Finite Group Databasebeta

← #11895671

Subgroups — #11895671

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic
4C3×#5075C211yesmaximal, characteristic
5#10591478C212yesmaximal, complemented
6#10591442C212yesmaximal, complemented
7Dic3×#214C212yesmaximal, complemented
8#10591409C212yesmaximal, complemented
9C4×#3718C211yesmaximal, characteristic, complemented
10#10590301C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83717—31nomaximal
13#80370—31nomaximal
14C32×#127C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#936—21no—
17C3×#936C2212yes—
18C3×#935—22no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3C2212yes—
21C2×C3×#214C2212yes—
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63869C2212yes—
26#63866—21no—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3718C2211yescharacteristic
31#63659C2212yes—
32#63659C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63576C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63565C2211yescharacteristic
41#63565C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5713D311yescharacteristic
45#5570—31no—
46#5567—31no—
47C3×#460—31no—
48#5166—32no—
49Dic3×SD16—32no—
50#5075D311yescharacteristic
51#5070—31no—
52#5070—31no—
53#5070—61no—
54#5056—32no—
55#5054—32no—
56C4×#216—31no—
57C4×#216—31no—
58Q8×C3⋊C8—31no—
59#5020—31no—
60C4×#214—32no—
61#5009—32no—
62#4851—31no—
63#4830—31no—
64#4768—32no—
65#4763—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634—21no—
70C22×C3×Dic3—22no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C32×C42C2311yescharacteristic
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×#217—22no—
80C3×#217—22no—
81C3×#217—22no—
82C3×#214—24no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—21no—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3718—22no—
98#3365—91noSylow
99C2×C3×SD16—32no—
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×Q8—31no—
109C3×C4×D4—32no—
110C3×C4×D4—61no—
111Q8×Dic3—32no—
112#944—61no—
113C2×#216—31no—
114C2×#216—31no—
115#936—21no—
116#936C2×D312yes—
117#935—22no—
118D4×Dic3—21no—
119D4×Dic3C2×D312yes—
120C2×#214C2×D312yes—
121#890—32no—
122#890—62no—
123#889—62no—
124#887—61no—
125#870—32no—
126#869—31no—
127#869—31no—
128#869—61no—
129#869—61no—
130C4×Dic6—32no—
131C4×Dic6—61no—
132C4×Dic6C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—31no—
136C3×#102—32no—
137#835—31no—
138#835—31no—
139#835—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—32no—
144#832—62no—
145#832—62no—
146#832C2×D312yes—
147#817—32no—
148#816—32no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#810—31no—
152#810—31no—
153#808—32no—
154#807—31no—
155#807—31no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8—61no—
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—22no—
171#634—42no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—82no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6#4112yes—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—21no—
186C3×C3⋊C8—22no—
187#559—31no—
188#557—91no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—31no—
195C8×Q8—91no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
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—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6#6711yescharacteristic
216C2×Dic6C22×D311yescharacteristic
217C2×Dic6C22×D311yescharacteristic
218C3×SD16—64no—
219C2×C3×C8—32no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—31no—
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×C42—61no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—22no—
236#217—22no—
237#217—22no—
238#216—62no—
239#216—62no—
240#214—24no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—121no—
249C4⋊Dic3#6711yescharacteristic
250C4⋊Dic3C22×D311yescharacteristic
251C4⋊Dic3C22×D311yescharacteristic
252Dic3⋊C4—21no—
253Dic3⋊C4—21no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4#6712yes—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3C22×D312yes—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8C22×D312yes—
271C22×C32—42no—
272C22×C32—42no—
273C22×C32—42no—
274C22×C32C22×D411yescharacteristic
275C32×C4—21no—
276C32×C4#13512yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C2×Q16—91no—
287C2×SD16—32no—
288C4⋊Q8—91no—
289C4⋊Q8—181no—
290#127D3211yescharacteristic
291#125—92no—
292#125—182no—
293#124—32no—
294#124—61no—
295#123—62no—
296C4×Q8—31no—
297C4×Q8—31no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×Q8—181no—
301C4×D4—32no—
302C4×D4—61no—
303#107—91no—
304#106—92no—
305C4⋊C8—31no—
306C4⋊C8—92no—
307#103—91no—
308#103—91no—
309#103—92no—
310#102—32no—
311#102—92no—
312#102—92no—
313C4×C8—92no—
314C4×C8—91no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—42no—
318C3×Q8—32no—
319C3×Q8—62no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×Q8—61no—
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—61no—
343C2×C3×C4—61no—
344C2×C3×C4—242no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—82no—
358C2×Dic3—122no—
359C2×Dic3C2×#6712yes—
360C2×Dic3C2×#6712yes—
361Dic6—22no—
362Dic6—21no—
363Dic6—21no—
364Dic6—21no—
365Dic6—122no—
366Dic6—122no—
367Dic6—242no—
368Dic6#23712yes—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—121no—
376C3⋊C8—121no—
377C2×C32—82no—
378C2×C32#54811yescharacteristic
379C2×C32C2×#13511yescharacteristic
380C2×C32#57711yescharacteristic
381C2×Q8—31no—
382C2×Q8—31no—
383C2×Q8—31no—
384C2×Q8—181no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4C2×D3212yes—
388C22×C4—62no—
389Q16—182no—
390SD16—64no—
391C2×C8—32no—
392C2×C8—91no—
393C2×C8—91no—
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—31no—
397C4⋊C4—31no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—92no—
401C4⋊C4—182no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C4⋊C4—181no—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—62no—
408C42—32no—
409C42—61no—
410C42—61no—
411C42—182no—
412C42C2×D3211yescharacteristic
413C22×C3—21no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—82no—
421C22×C3—82no—
422C22×C3—82no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4#91612yes—
438C3×C4#95012yes—
439C3×C4C2×#23711yescharacteristic
440C3×C4D3×#4111yescharacteristic
441C3×C4#101011yescharacteristic
442C3×C4#101011yescharacteristic
443Dic3—22no—
444Dic3—22no—
445Dic3—22no—
446Dic3—41no—
447Dic3—41no—
448Dic3—41no—
449Dic3—122no—
450Dic3—122no—
451Dic3—242no—
452C32#336511yescharacteristic, complemented, Sylow
453C23—22no—
454Q8—32no—
455Q8—61no—
456Q8—62no—
457Q8—61no—
458Q8—61no—
459Q8—362no—
460D4—22no—
461D4—22no—
462D4—42no—
463D4—81no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—182no—
471C2×C4—242no—
472C2×C4D3×#6711yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—62no—
476C8—181no—
477C8—181no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—82no—
482C2×C3—82no—
483C2×C3—162no—
484C2×C3#559811yescharacteristic
485C2×C3C2×#91611yescharacteristic
486C2×C3#577511yescharacteristic
487C2×C3C2×#95011yescharacteristic
488C2×C3#583111yescharacteristic
489C2×C3#583611yescharacteristic
490C22—42no—
491C22—42no—
492C22—42no—
493C22C2×D3×#6711yescharacteristic
494C4—21no—
495C4—62no—
496C4—62no—
497C4—62no—
498C4—121no—
499C4—121no—
500C4—121no—
501C4—362no—
502C4#6393512yes—
503C4#6430911yescharacteristic
504C4D3×#23711yescharacteristic
505C3—21no—
506C3#8037011yescharacteristic, complemented
507C3#8371711yescharacteristic, complemented
508C2—82no—
509C2#1059510611yescharacteristic
510C2C2×#6393511yescharacteristic
511C2#1059515711yescharacteristic
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. #10593860C2semidirect
5. #10591478C2semidirect
6. #10591442C2semidirect
7. Dic3×#214C2semidirect
8. #10591409C2semidirect
9. C4×#3718C2semidirect
10. #10590301C2semidirect
11. #10590250C2semidirect
452. C32#3365semidirect
506. C3#80370semidirect
507. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
#105938602
#105927692
C3×#50752
#105914782
#105914422
Dic3×#2142
#105914092
C4×#37182
#105903012
#105902502
#837173
#803703