Finite Group Databasebeta

← #11884082

Subgroups — #11884082

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×#64118C211yesmaximal, characteristic, complemented
2C22×#3744C211yesmaximal, characteristic, complemented
3#10596021C211yesmaximal, characteristic
4D4×#634C211yesmaximal, characteristic, complemented
5C32×#435C211yesmaximal, characteristic, complemented
6#10592833C211yesmaximal, characteristic, complemented
7#10592815C211yesmaximal, characteristic, complemented
8#10592544C211yesmaximal, characteristic, complemented
9#10592540C211yesmaximal, characteristic, complemented
10#10592438C211yesmaximal, characteristic, complemented
11#10592437C211yesmaximal, characteristic, complemented
12#10592432C211yesmaximal, characteristic, complemented
13#10592430C211yesmaximal, characteristic, complemented
14#10592414C211yesmaximal, characteristic, complemented
15#10592409C211yesmaximal, characteristic, complemented
16#79495—34nomaximal
17C2×#3828C2211yescharacteristic
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×#634C2211yescharacteristic, complemented
21C2×C32×M16C2211yescharacteristic, complemented
22C22×C32×C8C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24#64146—21no—
25D4×C3⋊Dic3—21no—
26#64139C2211yescharacteristic
27#64133C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic, complemented
30#64118—24no—
31C2×#3746C2211yescharacteristic, complemented
32C2×#3746C2211yescharacteristic, complemented
33C2×#3746C2211yescharacteristic, complemented
34C2×#3744—24no—
35C2×#3744C2211yescharacteristic
36C2×#3744C2211yescharacteristic
37C2×#3744C2211yescharacteristic
38C2×#3744C2211yescharacteristic
39C2×#3744C2211yescharacteristic
40C2×#3744C2211yescharacteristic
41#64103—21no—
42#64097—21no—
43#64093—21no—
44C22⋊C4×C3⋊D3—21no—
45#64087—21no—
46#64087—21no—
47#64084C2211yescharacteristic
48C4×C4⋊(C3⋊D3)C2211yescharacteristic
49#64078C2211yescharacteristic, complemented
50C4×#634C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×C22⋊C8C2211yescharacteristic
53C32×C22⋊C8C2211yescharacteristic, complemented
54C32×#97C2211yescharacteristic, complemented
55#63648C2211yescharacteristic
56#63648C2211yescharacteristic
57#63645C2211yescharacteristic, complemented
58#63643C2211yescharacteristic, complemented
59#63643C2211yescharacteristic, complemented
60#63643C2211yescharacteristic, complemented
61#63643C2211yescharacteristic, complemented
62C2×#909—34no—
63C22×#204—34no—
64#5550—34no—
65D4×Dic6—34no—
66C3×#435D314yescomplemented
67#5134—34no—
68#5116—34no—
69#4845—34no—
70#4841—34no—
71#4739—34no—
72#4738—34no—
73#4733—34no—
74#4731—34no—
75#4715—34no—
76#4710—34no—
77C23×C3⋊D3—21no—
78C2×C32×D4D411yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×#638—21no—
82C2×#638—21no—
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—21no—
85#3828—22no—
86#3828—41no—
87C2×C4⋊(C3⋊D3)—22no—
88C2×C4⋊(C3⋊D3)—21no—
89C2×C4⋊(C3⋊D3)—41no—
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—21no—
94C2×#634—22no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—21no—
98C2×#634—41no—
99C2×#634—41no—
100C2×#634C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C32×M16—22no—
105C2×C32×C8—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116#3757—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3750—21no—
127#3750—21no—
128#3750—21no—
129C4×C3⋊Dic3—21no—
130#3746—22no—
131#3746—22no—
132#3746—41no—
133#3744—22no—
134#3744—22no—
135#3744—22no—
136#3744—22no—
137#3744—41no—
138#3744D414yescomplemented
139#3266—91noSylow
140C2×#235—34no—
141C22×D12—34no—
142C22×Dic6—34no—
143C22×Dic6—34no—
144C2×C3×M16C2×D314yescomplemented
145C22×C3×C8C2×D314yes—
146C3×C4×D4C2×D314yes—
147#937—64no—
148D4×Dic3—64no—
149#930—34no—
150#924—34no—
151#924—34no—
152#924—34no—
153#909—616no—
154C2×Dic12—34no—
155C2×Dic12—34no—
156C2×Dic12—34no—
157C2×#204—34no—
158C2×#204—34no—
159C2×#204—34no—
160C2×#204—34no—
161C2×#204—34no—
162C2×#204—34no—
163C2×#204—616no—
164#894—64no—
165#888—64no—
166#884—64no—
167D3×C22⋊C4—64no—
168#878—64no—
169#878—64no—
170#875—34no—
171C4×D12—34no—
172#869—34no—
173C4×Dic6—34no—
174C3×C4⋊C8C2×D314yescomplemented
175C3×C22⋊C8C2×D314yes—
176C3×C22⋊C8C2×D314yescomplemented
177C3×#97C2×D314yescomplemented
178#821—34no—
179#821—34no—
180#818—34no—
181#816—34no—
182#816—34no—
183#816—34no—
184#816—34no—
185C23×C32C2×D411yescharacteristic
186C23×C32C2×D411yescharacteristic
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—42no—
190C22×C3⋊D3—42no—
191C22×C3⋊D3—81no—
192C32×D4—22no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2411yescharacteristic
202#638—42no—
203#638—81no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—42no—
211C2×C3⋊Dic3—42no—
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—42no—
216C4⋊(C3⋊D3)C2×D412yes—
217C4×C3⋊D3—42no—
218C4×C3⋊D3—81no—
219#634—21no—
220#634—21no—
221#634—21no—
222#634—21no—
223#634—21no—
224#634—21no—
225#634—21no—
226#634—42no—
227#634—42no—
228#634C2×D412yes—
229C32×C8—21no—
230C32×C8—21no—
231C32×C8—21no—
232C32×C8C2×D412yes—
233C2×#137—91no—
234C22×SD16—91no—
235D4×Q8—91no—
236#546—91no—
237#497—91no—
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#435C3⋊D311yescharacteristic, complemented
248C23×D3—64no—
249C2×C3×D4D1214yes—
250C22×C3×C4C22×D314yes—
251C22×C3×C4C22×D314yes—
252C2×#67—64no—
253C2×#67—64no—
254C22×Dic3—64no—
255C22×Dic3—64no—
256#235—68no—
257#235—124no—
258C2×D12—34no—
259C2×D12—34no—
260C2×D12—68no—
261C2×D12—64no—
262C2×D12—124no—
263C2×C4×D3—64no—
264C2×C4×D3—64no—
265C2×Dic6—34no—
266C2×Dic6—34no—
267C2×Dic6—34no—
268C2×Dic6—34no—
269C2×Dic6—68no—
270C2×Dic6—68no—
271C2×Dic6—64no—
272C2×Dic6—64no—
273C2×Dic6—124no—
274C2×Dic6—124no—
275C3×M16—28no—
276C2×C3×C8—28no—
277C2×C3×C8C22×D314yes—
278C2×C3×C8C22×D314yes—
279C2×C3×C8C22×D314yes—
280C2×C3×C8C22×D314yes—
281C3×C4⋊C4D1214yes—
282C3×C22⋊C4D1214yes—
283C3×C22⋊C4D1214yes—
284C3×C42C22×D314yes—
285#217—64no—
286#217—64no—
287#217—64no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—64no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—64no—
292C4⋊Dic3—34no—
293C4⋊Dic3—34no—
294C4⋊Dic3—64no—
295C4⋊Dic3—64no—
296Dic3⋊C4—64no—
297Dic3⋊C4—64no—
298Dic3⋊C4—64no—
299Dic3⋊C4—64no—
300C4×Dic3—64no—
301Dic12—68no—
302Dic12—68no—
303Dic12—124no—
304#204—316no—
305#204—68no—
306#204—68no—
307#204—68no—
308#204—68no—
309#204—124no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32#13712yescomplemented
316C22×C32C22×D411yescharacteristic
317C2×C3⋊D3—22no—
318C2×C3⋊D3—41no—
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—84no—
324C32×C4—21no—
325C32×C4—21no—
326C32×C4—21no—
327C32×C4—21no—
328C32×C4C22×D411yescharacteristic
329C32×C4H(5,𝔽2)11yescharacteristic
330C3⋊Dic3—22no—
331C3⋊Dic3—41no—
332C3⋊Dic3—41no—
333C3⋊Dic3—41no—
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×Q16—91no—
343C2×Q16—91no—
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—91no—
350C2×SD16—184no—
351C2×M16C2×C3⋊D311yescharacteristic, complemented
352C22×C8C2×C3⋊D311yescharacteristic
353C4⋊Q8—91no—
354C4⋊Q8—181no—
355#124—91no—
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—181no—
368C4×D4C2×C3⋊D311yescharacteristic
369C2×C22⋊C4—181no—
370#107—91no—
371C4⋊C8C2×C3⋊D311yescharacteristic, complemented
372#103—91no—
373#103—91no—
374#103—91no—
375#103—91no—
376#102—91no—
377#102—91no—
378C22⋊C8C2×C3⋊D311yescharacteristic
379C22⋊C8C2×C3⋊D311yescharacteristic, complemented
380#97C2×C3⋊D311yescharacteristic, complemented
381C23×C3C2×D1214yes—
382C23×C3C2×D1214yes—
383C22×D3—64no—
384C22×D3—64no—
385C22×D3—128no—
386C22×D3—128no—
387C22×D3—244no—
388C3×D4—28no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4C2×D1214yes—
394C2×C3×C4C2×D1214yes—
395C2×C3×C4C2×D1214yes—
396C2×C3×C4C2×D1214yes—
397C2×C3×C4C23×D314yes—
398#67—128no—
399#67—244no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—128no—
407C2×Dic3—128no—
408D12—38no—
409D12—64no—
410D12—64no—
411D12—64no—
412D12—128no—
413C4×D3—128no—
414C4×D3—244no—
415Dic6—38no—
416Dic6—64no—
417Dic6—64no—
418Dic6—64no—
419Dic6—64no—
420Dic6—64no—
421Dic6—64no—
422Dic6—64no—
423Dic6—128no—
424Dic6—128no—
425C3×C8—24no—
426C3×C8—24no—
427C3×C8—24no—
428C3×C8D3×D418yes—
429C2×C32—22no—
430C2×C32—41no—
431C2×C32D4211yescharacteristic
432C2×C32C2×#13711yescharacteristic
433C2×C32#57711yescharacteristic
434C3⋊D3—42no—
435C3⋊D3—81no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—91no—
440C2×Q8—91no—
441C2×Q8—91no—
442C2×Q8—91no—
443C2×Q8—182no—
444C2×Q8—182no—
445C2×Q8—181no—
446C2×Q8—181no—
447C2×Q8—361no—
448C2×Q8—361no—
449C2×D4—91no—
450C2×D4—91no—
451C2×D4—182no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—181no—
455C2×D4—361no—
456C2×D4C4⋊(C3⋊D3)11yescharacteristic
457C22×C4—181no—
458C22×C4—181no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4C22×C3⋊D311yescharacteristic
462C22×C4C22×C3⋊D311yescharacteristic
463Q16—182no—
464Q16—182no—
465Q16—361no—
466SD16—94no—
467SD16—182no—
468SD16—182no—
469SD16—182no—
470SD16—182no—
471SD16—361no—
472M16—22no—
473C2×C8—22no—
474C2×C8C22×C3⋊D311yescharacteristic
475C2×C8C22×C3⋊D311yescharacteristic
476C2×C8C22×C3⋊D311yescharacteristic
477C2×C8C22×C3⋊D311yescharacteristic
478C4⋊C4—91no—
479C4⋊C4—91no—
480C4⋊C4—181no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
487C22⋊C4—181no—
488C22⋊C4—181no—
489C22⋊C4—181no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
495C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
496C42—181no—
497C42C22×C3⋊D311yescharacteristic
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—24no—
503C22×C3#90918yescomplemented
504C22×C3C22×D1214yes—
505C2×D3—68no—
506C2×D3—124no—
507C2×D3—124no—
508C2×D3—124no—
509C2×D3—124no—
510C2×D3—124no—
511C2×D3—2416no—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—24no—
515C3×C4—24no—
516C3×C4C2×D3×D414yes—
517C3×C4#100914yes—
518Dic3—68no—
519Dic3—124no—
520Dic3—124no—
521Dic3—124no—
522Dic3—124no—
523Dic3—124no—
524C32#326611yescharacteristic, complemented, Sylow
525C23—181no—
526C23—181no—
527C23—362no—
528C23—362no—
529C23—721no—
530C23C2×C4⋊(C3⋊D3)11yescharacteristic
531C23C2×C4⋊(C3⋊D3)11yescharacteristic
532Q8—92no—
533Q8—181no—
534Q8—181no—
535Q8—181no—
536Q8—181no—
537Q8—181no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8—362no—
542D4—22no—
543D4—92no—
544D4—181no—
545D4—181no—
546D4—181no—
547D4—362no—
548D4—362no—
549D4—721no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—362no—
561C2×C4—362no—
562C2×C4—362no—
563C2×C4—721no—
564C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
565C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
566C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
567C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
568C2×C4C23×C3⋊D311yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8D4×C3⋊D312yes—
573C2×C3—28no—
574C2×C3—44no—
575C2×C3D4×D1214yes—
576C2×C3C2×#90914yes—
577C2×C3#575114yes—
578D3—128no—
579D3—244no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—182no—
586C22—361no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22—361no—
591C22—724no—
592C22#6411812yescomplemented
593C22C22×C4⋊(C3⋊D3)11yescharacteristic
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—182no—
599C4—361no—
600C4—361no—
601C4—361no—
602C4—361no—
603C4—361no—
604C4C2×D4×C3⋊D311yescharacteristic
605C4#6436611yescharacteristic
606C3#7949514yescomplemented
607C2—22no—
608C2—41no—
609C2—362no—
610C2—721no—
611C2D4×C4⋊(C3⋊D3)11yescharacteristic
612C2C2×#6411811yescharacteristic
613C2#1059622211yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#435C2
socleC22×C32C22×D4
prime radical#10596021C2
hypercenter#435C3⋊D3
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#64118C2semidirect
2. C22×#3744C2semidirect
4. D4×#634C2semidirect
5. C32×#435C2semidirect
6. #10592833C2semidirect
7. #10592815C2semidirect
8. #10592544C2semidirect
9. #10592540C2semidirect
10. #10592438C2semidirect
11. #10592437C2semidirect
12. #10592432C2semidirect
13. #10592430C2semidirect
14. #10592414C2semidirect
15. #10592409C2semidirect
20. C22×#634C22semidirect
21. C2×C32×M16C22semidirect
29. #64133C22semidirect
31. C2×#3746C22semidirect
32. C2×#3746C22semidirect
33. C2×#3746C22semidirect
49. #64078C22semidirect
50. C4×#634C22semidirect
51. C32×C4⋊C8C22semidirect
53. C32×C22⋊C8C22semidirect
54. C32×#97C22semidirect
57. #63645C22semidirect
58. #63643C22semidirect
59. #63643C22semidirect
60. #63643C22semidirect
61. #63643C22semidirect
66. C3×#435D3semidirect
138. #3744D4semidirect
144. C2×C3×M16C2×D3semidirect
174. C3×C4⋊C8C2×D3semidirect
176. C3×C22⋊C8C2×D3semidirect
177. C3×#97C2×D3semidirect
247. #435C3⋊D3semidirect
315. C22×C32#137semidirect
351. C2×M16C2×C3⋊D3semidirect
371. C4⋊C8C2×C3⋊D3semidirect
379. C22⋊C8C2×C3⋊D3semidirect
380. #97C2×C3⋊D3semidirect
503. C22×C3#909semidirect
524. C32#3266semidirect
592. C22#64118semidirect
606. C3#79495semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
C22×#37442
#105960212
D4×#6342
C32×#4352
#105928332
#105928152
#105925442
#105925402
#105924382
#105924372
#105924322
#105924302
#105924142
#105924092
#794953