Finite Group Databasebeta

← #11895369

Subgroups — #11895369

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
1#10593960C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic, complemented
3#10592549C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590863C212yesmaximal, complemented
7#10590767C212yesmaximal, complemented
8Dic3×D24C212yesmaximal, complemented
9#10590755C212yesmaximal, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic, complemented
12#80319—31nomaximal
13#79927—31nomaximal
14#64078C2211yescharacteristic
15C4×#634C2211yescharacteristic
16C2×C3×D24C2212yes—
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63898—21no—
21#63896—22no—
22Dic3×D12C2212yes—
23Dic3×D12C2212yes—
24D3×C4⋊Dic3—21no—
25#63884—22no—
26#63869C2212yes—
27#63863—21no—
28#63860C2212yes—
29#63856—21no—
30C2×#3716C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63645C2212yes—
33#63643C2212yes—
34C3×#821C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63567C2211yescharacteristic
40#63563C2212yes—
41#63563C2211yescharacteristic
42#63563C2212yes—
43#5713—31no—
44#5585—31no—
45#5579—31no—
46#5543—31no—
47C3×#459—31no—
48C3×C8×Q8—31no—
49#5153—32no—
50Dic3×D8—32no—
51#5070—31no—
52C4×#214—31no—
53#4850—31no—
54#4850—31no—
55#4850—61no—
56#4847—32no—
57#4844—32no—
58#4843D311yescharacteristic
59#4830D311yescharacteristic, complemented
60#4768—32no—
61#4766—32no—
62#4697—32no—
63#4694—31no—
64C4×D24—32no—
65C4×#204—31no—
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C3×D24—24no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3716—22no—
98#3361—91noSylow
99C2×C3×D8—32no—
100C3×#127—31no—
101C3×C4×Q8—31no—
102C3×C4×D4—31no—
103#947—61no—
104#946—61no—
105#936—32no—
106#936—61no—
107#935—62no—
108D4×Dic3—32no—
109D4×Dic3—32no—
110D4×Dic3—61no—
111C2×#214—31no—
112C2×C4⋊Dic3—61no—
113#924—61no—
114C2×D24C2×D312yes—
115C2×#204—31no—
116#896—62no—
117#894—62no—
118#893—61no—
119D3×C4⋊C4—61no—
120#890—32no—
121#878—62no—
122#875—32no—
123#874C2×D311yescharacteristic
124C4×D12—32no—
125C4×D12—32no—
126C4×D12C2×D311yescharacteristic
127#870—32no—
128#869—31no—
129#869—31no—
130#869—61no—
131C4×Dic6—31no—
132C4×Dic6—31no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—21no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#102—32no—
140C3×C4×C8—32no—
141C3×C4×C8—31no—
142#832—31no—
143#832—32no—
144#832—32no—
145#821—31no—
146#821—32no—
147#821—32no—
148#821C2×D312yes—
149#818—32no—
150#818—32no—
151#818—62no—
152#817—31no—
153#816—32no—
154#816—32no—
155#816—31no—
156#816—62no—
157Dic3⋊C8C2×D312yes—
158C8×Dic3C2×D312yes—
159#810—31no—
160#808—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170#634—21no—
171#634—21no—
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×Dic6—22no—
184D3×Dic3—82no—
185D3×Dic3—82no—
186C32×C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—91no—
190#554—91no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—31no—
197C8×Q8—31no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×D4—31no—
202C2×C3×D4—32no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C22×C3×C4—61no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—121no—
221C2×Dic6D1211yescharacteristic
222C3×D8—64no—
223C2×C3×C8—22no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C22⋊C4—61no—
232C3×C42—21no—
233C3×C42—32no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#217—62no—
237#217—62no—
238#217—62no—
239#217—62no—
240#214—62no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—31no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—31no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—121no—
256C4⋊Dic3D1211yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—62no—
263Dic3⋊C4—121no—
264Dic3⋊C4D1212yes—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—121no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271D24—24no—
272#204—62no—
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#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—42no—
287C3×Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—41no—
290C2×SD16—91no—
291C2×D8—32no—
292C4⋊Q8—91no—
293#127—31no—
294#125—92no—
295#124—92no—
296#124—181no—
297#123—182no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—91no—
302C4×D4—31no—
303C4×D4—92no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C4⋊C4—181no—
307#107—92no—
308#106—91no—
309C4⋊C8—32no—
310C4⋊C8D3211yescharacteristic
311#103—91no—
312#103—92no—
313#102—32no—
314#102—91no—
315#102—92no—
316#102—92no—
317C4×C8—32no—
318C4×C8—31no—
319C23×C3—61no—
320C23×C3—62no—
321C22×D3—21no—
322C22×D3—22no—
323C3×Q8—62no—
324C3×D4—32no—
325C3×D4—61no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—122no—
329C3×D4—241no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—61no—
336C2×C3×C4—122no—
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—21no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—62no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—62no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—122no—
353C2×Dic3—242no—
354C2×Dic3—242no—
355C2×Dic3C2×D1212yes—
356C2×Dic3C2×D1212yes—
357D12—22no—
358D12—21no—
359D12—22no—
360D12—42no—
361D12—81no—
362D12#23712yes—
363C4×D3—42no—
364C4×D3—242no—
365C4×D3—242no—
366Dic6—22no—
367Dic6—62no—
368Dic6—61no—
369Dic6—61no—
370Dic6—61no—
371Dic6—61no—
372Dic6—121no—
373Dic6—241no—
374Dic6—241no—
375Dic6—242no—
376C3×C8—22no—
377C3×C8—22no—
378C3×C8—42no—
379C3×C8—61no—
380C3×C8—61no—
381C3⋊C8—21no—
382C3⋊C8—21no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57611yescharacteristic
386C3×D3—42no—
387C3×D3—82no—
388C2×Q8—31no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—31no—
392C2×D4—32no—
393C2×D4—61no—
394C2×D4—61no—
395C22×C4—61no—
396C22×C4—182no—
397C22×C4—182no—
398SD16—182no—
399D8—64no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8C2×D3212yes—
403C4⋊C4—31no—
404C4⋊C4—32no—
405C4⋊C4—31no—
406C4⋊C4—92no—
407C4⋊C4—91no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C22⋊C4—61no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C42—32no—
418C42—181no—
419C42C2×D3211yescharacteristic
420C22×C3—21no—
421C22×C3—62no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C22×D1211yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
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—62no—
442C3×C4—62no—
443C3×C4—121no—
444C3×C4#90412yes—
445C3×C4#91212yes—
446C3×C4C2×#23711yescharacteristic
447C3×C4#100711yescharacteristic
448C3×C4D3×#4111yescharacteristic
449C3×C4#101011yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—41no—
453Dic3—122no—
454Dic3—122no—
455Dic3—121no—
456Dic3—122no—
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460Dic3—242no—
461Dic3—241no—
462C32#336111yescharacteristic, complemented, Sylow
463C23—61no—
464C23—62no—
465Q8—62no—
466Q8—181no—
467Q8—181no—
468Q8—721no—
469D4—32no—
470D4—62no—
471D4—61no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—61no—
478C2×C4—122no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—182no—
482C2×C4—722no—
483C2×C4—722no—
484C2×C4D3×D1211yescharacteristic
485C2×C4D3×D1211yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—22no—
488C8—61no—
489C8—61no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3—242no—
495C2×C3#557611yescharacteristic
496C2×C3#559811yescharacteristic
497C2×C3C2×#90411yescharacteristic
498C2×C3#575211yescharacteristic
499C2×C3C2×#91211yescharacteristic
500C2×C3#577411yescharacteristic
501D3—42no—
502D3—82no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22C2×D3×D1211yescharacteristic
510C4—21no—
511C4—62no—
512C4—62no—
513C4—121no—
514C4—361no—
515C4—361no—
516C4—362no—
517C4#6380712yes—
518C4D3×#23711yescharacteristic
519C4#6431511yescharacteristic
520C3—21no—
521C3#7992711yescharacteristic, complemented
522C3#8031911yescharacteristic, complemented
523C2—122no—
524C2—242no—
525C2#1059438211yescharacteristic
526C2C2×#6380711yescharacteristic
527C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC3×#4843C2
hypercenterC4⋊C8D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593960C2semidirect
2. #10593951C2semidirect
3. #10592549C2semidirect
5. C3×#4830C2semidirect
6. #10590863C2semidirect
7. #10590767C2semidirect
8. Dic3×D24C2semidirect
9. #10590755C2semidirect
10. C4×#3716C2semidirect
11. #10590273C2semidirect
59. #4830D3semidirect
462. C32#3361semidirect
521. C3#79927semidirect
522. C3#80319semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105939512
#105925492
C3×#48432
C3×#48302
#105908632
#105907672
Dic3×D242
#105907552
C4×#37162
#105902732
#803193
#799273