Finite Group Databasebeta

← #11867035

Subgroups — #11867035

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64125C211yesmaximal, characteristic, complemented
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596098C211yesmaximal, characteristic, complemented
4#10596077C211yesmaximal, characteristic, complemented
5C32×#468C211yesmaximal, characteristic, complemented
6#10592873C211yesmaximal, characteristic, complemented
7#10592833C211yesmaximal, characteristic, complemented
8#10592751C211yesmaximal, characteristic, complemented
9#10592738C211yesmaximal, characteristic, complemented
10#10592585C211yesmaximal, characteristic, complemented
11#10592579C211yesmaximal, characteristic, complemented
12#10592515C211yesmaximal, characteristic, complemented
13#10592503C211yesmaximal, characteristic, complemented
14#10592481C211yesmaximal, characteristic, complemented
15#10592471C211yesmaximal, characteristic, complemented
16#80804—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic, complemented
21C2×C32×M16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121C2211yescharacteristic
24#64155C2211yescharacteristic
25C2×#3756C2211yescharacteristic, complemented
26#64147C2211yescharacteristic
27#64146—21no—
28D4×C3⋊Dic3—21no—
29C2×#3753C2211yescharacteristic, complemented
30#64139C2211yescharacteristic
31#64133C2211yescharacteristic
32C2×#3748C2211yescharacteristic
33#64125—24no—
34M16×C3⋊D3—24no—
35C2×#3744C2211yescharacteristic, complemented
36C2×#3743C2211yescharacteristic
37C2×#3743C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic
39C2×C8×C3⋊D3C2211yescharacteristic
40#64106C2211yescharacteristic
41#64104C2211yescharacteristic
42#64103—21no—
43#64102—21no—
44#64101C2211yescharacteristic
45#64101C2211yescharacteristic
46#64092—21no—
47#64091—21no—
48#64090—21no—
49#64090—21no—
50C32×#107C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63645C2211yescharacteristic, complemented
57#63643C2211yescharacteristic, complemented
58#63637C2211yescharacteristic, complemented
59#63636C2211yescharacteristic, complemented
60#63635C2211yescharacteristic, complemented
61#63635C2211yescharacteristic, complemented
62C2×#916—34no—
63C2×D3×M16—34no—
64#5627—34no—
65#5606—34no—
66C3×#468D314yescomplemented
67#5174—34no—
68#5134—34no—
69#5052—34no—
70#5039—34no—
71#4886—34no—
72#4880—34no—
73#4816—34no—
74#4804—34no—
75#4782—34no—
76#4772—34no—
77C23×C3⋊D3D411yescharacteristic
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C2×#638—21no—
83C2×#638—21no—
84C2×#638—21no—
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3D411yescharacteristic
87#3832—22no—
88#3832—22no—
89#3830—22no—
90#3830—22no—
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3D411yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C32×SD16—22no—
103C32×M16—22no—
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C22⋊C4—21no—
111#3757—21no—
112#3757—21no—
113#3756—22no—
114#3753—22no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3—21no—
128#3748—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3744—22no—
132#3743—22no—
133#3743—22no—
134C8×C3⋊D3—22no—
135C8×C3⋊D3D414yescomplemented
136#3054—91noSylow
137C2×#239—34no—
138C2×#237—34no—
139C22×C4×D3—34no—
140C2×C3×SD16C2×D314yescomplemented
141C2×C3×M16C2×D314yes—
142C3×C22⋊Q8C2×D314yes—
143C3×#121C2×D314yes—
144#946—34no—
145C2×#216—34no—
146#938—34no—
147#937—64no—
148D4×Dic3—64no—
149C2×#213—34no—
150#930—34no—
151#924—34no—
152C2×#208—34no—
153#916—616no—
154D3×M16—616no—
155C2×#204—34no—
156C2×ΓL(1,𝔽25)—34no—
157C2×ΓL(1,𝔽25)—34no—
158C2×D3×C8—34no—
159C2×D3×C8—34no—
160#897—34no—
161#895—34no—
162#894—64no—
163#893—64no—
164#892—34no—
165#892—34no—
166#883—64no—
167#882—64no—
168#67⋊C4—64no—
169#67⋊C4—64no—
170C3×#107C2×D314yescomplemented
171C3×#103C2×D314yescomplemented
172C3×#102C2×D314yescomplemented
173#835—34no—
174#832—34no—
175#821—34no—
176#818—34no—
177#816—34no—
178#810—34no—
179#809—34no—
180#808—34no—
181#808—34no—
182C23×C32—21no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—22no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—41no—
187C22×C3⋊D3—41no—
188C22×C3⋊D3C2×D411yescharacteristic
189C22×C3⋊D3C2×D411yescharacteristic
190C32×Q8—21no—
191C32×Q8—21no—
192C32×D4—21no—
193C32×D4—21no—
194C32×D4—42no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2411yescharacteristic
202#638—42no—
203#638—42no—
204#638—42no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—42no—
210C2×C3⋊Dic3C2×D411yescharacteristic
211C2×C3⋊Dic3C2×D411yescharacteristic
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—42no—
215C4⋊(C3⋊D3)—42no—
216C4×C3⋊D3—22no—
217C4×C3⋊D3—21no—
218C4×C3⋊D3—21no—
219C4×C3⋊D3—22no—
220C4×C3⋊D3—42no—
221C4×C3⋊D3C2×D412yes—
222C4×C3⋊D3#4112yes—
223#634—21no—
224#634—21no—
225C32×C8—21no—
226C32×C8C2×D412yes—
227C3⋊(C3⋊C8)—21no—
228C3⋊(C3⋊C8)C2×D412yes—
229C2×#135—91no—
230C22×M16—91no—
231#525—91no—
232#525—91no—
233#470—91no—
234#470—91no—
235#469—91no—
236#469—91no—
237#468—91no—
238#468—91no—
239#468—91no—
240#468C3⋊D311yescharacteristic, complemented
241#427—91no—
242#416—91no—
243#416—91no—
244C23×D3—34no—
245C2×C3×Q8C22×D314yes—
246C2×C3×D4—24no—
247C2×C3×D4C22×D314yes—
248C22×C3×C4C22×D314yes—
249C2×#67—64no—
250C2×#67—64no—
251C2×#67—64no—
252C22×Dic3—34no—
253C22×Dic3—64no—
254#239—68no—
255#239—68no—
256#237—68no—
257#237—68no—
258C2×D12—34no—
259C2×D12—64no—
260C2×D12—64no—
261C2×C4×D3—34no—
262C2×C4×D3—34no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—68no—
266C2×C4×D3—68no—
267C2×C4×D3—64no—
268C2×Dic6—34no—
269C3×SD16—28no—
270C3×M16—28no—
271C2×C3×C8C22×D314yes—
272C2×C3×C8C22×D314yes—
273C3×C4⋊C4—24no—
274C3×C4⋊C4C22×D314yes—
275C3×C4⋊C4C22×D314yes—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—24no—
278#217—64no—
279#217—64no—
280#216—68no—
281#213—68no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285(C2×D3)⋊C4—64no—
286(C2×D3)⋊C4—64no—
287(C2×D3)⋊C4—64no—
288C4⋊Dic3—34no—
289C4⋊Dic3—34no—
290C4⋊Dic3—64no—
291Dic3⋊C4—64no—
292Dic3⋊C4—64no—
293C4×Dic3—64no—
294C4×Dic3—64no—
295#208—68no—
296C2×C3⋊C8—34no—
297C2×C3⋊C8—34no—
298#204—68no—
299ΓL(1,𝔽25)—68no—
300ΓL(1,𝔽25)—68no—
301D3×C8—316no—
302D3×C8—68no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—21no—
311C2×C3⋊D3—21no—
312C2×C3⋊D3—21no—
313C2×C3⋊D3—21no—
314C2×C3⋊D3—21no—
315C2×C3⋊D3—44no—
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3⋊D3#12112yes—
320C32×C4—21no—
321C32×C4—41no—
322C32×C4—41no—
323C32×C4—41no—
324C32×C4C22×D411yescharacteristic
325C32×C4C2×#4111yescharacteristic
326C3⋊Dic3—21no—
327C3⋊Dic3—41no—
328C3⋊Dic3—41no—
329C3⋊Dic3—41no—
330C3⋊Dic3#12112yes—
331C2×#41—91no—
332C2×#41—91no—
333C23×C4—91no—
334#135—184no—
335C2×Q16—91no—
336C2×SD16—91no—
337C2×SD16C2×C3⋊D311yescharacteristic, complemented
338C2×D8—91no—
339C2×M16—91no—
340C2×M16—91no—
341C2×M16—91no—
342C2×M16—184no—
343C2×M16C2×C3⋊D311yescharacteristic
344C22×C8—91no—
345C22×C8—91no—
346#123—181no—
347#123—181no—
348C22⋊Q8—91no—
349C22⋊Q8—91no—
350C22⋊Q8—91no—
351C22⋊Q8C2×C3⋊D311yescharacteristic
352#121—91no—
353#121—91no—
354#121—91no—
355#121C2×C3⋊D311yescharacteristic
356#120—181no—
357#120—181no—
358C4×D4—181no—
359C4×D4—181no—
360C4×D4—181no—
361C4×D4—181no—
362#117—91no—
363#117—91no—
364#107—91no—
365#107C2×C3⋊D311yescharacteristic, complemented
366#106—91no—
367#106—91no—
368#103—91no—
369#103—91no—
370#103—91no—
371#103C2×C3⋊D311yescharacteristic, complemented
372#102—91no—
373#102—91no—
374#102—91no—
375#102C2×C3⋊D311yescharacteristic, complemented
376C23×C3—24no—
377C23×C3D3×D414yes—
378C22×D3—34no—
379C22×D3—34no—
380C22×D3—68no—
381C22×D3—64no—
382C22×D3—124no—
383C22×D3—124no—
384C3×Q8—24no—
385C3×Q8—24no—
386C3×D4—24no—
387C3×D4—24no—
388C3×D4—48no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4D3×D414yes—
395C2×C3×C4C23×D314yes—
396#67—128no—
397#67—128no—
398#67—128no—
399C2×Dic3—34no—
400C2×Dic3—34no—
401C2×Dic3—68no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—128no—
406D12—64no—
407D12—64no—
408D12—128no—
409D12—128no—
410C4×D3—38no—
411C4×D3—38no—
412C4×D3—68no—
413C4×D3—68no—
414C4×D3—64no—
415C4×D3—64no—
416C4×D3—128no—
417Dic6—64no—
418Dic6—64no—
419C3×C8—24no—
420C3×C8D3×D418yes—
421C3⋊C8—38no—
422C3⋊C8—64no—
423C2×C32—41no—
424C2×C32—81no—
425C2×C32C2×#12111yescharacteristic
426C2×C32#57511yescharacteristic
427C2×C32#57511yescharacteristic
428C3⋊D3—22no—
429C3⋊D3—41no—
430C3⋊D3—81no—
431C24—91no—
432#41—182no—
433#41—182no—
434#41—182no—
435#41—182no—
436C2×Q8—91no—
437C2×Q8C22×C3⋊D311yescharacteristic
438C2×D4—21no—
439C2×D4—91no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—181no—
443C2×D4—181no—
444C2×D4—181no—
445C2×D4C22×C3⋊D311yescharacteristic
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—182no—
452C22×C4—182no—
453C22×C4—181no—
454C22×C4—181no—
455C22×C4C22×C3⋊D311yescharacteristic
456Q16—182no—
457SD16—22no—
458SD16—182no—
459D8—182no—
460M16—22no—
461M16—182no—
462M16—182no—
463M16—182no—
464C2×C8—91no—
465C2×C8—94no—
466C2×C8—91no—
467C2×C8—182no—
468C2×C8C22×C3⋊D311yescharacteristic
469C2×C8C22×C3⋊D311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—91no—
472C4⋊C4—91no—
473C4⋊C4—181no—
474C4⋊C4—181no—
475C4⋊C4—181no—
476C4⋊C4C22×C3⋊D311yescharacteristic
477C4⋊C4C22×C3⋊D311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—181no—
481C22⋊C4—181no—
482C22⋊C4—181no—
483C22⋊C4—181no—
484C22⋊C4—181no—
485C22⋊C4—181no—
486C22⋊C4—181no—
487C22⋊C4—181no—
488C42—181no—
489C42—181no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—44no—
494C22×C3—44no—
495C22×C3—44no—
496C22×C3C2×D3×D414yes—
497C2×D3—38no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—64no—
503C2×D3—1216no—
504C2×D3—124no—
505C2×D3—124no—
506C2×D3—124no—
507C3×C4—24no—
508C3×C4—44no—
509C3×C4—44no—
510C3×C4—44no—
511C3×C4C2×D3×D414yes—
512C3×C4D3×#4114yes—
513Dic3—38no—
514Dic3—64no—
515Dic3—124no—
516Dic3—124no—
517Dic3—124no—
518C32#305411yescharacteristic, complemented, Sylow
519C23—21no—
520C23—91no—
521C23—91no—
522C23—182no—
523C23—181no—
524C23—361no—
525C23—361no—
526C23D4×C3⋊D311yescharacteristic
527Q8—21no—
528Q8—21no—
529Q8—181no—
530Q8—181no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—181no—
535D4—181no—
536D4—362no—
537D4—362no—
538D4—362no—
539D4—362no—
540D4—362no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—91no—
547C2×C4—92no—
548C2×C4—92no—
549C2×C4—91no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—362no—
559C2×C4—362no—
560C2×C4D4×C3⋊D311yescharacteristic
561C2×C4C23×C3⋊D311yescharacteristic
562C8—21no—
563C8—92no—
564C8—181no—
565C8D4×C3⋊D312yes—
566C2×C3—44no—
567C2×C3—84no—
568C2×C3D3×#12114yes—
569C2×C3#577314yes—
570C2×C3#577714yes—
571D3—68no—
572D3—124no—
573D3—244no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—92no—
581C22—181no—
582C22—181no—
583C22—181no—
584C22—181no—
585C22—181no—
586C22—364no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22C2×D4×C3⋊D311yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—92no—
596C4—181no—
597C4—361no—
598C4—361no—
599C4—361no—
600C4C2×D4×C3⋊D311yescharacteristic
601C4#41×C3⋊D311yescharacteristic
602C3#8080414yescomplemented
603C2—41no—
604C2—81no—
605C2—182no—
606C2—361no—
607C2—721no—
608C2C3⋊D3×#12111yescharacteristic
609C2#1059624411yescharacteristic
610C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#468C2
socleC22×C32C22×D4
hypercenter#468C3⋊D3
hypocenterC32#3054
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#64125C2semidirect
2. C2×M16×C3⋊D3C2semidirect
3. #10596098C2semidirect
4. #10596077C2semidirect
5. C32×#468C2semidirect
6. #10592873C2semidirect
7. #10592833C2semidirect
8. #10592751C2semidirect
9. #10592738C2semidirect
10. #10592585C2semidirect
11. #10592579C2semidirect
12. #10592515C2semidirect
13. #10592503C2semidirect
14. #10592481C2semidirect
15. #10592471C2semidirect
20. C2×C32×SD16C22semidirect
25. C2×#3756C22semidirect
29. C2×#3753C22semidirect
35. C2×#3744C22semidirect
50. C32×#107C22semidirect
51. C32×#103C22semidirect
52. C32×#102C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63645C22semidirect
57. #63643C22semidirect
58. #63637C22semidirect
59. #63636C22semidirect
60. #63635C22semidirect
61. #63635C22semidirect
66. C3×#468D3semidirect
135. C8×C3⋊D3D4semidirect
140. C2×C3×SD16C2×D3semidirect
170. C3×#107C2×D3semidirect
171. C3×#103C2×D3semidirect
172. C3×#102C2×D3semidirect
240. #468C3⋊D3semidirect
337. C2×SD16C2×C3⋊D3semidirect
365. #107C2×C3⋊D3semidirect
371. #103C2×C3⋊D3semidirect
375. #102C2×C3⋊D3semidirect
518. C32#3054semidirect
602. C3#80804semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
C2×M16×C3⋊D32
#105960982
#105960772
C32×#4682
#105928732
#105928332
#105927512
#105927382
#105925852
#105925792
#105925152
#105925032
#105924812
#105924712
#808043