Finite Group Databasebeta

← #11872418

Subgroups — #11872418

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596096C211yesmaximal, characteristic, complemented
2#10595975C211yesmaximal, characteristic
3C32×#483C211yesmaximal, characteristic, complemented
4#10592746C211yesmaximal, characteristic
5#10592669C211yesmaximal, characteristic, complemented
6#10592570C211yesmaximal, characteristic, complemented
7#10592556C211yesmaximal, characteristic, complemented
8#10592552C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592517C211yesmaximal, characteristic, complemented
11#10592516C211yesmaximal, characteristic, complemented
12#10592494C211yesmaximal, characteristic, complemented
13#10592489C211yesmaximal, characteristic, complemented
14#10592432C211yesmaximal, characteristic
15#10592419C211yesmaximal, characteristic, complemented
16#81416—34nomaximal
17C2×#3828C2211yescharacteristic
18C32×C22⋊Q8C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64153C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C4×#638—21no—
25C4×#638—21no—
26#64135C2211yescharacteristic
27#64133C2211yescharacteristic
28C2×#3746C2211yescharacteristic
29C2×#3744C2211yescharacteristic
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64101—21no—
33C4⋊C4×C3⋊D3—21no—
34#64099—21no—
35#64099C2211yescharacteristic
36#64098—21no—
37#64096C2211yescharacteristic
38#64096C2211yescharacteristic
39#64096C2211yescharacteristic
40#64088—21no—
41#64088—21no—
42C32×#106C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47#63657C2211yescharacteristic
48#63648C2211yescharacteristic
49#63643C2211yescharacteristic
50#63642C2211yescharacteristic
51#63641C2211yescharacteristic
52#63641C2211yescharacteristic
53C8×C3⋊Dic3C2211yescharacteristic
54#63637C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic
59#63634C2211yescharacteristic
60#5625—34no—
61#5504—34no—
62C3×#483D314yescomplemented
63#5047—34no—
64#4970—34no—
65#4871—34no—
66#4857—34no—
67#4853—34no—
68#4852—34no—
69#4818—34no—
70#4817—34no—
71#4795—34no—
72#4790—34no—
73#4733—34no—
74#4720—34no—
75C2×C32×Q8C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79#3828—22no—
80#3828—22no—
81C2×C4⋊(C3⋊D3)C2311yescharacteristic
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×#634C2311yescharacteristic
86C2×#634C2311yescharacteristic
87C2×C32×C8C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C32×C4⋊C4—21no—
90C32×C4⋊C4—21no—
91C32×C4⋊C4C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C22⋊C4—21no—
95#3757—21no—
96#3757D411yescharacteristic
97#3757D411yescharacteristic
98#3756—22no—
99#3755—22no—
100#3752—21no—
101#3752—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)D411yescharacteristic
105C4⋊(C3⋊Dic3)D411yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3746—22no—
123#3744—22no—
124#3120—91noSylow
125C2×#235—34no—
126C3×C22⋊Q8C2×D314yes—
127C2×C3×C4⋊C4C2×D314yes—
128Q8×Dic3—34no—
129#944—34no—
130C2×#216—34no—
131C2×#215—34no—
132C4×#67—64no—
133C4×#67—64no—
134#926—34no—
135#924—34no—
136C2×Dic12—34no—
137C2×#204—34no—
138#893—34no—
139#893—34no—
140#892—64no—
141D3×C4⋊C4—64no—
142#890—34no—
143#890—64no—
144#889—64no—
145#887—34no—
146#887—34no—
147#887—34no—
148#879—64no—
149#879—64no—
150C3×#106C2×D314yes—
151C3×#106C2×D314yes—
152C3×#103C2×D314yes—
153C3×#103C2×D314yes—
154C3×C22⋊C8C2×D314yes—
155#830—34no—
156#821—34no—
157#816—34no—
158#815—34no—
159Dic3⋊C8—34no—
160Dic3⋊C8—34no—
161C8×Dic3—34no—
162#810—34no—
163#810—34no—
164#810—34no—
165#809—34no—
166#807—34no—
167#807—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C32×Q8—21no—
171C32×Q8—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—81no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—24no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)#4112yes—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—81no—
193C4×C3⋊D3—81no—
194#634—21no—
195#634—21no—
196#634—21no—
197#634#4112yes—
198C32×C8—21no—
199C32×C8—21no—
200C3⋊(C3⋊C8)—21no—
201C3⋊(C3⋊C8)—21no—
202#541—91no—
203#520—91no—
204#484—91no—
205#483C3⋊D311yescharacteristic, complemented
206#479—91no—
207#478—91no—
208#462—91no—
209#461—91no—
210#452—91no—
211#452—91no—
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433—91no—
217C2×C3×Q8C22×D314yes—
218C22×C3×C4—24no—
219C22×C3×C4C22×D314yes—
220C2×#67—64no—
221#235—68no—
222#235—68no—
223C2×D12—34no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×Dic6—34no—
228C2×Dic6—34no—
229C2×C3×C8C22×D314yes—
230C2×C3×C8C22×D314yes—
231C3×C4⋊C4—24no—
232C3×C4⋊C4—24no—
233C3×C4⋊C4C22×D314yes—
234C3×C4⋊C4C22×D314yes—
235C3×C4⋊C4C22×D314yes—
236C3×C22⋊C4—24no—
237#217—34no—
238#217—34no—
239#217—64no—
240#216—68no—
241#215—68no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—34no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—64no—
248C4⋊Dic3—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256C4×Dic3—34no—
257C4×Dic3—34no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C2×C3⋊C8—34no—
263C2×C3⋊C8—34no—
264Dic12—68no—
265#204—68no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32—21no—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—22no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C32×C4—21no—
274C32×C4—41no—
275C32×C4—41no—
276C32×C4—41no—
277C32×C4—41no—
278C32×C4C2×#4111yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—21no—
282C3⋊Dic3—21no—
283C3⋊Dic3—21no—
284C3⋊Dic3—21no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C2×#41—91no—
288C2×Q16—91no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#126—181no—
295#125—91no—
296#125—181no—
297#125—181no—
298C22⋊Q8—91no—
299C22⋊Q8C2×C3⋊D311yescharacteristic
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—181no—
307C4×D4—181no—
308#117—91no—
309#117—181no—
310C2×C4⋊C4—181no—
311C2×C4⋊C4C2×C3⋊D311yescharacteristic
312#107—91no—
313#107—91no—
314#106C2×C3⋊D311yescharacteristic
315#106C2×C3⋊D311yescharacteristic
316C4⋊C8—91no—
317C4⋊C8—91no—
318#103—91no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103C2×C3⋊D311yescharacteristic
323#103C2×C3⋊D311yescharacteristic
324#102—91no—
325#102—91no—
326C22⋊C8—91no—
327C22⋊C8C2×C3⋊D311yescharacteristic
328#97—91no—
329C4×C8—91no—
330C23×C3D3×D414yes—
331C22×D3—64no—
332C3×Q8—24no—
333C3×Q8—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—84no—
341C2×C3×C4D3×D414yes—
342C2×C3×C4C23×D314yes—
343#67—616no—
344C2×Dic3—34no—
345C2×Dic3—34no—
346C2×Dic3—34no—
347C2×Dic3—34no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—64no—
351D12—38no—
352D12—64no—
353C4×D3—616no—
354C4×D3—244no—
355C4×D3—244no—
356Dic6—38no—
357Dic6—64no—
358Dic6—64no—
359Dic6—64no—
360C3×C8—24no—
361C3×C8—24no—
362C3⋊C8—64no—
363C3⋊C8—64no—
364C2×C32—41no—
365C2×C32#52511yescharacteristic
366C2×C32#57711yescharacteristic
367C2×C32#57811yescharacteristic
368C3⋊D3—42no—
369#41—182no—
370#41—182no—
371C2×Q8—91no—
372C2×Q8—91no—
373C2×Q8C22×C3⋊D311yescharacteristic
374C2×D4—91no—
375C2×D4—181no—
376C22×C4—21no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4C22×C3⋊D311yescharacteristic
381Q16—182no—
382Q16—182no—
383SD16—182no—
384SD16—182no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8C22×C3⋊D311yescharacteristic
388C2×C8C22×C3⋊D311yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4C22×C3⋊D311yescharacteristic
404C4⋊C4C22×C3⋊D311yescharacteristic
405C4⋊C4C22×C3⋊D311yescharacteristic
406C22⋊C4—21no—
407C22⋊C4—91no—
408C22⋊C4—91no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C42—91no—
413C42—91no—
414C42—181no—
415C42—181no—
416C42—181no—
417C42—181no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3C2×D3×D414yes—
422C2×D3—68no—
423C2×D3—124no—
424C2×D3—124no—
425C3×C4—24no—
426C3×C4—44no—
427C3×C4—44no—
428C3×C4—44no—
429C3×C4—44no—
430C3×C4D3×#4114yes—
431C3×C4D3×#4114yes—
432Dic3—68no—
433Dic3—64no—
434Dic3—64no—
435Dic3—64no—
436Dic3—64no—
437Dic3—124no—
438Dic3—124no—
439C32#312011yescharacteristic, complemented, Sylow
440C23—181no—
441C23D4×C3⋊D311yescharacteristic
442Q8—21no—
443Q8—21no—
444Q8—92no—
445Q8—181no—
446Q8—181no—
447Q8—181no—
448D4—92no—
449D4—184no—
450D4—181no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—81no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—91no—
461C2×C4—91no—
462C2×C4—184no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—721no—
467C2×C4—721no—
468C2×C4D4×C3⋊D311yescharacteristic
469C2×C4C23×C3⋊D311yescharacteristic
470C8—21no—
471C8—21no—
472C8—181no—
473C8—181no—
474C2×C3—44no—
475C2×C3#565614yes—
476C2×C3#576214yes—
477C2×C3#577914yes—
478D3—128no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—182no—
483C22—361no—
484C22—361no—
485C22C2×D4×C3⋊D311yescharacteristic
486C4—21no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—182no—
492C4—181no—
493C4—181no—
494C4—181no—
495C4—181no—
496C4—361no—
497C4—361no—
498C4#41×C3⋊D311yescharacteristic
499C4#41×C3⋊D311yescharacteristic
500C3#8141614yescomplemented
501C2—41no—
502C2—362no—
503C2#1059612711yescharacteristic
504C2#1059623311yescharacteristic
505C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#483C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#483C3⋊D3
hypocenterC32#3120
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #10596096C2semidirect
3. C32×#483C2semidirect
5. #10592669C2semidirect
6. #10592570C2semidirect
7. #10592556C2semidirect
8. #10592552C2semidirect
9. #10592551C2semidirect
10. #10592517C2semidirect
11. #10592516C2semidirect
12. #10592494C2semidirect
13. #10592489C2semidirect
15. #10592419C2semidirect
62. C3×#483D3semidirect
205. #483C3⋊D3semidirect
439. C32#3120semidirect
500. C3#81416semidirect

Maximal subgroups

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

subgroupindex
#105960962
#105959752
C32×#4832
#105927462
#105926692
#105925702
#105925562
#105925522
#105925512
#105925172
#105925162
#105924942
#105924892
#105924322
#105924192
#814163