Finite Group Databasebeta

← #11898303

Subgroups — #11898303

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593906C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3#10592529C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6#10590884C212yesmaximal, complemented
7#10590876C212yesmaximal, complemented
8#10590748C212yesmaximal, complemented
9#10590742C212yesmaximal, complemented
10#10590375C211yesmaximal, characteristic, complemented
11C4×#3715C211yesmaximal, characteristic, complemented
12#80420—31nomaximal
13#80378—31nomaximal
14C2×#3795—21no—
15C4×#634C2211yescharacteristic
16C2×C3×#204C2212yes—
17C2×C3×#204C2212yes—
18C3×#874C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63914C2212yes—
23#63908—21no—
24#63898C2212yes—
25#63885—22no—
26#63873C2212yes—
27#63869—21no—
28#63847—22no—
29#63844—21no—
30#63843C2212yes—
31C2×#3715C2212yes—
32C2×#3715C2211yescharacteristic
33C2×#3715C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37C4×C3⋊(C3⋊C8)C2211yescharacteristic
38C3×#821C2212yes—
39C3×#816C2212yes—
40#63574C2211yescharacteristic
41#63565C2211yescharacteristic
42#63562C2211yescharacteristic
43#5721—31no—
44#5718—31no—
45#5567—31no—
46#5553—31no—
47C3×#461—31no—
48C3×#460—31no—
49#5175—32no—
50#5175—32no—
51#5163—32no—
52#5162—32no—
53#5085—31no—
54#5076—31no—
55C4×#215—31no—
56C4×#214—31no—
57#4848D311yescharacteristic, complemented
58#4841D311yescharacteristic, complemented
59#4830—31no—
60#4830—31no—
61#4830—61no—
62#4818—32no—
63#4788—32no—
64#4762—32no—
65#4758—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×#625—22no—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)D411yescharacteristic
81#3750D412yes—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C3×#204—42no—
93C3×#204—42no—
94#3724—22no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99#3715—24no—
100#3715—22no—
101#3715—42no—
102#3392—91noSylow
103C2×#237—61no—
104C2×#235—61no—
105C2×C3×SD16—32no—
106C2×C3×SD16—32no—
107C3×C4⋊Q8—31no—
108C3×#127—31no—
109C3×C4×Q8—31no—
110C3×C4×D4—31no—
111Q8×Dic3—32no—
112#944—32no—
113#944—32no—
114C2×#215—31no—
115C2×#215—32no—
116C2×#215—32no—
117#940—32no—
118#940—32no—
119#939—62no—
120#938—61no—
121D4×Dic3—32no—
122C2×#214—31no—
123C2×#214—32no—
124C2×#214—32no—
125#930—61no—
126C2×#204C2×D312yes—
127C2×#204C2×D312yes—
128#893—32no—
129#890—61no—
130#889—62no—
131#889—62no—
132#887—32no—
133#887—61no—
134#884—62no—
135#874C2×D311yescharacteristic
136C4×D12C2×D311yescharacteristic
137#870—61no—
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C4×Dic6—61no—
143C4×Dic6C2×D311yescharacteristic
144C3×C4⋊C8—21no—
145C3×C4⋊C8C2×D311yescharacteristic
146C3×C4⋊C8C2×D311yescharacteristic
147C3×#103—32no—
148C3×#102—32no—
149#835—31no—
150#832—31no—
151#821C2×D312yes—
152#816C2×D312yes—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—62no—
156C8×Dic3—32no—
157C8×Dic3—32no—
158C8×Dic3—62no—
159#810—31no—
160#809—31no—
161#808—31no—
162#808—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—61no—
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3C2×D412yes—
172C2×C3⋊Dic3C2×D412yes—
173#634SD1614yescomplemented
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—22no—
181C3×D12—21no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—42no—
185C3×Dic6—21no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6—21no—
189#625—44no—
190#625—82no—
191D3×Dic3—44no—
192C32×C8—22no—
193C3⋊(C3⋊C8)—21no—
194C3⋊(C3⋊C8)#4112yescomplemented
195#557—91no—
196#550—91no—
197#492—91no—
198#492—92no—
199#461—31no—
200#461—92no—
201#460—31no—
202#460—92no—
203C8×Q8—91no—
204C4×SD16—92no—
205C4×SD16—91no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C22×Dic3—62no—
218#237—124no—
219#235—124no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C22×D311yescharacteristic
223C2×D12C22×D312yes—
224C2×C4×D3—21no—
225C2×C4×D3—62no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6C22×D311yescharacteristic
230C2×Dic6C22×D312yes—
231C3×SD16—122no—
232C3×SD16—122no—
233C2×C3×C8—22no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C22×D312yes—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C42—21no—
243C3×C42—61no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#215—62no—
248#215—64no—
249#215—122no—
250#214—64no—
251#214—62no—
252#214—122no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—32no—
265Dic3⋊C4—32no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272C4×Dic3—21no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—61no—
284#204—42no—
285#204—42no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—42no—
288C2×C3×D3—41no—
289C2×C3×D3—42no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—42no—
293C32×C4—21no—
294C32×C4C2×SD1612yes—
295C32×C4C2×#4111yescharacteristic
296C32×C4H(5,𝔽2)11yescharacteristic
297C3⋊Dic3—22no—
298C3⋊Dic3C2×SD1614yes—
299C3×Dic3—42no—
300C3×Dic3—41no—
301C3×Dic3—41no—
302C3×Dic3—41no—
303C2×#41—181no—
304C2×SD16—32no—
305C2×SD16—32no—
306C2×SD16—92no—
307C2×SD16—91no—
308C2×SD16—92no—
309C4⋊Q8—31no—
310C4⋊Q8—92no—
311#127—31no—
312#127—92no—
313#125—181no—
314#125—182no—
315#121—182no—
316#121—181no—
317C4×Q8—31no—
318C4×Q8—91no—
319C4×Q8—92no—
320C4×Q8—181no—
321C4×D4—31no—
322C4×D4—92no—
323#106—91no—
324C4⋊C8—92no—
325C4⋊C8D3211yescharacteristic
326#103—32no—
327#103—91no—
328#102—32no—
329#102—91no—
330C4×C8—92no—
331C4×C8—91no—
332C23×C3—62no—
333C23×C3—61no—
334C22×D3—21no—
335C22×D3—22no—
336C3×Q8—62no—
337C3×Q8—61no—
338C3×Q8—61no—
339C3×Q8—62no—
340C3×D4—62no—
341C3×D4—61no—
342C3×D4—62no—
343C3×D4—61no—
344C3×D4—122no—
345C3×D4—241no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—124no—
361#67—124no—
362#67—242no—
363#67—242no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—124no—
375D12—21no—
376D12—22no—
377D12—21no—
378D12—22no—
379D12—42no—
380D12—81no—
381C4×D3—42no—
382C4×D3—124no—
383Dic6—21no—
384Dic6—22no—
385Dic6—22no—
386Dic6—21no—
387Dic6—34no—
388Dic6—34no—
389Dic6—64no—
390C3×C8—22no—
391C3×C8—22no—
392C3×C8—42no—
393C3⋊C8—32no—
394C3⋊C8—32no—
395C3⋊C8—62no—
396C3⋊C8—61no—
397C3⋊C8—61no—
398C3⋊C8—121no—
399C2×C32#55011yescharacteristic
400C2×C32C22×SD1611yescharacteristic
401C2×C32#57711yescharacteristic
402C3×D3—81no—
403C3×D3—82no—
404#41—364no—
405C2×Q8—32no—
406C2×Q8—31no—
407C2×Q8—91no—
408C2×D4—32no—
409C2×D4—31no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—182no—
413C2×D4—182no—
414C22×C4—61no—
415C22×C4—182no—
416SD16—122no—
417SD16—122no—
418SD16—184no—
419SD16—182no—
420SD16—362no—
421C2×C8—91no—
422C2×C8—91no—
423C2×C8C2×D3212yes—
424C4⋊C4—31no—
425C4⋊C4—31no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—92no—
430C4⋊C4—91no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—182no—
434C22⋊C4—61no—
435C22⋊C4—182no—
436C42—61no—
437C42—92no—
438C42—182no—
439C42C2×D3211yescharacteristic
440C22×C3—21no—
441C22×C3—122no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—121no—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C2×D3×D411yescharacteristic
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—41no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4D3×SD1612yes—
466C3×C4D3×SD1612yes—
467C3×C4#100411yescharacteristic
468C3×C4#100411yescharacteristic
469C3×C4D3×#4111yescharacteristic
470C3×C4D3×#4111yescharacteristic
471Dic3—34no—
472Dic3—34no—
473Dic3—41no—
474Dic3—41no—
475Dic3—42no—
476Dic3—41no—
477Dic3—64no—
478Dic3—62no—
479Dic3—62no—
480Dic3—122no—
481C32#339211yescharacteristic, complemented, Sylow
482C23—61no—
483C23—62no—
484Q8—61no—
485Q8—62no—
486Q8—62no—
487Q8—61no—
488Q8—94no—
489D4—61no—
490D4—62no—
491D4—62no—
492D4—61no—
493D4—122no—
494D4—241no—
495D4—364no—
496D4—722no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—122no—
504C2×C4—364no—
505C2×C4#380211yescharacteristic
506C2×C4#380211yescharacteristic
507C2×C4C22×D3211yescharacteristic
508C8—22no—
509C8—92no—
510C8—181no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—242no—
515C2×C3—241no—
516C2×C3#559911yescharacteristic
517C2×C3#559911yescharacteristic
518C2×C3C2×D3×SD1611yescharacteristic
519C2×C3C2×D3×SD1611yescharacteristic
520C2×C3#577511yescharacteristic
521C2×C3#577811yescharacteristic
522D3—81no—
523D3—82no—
524C22—121no—
525C22—122no—
526C22—122no—
527C22—121no—
528C22—121no—
529C22—122no—
530C22C2×#380211yescharacteristic
531C4—21no—
532C4—94no—
533C4—121no—
534C4—121no—
535C4—121no—
536C4—122no—
537C4—182no—
538C4#6379612yes—
539C4#6431311yescharacteristic
540C4#6431911yescharacteristic
541C3—21no—
542C3#8037811yescharacteristic, complemented
543C3#8042011yescharacteristic, complemented
544C2—241no—
545C2—242no—
546C2#1059452711yescharacteristic
547C2C2×#6379611yescharacteristic
548C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4⋊C8D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593864C2semidirect
3. #10592529C2semidirect
4. C3×#4848C2semidirect
5. C3×#4841C2semidirect
6. #10590884C2semidirect
7. #10590876C2semidirect
8. #10590748C2semidirect
9. #10590742C2semidirect
10. #10590375C2semidirect
11. C4×#3715C2semidirect
57. #4848D3semidirect
58. #4841D3semidirect
173. #634SD16semidirect
194. C3⋊(C3⋊C8)#41semidirect
481. C32#3392semidirect
542. C3#80378semidirect
543. C3#80420semidirect

Maximal subgroups

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

subgroupindex
#105939062
#105938642
#105925292
C3×#48482
C3×#48412
#105908842
#105908762
#105907482
#105907422
#105903752
C4×#37152
#804203
#803783