Finite Group Databasebeta

← #11895256

Subgroups — #11895256

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591468C212yesmaximal
6#10591401C212yesmaximal, complemented
7#10590533C212yesmaximal, complemented
8#10590492C212yesmaximal, complemented
9#10590288C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83637—31nomaximal
13#79568—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3754C2212yes—
16#64078C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×#213C2211yescharacteristic
19C2×C3×C4⋊Dic3—21no—
20C3×#924—21no—
21C3×#890C2212yes—
22C3×#878—22no—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63861—22no—
27#63860C2212yes—
28#63856—21no—
29#63844C2212yes—
30#63841—21no—
31#63637C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5584—31no—
45#5543D311yescharacteristic, complemented
46#5542—31no—
47C3×C4×D8—31no—
48#5153—32no—
49#5093—31no—
50#5084—31no—
51#5068—32no—
52#5063—32no—
53Q8×C3⋊C8—31no—
54#5019—31no—
55#5019—31no—
56#5019—61no—
57C4×#214—32no—
58#5016—32no—
59C4×#213D311yescharacteristic
60#5008—31no—
61#4877—32no—
62#4768—32no—
63#4758—32no—
64#4681—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2312yes—
69C22×C3×Dic3—22no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3754—24no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×#217—22no—
82C3×#213—22no—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3360—91noSylow
99C2×C3×D8—31no—
100C3×C4⋊Q8—31no—
101C3×#125—32no—
102C3×C22⋊Q8—62no—
103C3×C22⋊Q8—61no—
104C3×C4×Q8—31no—
105C3×C4×D4—21no—
106C3×C4×D4—32no—
107C3×C4×D4—31no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110C2×C3×C4⋊C4—61no—
111#946—61no—
112#936—32no—
113D4×Dic3C2×D312yes—
114C2×#214—32no—
115C2×#214—32no—
116C2×#214—62no—
117C2×#213C2×D311yescharacteristic
118#926—61no—
119C2×C4⋊Dic3—21no—
120#924—21no—
121#924—61no—
122#898—62no—
123#892—61no—
124#890C2×D312yes—
125#887—32no—
126#879—62no—
127#878—22no—
128#875—32no—
129C4×D12C2×D311yescharacteristic
130#869—31no—
131#869—31no—
132#869—61no—
133#869C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×#107—31no—
137C3×#102—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#832—32no—
141#832C2×D311yescharacteristic
142#816—32no—
143#816—32no—
144Dic3⋊C8—32no—
145C8×Dic3—32no—
146#810—32no—
147#810—32no—
148#810—32no—
149#810—32no—
150#810—62no—
151#809—32no—
152#809C2×D311yescharacteristic
153#808—32no—
154#808—32no—
155#807C2×D311yescharacteristic
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—21no—
163C22×C3×D3—21no—
164C32×D4—21no—
165C32×D4#4112yes—
166C2×C32×C4—21no—
167C2×C32×C4—42no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172#634—22no—
173#634—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—82no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—81no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#556—91no—
188#554—31no—
189#488—92no—
190#487—91no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—91no—
195C8×Q8—91no—
196C4×SD16—92no—
197C4×D8—31no—
198C2×C3×Q8—31no—
199C2×C3×Q8—61no—
200C2×C3×D4—21no—
201C2×C3×D4—31no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—41no—
207C22×C3×C4—62no—
208C22×C3×C4—61no—
209C22×Dic3—22no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6#6711yescharacteristic
217C3×D8—62no—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C4⋊C4C22×D311yescharacteristic
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—41no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—22no—
240#217—62no—
241#217—62no—
242#214—64no—
243#214—64no—
244#214—124no—
245#213—22no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—22no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—121no—
256C4⋊Dic3—121no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—22no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—41no—
281C32×C4#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C2×SD16—92no—
290C2×D8—31no—
291C4⋊Q8—31no—
292C4⋊Q8—91no—
293#126—182no—
294#125—32no—
295#124—92no—
296C22⋊Q8—62no—
297C22⋊Q8—61no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×Q8—92no—
301C4×D4—32no—
302C4×D4—31no—
303C4×D4D3211yescharacteristic
304#117—181no—
305C2×C4⋊C4—61no—
306#107—31no—
307#106—92no—
308C4⋊C8—92no—
309C4⋊C8—91no—
310#103—92no—
311#103—92no—
312#103—92no—
313#102—31no—
314#102—31no—
315#102—92no—
316C4×C8—31no—
317C4×C8—92no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—41no—
321C23×C3—61no—
322C22×D3—21no—
323C3×Q8—62no—
324C3×Q8—241no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—22no—
328C3×D4—41no—
329C3×D4—61no—
330C3×D4—61no—
331C3×D4#23512yes—
332C3×D4#23912yes—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—82no—
346C2×C3×C4—122no—
347C2×C3×C4—242no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—82no—
359C2×Dic3—122no—
360C2×Dic3C2×#6712yes—
361C2×Dic3C2×#6712yes—
362D12—21no—
363D12—21no—
364C4×D3—42no—
365Dic6—22no—
366Dic6—62no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—81no—
371Dic6—122no—
372Dic6—122no—
373C3×C8—61no—
374C3×C8—61no—
375C3⋊C8—21no—
376C3⋊C8—21no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C3⋊C8—122no—
380C2×C32—42no—
381C2×C32#54811yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C2×C32#57711yescharacteristic
384C3×D3—81no—
385C2×Q8—31no—
386C2×Q8—61no—
387C2×Q8—92no—
388C2×D4—31no—
389C2×D4C2×D3211yescharacteristic
390C22×C4—21no—
391C22×C4—62no—
392C22×C4—61no—
393SD16—184no—
394D8—62no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—92no—
398C4⋊C4—31no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—182no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4C2×D3211yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—62no—
411C22⋊C4—61no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C42—32no—
415C42—182no—
416C42C2×D3211yescharacteristic
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—42no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3—121no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C22×#6711yescharacteristic
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—62no—
444C3×C4—62no—
445C3×C4—81no—
446C3×C4—122no—
447C3×C4—121no—
448C3×C4#91212yes—
449C3×C4#95012yes—
450C3×C4C2×#23511yescharacteristic
451C3×C4C2×#23911yescharacteristic
452C3×C4#100711yescharacteristic
453C3×C4#101011yescharacteristic
454Dic3—22no—
455Dic3—22no—
456Dic3—41no—
457Dic3—42no—
458Dic3—122no—
459Dic3—122no—
460Dic3—242no—
461C32#336011yescharacteristic, complemented, Sylow
462C23—21no—
463C23—61no—
464Q8—62no—
465Q8—182no—
466Q8—182no—
467Q8—241no—
468D4—21no—
469D4—61no—
470D4—61no—
471D4#379912yes—
472C2×C4—21no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—42no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—122no—
479C2×C4—182no—
480C2×C4—242no—
481C2×C4D3×#6711yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—61no—
485C8—61no—
486C8—182no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—42no—
491C2×C3—42no—
492C2×C3—82no—
493C2×C3—241no—
494C2×C3#555211yescharacteristic
495C2×C3C2×#91211yescharacteristic
496C2×C3#577011yescharacteristic
497C2×C3#581711yescharacteristic
498C2×C3C2×#95011yescharacteristic
499C2×C3#583611yescharacteristic
500D3—81no—
501C22—22no—
502C22—41no—
503C22—41no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22C2×D3×#6711yescharacteristic
508C4—21no—
509C4—41no—
510C4—62no—
511C4—62no—
512C4—121no—
513C4—122no—
514C4—362no—
515C4#6393312yes—
516C4#6429711yescharacteristic
517C4C2×#379911yescharacteristic
518C3—21no—
519C3#7956811yescharacteristic, complemented
520C3#8363711yescharacteristic, complemented
521C2—42no—
522C2—241no—
523C2#1059490211yescharacteristic
524C2C2×#6393311yescharacteristic
525C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5543C2semidirect
2. #10593879C2semidirect
3. #10592718C2semidirect
6. #10591401C2semidirect
7. #10590533C2semidirect
8. #10590492C2semidirect
9. #10590288C2semidirect
10. #10590266C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5543D3semidirect
461. C32#3360semidirect
519. C3#79568semidirect
520. C3#83637semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105938792
#105927182
C3×C4×#2132
#105914682
#105914012
#105905332
#105904922
#105902882
#105902662
C3⋊C8×Dic62
#836373
#795683