Finite Group Databasebeta

← #11896289

Subgroups — #11896289

Order 1152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic
2#10596040C211yesmaximal, characteristic, complemented
3C32×#441C211yesmaximal, characteristic, complemented
4#10592884C211yesmaximal, characteristic, complemented
5#10592884C211yesmaximal, characteristic, complemented
6#10592726C211yesmaximal, characteristic
7#10592721C211yesmaximal, characteristic, complemented
8#10592570C211yesmaximal, characteristic, complemented
9#10592569C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592499C211yesmaximal, characteristic, complemented
12#10592493C211yesmaximal, characteristic, complemented
13#10592487C211yesmaximal, characteristic, complemented
14#10592412C211yesmaximal, characteristic
15#10592400C211yesmaximal, characteristic, complemented
16#79816—34nomaximal
17C2×C32×Q16C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64156C2211yescharacteristic
21#64156C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26#64103—21no—
27#64103—21no—
28#64102C2211yescharacteristic
29#64102C2211yescharacteristic
30#64099—21no—
31#64099C2211yescharacteristic
32#64097—21no—
33#64097C2211yescharacteristic
34#64084—21no—
35#64083C2211yescharacteristic
36C4×C4⋊(C3⋊D3)—21no—
37#64079—21no—
38#64079C2211yescharacteristic
39C4×#634—21no—
40C4×#634C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#97C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63642C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54C8×C3⋊Dic3C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5585—34no—
61#5569—34no—
62C3×#441D314yescomplemented
63#5185—34no—
64#5185—34no—
65#5027—34no—
66#5022—34no—
67#4871—34no—
68#4870—34no—
69#4817—34no—
70#4800—34no—
71#4794—34no—
72#4788—34no—
73#4713—34no—
74#4701—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C2×C4⋊(C3⋊D3)—21no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×C4×C3⋊D3—21no—
83C2×#634—21no—
84C2×#634D411yescharacteristic
85C32×Q16—22no—
86C2×C32×C8C2311yescharacteristic
87C2×C32×C8C2311yescharacteristic
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C4⋊C4C2311yescharacteristic
92C32×C42—21no—
93C32×C42—21no—
94C32×C42C2311yescharacteristic
95#3755—22no—
96#3755—22no—
97#3752—21no—
98#3752—21no—
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)D411yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3371—91noSylow
122C2×C3×Q16C2×D314yes—
123C3×C4×Q8C2×D314yes—
124C3×C4×Q8C2×D314yes—
125#947—34no—
126#947—34no—
127Q8×Dic3—34no—
128Q8×Dic3—34no—
129C2×#215—34no—
130C2×#215—34no—
131#894—64no—
132#894—64no—
133#893—34no—
134#893—34no—
135#890—34no—
136#890—64no—
137#888—34no—
138#888—64no—
139#875—64no—
140#874—34no—
141C4×D12—64no—
142#870—34no—
143#870—64no—
144C4×Dic6—34no—
145C4×Dic6—64no—
146C3×#106C2×D314yes—
147C3×#103C2×D314yes—
148C3×#103C2×D314yes—
149C3×#97C2×D314yes—
150#835—34no—
151#835—34no—
152#821—34no—
153#821—34no—
154#821—34no—
155#821—34no—
156#815—34no—
157Dic3⋊C8—34no—
158Dic3⋊C8—34no—
159C8×Dic3—34no—
160#809—34no—
161#809—34no—
162#808—34no—
163#807—34no—
164C4⋊(C3⋊C8)—34no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C32×Q8—21no—
168C32×Q8—21no—
169C32×Q8—21no—
170C32×Q8#4112yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)—42no—
189C4⋊(C3⋊D3)—81no—
190C4×C3⋊D3—81no—
191C4×C3⋊D3—81no—
192#634—41no—
193#634—42no—
194C32×C8—21no—
195C32×C8—21no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198#559—91no—
199#557—91no—
200#490—91no—
201#489—91no—
202#488—91no—
203#479—91no—
204#478—91no—
205#476—91no—
206#464—91no—
207#464—91no—
208#460—91no—
209#446—91no—
210#441C3⋊D311yescharacteristic, complemented
211#440—91no—
212C4×SD16—91no—
213C2×C3×Q8C22×D314yes—
214C2×C3×Q8C22×D314yes—
215C2×D12—34no—
216C2×D12—34no—
217C2×D12—64no—
218C2×D12—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×Dic6—34no—
222C2×Dic6—64no—
223C3×Q16—28no—
224C2×C3×C8C22×D314yes—
225C2×C3×C8C22×D314yes—
226C3×C4⋊C4—24no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4C22×D314yes—
229C3×C4⋊C4C22×D314yes—
230C3×C42—24no—
231C3×C42—24no—
232C3×C42C22×D314yes—
233#215—68no—
234#215—68no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—34no—
242C4⋊Dic3—34no—
243C4⋊Dic3—34no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246C4⋊Dic3—64no—
247Dic3⋊C4—34no—
248Dic3⋊C4—34no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253C4×Dic3—34no—
254C4×Dic3—34no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C2×C3⋊C8—34no—
258C2×C3⋊C8—34no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—41no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C2×C3⋊D3—41no—
266C32×C4—22no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4—41no—
270C32×C4—41no—
271C32×C4—41no—
272C32×C4C2×#4111yescharacteristic
273C32×C42−1+411yescharacteristic
274C3⋊Dic3—21no—
275C3⋊Dic3—21no—
276C3⋊Dic3—21no—
277C3⋊Dic3—21no—
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C2×Q16C2×C3⋊D311yescharacteristic
281C2×SD16—91no—
282C2×SD16—91no—
283C4⋊Q8—91no—
284C4⋊Q8—181no—
285#127—91no—
286#125—91no—
287#125—91no—
288#125—181no—
289#125—181no—
290#124—91no—
291#124—91no—
292#124—181no—
293#123—181no—
294#123—181no—
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—181no—
299C4×Q8C2×C3⋊D311yescharacteristic
300C4×Q8C2×C3⋊D311yescharacteristic
301C4×D4—91no—
302C4×D4—91no—
303C4×D4—181no—
304#107—91no—
305#106—91no—
306#106C2×C3⋊D311yescharacteristic
307C4⋊C8—91no—
308C4⋊C8—91no—
309C4⋊C8—91no—
310#103—91no—
311#103—91no—
312#103C2×C3⋊D311yescharacteristic
313#103C2×C3⋊D311yescharacteristic
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102—91no—
319#102—91no—
320#97—91no—
321#97C2×C3⋊D311yescharacteristic
322C4×C8—91no—
323C22×D3—64no—
324C22×D3—64no—
325C3×Q8—24no—
326C3×Q8—24no—
327C3×Q8—24no—
328C3×Q8#23518yes—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4D3×D414yes—
334C2×C3×C4D3×D414yes—
335C2×C3×C4C23×D314yes—
336C2×Dic3—34no—
337C2×Dic3—34no—
338C2×Dic3—34no—
339C2×Dic3—34no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342D12—64no—
343D12—64no—
344D12—64no—
345D12—64no—
346D12—128no—
347D12—244no—
348C4×D3—244no—
349C4×D3—244no—
350Dic6—124no—
351Dic6—128no—
352C3×C8—24no—
353C3×C8—24no—
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32#54811yescharacteristic
357C2×C32#57511yescharacteristic
358C2×C32#57711yescharacteristic
359C3⋊D3—81no—
360C3⋊D3—81no—
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8C22×C3⋊D311yescharacteristic
364C2×Q8C22×C3⋊D311yescharacteristic
365C2×D4—91no—
366C2×D4—91no—
367C2×D4—181no—
368C2×D4—181no—
369C22×C4—181no—
370C22×C4—181no—
371Q16—22no—
372SD16—182no—
373SD16—182no—
374C2×C8—91no—
375C2×C8—91no—
376C2×C8C22×C3⋊D311yescharacteristic
377C2×C8C22×C3⋊D311yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4C22×C3⋊D311yescharacteristic
393C4⋊C4C22×C3⋊D311yescharacteristic
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—21no—
401C42—21no—
402C42—91no—
403C42—91no—
404C42—181no—
405C42—181no—
406C42C22×C3⋊D311yescharacteristic
407C22×C3C2×D3×D414yes—
408C2×D3—124no—
409C2×D3—124no—
410C2×D3—124no—
411C2×D3—124no—
412C2×D3—124no—
413C2×D3—124no—
414C3×C4—24no—
415C3×C4—24no—
416C3×C4—28no—
417C3×C4—44no—
418C3×C4—44no—
419C3×C4—44no—
420C3×C4C2×#23514yes—
421C3×C4#101014yes—
422Dic3—64no—
423Dic3—64no—
424Dic3—64no—
425Dic3—64no—
426Dic3—124no—
427Dic3—124no—
428C32#337111yescharacteristic, complemented, Sylow
429C23—181no—
430C23—181no—
431Q8—21no—
432Q8—21no—
433Q8—21no—
434Q8—361no—
435Q8—362no—
436Q8#382812yes—
437D4—181no—
438D4—181no—
439D4—181no—
440D4—181no—
441D4—362no—
442D4—721no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—91no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—721no—
454C2×C4—721no—
455C2×C4D4×C3⋊D311yescharacteristic
456C2×C4D4×C3⋊D311yescharacteristic
457C2×C4C23×C3⋊D311yescharacteristic
458C8—21no—
459C8—21no—
460C8—181no—
461C8—181no—
462C2×C3#555214yes—
463C2×C3#577714yes—
464C2×C3#577814yes—
465D3—244no—
466D3—244no—
467C22—361no—
468C22—361no—
469C22—361no—
470C22—361no—
471C22—361no—
472C22—361no—
473C22C2×D4×C3⋊D311yescharacteristic
474C4—21no—
475C4—21no—
476C4—22no—
477C4—41no—
478C4—41no—
479C4—41no—
480C4—181no—
481C4—181no—
482C4—181no—
483C4—181no—
484C4—361no—
485C4—361no—
486C4C2×#382811yescharacteristic
487C4#6436711yescharacteristic
488C3#7981614yescomplemented
489C2—721no—
490C2—721no—
491C2#1059602311yescharacteristic
492C2#1059624811yescharacteristic
493C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radical#64083C22
hypercenter#441C3⋊D3
hypocenterC32#3371
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #10596040C2semidirect
3. C32×#441C2semidirect
4. #10592884C2semidirect
5. #10592884C2semidirect
7. #10592721C2semidirect
8. #10592570C2semidirect
9. #10592569C2semidirect
10. #10592516C2semidirect
11. #10592499C2semidirect
12. #10592493C2semidirect
13. #10592487C2semidirect
15. #10592400C2semidirect
62. C3×#441D3semidirect
210. #441C3⋊D3semidirect
428. C32#3371semidirect
488. C3#79816semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105960402
C32×#4412
#105928842
#105927262
#105927212
#105925702
#105925692
#105925162
#105924992
#105924932
#105924872
#105924122
#105924002
#798163