Finite Group Databasebeta

← #11895871

Subgroups — #11895871

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic, complemented
3C3×#5083C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591632C212yesmaximal, complemented
6#10591631C212yesmaximal, complemented
7#10591572C212yesmaximal, complemented
8#10591570C212yesmaximal
9C4×#3714C211yesmaximal, characteristic
10#10590313C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81622—31nomaximal
13#80416—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64156C2212yes—
17Q8×C3⋊Dic3C2212yes—
18#64107—22no—
19#64106—21no—
20#64101—21no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#215C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63919C2212yes—
27#63899—22no—
28#63898C2212yes—
29#63856—21no—
30C2×#3714C2211yescharacteristic
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2212yes—
37#63575C2211yescharacteristic
38#63572C2212yes—
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5732—31no—
44#5732—31no—
45#5732—61no—
46#5727—31no—
47D4×Dic6—31no—
48C3×#487—31no—
49C3×#461—31no—
50#5165—32no—
51#5164—32no—
52#5087—31no—
53#5083D311yescharacteristic, complemented
54#5079D311yescharacteristic, complemented
55C4×#213—31no—
56#4846—31no—
57#4831—31no—
58#4819—32no—
59#4817—32no—
60#4794—32no—
61#4794—32no—
62#4793—32no—
63#4793—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634D411yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—44no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3752—21no—
80#3752—22no—
81#3752—22no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750D412yes—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3C2312yes—
88C3×#215—24no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98#3714—22no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4×D4—31no—
108#947—32no—
109#947—32no—
110#947—62no—
111#946—61no—
112Q8×Dic3—32no—
113Q8×Dic3—32no—
114Q8×Dic3—62no—
115C2×#215C2×D312yes—
116D4×Dic3—32no—
117C2×#213—31no—
118#924—61no—
119C2×D24—31no—
120#898—62no—
121#898—62no—
122#898—64no—
123#897—61no—
124#897—61no—
125#897—62no—
126#896—62no—
127#893—32no—
128#892—61no—
129#892—61no—
130#892—62no—
131#888—32no—
132#888—32no—
133#878—62no—
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137C4×D12C2×D311yescharacteristic
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#103—32no—
146C3×C4×C8—31no—
147#835C2×D312yes—
148#835C2×D312yes—
149#835C2×D312yes—
150#832—31no—
151#821—31no—
152#821—32no—
153#821—31no—
154#818—32no—
155#818—31no—
156#815—32no—
157#815—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#809—31no—
161#809—32no—
162#807—31no—
163#807—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—21no—
168C32×Q8—22no—
169C32×Q8—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×D412yes—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)—21no—
179C4×C3⋊D3—42no—
180#634—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12#4112yes—
185C3×C4×D3—42no—
186C3×Dic6—42no—
187#627—44no—
188D3×Dic3—44no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192#556—91no—
193D4×Q8—91no—
194#489—92no—
195#487—31no—
196#477—92no—
197#474—91no—
198#463—92no—
199#461—31no—
200#446—91no—
201#440—92no—
202C4×D8—91no—
203C2×C3×Q8—22no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D312yes—
206C2×C3×Q8C22×D312yes—
207C2×C3×D4—31no—
208C22×C3×C4—61no—
209C22×Dic3—62no—
210D3×Q8—124no—
211C2×D12—31no—
212C2×D12—31no—
213C2×D12—61no—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×Dic6—21no—
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—124no—
227C3×SD16—64no—
228C2×C3×C8—31no—
229C2×C3×C8—32no—
230C2×C3×C8—31no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C22⋊C4—61no—
241C3×C42—21no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#215—24no—
246#213—62no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—21no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—64no—
268C4⋊Dic3C22×D312yes—
269C4⋊Dic3C22×D311yescharacteristic
270Dic3⋊C4—32no—
271Dic3⋊C4—32no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3—64no—
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D312yes—
284D24—62no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—41no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C32×C4—21no—
293C32×C4—42no—
294C32×C4AGL(1,ℤ/8)12yes—
295C32×C4C2×#4111yescharacteristic
296C32×C42−1+411yescharacteristic
297C3⋊Dic3—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—41no—
300C3×Dic3—42no—
301C3×Dic3—41no—
302C22×Q8—181no—
303C2×SD16—32no—
304C2×D8—91no—
305C4⋊Q8—31no—
306C4⋊Q8—92no—
307C4⋊Q8D3211yescharacteristic
308#126—182no—
309#124—92no—
310C22⋊Q8—182no—
311C22⋊Q8—181no—
312C22⋊Q8—181no—
313C4×Q8—91no—
314C4×Q8—92no—
315C4×D4—31no—
316C4×D4—92no—
317C4×D4—91no—
318#117—181no—
319#107—91no—
320#107—92no—
321C4⋊C8—31no—
322C4⋊C8—92no—
323#103—32no—
324#103—32no—
325#103—32no—
326#102—91no—
327#102—92no—
328#102—91no—
329#97—92no—
330C4×C8—31no—
331C23×C3—61no—
332C22×D3—21no—
333C22×D3—62no—
334C22×D3—61no—
335C22×D3—61no—
336C3×Q8—22no—
337C3×Q8—22no—
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—42no—
341C3×Q8—42no—
342C3×Q8—122no—
343C3×D4—32no—
344C3×D4—61no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
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
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—124no—
372D12—21no—
373D12—61no—
374D12—61no—
375D12—61no—
376D12—61no—
377D12—121no—
378D12—121no—
379D12#23712yes—
380C4×D3—42no—
381C4×D3—124no—
382C4×D3—124no—
383C4×D3—122no—
384C4×D3—122no—
385Dic6—42no—
386Dic6—62no—
387Dic6—62no—
388Dic6—122no—
389Dic6—124no—
390Dic6—124no—
391C3×C8—61no—
392C3×C8—62no—
393C3×C8—61no—
394C3⋊C8—22no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C2×C32#54811yescharacteristic
398C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
399C2×C32#57811yescharacteristic
400C3⋊D3—81no—
401C3×D3—42no—
402C2×Q8—61no—
403C2×Q8—91no—
404C2×Q8—182no—
405C2×Q8—364no—
406C2×Q8C2×D3212yes—
407C2×D4—31no—
408C2×D4—91no—
409C22×C4—61no—
410C22×C4—182no—
411C22×C4—181no—
412SD16—64no—
413D8—182no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—31no—
420C4⋊C4—32no—
421C4⋊C4—61no—
422C4⋊C4—91no—
423C4⋊C4—92no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C22⋊C4—61no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22⋊C4—181no—
432C42—92no—
433C42—182no—
434C42C2×D3211yescharacteristic
435C22×C3—21no—
436C22×C3—62no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C2×D3×D411yescharacteristic
441C2×D3—22no—
442C2×D3—41no—
443C2×D3—41no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—41no—
459C3×C4—44no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—121no—
463C3×C4—122no—
464C3×C4#91412yes—
465C3×C4#91412yes—
466C3×C4C2×#23711yescharacteristic
467C3×C4D3×#4111yescharacteristic
468C3×C4#101011yescharacteristic
469C3×C4#101011yescharacteristic
470Dic3—42no—
471Dic3—41no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—122no—
477Dic3—122no—
478Dic3—122no—
479Dic3—121no—
480Dic3—121no—
481C32#336711yescharacteristic, complemented, Sylow
482C23—61no—
483C23—181no—
484Q8—22no—
485Q8—22no—
486Q8—122no—
487Q8—182no—
488Q8—364no—
489D4—32no—
490D4—61no—
491D4—181no—
492D4—181no—
493C2×C4—22no—
494C2×C4—61no—
495C2×C4—62no—
496C2×C4—92no—
497C2×C4—92no—
498C2×C4—122no—
499C2×C4—181no—
500C2×C4—364no—
501C2×C4—362no—
502C2×C4#381111yescharacteristic
503C2×C4#381111yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—61no—
507C8—62no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—122no—
512C2×C3#559811yescharacteristic
513C2×C3#567711yescharacteristic
514C2×C3C2×#91411yescharacteristic
515C2×C3C2×#91411yescharacteristic
516C2×C3#576611yescharacteristic
517C2×C3#577911yescharacteristic
518D3—42no—
519D3—242no—
520D3—241no—
521D3—241no—
522C22—62no—
523C22—121no—
524C22—121no—
525C22—361no—
526C22—361no—
527C22—361no—
528C22C2×#381111yescharacteristic
529C4—21no—
530C4—42no—
531C4—121no—
532C4—122no—
533C4—182no—
534C4—182no—
535C4—361no—
536C4#6394112yes—
537C4#6430911yescharacteristic
538C4D3×#23711yescharacteristic
539C3—21no—
540C3#8041611yescharacteristic, complemented
541C3#8162211yescharacteristic, complemented
542C2—122no—
543C2—721no—
544C2#1059516111yescharacteristic
545C2C2×#6394111yescharacteristic
546C2#1059533711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
2. #10593904C2semidirect
3. C3×#5083C2semidirect
4. C3×#5079C2semidirect
5. #10591632C2semidirect
6. #10591631C2semidirect
7. #10591572C2semidirect
10. #10590313C2semidirect
11. #10590296C2semidirect
53. #5083D3semidirect
54. #5079D3semidirect
481. C32#3367semidirect
540. C3#80416semidirect
541. C3#81622semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105939042
C3×#50832
C3×#50792
#105916322
#105916312
#105915722
#105915702
C4×#37142
#105903132
#105902962
#816223
#804163