Finite Group Databasebeta

← #11895670

Subgroups — #11895670

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic
4C3×#5070C211yesmaximal, characteristic
5#10591478C212yesmaximal, complemented
6#10591441C212yesmaximal, complemented
7#10591411C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9C4×#3719C211yesmaximal, characteristic, complemented
10#10590285C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83717—31nomaximal
13#81589—31nomaximal
14C32×#127C2211yescharacteristic
15C2×#3754C2212yes—
16C4×#634C2211yescharacteristic
17C3×#936—21no—
18C3×#936C2212yes—
19C3×#935—22no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63873—21no—
26#63869C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3719C2211yescharacteristic
31#63659C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5721—31no—
45#5713D311yescharacteristic
46#5567—31no—
47C3×#486—31no—
48#5094—31no—
49#5075—31no—
50#5075—31no—
51#5075—61no—
52#5070D311yescharacteristic
53#5056—32no—
54#5054—32no—
55C4×#216—31no—
56Q8×C3⋊C8—31no—
57#5020—31no—
58C4×#214—32no—
59#5009—32no—
60#4768—32no—
61#4767—32no—
62#4766—32no—
63#4758—32no—
64C4×Dic12—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634C2311yescharacteristic
70C22×C3×Dic3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C32×C42C2311yescharacteristic
75#3754—24no—
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78C4×C3⋊Dic3—21no—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#217—22no—
81C3×#217—22no—
82C3×#217—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—21no—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93#3724—22no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3719—22no—
98#3365—91noSylow
99C3×C4⋊Q8—31no—
100C3×#127—21no—
101C3×#127C2×D311yescharacteristic
102C3×#127C2×D311yescharacteristic
103C3×#124—32no—
104C3×#124—61no—
105C3×#123—62no—
106C3×C4×Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—32no—
109C3×C4×D4—61no—
110Q8×Dic3—61no—
111#944—61no—
112#944—61no—
113C2×#216—31no—
114#936—21no—
115#936C2×D312yes—
116#935—22no—
117D4×Dic3—21no—
118D4×Dic3C2×D312yes—
119C2×#214—32no—
120C2×#214—32no—
121C2×#214—62no—
122C2×Dic12—31no—
123#890—32no—
124#889—62no—
125#889—62no—
126#887—32no—
127#887—61no—
128#870—32no—
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#102—32no—
137C3×#102—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—31no—
141#832—32no—
142#832—32no—
143#832—62no—
144#832C2×D312yes—
145#832C2×D312yes—
146#818—31no—
147#816—31no—
148#816—31no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#810—32no—
152#810—31no—
153#808—32no—
154#808—32no—
155#807—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C23×C32—22no—
163C32×D4—22no—
164C32×D4—22no—
165C32×D4—42no—
166C32×D4—81no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172#634—21no—
173#634#4112yes—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—82no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—42no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—31no—
188#557—91no—
189#488—92no—
190#486—31no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—22no—
206C2×C3×D4—41no—
207C2×C3×D4—41no—
208C2×C3×D4C22×D312yes—
209C2×C3×D4C22×D312yes—
210C22×C3×C4—62no—
211C22×Dic3—22no—
212C2×Dic6—21no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6#6711yescharacteristic
217C2×Dic6C22×D311yescharacteristic
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4—62no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42—61no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—22no—
235#217—22no—
236#217—22no—
237#216—62no—
238#214—64no—
239#214—64no—
240#214—124no—
241C4⋊Dic3—21no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—62no—
246C4⋊Dic3#6711yescharacteristic
247C4⋊Dic3C22×D311yescharacteristic
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—21no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—121no—
258Dic3⋊C4#6712yes—
259C4×Dic3—21no—
260C4×Dic3—62no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—62no—
264C4×Dic3—121no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271Dic12—62no—
272C22×C32—42no—
273C22×C32—42no—
274C22×C32—42no—
275C22×C32C22×D411yescharacteristic
276C32×C4—21no—
277C32×C4#13512yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C2×Q16—91no—
288C2×SD16—92no—
289C4⋊Q8—31no—
290C4⋊Q8—181no—
291#127D3211yescharacteristic
292#125—92no—
293#125—182no—
294#124—32no—
295#124—61no—
296#123—62no—
297C4×Q8—31no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×Q8—91no—
301C4×Q8—181no—
302C4×D4—32no—
303C4×D4—61no—
304#107—91no—
305#106—92no—
306C4⋊C8—92no—
307C4⋊C8—91no—
308#103—91no—
309#103—92no—
310#103—91no—
311#102—32no—
312#102—32no—
313#102—92no—
314C4×C8—31no—
315C4×C8—92no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—42no—
319C3×Q8—62no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×Q8—122no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—42no—
331C3×D4—82no—
332C3×D4—81no—
333C3×D4—81no—
334C3×D4—82no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—242no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—82no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3C2×#6712yes—
361C2×Dic3C2×#6712yes—
362Dic6—22no—
363Dic6—21no—
364Dic6—21no—
365Dic6—32no—
366Dic6—32no—
367Dic6—42no—
368Dic6—62no—
369Dic6—61no—
370Dic6—61no—
371Dic6—121no—
372C3×C8—61no—
373C3×C8—61no—
374C3⋊C8—21no—
375C3⋊C8—21no—
376C3⋊C8—62no—
377C3⋊C8—62no—
378C3⋊C8—122no—
379C2×C32—82no—
380C2×C32#54811yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C2×C32#57711yescharacteristic
383C2×Q8—31no—
384C2×Q8—31no—
385C2×Q8—61no—
386C2×Q8—91no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4C2×D3212yes—
390C22×C4—62no—
391Q16—182no—
392SD16—184no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8—92no—
396C4⋊C4—31no—
397C4⋊C4—32no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—91no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—181no—
407C22⋊C4—62no—
408C22⋊C4—62no—
409C22⋊C4—62no—
410C42—32no—
411C42—61no—
412C42—182no—
413C42—181no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—82no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C22×#6711yescharacteristic
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4—122no—
438C3×C4#91212yes—
439C3×C4#95012yes—
440C3×C4D3×#4111yescharacteristic
441C3×C4D3×#4111yescharacteristic
442C3×C4#101011yescharacteristic
443C3×C4#101011yescharacteristic
444Dic3—22no—
445Dic3—22no—
446Dic3—42no—
447Dic3—41no—
448Dic3—41no—
449Dic3—62no—
450Dic3—62no—
451Dic3—122no—
452Dic3—121no—
453Dic3—121no—
454Dic3—241no—
455C32#336511yescharacteristic, complemented, Sylow
456C23—22no—
457Q8—62no—
458Q8—61no—
459Q8—61no—
460Q8—92no—
461Q8—122no—
462Q8—181no—
463D4—22no—
464D4—22no—
465D4—42no—
466D4—81no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—242no—
475C2×C4D3×#6711yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—61no—
479C8—61no—
480C8—182no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3—162no—
487C2×C3#567711yescharacteristic
488C2×C3C2×#91211yescharacteristic
489C2×C3#576211yescharacteristic
490C2×C3C2×#95011yescharacteristic
491C2×C3#583111yescharacteristic
492C2×C3#583611yescharacteristic
493C22—42no—
494C22—42no—
495C22—42no—
496C22C2×D3×#6711yescharacteristic
497C4—21no—
498C4—62no—
499C4—62no—
500C4—121no—
501C4—122no—
502C4—121no—
503C4—182no—
504C4—361no—
505C4#6393312yes—
506C4#6430911yescharacteristic
507C4#6431211yescharacteristic
508C3—21no—
509C3#8158911yescharacteristic, complemented
510C3#8371711yescharacteristic, complemented
511C2—82no—
512C2#1059510511yescharacteristic
513C2C2×#6393311yescharacteristic
514C2#1059523711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593864C2semidirect
5. #10591478C2semidirect
6. #10591441C2semidirect
7. #10591411C2semidirect
8. #10591401C2semidirect
9. C4×#3719C2semidirect
10. #10590285C2semidirect
11. C3⋊C8×Dic6C2semidirect
455. C32#3365semidirect
509. C3#81589semidirect
510. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
#105938642
#105927742
C3×#50702
#105914782
#105914412
#105914112
#105914012
C4×#37192
#105902852
C3⋊C8×Dic62
#837173
#815893