Finite Group Databasebeta

← #11895927

Subgroups — #11895927

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596040C211yesmaximal, characteristic, complemented
2#10596024C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4#10592862C211yesmaximal, characteristic, complemented
5#10592862C211yesmaximal, characteristic, complemented
6#10592726C211yesmaximal, characteristic, complemented
7#10592708C211yesmaximal, characteristic, complemented
8#10592590C211yesmaximal, characteristic, complemented
9#10592589C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592487C211yesmaximal, characteristic, complemented
12#10592463C211yesmaximal, characteristic, complemented
13#10592459C211yesmaximal, characteristic, complemented
14#10592412C211yesmaximal, characteristic, complemented
15#10592400C211yesmaximal, characteristic, complemented
16#79752—34nomaximal
17C2×#3828—21no—
18C2×C32×SD16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25#64149C2211yescharacteristic
26#64149C2211yescharacteristic
27#64139—21no—
28#64102C2211yescharacteristic
29#64102C2211yescharacteristic
30#64099—21no—
31#64099C2211yescharacteristic
32#64097—21no—
33#64097C2211yescharacteristic
34#64093—21no—
35#64093—21no—
36#64083C2211yescharacteristic
37#64079—21no—
38#64079C2211yescharacteristic
39C4×#634—21no—
40C4×#634C2211yescharacteristic
41C32×#107C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#97C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
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#5569—34no—
61#5553—34no—
62C3×#440D314yescomplemented
63#5163—34no—
64#5163—34no—
65#5027—34no—
66#5009—34no—
67#4891—34no—
68#4890—34no—
69#4817—34no—
70#4788—34no—
71#4764—34no—
72#4760—34no—
73#4713—34no—
74#4701—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C2×#638—21no—
79C2×#638—21no—
80C2×#638—21no—
81C2×#638—21no—
82#3828—44no—
83C2×C4⋊(C3⋊D3)—21no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4⋊(C3⋊D3)C2311yescharacteristic
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×#634—21no—
90C2×#634D411yescharacteristic
91C32×SD16—22no—
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C22⋊C4—21no—
98C32×C42—21no—
99C32×C42C2311yescharacteristic
100#3755—22no—
101#3755—22no—
102#3752—21no—
103#3752—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)D411yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750D411yescharacteristic
115#3750D411yescharacteristic
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#3368—91noSylow
123C2×#235—64no—
124C2×C3×SD16C2×D314yes—
125C3×C4×Q8C2×D314yes—
126C3×C4×D4C2×D314yes—
127Q8×Dic3—34no—
128Q8×Dic3—34no—
129C2×#215—34no—
130C2×#215—34no—
131#940—34no—
132#940—34no—
133#930—64no—
134#893—34no—
135#893—34no—
136#890—34no—
137#890—64no—
138#888—34no—
139#888—64no—
140#884—64no—
141#884—64no—
142#874—34no—
143#870—34no—
144#870—64no—
145C4×Dic6—34no—
146C4×Dic6—64no—
147C3×#107C2×D314yes—
148C3×#103C2×D314yes—
149C3×#102C2×D314yes—
150C3×#97C2×D314yes—
151#832—34no—
152#832—34no—
153#821—34no—
154#821—34no—
155#821—34no—
156#821—34no—
157#815—34no—
158Dic3⋊C8—34no—
159Dic3⋊C8—34no—
160C8×Dic3—34no—
161#809—34no—
162#809—34no—
163#808—34no—
164#807—34no—
165C4⋊(C3⋊C8)—34no—
166C23×C32—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C32×Q8—21no—
170C32×Q8#4112yescomplemented
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—42no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180#638—42no—
181#638—42no—
182#638—81no—
183#638—81no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—42no—
195C4⋊(C3⋊D3)—81no—
196C4×C3⋊D3—42no—
197C4×C3⋊D3—42no—
198#634—22no—
199#634—42no—
200C32×C8—21no—
201C32×C8—21no—
202C3⋊(C3⋊C8)—21no—
203C3⋊(C3⋊C8)—21no—
204#557—91no—
205#550—91no—
206#490—91no—
207#490—91no—
208#486—91no—
209#478—91no—
210#478—91no—
211#474—91no—
212#460—91no—
213#460—91no—
214#460—91no—
215#446—91no—
216#440—91no—
217#440C3⋊D311yescharacteristic, complemented
218C4×SD16—91no—
219C2×C3×Q8C22×D314yes—
220C2×C3×D4C22×D314yes—
221C22×C3×C4—24no—
222C2×#67—64no—
223C2×#67—64no—
224C2×#67—64no—
225C2×#67—64no—
226#235—1216no—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—64no—
230C2×D12—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×Dic6—34no—
234C2×Dic6—64no—
235C3×SD16—28no—
236C2×C3×C8C22×D314yes—
237C2×C3×C8C22×D314yes—
238C3×C4⋊C4—24no—
239C3×C4⋊C4C22×D314yes—
240C3×C4⋊C4C22×D314yes—
241C3×C22⋊C4—24no—
242C3×C42—24no—
243C3×C42C22×D314yes—
244#215—68no—
245#215—68no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—34no—
249C4⋊Dic3—34no—
250C4⋊Dic3—34no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—64no—
254Dic3⋊C4—34no—
255Dic3⋊C4—34no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260C4×Dic3—34no—
261C4×Dic3—34no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C2×C3⋊C8—34no—
265C2×C3⋊C8—34no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32—41no—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—41no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C32×C4—22no—
277C32×C4—21no—
278C32×C4—21no—
279C32×C4—41no—
280C32×C4—41no—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—21no—
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3⋊Dic3AGL(1,ℤ/8)12yes—
289C2×#41—181no—
290C2×SD16—91no—
291C2×SD16—91no—
292C2×SD16C2×C3⋊D311yescharacteristic
293C4⋊Q8—91no—
294C4⋊Q8—181no—
295#127—91no—
296#127—91no—
297#127—91no—
298#125—91no—
299#125—91no—
300#125—181no—
301#125—181no—
302#121—181no—
303#121—181no—
304#121—181no—
305C4×Q8—91no—
306C4×Q8—91no—
307C4×Q8—91no—
308C4×Q8—181no—
309C4×Q8C2×C3⋊D311yescharacteristic
310C4×D4—91no—
311C4×D4—91no—
312C4×D4C2×C3⋊D311yescharacteristic
313#107—91no—
314#107C2×C3⋊D311yescharacteristic
315#106—91no—
316C4⋊C8—91no—
317C4⋊C8—91no—
318C4⋊C8—91no—
319#103C2×C3⋊D311yescharacteristic
320#102—91no—
321#102—91no—
322#102—91no—
323#102—91no—
324#102—91no—
325#102—91no—
326#102—91no—
327#102—91no—
328#102C2×C3⋊D311yescharacteristic
329#97—91no—
330#97C2×C3⋊D311yescharacteristic
331C4×C8—91no—
332C23×C3—24no—
333C22×D3—64no—
334C22×D3—64no—
335C3×Q8—24no—
336C3×Q8#23518yescomplemented
337C3×D4—24no—
338C3×D4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—48no—
343C2×C3×C4D3×D414yes—
344C2×C3×C4D3×D414yes—
345C2×C3×C4C23×D314yes—
346#67—128no—
347#67—128no—
348#67—244no—
349#67—244no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356D12—64no—
357D12—64no—
358D12—64no—
359D12—64no—
360D12—128no—
361D12—244no—
362C4×D3—128no—
363C4×D3—128no—
364Dic6—68no—
365Dic6—128no—
366C3×C8—24no—
367C3×C8—24no—
368C3⋊C8—64no—
369C3⋊C8—64no—
370C2×C32—81no—
371C2×C32#54811yescharacteristic
372C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
373C2×C32#57711yescharacteristic
374C3⋊D3—81no—
375C3⋊D3—81no—
376#41—364no—
377C2×Q8—91no—
378C2×Q8—181no—
379C2×Q8C22×C3⋊D311yescharacteristic
380C2×D4—91no—
381C2×D4—91no—
382C2×D4—181no—
383C2×D4—181no—
384C2×D4—181no—
385C2×D4—181no—
386C2×D4—181no—
387C2×D4—181no—
388C2×D4C22×C3⋊D311yescharacteristic
389C22×C4—21no—
390C22×C4—181no—
391C22×C4—181no—
392SD16—22no—
393SD16—182no—
394SD16—182no—
395C2×C8—91no—
396C2×C8—91no—
397C2×C8C22×C3⋊D311yescharacteristic
398C2×C8C22×C3⋊D311yescharacteristic
399C4⋊C4—21no—
400C4⋊C4—91no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4C22×C3⋊D311yescharacteristic
413C4⋊C4C22×C3⋊D311yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C42—21no—
418C42—91no—
419C42—91no—
420C42—181no—
421C42—181no—
422C42C22×C3⋊D311yescharacteristic
423C22×C3—44no—
424C22×C3—44no—
425C22×C3—44no—
426C22×C3C2×D3×D414yes—
427C2×D3—124no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—124no—
433C3×C4—24no—
434C3×C4—24no—
435C3×C4—28no—
436C3×C4—44no—
437C3×C4—44no—
438C3×C4C2×#23514yes—
439C3×C4#101014yes—
440Dic3—38no—
441Dic3—64no—
442Dic3—64no—
443Dic3—64no—
444Dic3—124no—
445Dic3—124no—
446C32#336811yescharacteristic, complemented, Sylow
447C23—21no—
448C23—181no—
449C23—181no—
450Q8—21no—
451Q8—182no—
452Q8—362no—
453Q8#382812yescomplemented
454D4—21no—
455D4—21no—
456D4—181no—
457D4—181no—
458D4—181no—
459D4—181no—
460D4—362no—
461D4—362no—
462D4—362no—
463D4—721no—
464D4—721no—
465D4—721no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—42no—
470C2×C4—91no—
471C2×C4—91no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—362no—
477C2×C4—362no—
478C2×C4D4×C3⋊D311yescharacteristic
479C2×C4D4×C3⋊D311yescharacteristic
480C2×C4C23×C3⋊D311yescharacteristic
481C8—21no—
482C8—21no—
483C8—181no—
484C8—181no—
485C2×C3—84no—
486C2×C3#555214yes—
487C2×C3D3×AGL(1,ℤ/8)14yes—
488C2×C3#577814yes—
489D3—244no—
490D3—244no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—361no—
495C22—361no—
496C22—361no—
497C22—361no—
498C22—361no—
499C22—361no—
500C22C2×D4×C3⋊D311yescharacteristic
501C4—21no—
502C4—21no—
503C4—22no—
504C4—41no—
505C4—41no—
506C4—92no—
507C4—181no—
508C4—181no—
509C4—181no—
510C4—361no—
511C4—361no—
512C4C2×#382811yescharacteristic
513C4#6436711yescharacteristic
514C3#7975214yescomplemented
515C2—81no—
516C2—721no—
517C2—721no—
518C2#1059602311yescharacteristic
519C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
520C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radical#10596024C2
hypercenter#440C3⋊D3
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10596040C2semidirect
3. C32×#440C2semidirect
4. #10592862C2semidirect
5. #10592862C2semidirect
6. #10592726C2semidirect
7. #10592708C2semidirect
8. #10592590C2semidirect
9. #10592589C2semidirect
10. #10592516C2semidirect
11. #10592487C2semidirect
12. #10592463C2semidirect
13. #10592459C2semidirect
14. #10592412C2semidirect
15. #10592400C2semidirect
62. C3×#440D3semidirect
170. C32×Q8#41semidirect
217. #440C3⋊D3semidirect
336. C3×Q8#235semidirect
446. C32#3368semidirect
453. Q8#3828semidirect
514. C3#79752semidirect

Maximal subgroups

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

subgroupindex
#105960402
#105960242
C32×#4402
#105928622
#105927262
#105927082
#105925902
#105925892
#105925162
#105924872
#105924632
#105924592
#105924122
#105924002
#797523