Finite Group Databasebeta

← #11895351

Subgroups — #11895351

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592720C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591567C212yesmaximal, complemented
7#10590545C212yesmaximal, complemented
8#10590452C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic
10#10590273C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83713—31nomaximal
13#79621—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#947C2212yes—
17C2×C3×#215C2211yescharacteristic
18C3×#894—22no—
19C3×#893C2212yes—
20C3×#875—21no—
21C3×#874C2211yescharacteristic
22C3×C4×D12—21no—
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3713C2212yes—
31#63662C2212yes—
32#63634C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#835C2211yescharacteristic
35C3×#809C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5585D311yescharacteristic, complemented
45#5579—31no—
46#5543—31no—
47C3×C4×SD16—31no—
48#5165—32no—
49#5072—31no—
50#5070—31no—
51#5057—32no—
52#5056—32no—
53C4×#215D311yescharacteristic, complemented
54Q8×C3⋊C8—31no—
55#5021—31no—
56#5021—31no—
57#5021—61no—
58#5015—31no—
59C4×#213—32no—
60#5009—32no—
61#4871—32no—
62#4800—32no—
63#4756—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6D411yescharacteristic
75C2×D3×Dic3—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C42—21no—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#215—22no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3713—24no—
98#3361—91noSylow
99C2×C3×SD16—31no—
100C3×#127—31no—
101C3×#124—32no—
102C3×#124—61no—
103C3×#123—62no—
104C3×C4×Q8—21no—
105C3×C4×Q8—31no—
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×D4—32no—
109C3×C4×D4—31no—
110C3×C4×D4—61no—
111#947C2×D312yes—
112#946—61no—
113C2×#215C2×D311yescharacteristic
114D4×Dic3—32no—
115C2×#213—32no—
116C2×#213—32no—
117C2×C4⋊Dic3—61no—
118#924—61no—
119#896—62no—
120#894—22no—
121#893C2×D312yes—
122D3×C4⋊C4—61no—
123#890—32no—
124#878—62no—
125#875—21no—
126#874C2×D311yescharacteristic
127C4×D12—21no—
128C4×D12—32no—
129C4×D12C2×D311yescharacteristic
130#870—32no—
131#869—31no—
132#869—31no—
133#869—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×#106—31no—
136C3×#103—31no—
137C3×#102—31no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—62no—
142#835C2×D311yescharacteristic
143#832—32no—
144#832—32no—
145#832—32no—
146#821—32no—
147#821—32no—
148Dic3⋊C8—32no—
149C8×Dic3—32no—
150#809—32no—
151#809C2×D311yescharacteristic
152#808C2×D311yescharacteristic
153#807—32no—
154#807—32no—
155#807—62no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C32×Q8—21no—
165C32×Q8—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172#634—81no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—42no—
180C3×D12—81no—
181C3×D12#4112yes—
182C3×C4×D3—42no—
183C3×C4×D3—82no—
184C3×Dic6—22no—
185D3×Dic3—82no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—31no—
190#554—91no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—31no—
199C4×D8—92no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×D4—31no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×Dic3—62no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12C22×D312yes—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×C4×D3—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—121no—
221C2×Dic6#6711yescharacteristic
222C3×SD16—62no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—61no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42—41no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#217—62no—
246#215—22no—
247#213—64no—
248#213—64no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—121no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4#6712yes—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—62no—
271C2×C3⋊C8C22×D311yescharacteristic
272C2×C3⋊C8C22×D311yescharacteristic
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—21no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4#13512yes—
284C32×C4C2×#4111yescharacteristic
285C32×C42−1+411yescharacteristic
286C3⋊Dic3—42no—
287C3×Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—41no—
290C2×SD16—31no—
291C2×D8—92no—
292C4⋊Q8—91no—
293#127—31no—
294#125—92no—
295#124—32no—
296#124—61no—
297#123—62no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8D3211yescharacteristic
302C4×D4—32no—
303C4×D4—31no—
304C4×D4—61no—
305C4×D4—92no—
306C2×C4⋊C4—181no—
307#107—92no—
308#106—31no—
309C4⋊C8—92no—
310C4⋊C8—91no—
311#103—31no—
312#103—92no—
313#102—31no—
314#102—92no—
315#102—92no—
316#102—92no—
317C4×C8—31no—
318C4×C8—92no—
319C23×C3—61no—
320C23×C3—62no—
321C22×D3—21no—
322C22×D3—22no—
323C3×Q8—22no—
324C3×Q8—21no—
325C3×Q8—21no—
326C3×Q8—21no—
327C3×Q8—21no—
328C3×Q8—41no—
329C3×Q8—62no—
330C3×D4—32no—
331C3×D4—62no—
332C3×D4—61no—
333C3×D4—62no—
334C3×D4—122no—
335C3×D4—241no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—61no—
348C2×C3×C4—122no—
349C2×C3×C4—242no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—242no—
361C2×Dic3C2×#6712yes—
362C2×Dic3C2×#6712yes—
363D12—22no—
364D12—21no—
365D12—22no—
366D12—42no—
367D12—81no—
368D12#23512yes—
369C4×D3—42no—
370C4×D3—82no—
371C4×D3—242no—
372Dic6—22no—
373Dic6—241no—
374Dic6—241no—
375Dic6—242no—
376C3×C8—61no—
377C3×C8—61no—
378C3⋊C8—21no—
379C3⋊C8—21no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C3⋊C8—122no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57611yescharacteristic
386C3×D3—42no—
387C3×D3—82no—
388C2×Q8—31no—
389C2×Q8—181no—
390C2×Q8C2×D3211yescharacteristic
391C2×D4—31no—
392C2×D4—32no—
393C2×D4—61no—
394C2×D4—61no—
395C22×C4—62no—
396C22×C4—61no—
397C22×C4—182no—
398SD16—62no—
399D8—184no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8—92no—
403C4⋊C4—21no—
404C4⋊C4—31no—
405C4⋊C4—32no—
406C4⋊C4—31no—
407C4⋊C4—92no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4C2×D3211yescharacteristic
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—61no—
416C22⋊C4—182no—
417C42—21no—
418C42—32no—
419C42C2×D3211yescharacteristic
420C22×C3—21no—
421C22×C3—62no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C22×#6711yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—81no—
449C3×C4—121no—
450C3×C4#91612yes—
451C3×C4#95012yes—
452C3×C4C2×#23511yescharacteristic
453C3×C4D3×#4111yescharacteristic
454C3×C4#101011yescharacteristic
455C3×C4#101011yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—41no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462C32#336111yescharacteristic, complemented, Sylow
463C23—61no—
464C23—62no—
465Q8—21no—
466Q8—21no—
467Q8—62no—
468Q8—721no—
469D4—32no—
470D4—61no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—61no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—242no—
483C2×C4—722no—
484C2×C4D3×#6711yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—61no—
488C8—61no—
489C8—182no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3—242no—
495C2×C3#555211yescharacteristic
496C2×C3C2×#91611yescharacteristic
497C2×C3#576911yescharacteristic
498C2×C3C2×#95011yescharacteristic
499C2×C3#583111yescharacteristic
500C2×C3#583511yescharacteristic
501D3—42no—
502D3—82no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22C2×D3×#6711yescharacteristic
510C4—21no—
511C4—41no—
512C4—41no—
513C4—62no—
514C4—62no—
515C4—121no—
516C4—362no—
517C4#6394712yes—
518C4#6429811yescharacteristic
519C4D3×#23511yescharacteristic
520C3—21no—
521C3#7962111yescharacteristic, complemented
522C3#8371311yescharacteristic, complemented
523C2—122no—
524C2—242no—
525C2#1059489911yescharacteristic
526C2C2×#6394711yescharacteristic
527C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590347C2
hypercenterC4×Q8D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5585C2semidirect
2. #10593960C2semidirect
3. #10592720C2semidirect
4. C3×C4×#215C2semidirect
5. #10591614C2semidirect
6. #10591567C2semidirect
7. #10590545C2semidirect
8. #10590452C2semidirect
10. #10590273C2semidirect
11. C3⋊C8×Dic6C2semidirect
44. #5585D3semidirect
53. C4×#215D3semidirect
462. C32#3361semidirect
521. C3#79621semidirect
522. C3#83713semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
#105939602
#105927202
C3×C4×#2152
#105916142
#105915672
#105905452
#105904522
#105903472
#105902732
C3⋊C8×Dic62
#837133
#796213