Finite Group Databasebeta

← #11884064

Subgroups — #11884064

Order 1152.

1482 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64127C211yesmaximal, characteristic, complemented
2C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596198C211yesmaximal, characteristic, complemented
4#10596147C211yesmaximal, characteristic
5C32×#497C211yesmaximal, characteristic, complemented
6#10592887C211yesmaximal, characteristic, complemented
7#10592886C211yesmaximal, characteristic, complemented
8#10592885C211yesmaximal, characteristic, complemented
9#10592873C211yesmaximal, characteristic, complemented
10#10592869C211yesmaximal, characteristic, complemented
11#10592868C211yesmaximal, characteristic, complemented
12#10592782C211yesmaximal, characteristic, complemented
13#10592753C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592405C211yesmaximal, characteristic, complemented
16#81881—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic, complemented
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic
24C2×C32×SD16C2211yescharacteristic
25C32×C4⋊Q8C2211yescharacteristic, complemented
26C32×#124C2211yescharacteristic
27#64155C2211yescharacteristic
28#64155C2211yescharacteristic
29#64155C2211yescharacteristic, complemented
30C2×#3756C2211yescharacteristic, complemented
31C2×#3755C2211yescharacteristic
32C2×#3755C2211yescharacteristic
33#64147C2211yescharacteristic
34C2×#3754C2211yescharacteristic
35#64127—24no—
36SD16×C3⋊D3—24no—
37C2×#3744C2211yescharacteristic
38C2×#3743C2211yescharacteristic, complemented
39C2×C8×C3⋊D3C2211yescharacteristic
40#64105—21no—
41#64105—21no—
42#64102—21no—
43#64097—21no—
44#64093—21no—
45#64092—21no—
46#64091—21no—
47C22⋊C4×C3⋊D3—21no—
48C4×C4⋊(C3⋊D3)C2211yescharacteristic
49C4×C4⋊(C3⋊D3)C2211yescharacteristic
50C4×#634C2211yescharacteristic, complemented
51C32×#97C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63659C2211yescharacteristic
56#63648C2211yescharacteristic
57#63647C2211yescharacteristic
58#63647C2211yescharacteristic, complemented
59#63645C2211yescharacteristic, complemented
60#63643C2211yescharacteristic, complemented
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#918—34no—
63C2×D3×SD16—34no—
64#5727—34no—
65#5676—34no—
66C3×#497D314yescomplemented
67#5188—34no—
68#5187—34no—
69#5186—34no—
70#5174—34no—
71#5170—34no—
72#5169—34no—
73#5083—34no—
74#5054—34no—
75#4710—34no—
76#4706—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C2×#638—21no—
83C2×#638—21no—
84#3832—22no—
85#3832—41no—
86Q8×C3⋊D3—22no—
87Q8×C3⋊D3—22no—
88Q8×C3⋊D3—41no—
89Q8×C3⋊D3—41no—
90D4×C3⋊D3—22no—
91D4×C3⋊D3—41no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)D411yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634—21no—
102C2×#634—21no—
103C2×#634C2311yescharacteristic
104C32×Q16—22no—
105C32×Q16—41no—
106C32×SD16—22no—
107C32×SD16—41no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3756—22no—
117#3755—22no—
118#3755—22no—
119#3754—22no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752—21no—
124#3752D411yescharacteristic
125#3752D411yescharacteristic
126C4⋊(C3⋊Dic3)D411yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3750—21no—
131#3750—21no—
132#3750—21no—
133C4×C3⋊Dic3—21no—
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3744D414yescomplemented
137#3743—22no—
138C8×C3⋊D3—22no—
139#3266—91noSylow
140C2×#239—34no—
141C2×D3×Q8—34no—
142C2×D3×Q8—34no—
143C2×D3×D4—34no—
144C2×C3×Q16C2×D314yescomplemented
145C2×C3×Q16C2×D314yescomplemented
146C2×C3×SD16C2×D314yes—
147C2×C3×SD16C2×D314yes—
148C3×C4⋊Q8C2×D314yescomplemented
149C3×#124C2×D314yes—
150#946—34no—
151#946—34no—
152#946—34no—
153C2×#216—34no—
154C2×#215—34no—
155C2×#215—34no—
156#938—34no—
157C2×#214—34no—
158#918—616no—
159D3×SD16—616no—
160C2×#204—34no—
161C2×ΓL(1,𝔽25)—34no—
162C2×D3×C8—34no—
163#896—64no—
164#896—64no—
165#893—64no—
166#888—64no—
167#884—64no—
168#883—64no—
169#882—64no—
170D3×C22⋊C4—64no—
171C4×D12—34no—
172C4×D12—34no—
173C4×Dic6—34no—
174C3×#97C2×D314yescomplemented
175#835—34no—
176#835—34no—
177#835—34no—
178#832—34no—
179#821—34no—
180(C2×D3)⋊C8—34no—
181(C2×D3)⋊C8—34no—
182#818—34no—
183#816—34no—
184C4⋊(C3⋊C8)—34no—
185C23×C32—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—42no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3—81no—
190C22×C3⋊D3C2×D411yescharacteristic
191C22×C3⋊D3C2×D411yescharacteristic
192C32×Q8—21no—
193C32×Q8—21no—
194C32×Q8—21no—
195C32×Q8—21no—
196C32×Q8—21no—
197C32×Q8—21no—
198C32×D4—21no—
199C32×D4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2411yescharacteristic
206#638—42no—
207#638—81no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3C2×D411yescharacteristic
212C2×C3⋊Dic3C2×D411yescharacteristic
213C4⋊(C3⋊D3)—22no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—42no—
216C4⋊(C3⋊D3)C2×D412yes—
217C4×C3⋊D3—21no—
218C4×C3⋊D3—21no—
219C4×C3⋊D3—21no—
220C4×C3⋊D3—21no—
221C4×C3⋊D3—42no—
222C4×C3⋊D3—42no—
223C4×C3⋊D3—42no—
224C4×C3⋊D3—81no—
225#634—21no—
226#634—42no—
227#634—42no—
228#634C2×D412yes—
229C32×C8—21no—
230C32×C8C2×D412yes—
231C3⋊(C3⋊C8)—21no—
232C3⋊(C3⋊C8)—21no—
233C2×#137—91no—
234C22×SD16—91no—
235D4×Q8—91no—
236#546—91no—
237#497C3⋊D311yescharacteristic, complemented
238#468—91no—
239#467—91no—
240#464—91no—
241#461—91no—
242#452—91no—
243#451—91no—
244#450—91no—
245#448—91no—
246#440—91no—
247#435—91no—
248C23×D3—64no—
249C2×C3×Q8C22×D314yes—
250C2×C3×Q8C22×D314yes—
251C2×C3×Q8C22×D314yes—
252C2×C3×D4C22×D314yes—
253C2×#67—64no—
254C2×#67—64no—
255#239—68no—
256#239—124no—
257D3×Q8—68no—
258D3×Q8—68no—
259D3×Q8—124no—
260D3×Q8—124no—
261D3×D4—68no—
262D3×D4—124no—
263C2×D12—34no—
264C2×D12—34no—
265C2×D12—64no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×Dic6—34no—
273C2×Dic6—64no—
274C2×Dic6—64no—
275C3×Q16—28no—
276C3×Q16—44no—
277C3×SD16—28no—
278C3×SD16—44no—
279C2×C3×C8C22×D314yes—
280C2×C3×C8C22×D314yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C42C22×D314yes—
286#217—64no—
287#216—68no—
288#215—68no—
289#215—68no—
290#214—68no—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—34no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297C4⋊Dic3—34no—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303Dic3⋊C4—64no—
304C4×Dic3—64no—
305C2×C3⋊C8—34no—
306C2×C3⋊C8—34no—
307#204—316no—
308ΓL(1,𝔽25)—68no—
309D3×C8—68no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—21no—
315C2×C3⋊D3—21no—
316C2×C3⋊D3—21no—
317C2×C3⋊D3—22no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—21no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—84no—
323C2×C3⋊D3#13712yescomplemented
324C32×C4—21no—
325C32×C4—21no—
326C32×C4—41no—
327C32×C4—41no—
328C32×C4—41no—
329C32×C4C22×D411yescharacteristic
330C32×C4H(5,𝔽2)11yescharacteristic
331C3⋊Dic3—22no—
332C3⋊Dic3—21no—
333C3⋊Dic3—21no—
334C3⋊Dic3—41no—
335C3⋊Dic3—41no—
336C2×#41—91no—
337C22×Q8—91no—
338C22×Q8—91no—
339C22×D4—91no—
340#137—184no—
341C2×Q16—91no—
342C2×Q16C2×C3⋊D311yescharacteristic, complemented
343C2×Q16C2×C3⋊D311yescharacteristic, complemented
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—184no—
349C2×SD16C2×C3⋊D311yescharacteristic
350C2×SD16C2×C3⋊D311yescharacteristic
351C2×M16—91no—
352C22×C8—91no—
353C4⋊Q8—181no—
354C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
355#124C2×C3⋊D311yescharacteristic
356#123—181no—
357C22⋊Q8—91no—
358C22⋊Q8—91no—
359C22⋊Q8—91no—
360C22⋊Q8—181no—
361C22⋊Q8—181no—
362#121—91no—
363#121—181no—
364#120—181no—
365C4×Q8—91no—
366C4×D4—91no—
367C4×D4—91no—
368C4×D4—181no—
369C2×C22⋊C4—181no—
370#107—91no—
371C4⋊C8—91no—
372#103—91no—
373#103—91no—
374#103—91no—
375#103—91no—
376#102—91no—
377#102—91no—
378C22⋊C8—91no—
379C22⋊C8—91no—
380#97C2×C3⋊D311yescharacteristic, complemented
381C23×C3—24no—
382C22×D3—34no—
383C22×D3—34no—
384C22×D3—64no—
385C22×D3—128no—
386C22×D3—128no—
387C22×D3—244no—
388C3×Q8—24no—
389C3×Q8—24no—
390C3×Q8—24no—
391C3×Q8—24no—
392C3×Q8—24no—
393C3×Q8—24no—
394C3×D4—24no—
395C3×D4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4D3×D414yes—
400C2×C3×C4D3×D414yes—
401C2×C3×C4C23×D314yes—
402#67—128no—
403#67—244no—
404C2×Dic3—34no—
405C2×Dic3—34no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409D12—38no—
410D12—68no—
411D12—64no—
412D12—128no—
413C4×D3—64no—
414C4×D3—64no—
415C4×D3—64no—
416C4×D3—64no—
417C4×D3—128no—
418C4×D3—128no—
419C4×D3—128no—
420C4×D3—244no—
421Dic6—38no—
422Dic6—64no—
423Dic6—128no—
424Dic6—128no—
425C3×C8—24no—
426C3×C8D3×D418yes—
427C3⋊C8—64no—
428C3⋊C8—64no—
429C2×C32—81no—
430C2×C32D4211yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C2×C32#57711yescharacteristic
433C3⋊D3—22no—
434C3⋊D3—41no—
435C3⋊D3—42no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—91no—
440C2×Q8—181no—
441C2×Q8—181no—
442C2×Q8—182no—
443C2×Q8—182no—
444C2×Q8—361no—
445C2×Q8—361no—
446C2×Q8C22×C3⋊D311yescharacteristic
447C2×Q8C22×C3⋊D311yescharacteristic
448C2×Q8C22×C3⋊D311yescharacteristic
449C2×D4—91no—
450C2×D4—91no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—182no—
454C2×D4—181no—
455C2×D4—361no—
456C2×D4C22×C3⋊D311yescharacteristic
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4—181no—
463Q16—22no—
464Q16—41no—
465Q16—182no—
466SD16—22no—
467SD16—41no—
468SD16—94no—
469SD16—182no—
470SD16—182no—
471SD16—182no—
472M16—182no—
473C2×C8—91no—
474C2×C8—91no—
475C2×C8—182no—
476C2×C8C22×C3⋊D311yescharacteristic
477C2×C8C22×C3⋊D311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—91no—
481C4⋊C4—91no—
482C4⋊C4—91no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—91no—
490C22⋊C4—91no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C42—181no—
497C42C22×C3⋊D311yescharacteristic
498C22×C3—44no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3C2×D3×D414yes—
502C2×D3—38no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—68no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—124no—
510C2×D3—124no—
511C2×D3—2416no—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—44no—
515C3×C4—44no—
516C3×C4—44no—
517C3×C4C2×D3×D414yes—
518C3×C4#100414yes—
519Dic3—68no—
520Dic3—64no—
521Dic3—64no—
522Dic3—124no—
523Dic3—124no—
524C32#326611yescharacteristic, complemented, Sylow
525C23—21no—
526C23—91no—
527C23—91no—
528C23—181no—
529C23—362no—
530C23—362no—
531C23—721no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—92no—
539Q8—181no—
540Q8—362no—
541Q8—362no—
542D4—21no—
543D4—21no—
544D4—92no—
545D4—182no—
546D4—181no—
547D4—362no—
548D4—362no—
549D4—721no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—91no—
554C2×C4—91no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—362no—
563C2×C4—362no—
564C2×C4—362no—
565C2×C4—721no—
566C2×C4D4×C3⋊D311yescharacteristic
567C2×C4D4×C3⋊D311yescharacteristic
568C2×C4C23×C3⋊D311yescharacteristic
569C8—21no—
570C8—181no—
571C8—181no—
572C8D4×C3⋊D312yes—
573C2×C3—84no—
574C2×C3#571714yes—
575C2×C3D3×#13714yes—
576C2×C3#577814yes—
577D3—68no—
578D3—124no—
579D3—128no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—92no—
584C22—181no—
585C22—181no—
586C22—181no—
587C22—182no—
588C22—181no—
589C22—181no—
590C22—361no—
591C22—361no—
592C22—724no—
593C22C2×D4×C3⋊D311yescharacteristic
594C4—21no—
595C4—21no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—181no—
600C4—181no—
601C4—182no—
602C4—361no—
603C4—361no—
604C4C2×D4×C3⋊D311yescharacteristic
605C4#6436111yescharacteristic
606C3#8188114yescomplemented
607C2—81no—
608C2—182no—
609C2—361no—
610C2—362no—
611C2#1059618811yescharacteristic
612C2C3⋊D3×#13711yescharacteristic
613C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#497C2
socleC22×C32C22×D4
prime radical#10596147C2
hypercenter#497C3⋊D3
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#64127C2semidirect
2. C2×SD16×C3⋊D3C2semidirect
3. #10596198C2semidirect
5. C32×#497C2semidirect
6. #10592887C2semidirect
7. #10592886C2semidirect
8. #10592885C2semidirect
9. #10592873C2semidirect
10. #10592869C2semidirect
11. #10592868C2semidirect
12. #10592782C2semidirect
13. #10592753C2semidirect
14. #10592409C2semidirect
15. #10592405C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
21. C2×C32×Q16C22semidirect
22. C2×C32×Q16C22semidirect
25. C32×C4⋊Q8C22semidirect
29. #64155C22semidirect
30. C2×#3756C22semidirect
38. C2×#3743C22semidirect
50. C4×#634C22semidirect
51. C32×#97C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
54. #63662C22semidirect
58. #63647C22semidirect
59. #63645C22semidirect
60. #63643C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#497D3semidirect
136. #3744D4semidirect
144. C2×C3×Q16C2×D3semidirect
145. C2×C3×Q16C2×D3semidirect
148. C3×C4⋊Q8C2×D3semidirect
174. C3×#97C2×D3semidirect
237. #497C3⋊D3semidirect
323. C2×C3⋊D3#137semidirect
342. C2×Q16C2×C3⋊D3semidirect
343. C2×Q16C2×C3⋊D3semidirect
354. C4⋊Q8C2×C3⋊D3semidirect
380. #97C2×C3⋊D3semidirect
524. C32#3266semidirect
606. C3#81881semidirect

Maximal subgroups

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

subgroupindex
C2×#641272
C2×SD16×C3⋊D32
#105961982
#105961472
C32×#4972
#105928872
#105928862
#105928852
#105928732
#105928692
#105928682
#105927822
#105927532
#105924092
#105924052
#818813