C2×C4semidirect
109. #3754C2×C4semidirect
110. #3753C2×C4semidirect
127. #3744C2×C4semidirect
129. #3743C2×C4semidirect
136. C3×C4×D4C2×D3semidirect
159. C3×#106C2×D3semidirect
161. C3×#102C2×D3semidirect
162. C3×#97C2×D3semidirect
185. C32×D4C22×C4semidirect
214. #634C22×C4semidirect
216. C32×C8C22×C4semidirect
218. C3⋊(C3⋊C8)C22×C4semidirect
223. #442C3⋊D3semidirect
257. C3×D8C4×D3semidirect
313. C3⋊Dic3AGL(1,ℤ/8)semidirect
335. C4×D4C2×C3⋊D3semidirect
345. #106C2×C3⋊D3semidirect
353. #102C2×C3⋊D3semidirect
355. #97C2×C3⋊D3semidirect
368. C3×D4C2×C4×D3semidirect
399. C3×C8C2×C4×D3semidirect
435. D8C4×C3⋊D3semidirect
489. C32C4×AGL(1,ℤ/8)semidirect
506. D4C2×C4×C3⋊D3semidirect
533. C8C2×C4×C3⋊D3semidirect
567. C3#79865semidirect

Maximal subgroups

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

subgroupindex
C2×#641202
C4×D4×C3⋊D32
C4×#38302
C32×#4422
D8×C3⋊Dic32
#105927172
#105927132
#105925602
#105925512
#105924702
#105924692
#105924572
#105924552
#105924092
#105924062
#798653