Finite Group Databasebeta

← #11895880

Subgroups — #11895880

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593904C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic, complemented
3#10592530C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6#10590866C212yesmaximal, complemented
7#10590817C212yesmaximal, complemented
8#10590779C212yesmaximal, complemented
9#10590750C212yesmaximal
10C4×#3713C211yesmaximal, characteristic
11#10590290C211yesmaximal, characteristic, complemented
12#80993—31nomaximal
13#80416—31nomaximal
14C2×D3×Dic6—21no—
15C4×#634C2211yescharacteristic
16C2×C3×#204C2212yes—
17C3×C4×D12C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×#869C2211yescharacteristic
21#63919C2212yes—
22#63899—22no—
23#63898C2212yes—
24#63863C2212yes—
25#63858—22no—
26#63857—21no—
27#63856—21no—
28#63843C2212yes—
29#63841—21no—
30C2×#3713C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63642C2212yes—
33#63641C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#818C2212yes—
37C3×#816C2212yes—
38#63576C2211yescharacteristic
39#63565C2212yes—
40#63565C2212yes—
41#63562C2211yescharacteristic
42#63562C2211yescharacteristic
43#5732—31no—
44#5727—31no—
45#5542—31no—
46D4×Dic6—31no—
47C3×#474—31no—
48C3×#461—31no—
49#5165—32no—
50#5164—32no—
51#5093—31no—
52#5079—31no—
53C4×#213—31no—
54C4×#213—31no—
55#4889—32no—
56#4875—32no—
57#4846D311yescharacteristic, complemented
58#4841D311yescharacteristic, complemented
59#4831—31no—
60#4831—31no—
61#4831—61no—
62#4794—32no—
63#4793—32no—
64#4787—32no—
65#4765—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—44no—
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)D411yescharacteristic
79#3750D412yes—
80C4×C3⋊Dic3C2312yes—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×#204—24no—
92#3724—22no—
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3713—22no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—31no—
105C3×C4×D4—31no—
106C3×C4×D4—31no—
107#947—32no—
108#946—61no—
109Q8×Dic3—32no—
110#936—32no—
111D4×Dic3—32no—
112C2×#213—31no—
113C2×#213—31no—
114#926—61no—
115#924—61no—
116#924—61no—
117C2×#204C2×D312yes—
118#898—62no—
119#897—61no—
120#896—62no—
121#893—32no—
122#892—61no—
123#888—32no—
124#888—32no—
125#887—32no—
126#879—62no—
127#878—62no—
128C4×D12C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130#869C2×D311yescharacteristic
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C3×#107—32no—
136C3×C4⋊C8—21no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#103—32no—
140C3×#102—32no—
141#835—32no—
142#835—32no—
143#832—31no—
144#832—31no—
145#821C2×D312yes—
146#818C2×D312yes—
147#816C2×D312yes—
148#815—32no—
149#815—32no—
150#815—62no—
151Dic3⋊C8—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8—62no—
154#810—32no—
155#810—32no—
156#809—31no—
157#809—31no—
158#807—31no—
159#807—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×D412yes—
170#634—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×C4×D3—42no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—42no—
184#627—44no—
185D3×Dic3—44no—
186C32×C8—22no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—21no—
189#556—91no—
190D4×Q8—91no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—31no—
195#463—92no—
196#461—31no—
197#446—91no—
198#440—92no—
199C4×D8—91no—
200C2×C3×Q8—32no—
201C2×C3×Q8—61no—
202C2×C3×D4—31no—
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×Dic3—62no—
207D3×Q8—124no—
208C2×D12C22×D311yescharacteristic
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×Dic6—21no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—124no—
220C2×Dic6C22×D312yes—
221C3×SD16—64no—
222C2×C3×C8—22no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C22×D312yes—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C42—21no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#217—62no—
237#217—62no—
238#217—62no—
239#213—62no—
240#213—62no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—61no—
252C4⋊Dic3—62no—
253C4⋊Dic3C22×D311yescharacteristic
254C4⋊Dic3C22×D311yescharacteristic
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262C4×Dic3—32no—
263C4×Dic3—32no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273#204—24no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C32×C4—21no—
282C32×C4AGL(1,ℤ/8)12yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3⋊Dic3—22no—
286C3⋊Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C22×Q8—181no—
292C2×SD16—32no—
293C2×D8—91no—
294C4⋊Q8—31no—
295C4⋊Q8—31no—
296C4⋊Q8—92no—
297#126—182no—
298#124—92no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C22⋊Q8—181no—
302C4×Q8—91no—
303C4×Q8—92no—
304C4×D4—31no—
305C4×D4—31no—
306C4×D4—92no—
307#117—181no—
308#107—32no—
309#107—91no—
310C4⋊C8—92no—
311C4⋊C8D3211yescharacteristic
312#103—32no—
313#103—92no—
314#103—92no—
315#102—32no—
316#102—91no—
317#102—91no—
318#97—92no—
319C4×C8—91no—
320C23×C3—61no—
321C23×C3—61no—
322C22×D3—21no—
323C22×D3—21no—
324C3×Q8—62no—
325C3×Q8—62no—
326C3×Q8—122no—
327C3×D4—32no—
328C3×D4—61no—
329C3×D4—61no—
330C3×D4—61no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—122no—
339C2×C3×C4—122no—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×Dic3—21no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—124no—
357D12—21no—
358D12—21no—
359D12—21no—
360D12#23712yes—
361C4×D3—42no—
362C4×D3—42no—
363C4×D3—124no—
364Dic6—22no—
365Dic6—22no—
366Dic6—42no—
367Dic6—62no—
368Dic6—62no—
369Dic6—122no—
370Dic6—124no—
371Dic6—124no—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3⋊C8—62no—
376C3⋊C8—61no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C3⋊C8—121no—
381C2×C32#54811yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32#57811yescharacteristic
384C3×D3—42no—
385C3×D3—81no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—91no—
389C2×Q8—182no—
390C2×Q8—364no—
391C2×D4—31no—
392C2×D4—31no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—182no—
396SD16—64no—
397D8—182no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8C2×D3212yes—
401C4⋊C4—32no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4—91no—
408C4⋊C4—92no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C42—92no—
417C42—182no—
418C42C2×D3211yescharacteristic
419C22×C3—21no—
420C22×C3—62no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—41no—
440C3×C4—122no—
441C3×C4—121no—
442C3×C4—122no—
443C3×C4—121no—
444C3×C4#91112yes—
445C3×C4#91412yes—
446C3×C4C2×#23711yescharacteristic
447C3×C4#100711yescharacteristic
448C3×C4D3×#4111yescharacteristic
449C3×C4#101011yescharacteristic
450Dic3—42no—
451Dic3—41no—
452Dic3—41no—
453Dic3—42no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—122no—
459Dic3—122no—
460C32#336711yescharacteristic, complemented, Sylow
461C23—61no—
462C23—61no—
463Q8—62no—
464Q8—62no—
465Q8—122no—
466Q8—182no—
467Q8—364no—
468D4—32no—
469D4—61no—
470D4—61no—
471D4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—122no—
479C2×C4—122no—
480C2×C4—364no—
481C2×C4#380211yescharacteristic
482C2×C4#380211yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—22no—
485C8—181no—
486C8—181no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—241no—
492C2×C3#559811yescharacteristic
493C2×C3#563311yescharacteristic
494C2×C3C2×#91111yescharacteristic
495C2×C3C2×#91411yescharacteristic
496C2×C3#577911yescharacteristic
497C2×C3#577911yescharacteristic
498D3—42no—
499D3—81no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22C2×#380211yescharacteristic
507C4—21no—
508C4—121no—
509C4—121no—
510C4—122no—
511C4—122no—
512C4—182no—
513C4—182no—
514C4#6379812yes—
515C4D3×#23711yescharacteristic
516C4#6431511yescharacteristic
517C3—21no—
518C3#8041611yescharacteristic, complemented
519C3#8099311yescharacteristic, complemented
520C2—122no—
521C2—241no—
522C2#1059452511yescharacteristic
523C2C2×#6379811yescharacteristic
524C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊C8D32
hypocenterC32#3367
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. #10593904C2semidirect
2. #10593863C2semidirect
3. #10592530C2semidirect
4. C3×#4846C2semidirect
5. C3×#4841C2semidirect
6. #10590866C2semidirect
7. #10590817C2semidirect
8. #10590779C2semidirect
11. #10590290C2semidirect
57. #4846D3semidirect
58. #4841D3semidirect
460. C32#3367semidirect
518. C3#80416semidirect
519. C3#80993semidirect

Maximal subgroups

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

subgroupindex
#105939042
#105938632
#105925302
C3×#48462
C3×#48412
#105908662
#105908172
#105907792
#105907502
C4×#37132
#105902902
#809933
#804163