Finite Group Databasebeta

← #11884076

Subgroups — #11884076

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
1Q8×#638C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic, complemented
3C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
4#10596083C211yesmaximal, characteristic
5C32×#448C211yesmaximal, characteristic, complemented
6#10592868C211yesmaximal, characteristic, complemented
7#10592866C211yesmaximal, characteristic, complemented
8#10592865C211yesmaximal, characteristic, complemented
9#10592741C211yesmaximal, characteristic, complemented
10#10592517C211yesmaximal, characteristic, complemented
11#10592516C211yesmaximal, characteristic, complemented
12#10592512C211yesmaximal, characteristic, complemented
13#10592508C211yesmaximal, characteristic, complemented
14#10592432C211yesmaximal, characteristic, complemented
15#10592427C211yesmaximal, characteristic, complemented
16#80061—34nomaximal
17C22×C32×Q8C2211yescharacteristic, complemented
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×#3828C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C32×#121C2211yescharacteristic
24#64155—21no—
25#64155C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic, complemented
27#64153—21no—
28#64153C2211yescharacteristic, complemented
29C2×#3756C2211yescharacteristic, complemented
30C2×#3756C2211yescharacteristic, complemented
31#64151—24no—
32C2×#3755C2211yescharacteristic
33C2×#3755C2211yescharacteristic
34#64147—21no—
35#64146—21no—
36#64145C2211yescharacteristic
37C2×#3754C2211yescharacteristic
38C4×#638—21no—
39C4×#638C2211yescharacteristic
40#64133—21no—
41#64133C2211yescharacteristic, complemented
42C2×#3748C2211yescharacteristic, complemented
43SD16×C3⋊D3—24no—
44C2×#3746C2211yescharacteristic, complemented
45C2×#3744C2211yescharacteristic
46C2×C8×C3⋊D3C2211yescharacteristic
47#64106C2211yescharacteristic
48#64102C2211yescharacteristic
49#64092—21no—
50C22⋊C4×C3⋊D3—21no—
51C32×#103C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63659C2211yescharacteristic
55#63648C2211yescharacteristic
56#63647C2211yescharacteristic
57#63643C2211yescharacteristic, complemented
58#63642C2211yescharacteristic, complemented
59#63641C2211yescharacteristic, complemented
60#63637C2211yescharacteristic, complemented
61#63634C2211yescharacteristic, complemented
62Q8×#67—34no—
63C2×#942—34no—
64C2×D3×SD16—34no—
65#5612—34no—
66C3×#448D314yescomplemented
67#5169—34no—
68#5167—34no—
69#5166—34no—
70#5042—34no—
71#4818—34no—
72#4817—34no—
73#4813—34no—
74#4809—34no—
75#4733—34no—
76#4728—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8—21no—
79C2×C32×Q8—22no—
80C2×C32×Q8—41no—
81C2×C32×Q8C2311yescharacteristic
82C2×C32×Q8C2311yescharacteristic
83C2×C32×D4—21no—
84C2×C32×D4C2311yescharacteristic
85C22×C32×C4—21no—
86C22×C32×C4C2311yescharacteristic
87C2×#638—21no—
88C2×#638—21no—
89C2×#638D411yescharacteristic
90Q8×C3⋊D3—22no—
91Q8×C3⋊D3—41no—
92D4×C3⋊D3—22no—
93D4×C3⋊D3—41no—
94#3828—22no—
95#3828—41no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634—21no—
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C32×SD16—22no—
105C32×SD16—41no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110#3757—21no—
111#3757—21no—
112#3757—21no—
113#3757D411yescharacteristic
114#3756—22no—
115#3756—22no—
116#3755—22no—
117#3755D414yescomplemented
118#3754—22no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752D411yescharacteristic
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3750—21no—
128#3750—21no—
129#3750—21no—
130#3750D411yescharacteristic
131C4×C3⋊Dic3—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133#3748—22no—
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3746—41no—
137#3744—22no—
138C8×C3⋊D3—22no—
139#3266—91noSylow
140C22×C3×Q8C2×D314yescomplemented
141C2×D3×Q8—34no—
142C2×D3×D4—34no—
143C2×#235—34no—
144C2×C3×SD16C2×D314yes—
145C2×C3×SD16C2×D314yes—
146C3×#121C2×D314yes—
147#946—34no—
148#946—64no—
149Q8×Dic3—34no—
150#944—34no—
151#944—64no—
152C2×#216—34no—
153C2×#216—34no—
154#942—616no—
155C2×#215—34no—
156C2×#215—34no—
157#938—64no—
158#937—64no—
159#936—34no—
160C2×#214—34no—
161C4×#67—34no—
162C4×#67—64no—
163#924—34no—
164#924—64no—
165C2×#208—34no—
166D3×SD16—616no—
167C2×Dic12—34no—
168C2×#204—34no—
169C2×D3×C8—34no—
170#897—34no—
171#893—34no—
172#883—64no—
173D3×C22⋊C4—64no—
174C3×#103C2×D314yescomplemented
175C3×#103C2×D314yescomplemented
176C3×C22⋊C8C2×D314yescomplemented
177#832—34no—
178#821—34no—
179(C2×D3)⋊C8—34no—
180#816—34no—
181#815—34no—
182Dic3⋊C8—34no—
183#810—34no—
184#807—34no—
185C23×C32—21no—
186C23×C32C2×D411yescharacteristic
187C22×C3⋊D3—21no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3—42no—
190C22×C3⋊D3—81no—
191C22×C3⋊D3C2×D411yescharacteristic
192C32×Q8—21no—
193C32×Q8—21no—
194C32×Q8—21no—
195C32×Q8—42no—
196C32×Q8C2×D412yes—
197C32×D4—21no—
198C32×D4—21no—
199C32×D4—81no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—42no—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2411yescharacteristic
208#638—22no—
209#638—42no—
210#638—42no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3C2×D411yescharacteristic
215C2×C3⋊Dic3C2×D411yescharacteristic
216C2×C3⋊Dic3C2×D411yescharacteristic
217C4⋊(C3⋊D3)—21no—
218C4⋊(C3⋊D3)C2×D412yes—
219C4×C3⋊D3—21no—
220C4×C3⋊D3—21no—
221C4×C3⋊D3—42no—
222C4×C3⋊D3—42no—
223C4×C3⋊D3—81no—
224#634—21no—
225#634—21no—
226#634—21no—
227#634—21no—
228#634—42no—
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#461—91no—
242#452—91no—
243#451—91no—
244#450—91no—
245#448C3⋊D311yescharacteristic, complemented
246#440—91no—
247#435—91no—
248C23×D3—64no—
249C2×C3×Q8—24no—
250C2×C3×Q8—28no—
251C2×C3×Q8—44no—
252C2×C3×Q8C22×D314yes—
253C2×C3×Q8C22×D314yes—
254C2×C3×D4—24no—
255C2×C3×D4C22×D314yes—
256C22×C3×C4—24no—
257C22×C3×C4C22×D314yes—
258C2×#67—34no—
259C2×#67—64no—
260C2×#67—64no—
261D3×Q8—68no—
262D3×Q8—124no—
263D3×D4—68no—
264D3×D4—124no—
265#235—68no—
266#235—124no—
267C2×D12—34no—
268C2×C4×D3—34no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×Dic6—34no—
273C2×Dic6—34no—
274C2×Dic6—64no—
275C3×SD16—28no—
276C3×SD16—44no—
277C2×C3×C8C22×D314yes—
278C2×C3×C8C22×D314yes—
279C3×C4⋊C4C22×D314yes—
280C3×C22⋊C4—24no—
281#217—34no—
282#217—64no—
283#217—64no—
284#217—64no—
285#216—68no—
286#216—68no—
287#215—316no—
288#215—68no—
289#214—68no—
290(C2×D3)⋊C4—34no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294C4⋊Dic3—34no—
295C4⋊Dic3—64no—
296C4⋊Dic3—64no—
297Dic3⋊C4—34no—
298Dic3⋊C4—64no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302C4×Dic3—34no—
303C4×Dic3—64no—
304#208—68no—
305C2×C3⋊C8—34no—
306C2×C3⋊C8—34no—
307Dic12—124no—
308#204—68no—
309D3×C8—68no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32C22×D411yescharacteristic
317C2×C3⋊D3—21no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—84no—
323C2×C3⋊D3#13712yescomplemented
324C32×C4—22no—
325C32×C4—21no—
326C32×C4—41no—
327C32×C4—41no—
328C32×C4C22×D411yescharacteristic
329C32×C4H(5,𝔽2)11yescharacteristic
330C3⋊Dic3—21no—
331C3⋊Dic3—21no—
332C3⋊Dic3—21no—
333C3⋊Dic3—41no—
334C3⋊Dic3—41no—
335C3⋊Dic3—41no—
336C2×#41—91no—
337C22×Q8—91no—
338C22×Q8C2×C3⋊D311yescharacteristic, complemented
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—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—181no—
363#121C2×C3⋊D311yescharacteristic
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#103C2×C3⋊D311yescharacteristic, complemented
375#103C2×C3⋊D311yescharacteristic, complemented
376#102—91no—
377#102—91no—
378C22⋊C8—91no—
379C22⋊C8C2×C3⋊D311yescharacteristic, complemented
380#97—91no—
381C23×C3—24no—
382C23×C3D3×D414yes—
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—48no—
392C3×Q8D3×D418yes—
393C3×D4—24no—
394C3×D4—24no—
395C3×D4—84no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—48no—
402C2×C3×C4D3×D414yes—
403C2×C3×C4C23×D314yes—
404#67—68no—
405#67—128no—
406#67—128no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412C2×Dic3—64no—
413D12—38no—
414D12—64no—
415C4×D3—64no—
416C4×D3—64no—
417C4×D3—128no—
418C4×D3—128no—
419C4×D3—244no—
420Dic6—64no—
421Dic6—64no—
422Dic6—64no—
423Dic6—64no—
424Dic6—128no—
425C3×C8—24no—
426C3×C8—24no—
427C3⋊C8—38no—
428C3⋊C8—64no—
429C2×C32—41no—
430C2×C32—81no—
431C2×C32D4211yescharacteristic
432C2×C32C2×#13711yescharacteristic
433C2×C32#57711yescharacteristic
434C3⋊D3—22no—
435C3⋊D3—42no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—91no—
443C2×Q8—91no—
444C2×Q8—181no—
445C2×Q8—182no—
446C2×Q8—361no—
447C2×Q8C22×C3⋊D311yescharacteristic
448C2×Q8C22×C3⋊D311yescharacteristic
449C2×D4—21no—
450C2×D4—91no—
451C2×D4—91no—
452C2×D4—181no—
453C2×D4—182no—
454C2×D4—181no—
455C2×D4—361no—
456C2×D4C22×C3⋊D311yescharacteristic
457C22×C4—21no—
458C22×C4—91no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4C22×C3⋊D311yescharacteristic
463Q16—182no—
464Q16—182no—
465Q16—361no—
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—91no—
479C4⋊C4—91no—
480C4⋊C4—181no—
481C4⋊C4—181no—
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—91no—
497C42—181no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—44no—
502C22×C3—44no—
503C22×C3—44no—
504C22×C3C2×D3×D414yes—
505C2×D3—38no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—68no—
509C2×D3—124no—
510C2×D3—124no—
511C2×D3—2416no—
512C3×C4—28no—
513C3×C4—24no—
514C3×C4—44no—
515C3×C4—44no—
516C3×C4C2×D3×D414yes—
517C3×C4#100414yes—
518Dic3—64no—
519Dic3—64no—
520Dic3—64no—
521Dic3—124no—
522Dic3—124no—
523Dic3—124no—
524C32#326611yescharacteristic, complemented, Sylow
525C23—21no—
526C23—91no—
527C23—181no—
528C23—362no—
529C23—362no—
530C23—721no—
531C23D4×C3⋊D311yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—42no—
536Q8—181no—
537Q8—181no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8D4×C3⋊D312yes—
542D4—21no—
543D4—21no—
544D4—81no—
545D4—92no—
546D4—182no—
547D4—181no—
548D4—362no—
549D4—362no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—91no—
557C2×C4—91no—
558C2×C4—91no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—362no—
565C2×C4—362no—
566C2×C4—721no—
567C2×C4D4×C3⋊D311yescharacteristic
568C2×C4C23×C3⋊D311yescharacteristic
569C8—21no—
570C8—21no—
571C8—92no—
572C8—181no—
573C2×C3—44no—
574C2×C3—84no—
575C2×C3#559014yes—
576C2×C3#576214yes—
577C2×C3D3×#13714yes—
578D3—68no—
579D3—128no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—92no—
587C22—181no—
588C22—181no—
589C22—182no—
590C22—361no—
591C22—361no—
592C22—724no—
593C22C2×D4×C3⋊D311yescharacteristic
594C4—21no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—181no—
599C4—181no—
600C4—181no—
601C4—361no—
602C4—361no—
603C4—361no—
604C4C2×D4×C3⋊D311yescharacteristic
605C4#6436111yescharacteristic
606C3#8006114yescomplemented
607C2—41no—
608C2—81no—
609C2—182no—
610C2—362no—
611C2#1059606111yescharacteristic
612C2#1059623311yescharacteristic
613C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#448C2
socleC22×C32C22×D4
prime radical#10596083C2
hypercenter#448C3⋊D3
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×#638C2semidirect
2. C2×#64151C2semidirect
3. C2×SD16×C3⋊D3C2semidirect
5. C32×#448C2semidirect
6. #10592868C2semidirect
7. #10592866C2semidirect
8. #10592865C2semidirect
9. #10592741C2semidirect
10. #10592517C2semidirect
11. #10592516C2semidirect
12. #10592512C2semidirect
13. #10592508C2semidirect
14. #10592432C2semidirect
15. #10592427C2semidirect
17. C22×C32×Q8C22semidirect
26. Q8×C3⋊Dic3C22semidirect
28. #64153C22semidirect
29. C2×#3756C22semidirect
30. C2×#3756C22semidirect
41. #64133C22semidirect
42. C2×#3748C22semidirect
44. C2×#3746C22semidirect
51. C32×#103C22semidirect
52. C32×#103C22semidirect
53. C32×C22⋊C8C22semidirect
57. #63643C22semidirect
58. #63642C22semidirect
59. #63641C22semidirect
60. #63637C22semidirect
61. #63634C22semidirect
66. C3×#448D3semidirect
117. #3755D4semidirect
140. C22×C3×Q8C2×D3semidirect
174. C3×#103C2×D3semidirect
175. C3×#103C2×D3semidirect
176. C3×C22⋊C8C2×D3semidirect
245. #448C3⋊D3semidirect
323. C2×C3⋊D3#137semidirect
338. C22×Q8C2×C3⋊D3semidirect
374. #103C2×C3⋊D3semidirect
375. #103C2×C3⋊D3semidirect
379. C22⋊C8C2×C3⋊D3semidirect
524. C32#3266semidirect
606. C3#80061semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
C2×#641512
C2×SD16×C3⋊D32
#105960832
C32×#4482
#105928682
#105928662
#105928652
#105927412
#105925172
#105925162
#105925122
#105925082
#105924322
#105924272
#800613