Finite Group Databasebeta

← #11866230

Subgroups — #11866230

Order 1152.

1482 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C211yesmaximal, characteristic
2C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596195C211yesmaximal, characteristic, complemented
4#10596016C211yesmaximal, characteristic, complemented
5C32×#461C211yesmaximal, characteristic, complemented
6#10592864C211yesmaximal, characteristic, complemented
7#10592861C211yesmaximal, characteristic, complemented
8#10592782C211yesmaximal, characteristic, complemented
9#10592715C211yesmaximal, characteristic, complemented
10#10592543C211yesmaximal, characteristic, complemented
11#10592538C211yesmaximal, characteristic, complemented
12#10592518C211yesmaximal, characteristic, complemented
13#10592517C211yesmaximal, characteristic, complemented
14#10592503C211yesmaximal, characteristic, complemented
15#10592501C211yesmaximal, characteristic, complemented
16#80430—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24#64156C2211yescharacteristic, complemented
25#64153C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27C2×#3755C2211yescharacteristic
28D4×C3⋊Dic3C2211yescharacteristic
29C2×#3754C2211yescharacteristic
30C2×#3753C2211yescharacteristic
31C4×#638—21no—
32C2×#3752—21no—
33#64123—24no—
34SD16×C3⋊D3—24no—
35C2×#3745C2211yescharacteristic
36C2×#3744C2211yescharacteristic
37C2×#3743C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic
39#64105—21no—
40#64105—21no—
41#64103—21no—
42#64103—21no—
43#64102C2211yescharacteristic
44#64101C2211yescharacteristic
45#64090—21no—
46C22⋊C4×C3⋊D3—21no—
47#64084C2211yescharacteristic, complemented
48C4×C4⋊(C3⋊D3)C2211yescharacteristic
49#64081C2211yescharacteristic
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63643C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63636C2211yescharacteristic, complemented
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#914—34no—
63C2×D3×SD16—34no—
64#5724—34no—
65#5545—34no—
66C3×#461D314yescomplemented
67#5165—34no—
68#5162—34no—
69#5083—34no—
70#5016—34no—
71#4844—34no—
72#4839—34no—
73#4819—34no—
74#4818—34no—
75#4804—34no—
76#4802—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C2×#638—21no—
83C22×C3⋊Dic3—21no—
84#3832—22no—
85#3832—22no—
86Q8×C3⋊D3—22no—
87Q8×C3⋊D3—22no—
88D4×C3⋊D3—22no—
89D4×C3⋊D3D414yes—
90C2×C4⋊(C3⋊D3)—21no—
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C32×SD16—22no—
101C32×SD16—22no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C42C2311yescharacteristic
109#3757—21no—
110#3755—22no—
111#3755—22no—
112#3754—22no—
113#3753—22no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752D411yescharacteristic
122#3752D411yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126#3750D411yescharacteristic
127#3750D411yescharacteristic
128C4×C3⋊Dic3—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3745—22no—
133#3744—22no—
134#3743—22no—
135C8×C3⋊D3—22no—
136#3042—91noSylow
137C2×#239—34no—
138C2×D3×Q8—34no—
139C2×D3×D4—34no—
140C2×C3×SD16C2×D314yes—
141C2×C3×SD16C2×D314yes—
142C3×C4⋊Q8C2×D314yescomplemented
143C3×C4×D4C2×D314yes—
144#947—34no—
145#944—34no—
146C2×#215—34no—
147C2×#215—34no—
148D4×Dic3—34no—
149C2×#214—34no—
150C2×#213—34no—
151C4×#67—64no—
152C2×(C2×D3)⋊C4—64no—
153#914—616no—
154D3×SD16—616no—
155C2×D24—34no—
156C2×#204—34no—
157C2×ΓL(1,𝔽25)—34no—
158C2×D3×C8—34no—
159#896—64no—
160#896—64no—
161#894—64no—
162#894—64no—
163#893—34no—
164#892—34no—
165#67⋊C4—64no—
166D3×C22⋊C4—64no—
167#875—34no—
168C4×D12—34no—
169#872—34no—
170C3×C4⋊C8C2×D314yescomplemented
171C3×#103C2×D314yescomplemented
172C3×#103C2×D314yescomplemented
173#835—34no—
174#835—34no—
175#821—34no—
176#816—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179#810—34no—
180#809—34no—
181C4⋊(C3⋊C8)—34no—
182C23×C32—21no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3—24no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—81no—
187C22×C3⋊D3—81no—
188C22×C3⋊D3C2×D411yescharacteristic
189C32×Q8—21no—
190C32×Q8—21no—
191C32×Q8—21no—
192C32×Q8—21no—
193C32×D4—21no—
194C32×D4C2×D412yes—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—81no—
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2411yescharacteristic
202#638—24no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—81no—
206C2×C3⋊Dic3C2×D411yescharacteristic
207C2×C3⋊Dic3C2×D411yescharacteristic
208C2×C3⋊Dic3C2×D411yescharacteristic
209C4⋊(C3⋊D3)—21no—
210C4⋊(C3⋊D3)—21no—
211C4⋊(C3⋊D3)—21no—
212C4⋊(C3⋊D3)—42no—
213C4⋊(C3⋊D3)C2×D412yes—
214C4×C3⋊D3—42no—
215C4×C3⋊D3—42no—
216C4×C3⋊D3—81no—
217C4×C3⋊D3—81no—
218C4×C3⋊D3C2×D412yes—
219C4×C3⋊D3#4112yes—
220#634—21no—
221#634—21no—
222#634—42no—
223C32×C8—21no—
224C32×C8—21no—
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)—21no—
227C2×AGL(1,ℤ/8)—91no—
228C22×SD16—91no—
229#536—91no—
230#518—91no—
231#463—91no—
232#463—91no—
233#463—91no—
234#463—91no—
235#461—91no—
236#461—91no—
237#461—91no—
238#461C3⋊D311yescharacteristic, complemented
239#424—91no—
240#419—91no—
241#416—91no—
242C23×D3—64no—
243C2×C3×Q8C22×D314yes—
244C2×C3×Q8C22×D314yes—
245C2×C3×D4C22×D314yes—
246C22×C3×C4—24no—
247C2×#67—64no—
248C22×Dic3—64no—
249#239—68no—
250#239—68no—
251D3×Q8—68no—
252D3×Q8—68no—
253D3×D4—316no—
254D3×D4—68no—
255C2×D12—34no—
256C2×D12—34no—
257C2×D12—64no—
258C2×C4×D3—34no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×Dic6—34no—
264C2×Dic6—64no—
265C3×SD16—28no—
266C3×SD16—28no—
267C2×C3×C8C22×D314yes—
268C2×C3×C8C22×D314yes—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4C22×D314yes—
272C3×C22⋊C4—24no—
273C3×C42C22×D314yes—
274#217—64no—
275#215—68no—
276#215—68no—
277#214—68no—
278#213—68no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—64no—
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—
289Dic3⋊C4—34no—
290Dic3⋊C4—34no—
291Dic3⋊C4—64no—
292Dic3⋊C4—64no—
293C4×Dic3—34no—
294C4×Dic3—64no—
295C2×C3⋊C8—34no—
296C2×C3⋊C8—34no—
297D24—68no—
298#204—68no—
299ΓL(1,𝔽25)—68no—
300D3×C8—68no—
301C22×C32—22no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—21no—
306C2×C3⋊D3—21no—
307C2×C3⋊D3—22no—
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C2×C3⋊D3—41no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—84no—
314C2×C3⋊D3#12112yes—
315C32×C4—21no—
316C32×C4—21no—
317C32×C4—41no—
318C32×C4—41no—
319C32×C4—41no—
320C32×C4C22×D411yescharacteristic
321C32×C4C2×#4111yescharacteristic
322C3⋊Dic3—21no—
323C3⋊Dic3—21no—
324C3⋊Dic3—41no—
325C3⋊Dic3—41no—
326C3⋊Dic3#12112yes—
327C2×#41—91no—
328C22×Q8—91no—
329C22×D4—91no—
330AGL(1,ℤ/8)—184no—
331C2×SD16—91no—
332C2×SD16—91no—
333C2×SD16—91no—
334C2×SD16—91no—
335C2×SD16—184no—
336C2×SD16C2×C3⋊D311yescharacteristic
337C2×SD16C2×C3⋊D311yescharacteristic
338C2×D8—91no—
339C2×D8—91no—
340C2×M16—91no—
341C22×C8—91no—
342C4⋊Q8—91no—
343C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
344#124—91no—
345#124—91no—
346#123—181no—
347#123—181no—
348C22⋊Q8—181no—
349C22⋊Q8—181no—
350C4×D4—91no—
351C4×D4—91no—
352C4×D4—91no—
353C4×D4—181no—
354C4×D4—181no—
355C4×D4C2×C3⋊D311yescharacteristic
356#117—91no—
357#117—91no—
358C2×C22⋊C4—181no—
359C2×C22⋊C4—181no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8—91no—
363C4⋊C8C2×C3⋊D311yescharacteristic, complemented
364#103—91no—
365#103—91no—
366#103—91no—
367#103—91no—
368#103C2×C3⋊D311yescharacteristic, complemented
369#103C2×C3⋊D311yescharacteristic, complemented
370#102—91no—
371#102—91no—
372C23×C3—24no—
373C22×D3—34no—
374C22×D3—616no—
375C22×D3—64no—
376C22×D3—64no—
377C22×D3—244no—
378C22×D3—244no—
379C3×Q8—24no—
380C3×Q8—24no—
381C3×Q8—24no—
382C3×Q8—24no—
383C3×D4—24no—
384C3×D4D3×D418yes—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—84no—
389C2×C3×C4D3×D414yes—
390C2×C3×C4D3×D414yes—
391C2×C3×C4C23×D314yes—
392#67—616no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—244no—
399D12—38no—
400D12—64no—
401D12—64no—
402D12—64no—
403D12—128no—
404C4×D3—38no—
405C4×D3—38no—
406C4×D3—128no—
407C4×D3—128no—
408C4×D3—244no—
409C4×D3—244no—
410Dic6—64no—
411Dic6—64no—
412Dic6—128no—
413C3×C8—24no—
414C3×C8—24no—
415C3⋊C8—64no—
416C3⋊C8—64no—
417C2×C32—42no—
418C2×C32C2×#12111yescharacteristic
419C2×C32#57711yescharacteristic
420C2×C32#57711yescharacteristic
421C3⋊D3—22no—
422C3⋊D3—42no—
423C3⋊D3—81no—
424C24—181no—
425#41—182no—
426#41—182no—
427C2×Q8—91no—
428C2×Q8—181no—
429C2×Q8—182no—
430C2×Q8—182no—
431C2×Q8C22×C3⋊D311yescharacteristic
432C2×Q8C22×C3⋊D311yescharacteristic
433C2×D4—94no—
434C2×D4—91no—
435C2×D4—91no—
436C2×D4—181no—
437C2×D4—182no—
438C2×D4—181no—
439C2×D4C22×C3⋊D311yescharacteristic
440C22×C4—21no—
441C22×C4—91no—
442C22×C4—181no—
443C22×C4—181no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—181no—
447SD16—22no—
448SD16—22no—
449SD16—182no—
450SD16—182no—
451SD16—182no—
452SD16—182no—
453D8—182no—
454D8—182no—
455M16—182no—
456C2×C8—91no—
457C2×C8—91no—
458C2×C8—182no—
459C2×C8C22×C3⋊D311yescharacteristic
460C2×C8C22×C3⋊D311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—91no—
464C4⋊C4—91no—
465C4⋊C4—91no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C4⋊C4C22×C3⋊D311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—91no—
471C22⋊C4—91no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C22⋊C4—181no—
477C22⋊C4—181no—
478C22⋊C4—181no—
479C22⋊C4—181no—
480C42—91no—
481C42—181no—
482C42C22×C3⋊D311yescharacteristic
483C22×C3—28no—
484C22×C3—44no—
485C22×C3—44no—
486C22×C3C2×D3×D414yes—
487C2×D3—38no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—68no—
491C2×D3—124no—
492C2×D3—124no—
493C2×D3—124no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—2416no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—44no—
500C3×C4—44no—
501C3×C4—44no—
502C3×C4C2×D3×D414yes—
503C3×C4D3×#4114yes—
504Dic3—38no—
505Dic3—64no—
506Dic3—64no—
507Dic3—124no—
508Dic3—124no—
509C32#304211yescharacteristic, complemented, Sylow
510C23—21no—
511C23—91no—
512C23—184no—
513C23—181no—
514C23—181no—
515C23—721no—
516C23—721no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—181no—
522Q8—181no—
523Q8—362no—
524D4—21no—
525D4—92no—
526D4—184no—
527D4—181no—
528D4—181no—
529D4—181no—
530D4—362no—
531D4D4×C3⋊D312yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—81no—
536C2×C4—91no—
537C2×C4—92no—
538C2×C4—92no—
539C2×C4—91no—
540C2×C4—91no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—362no—
544C2×C4—362no—
545C2×C4—721no—
546C2×C4—721no—
547C2×C4—721no—
548C2×C4D4×C3⋊D311yescharacteristic
549C2×C4D4×C3⋊D311yescharacteristic
550C2×C4C23×C3⋊D311yescharacteristic
551C8—21no—
552C8—21no—
553C8—181no—
554C8—181no—
555C2×C3—48no—
556C2×C3D3×#12114yes—
557C2×C3#576214yes—
558C2×C3#577814yes—
559D3—68no—
560D3—128no—
561D3—244no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—92no—
566C22—181no—
567C22—181no—
568C22—182no—
569C22—361no—
570C22—361no—
571C22—361no—
572C22—361no—
573C22—361no—
574C22—724no—
575C22C2×D4×C3⋊D311yescharacteristic
576C4—21no—
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—92no—
582C4—181no—
583C4—181no—
584C4—361no—
585C4—361no—
586C4C2×D4×C3⋊D311yescharacteristic
587C4#41×C3⋊D311yescharacteristic
588C3#8043014yescomplemented
589C2—42no—
590C2—182no—
591C2—362no—
592C2—721no—
593C2C3⋊D3×#12111yescharacteristic
594C2#1059623311yescharacteristic
595C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×#64123C2
hypercenter#461C3⋊D3
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C2×SD16×C3⋊D3C2semidirect
3. #10596195C2semidirect
4. #10596016C2semidirect
5. C32×#461C2semidirect
6. #10592864C2semidirect
7. #10592861C2semidirect
8. #10592782C2semidirect
9. #10592715C2semidirect
10. #10592543C2semidirect
11. #10592538C2semidirect
12. #10592518C2semidirect
13. #10592517C2semidirect
14. #10592503C2semidirect
15. #10592501C2semidirect
22. C32×C4⋊Q8C22semidirect
24. #64156C22semidirect
25. #64153C22semidirect
47. #64084C22semidirect
50. C32×C4⋊C8C22semidirect
51. C32×#103C22semidirect
52. C32×#103C22semidirect
53. #63662C22semidirect
54. #63662C22semidirect
55. #63648C22semidirect
56. #63643C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63637C22semidirect
60. #63636C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#461D3semidirect
142. C3×C4⋊Q8C2×D3semidirect
170. C3×C4⋊C8C2×D3semidirect
171. C3×#103C2×D3semidirect
172. C3×#103C2×D3semidirect
238. #461C3⋊D3semidirect
343. C4⋊Q8C2×C3⋊D3semidirect
363. C4⋊C8C2×C3⋊D3semidirect
368. #103C2×C3⋊D3semidirect
369. #103C2×C3⋊D3semidirect
509. C32#3042semidirect
588. C3#80430semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
C2×SD16×C3⋊D32
#105961952
#105960162
C32×#4612
#105928642
#105928612
#105927822
#105927152
#105925432
#105925382
#105925182
#105925172
#105925032
#105925012
#804303