Finite Group Databasebeta

← #11884085

Subgroups — #11884085

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×#64124C211yesmaximal, characteristic, complemented
2C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596198C211yesmaximal, characteristic, complemented
4#10596025C211yesmaximal, characteristic
5C32×#461C211yesmaximal, characteristic, complemented
6#10592872C211yesmaximal, characteristic, complemented
7#10592868C211yesmaximal, characteristic, complemented
8#10592785C211yesmaximal, characteristic, complemented
9#10592717C211yesmaximal, characteristic, complemented
10#10592544C211yesmaximal, characteristic, complemented
11#10592535C211yesmaximal, characteristic, complemented
12#10592512C211yesmaximal, characteristic, complemented
13#10592511C211yesmaximal, characteristic, complemented
14#10592508C211yesmaximal, characteristic, complemented
15#10592505C211yesmaximal, characteristic, complemented
16#80444—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic
25#64155C2211yescharacteristic
26#64155C2211yescharacteristic, complemented
27C2×#3756C2211yescharacteristic, complemented
28C2×#3756C2211yescharacteristic, complemented
29C2×#3755C2211yescharacteristic
30C2×#3755C2211yescharacteristic
31C2×#3754C2211yescharacteristic
32#64139—21no—
33C2×#3752—21no—
34#64124—24no—
35SD16×C3⋊D3—24no—
36C2×#3746C2211yescharacteristic, complemented
37C2×#3744C2211yescharacteristic
38C2×#3743C2211yescharacteristic, complemented
39C2×C8×C3⋊D3C2211yescharacteristic
40#64106C2211yescharacteristic
41#64105—21no—
42#64105—21no—
43#64104C2211yescharacteristic
44#64102—21no—
45#64097—21no—
46#64095—21no—
47#64091—21no—
48#64084C2211yescharacteristic
49C4×C4⋊(C3⋊D3)C2211yescharacteristic
50C4×#634C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54#63659C2211yescharacteristic
55#63648C2211yescharacteristic
56#63647C2211yescharacteristic
57#63647C2211yescharacteristic, complemented
58#63643C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63634C2211yescharacteristic, complemented
61#63630C2211yescharacteristic, complemented
62C2×#915—34no—
63C2×D3×SD16—34no—
64#5727—34no—
65#5554—34no—
66C3×#461D314yescomplemented
67#5173—34no—
68#5169—34no—
69#5086—34no—
70#5018—34no—
71#4845—34no—
72#4836—34no—
73#4813—34no—
74#4812—34no—
75#4809—34no—
76#4806—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C2×#638—21no—
83C2×#638—21no—
84C22×C3⋊Dic3—21no—
85Q8×C3⋊D3—22no—
86Q8×C3⋊D3—22no—
87Q8×C3⋊D3—41no—
88Q8×C3⋊D3—41no—
89#3830—22no—
90#3830—41no—
91D4×C3⋊D3—22no—
92D4×C3⋊D3—41no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)D411yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634—21no—
101C2×#634—21no—
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C32×SD16—22no—
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3756—22no—
114#3756—41no—
115#3755—22no—
116#3755—41no—
117#3754D414yescomplemented
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752—21no—
124#3752D411yescharacteristic
125#3752D411yescharacteristic
126C4⋊(C3⋊Dic3)—21no—
127C4⋊(C3⋊Dic3)D411yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3750—21no—
131#3750—21no—
132C4×C3⋊Dic3—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135#3746—22no—
136#3744—22no—
137#3743—22no—
138C8×C3⋊D3—22no—
139#3266—91noSylow
140C2×D3×Q8—34no—
141C2×D3×Q8—34no—
142C2×#237—34no—
143C2×D3×D4—34no—
144C2×C3×SD16C2×D314yes—
145C2×C3×SD16C2×D314yes—
146C3×C4⋊Q8C2×D314yescomplemented
147C3×C4×D4C2×D314yes—
148#946—34no—
149#946—34no—
150C2×#216—34no—
151C2×#216—34no—
152C2×#215—34no—
153C2×#215—34no—
154C2×#214—34no—
155#930—64no—
156C2×(C2×D3)⋊C4—64no—
157#915—616no—
158D3×SD16—616no—
159C2×Dic12—34no—
160C2×#204—34no—
161C2×ΓL(1,𝔽25)—34no—
162C2×D3×C8—34no—
163#897—34no—
164#896—64no—
165#896—64no—
166#895—34no—
167#893—64no—
168#888—64no—
169#886—64no—
170#882—64no—
171#875—34no—
172C4×D12—34no—
173C4×Dic6—34no—
174C3×C4⋊C8C2×D314yescomplemented
175C3×#103C2×D314yescomplemented
176C3×#103C2×D314yescomplemented
177#832—34no—
178#821—34no—
179(C2×D3)⋊C8—34no—
180(C2×D3)⋊C8—34no—
181#816—34no—
182#810—34no—
183#807—34no—
184#803—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×D4—21no—
197C32×D4C2×D412yes—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—81no—
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2411yescharacteristic
205#638—42no—
206#638—42no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—42no—
211C2×C3⋊Dic3C2×D411yescharacteristic
212C2×C3⋊Dic3C2×D411yescharacteristic
213C4⋊(C3⋊D3)—22no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—21no—
216C4⋊(C3⋊D3)—81no—
217C4×C3⋊D3—21no—
218C4×C3⋊D3—21no—
219C4×C3⋊D3—21no—
220C4×C3⋊D3—21no—
221C4×C3⋊D3—42no—
222C4×C3⋊D3—42no—
223#634—21no—
224#634—21no—
225#634—21no—
226#634—42no—
227#634—42no—
228#634C2×D412yes—
229C32×C8—21no—
230C32×C8—21no—
231C3⋊(C3⋊C8)—21no—
232C3⋊(C3⋊C8)C2×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#461C3⋊D311yescharacteristic, complemented
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×D4C22×D314yes—
252C22×C3×C4—24no—
253C2×#67—64no—
254C2×#67—64no—
255C22×Dic3—64no—
256D3×Q8—68no—
257D3×Q8—68no—
258D3×Q8—124no—
259D3×Q8—124no—
260#237—68no—
261#237—124no—
262D3×D4—68no—
263D3×D4—124no—
264C2×D12—34no—
265C2×D12—34no—
266C2×D12—64no—
267C2×C4×D3—34no—
268C2×C4×D3—34no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×Dic6—34no—
272C2×Dic6—34no—
273C2×Dic6—64no—
274C2×Dic6—64no—
275C3×SD16—28no—
276C3×SD16—28no—
277C2×C3×C8C22×D314yes—
278C2×C3×C8C22×D314yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4C22×D314yes—
282C3×C22⋊C4—24no—
283C3×C42C22×D314yes—
284#216—68no—
285#216—124no—
286#215—68no—
287#215—124no—
288#214—316no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—34no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
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—64no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303C4×Dic3—64no—
304C2×C3⋊C8—34no—
305C2×C3⋊C8—34no—
306Dic12—68no—
307#204—68no—
308ΓL(1,𝔽25)—68no—
309D3×C8—68no—
310C22×C32—22no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—21no—
315C2×C3⋊D3—21no—
316C2×C3⋊D3—21no—
317C2×C3⋊D3—21no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—41no—
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×Q16—91no—
343C2×Q16—91no—
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#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#103C2×C3⋊D311yescharacteristic, complemented
375#103C2×C3⋊D311yescharacteristic, complemented
376#102—91no—
377#102—91no—
378C22⋊C8—91no—
379C22⋊C8—91no—
380#97—91no—
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×D4—24no—
393C3×D4D3×D418yes—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—84no—
398C2×C3×C4D3×D414yes—
399C2×C3×C4D3×D414yes—
400C2×C3×C4C23×D314yes—
401#67—128no—
402#67—128no—
403C2×Dic3—34no—
404C2×Dic3—34no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—128no—
409D12—68no—
410D12—64no—
411D12—64no—
412D12—244no—
413C4×D3—64no—
414C4×D3—64no—
415C4×D3—64no—
416C4×D3—64no—
417C4×D3—128no—
418C4×D3—128no—
419Dic6—38no—
420Dic6—64no—
421Dic6—64no—
422Dic6—64no—
423Dic6—128no—
424Dic6—128no—
425C3×C8—24no—
426C3×C8—24no—
427C3⋊C8—38no—
428C3⋊C8—64no—
429C2×C32—42no—
430C2×C32D4211yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C2×C32#57711yescharacteristic
433C3⋊D3—22no—
434C3⋊D3—41no—
435C3⋊D3—81no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—91no—
440C2×Q8—91no—
441C2×Q8—181no—
442C2×Q8—181no—
443C2×Q8—182no—
444C2×Q8—182no—
445C2×Q8—361no—
446C2×Q8—361no—
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—21no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4—181no—
463Q16—182no—
464Q16—182no—
465Q16—361no—
466SD16—22no—
467SD16—22no—
468SD16—94no—
469SD16—182no—
470SD16—182no—
471SD16—361no—
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—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4C22×C3⋊D311yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—91no—
489C22⋊C4—91no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C42—181no—
497C42C22×C3⋊D311yescharacteristic
498C22×C3—28no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3C2×D3×D414yes—
502C2×D3—38no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—124no—
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#100914yes—
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—92no—
537Q8—181no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8—362no—
542D4—21no—
543D4—182no—
544D4—181no—
545D4—181no—
546D4—362no—
547D4—362no—
548D4—721no—
549D4D4×C3⋊D312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—81no—
554C2×C4—91no—
555C2×C4—91no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—362no—
564C2×C4—362no—
565C2×C4—362no—
566C2×C4D4×C3⋊D311yescharacteristic
567C2×C4D4×C3⋊D311yescharacteristic
568C2×C4C23×C3⋊D311yescharacteristic
569C8—21no—
570C8—21no—
571C8—92no—
572C8—181no—
573C2×C3—48no—
574C2×C3#560914yes—
575C2×C3#576214yes—
576C2×C3D3×#13714yes—
577D3—68no—
578D3—124no—
579D3—244no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—92no—
584C22—181no—
585C22—181no—
586C22—181no—
587C22—181no—
588C22—181no—
589C22—361no—
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#6436611yescharacteristic
606C3#8044414yescomplemented
607C2—42no—
608C2—182no—
609C2—361no—
610C2—721no—
611C2#1059608011yescharacteristic
612C2#1059623311yescharacteristic
613C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radical#10596025C2
hypercenter#461C3⋊D3
hypocenterC32#3266
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
1. C2×#64124C2semidirect
2. C2×SD16×C3⋊D3C2semidirect
3. #10596198C2semidirect
5. C32×#461C2semidirect
6. #10592872C2semidirect
7. #10592868C2semidirect
8. #10592785C2semidirect
9. #10592717C2semidirect
10. #10592544C2semidirect
11. #10592535C2semidirect
12. #10592512C2semidirect
13. #10592511C2semidirect
14. #10592508C2semidirect
15. #10592505C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
23. C32×C4⋊Q8C22semidirect
26. #64155C22semidirect
27. C2×#3756C22semidirect
28. C2×#3756C22semidirect
36. C2×#3746C22semidirect
38. C2×#3743C22semidirect
50. C4×#634C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#103C22semidirect
53. C32×#103C22semidirect
57. #63647C22semidirect
58. #63643C22semidirect
59. #63637C22semidirect
60. #63634C22semidirect
61. #63630C22semidirect
66. C3×#461D3semidirect
117. #3754D4semidirect
146. C3×C4⋊Q8C2×D3semidirect
174. C3×C4⋊C8C2×D3semidirect
175. C3×#103C2×D3semidirect
176. C3×#103C2×D3semidirect
241. #461C3⋊D3semidirect
323. C2×C3⋊D3#137semidirect
354. C4⋊Q8C2×C3⋊D3semidirect
371. C4⋊C8C2×C3⋊D3semidirect
374. #103C2×C3⋊D3semidirect
375. #103C2×C3⋊D3semidirect
524. C32#3266semidirect
606. C3#80444semidirect

Maximal subgroups

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

subgroupindex
C2×#641242
C2×SD16×C3⋊D32
#105961982
#105960252
C32×#4612
#105928722
#105928682
#105927852
#105927172
#105925442
#105925352
#105925122
#105925112
#105925082
#105925052
#804443