Finite Group Databasebeta

← #11872566

Subgroups — #11872566

Order 1152.

1110 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#10596283C211yesmaximal, characteristic, complemented
2#10596114C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4#10592926C211yesmaximal, characteristic
5#10592884C211yesmaximal, characteristic, complemented
6#10592884C211yesmaximal, characteristic, complemented
7#10592883C211yesmaximal, characteristic, complemented
8Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#10592744C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592492C211yesmaximal, characteristic, complemented
12#10592490C211yesmaximal, characteristic, complemented
13#10592487C211yesmaximal, characteristic, complemented
14#10592436C211yesmaximal, characteristic
15#10592419C211yesmaximal, characteristic, complemented
16#80176—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×C32×Q16C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64156C2211yescharacteristic
22Q8×C3⋊Dic3—21no—
23Q8×C3⋊Dic3—21no—
24Q8×C3⋊Dic3C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic
27Q8×C3⋊Dic3C2211yescharacteristic
28Q8×C3⋊Dic3C2211yescharacteristic
29C2×#3755C2211yescharacteristic
30C2×#3755C2211yescharacteristic
31#64139C2211yescharacteristic
32#64135—21no—
33#64135—21no—
34#64135C2211yescharacteristic
35#64135C2211yescharacteristic
36#64107—21no—
37#64106—21no—
38#64102C2211yescharacteristic
39#64097C2211yescharacteristic
40#64094—21no—
41#64092—21no—
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63657C2211yescharacteristic
50#63648C2211yescharacteristic
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic
53#63644C2211yescharacteristic
54#63642C2211yescharacteristic
55#63641C2211yescharacteristic
56#63641C2211yescharacteristic
57C8×C3⋊Dic3C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60#5812—34no—
61#5643—34no—
62C3×#451D314yescomplemented
63#5227—34no—
64#5185—34no—
65#5185—34no—
66#5184—34no—
67Dic3×Q16—34no—
68#5045—34no—
69#4817—34no—
70#4793—34no—
71#4791—34no—
72#4788—34no—
73#4737—34no—
74#4720—34no—
75C2×C32×Q8—22no—
76C2×C32×Q8—22no—
77C2×C32×Q8—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—21no—
86C2×#634—21no—
87C32×Q16—22no—
88C32×Q16—22no—
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C22⋊C4—21no—
94#3757—21no—
95#3757D411yescharacteristic
96#3757D411yescharacteristic
97#3755—22no—
98#3755—22no—
99#3752—21no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)D411yescharacteristic
109C4⋊(C3⋊Dic3)D411yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3121—91noSylow
125C22×C3×Q8C2×D314yes—
126C2×C3×Q16C2×D314yes—
127C2×C3×Q16C2×D314yes—
128C3×C22⋊Q8C2×D314yes—
129#947—34no—
130Q8×Dic3—34no—
131Q8×Dic3—34no—
132Q8×Dic3—34no—
133Q8×Dic3—34no—
134Q8×Dic3—34no—
135Q8×Dic3—64no—
136Q8×Dic3—64no—
137C2×#215—34no—
138C2×#215—34no—
139#930—34no—
140#926—34no—
141#926—34no—
142#926—64no—
143#926—64no—
144#898—64no—
145#897—64no—
146#893—34no—
147#888—34no—
148#885—64no—
149#883—64no—
150C3×#103C2×D314yes—
151C3×#103C2×D314yes—
152C3×C22⋊C8C2×D314yes—
153#835—34no—
154#835—34no—
155#835—34no—
156#835—34no—
157#830—34no—
158#821—34no—
159#821—34no—
160#818—34no—
161#817—34no—
162#815—34no—
163Dic3⋊C8—34no—
164Dic3⋊C8—34no—
165C8×Dic3—34no—
166#808—34no—
167#807—34no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C32×Q8—24no—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×Q8—21no—
174C32×Q8—21no—
175C32×Q8#4112yes—
176C32×Q8#4112yes—
177C2×C32×C4—24no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—81no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)—21no—
196C4×C3⋊D3—81no—
197#634—81no—
198C32×C8—21no—
199C32×C8—21no—
200C3⋊(C3⋊C8)—21no—
201C3⋊(C3⋊C8)—21no—
202#542—91no—
203#519—91no—
204#485—91no—
205#482—91no—
206#477—91no—
207#475—91no—
208#464—91no—
209#464—91no—
210#451C3⋊D311yescharacteristic, complemented
211#448—91no—
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433—91no—
217C2×C3×Q8—28no—
218C2×C3×Q8—28no—
219C2×C3×Q8—24no—
220C2×C3×Q8C22×D314yes—
221C2×C3×Q8C22×D314yes—
222C2×C3×Q8C22×D314yes—
223C22×C3×C4—24no—
224C22×C3×C4C22×D314yes—
225C2×#67—64no—
226C2×D12—34no—
227C2×C4×D3—64no—
228C2×Dic6—64no—
229C3×Q16—28no—
230C3×Q16—28no—
231C2×C3×C8C22×D314yes—
232C2×C3×C8C22×D314yes—
233C3×C4⋊C4—24no—
234C3×C4⋊C4C22×D314yes—
235C3×C22⋊C4—24no—
236#217—34no—
237#217—34no—
238#217—64no—
239#215—68no—
240#215—68no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—34no—
248C4⋊Dic3—34no—
249C4⋊Dic3—34no—
250C4⋊Dic3—64no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—64no—
254C4⋊Dic3—64no—
255Dic3⋊C4—64no—
256C4×Dic3—34no—
257C4×Dic3—34no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C2×C3⋊C8—34no—
265C2×C3⋊C8—34no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32—21no—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—41no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—21no—
276C32×C4—41no—
277C32×C4—41no—
278C32×C4C2×#4111yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3⋊Dic3—21no—
281C3⋊Dic3—21no—
282C3⋊Dic3—21no—
283C3⋊Dic3—21no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C22×Q8C2×C3⋊D311yescharacteristic
288C2×Q16C2×C3⋊D311yescharacteristic
289C2×Q16C2×C3⋊D311yescharacteristic
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#124—91no—
295#124—181no—
296#123—181no—
297C22⋊Q8—181no—
298C22⋊Q8C2×C3⋊D311yescharacteristic
299#121—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—181no—
306C4×Q8—181no—
307C4×D4—91no—
308#117—91no—
309#117—91no—
310#117—181no—
311#117—181no—
312#107—91no—
313#107—91no—
314#106—91no—
315#106—91no—
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—216no—
333C3×Q8—24no—
334C3×Q8—24no—
335C3×Q8—24no—
336C3×Q8—24no—
337C3×Q8#23718yes—
338C3×Q8#23718yes—
339C2×C3×C4—216no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4D3×D414yes—
347C2×C3×C4C23×D314yes—
348#67—244no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356D12—64no—
357D12—64no—
358C4×D3—244no—
359Dic6—244no—
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—81no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—181no—
373C2×Q8C22×C3⋊D311yescharacteristic
374C2×Q8C22×C3⋊D311yescharacteristic
375C2×Q8C22×C3⋊D311yescharacteristic
376C2×D4—91no—
377C2×D4—181no—
378C22×C4—21no—
379C22×C4—181no—
380C22×C4C22×C3⋊D311yescharacteristic
381Q16—22no—
382Q16—22no—
383SD16—182no—
384SD16—182no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8C22×C3⋊D311yescharacteristic
388C2×C8C22×C3⋊D311yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4C22×C3⋊D311yescharacteristic
402C22⋊C4—21no—
403C22⋊C4—91no—
404C22⋊C4—91no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C42—91no—
411C42—91no—
412C42—181no—
413C42—181no—
414C42—181no—
415C42—181no—
416C42—181no—
417C42—181no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3C2×D3×D414yes—
422C2×D3—124no—
423C2×D3—124no—
424C2×D3—124no—
425C3×C4—28no—
426C3×C4—28no—
427C3×C4—24no—
428C3×C4—44no—
429C3×C4—44no—
430C3×C4C2×#23714yes—
431C3×C4C2×#23714yes—
432Dic3—64no—
433Dic3—64no—
434Dic3—64no—
435Dic3—64no—
436Dic3—124no—
437Dic3—124no—
438Dic3—124no—
439C32#312111yescharacteristic, complemented, Sylow
440C23—181no—
441C23D4×C3⋊D311yescharacteristic
442Q8—24no—
443Q8—21no—
444Q8—21no—
445Q8—21no—
446Q8—21no—
447Q8—721no—
448Q8#383012yes—
449Q8#383012yes—
450D4—181no—
451D4—181no—
452D4—721no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—91no—
461C2×C4—91no—
462C2×C4—91no—
463C2×C4—91no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—721no—
468C2×C4D4×C3⋊D311yescharacteristic
469C2×C4C23×C3⋊D311yescharacteristic
470C8—21no—
471C8—21no—
472C8—181no—
473C8—181no—
474C2×C3—44no—
475C2×C3#558614yes—
476C2×C3#576614yes—
477C2×C3#577814yes—
478D3—244no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—361no—
483C22—361no—
484C22—361no—
485C22C2×D4×C3⋊D311yescharacteristic
486C4—22no—
487C4—22no—
488C4—21no—
489C4—41no—
490C4—41no—
491C4—181no—
492C4—181no—
493C4—181no—
494C4—181no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4C2×#383011yescharacteristic
499C4C2×#383011yescharacteristic
500C3#8017614yescomplemented
501C2—41no—
502C2—721no—
503C2#1059605711yescharacteristic
504C2#1059623711yescharacteristic
505C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radical#64139C22
hypercenter#451C3⋊D3
hypocenterC32#3121
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #10596283C2semidirect
3. C32×#451C2semidirect
5. #10592884C2semidirect
6. #10592884C2semidirect
7. #10592883C2semidirect
8. Q16×C3⋊Dic3C2semidirect
9. #10592744C2semidirect
10. #10592516C2semidirect
11. #10592492C2semidirect
12. #10592490C2semidirect
13. #10592487C2semidirect
15. #10592419C2semidirect
62. C3×#451D3semidirect
210. #451C3⋊D3semidirect
439. C32#3121semidirect
500. C3#80176semidirect

Maximal subgroups

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

subgroupindex
#105962832
#105961142
C32×#4512
#105929262
#105928842
#105928832
Q16×C3⋊Dic32
#105927442
#105925162
#105924922
#105924902
#105924872
#105924362
#105924192
#801763