Finite Group Databasebeta

← #11895361

Subgroups — #11895361

Order 1152.

775 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#10593956C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic, complemented
3C8×#634C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6#10590868C212yesmaximal, complemented
7#10590782C212yesmaximal, complemented
8#10590750C212yesmaximal, complemented
9#10590740C212yesmaximal, complemented
10#10590347C211yesmaximal, characteristic
11#10590310C211yesmaximal, characteristic, complemented
12#81585—31nomaximal
13#79621—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×#204C2211yescharacteristic
16C3×#874C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63898C2212yes—
21#63898C2212yes—
22Dic3×D12—21no—
23D3×C4⋊Dic3—21no—
24#63887—22no—
25#63884—22no—
26#63872C2212yes—
27#63863C2212yes—
28#63860—21no—
29#63857—21no—
30C2×#3713C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×#817C2211yescharacteristic
39C3×#816C2211yescharacteristic
40#63576C2212yes—
41#63565C2212yes—
42#63562C2212yes—
43#5730—31no—
44#5713—31no—
45#5585—31no—
46#5543—31no—
47C3×#486—31no—
48C3×C4×SD16—31no—
49#5165—32no—
50#5091—31no—
51#5072—31no—
52#5021—31no—
53#5015—31no—
54#4871—32no—
55#4800—32no—
56#4787—32no—
57#4768—32no—
58#4763—32no—
59#4756—32no—
60#4756—32no—
61#4694D311yescharacteristic, complemented
62C4×#204D311yescharacteristic, complemented
63C8×Dic6—31no—
64C8×Dic6—31no—
65C8×Dic6—61no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)D411yescharacteristic
80#3750D412yes—
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C3×#204—22no—
91Dic3⋊Dic3—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#3713—24no—
98#3361—91noSylow
99C2×C3×SD16—31no—
100C3×C4⋊Q8—31no—
101C3×#127—31no—
102C3×C4×Q8—31no—
103C3×C4×D4—31no—
104#947—32no—
105#946—62no—
106#936—32no—
107#936—61no—
108#935—62no—
109D4×Dic3—32no—
110D4×Dic3—32no—
111D4×Dic3—61no—
112C2×#213—32no—
113C2×#213—32no—
114C2×C4⋊Dic3—61no—
115#924—61no—
116C2×#204C2×D311yescharacteristic
117#897—61no—
118#894—62no—
119#893—32no—
120#893—32no—
121D3×C4⋊C4—61no—
122#890—32no—
123#890—32no—
124#878—62no—
125#875—61no—
126#874C2×D311yescharacteristic
127C4×D12—61no—
128C4×D12C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C3×#106—31no—
135C3×#103—31no—
136C3×#102—31no—
137C3×#102—32no—
138C3×#102—32no—
139C3×C4×C8—21no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#835—32no—
143#832—32no—
144#821C2×D312yes—
145#821C2×D311yescharacteristic
146#821C2×D312yes—
147#817C2×D311yescharacteristic
148#816C2×D311yescharacteristic
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—62no—
152C8×Dic3—32no—
153C8×Dic3—32no—
154C8×Dic3—62no—
155#810—32no—
156#809—32no—
157#807—32no—
158#807—32no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—61no—
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×D412yes—
169#634—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C3×D12—22no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—42no—
178C3×D12—81no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—81no—
184D3×Dic3—82no—
185D3×Dic3—82no—
186C32×C8—21no—
187C32×C8—21no—
188C3⋊(C3⋊C8)—22no—
189#559—91no—
190#554—91no—
191#488—92no—
192#486—31no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—31no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×D4—31no—
203C2×C3×D4—32no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C22×C3×C4—61no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C22×D312yes—
212C2×D12C22×D311yescharacteristic
213C2×C4×D3—21no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×Dic6—21no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C2×Dic6C22×D311yescharacteristic
221C3×SD16—62no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C42—21no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#217—62no—
240#217—62no—
241#217—62no—
242#213—64no—
243#213—64no—
244(C2×D3)⋊C4—21no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257C4⋊Dic3C22×D311yescharacteristic
258Dic3⋊C4—21no—
259Dic3⋊C4—32no—
260Dic3⋊C4—32no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264C4×Dic3—21no—
265C4×Dic3—32no—
266C4×Dic3—32no—
267C4×Dic3—62no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—62no—
271#204—22no—
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C32×C4—21no—
280C32×C4#13512yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—22no—
284C3⋊Dic3—22no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C2×SD16—31no—
290C2×D8—92no—
291C4⋊Q8—31no—
292#127—31no—
293#125—92no—
294#124—92no—
295#124—181no—
296#123—182no—
297C22⋊Q8—182no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×Q8—91no—
301C4×D4—31no—
302C4×D4—92no—
303C4×D4—92no—
304C4×D4—181no—
305C2×C4⋊C4—181no—
306#107—92no—
307#106—31no—
308C4⋊C8—92no—
309C4⋊C8—91no—
310#103—31no—
311#103—92no—
312#102—31no—
313#102—32no—
314#102—32no—
315#102—92no—
316C4×C8—92no—
317C4×C8D3211yescharacteristic
318C23×C3—61no—
319C23×C3—62no—
320C22×D3—21no—
321C22×D3—22no—
322C3×Q8—61no—
323C3×Q8—61no—
324C3×Q8—241no—
325C3×D4—32no—
326C3×D4—62no—
327C3×D4—61no—
328C3×D4—62no—
329C3×D4—122no—
330C3×D4—241no—
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—61no—
338C2×C3×C4—122no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—22no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—242no—
356C2×Dic3—242no—
357D12—22no—
358D12—21no—
359D12—22no—
360D12—42no—
361D12—81no—
362D12#23512yes—
363C4×D3—42no—
364C4×D3—242no—
365C4×D3—242no—
366Dic6—21no—
367Dic6—21no—
368Dic6—64no—
369Dic6—62no—
370Dic6—62no—
371Dic6—81no—
372C3×C8—22no—
373C3×C8—21no—
374C3×C8—21no—
375C3×C8—21no—
376C3×C8—21no—
377C3×C8—41no—
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—122no—
381C2×C32#54811yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C2×C32#57611yescharacteristic
384C3×D3—42no—
385C3×D3—82no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8—91no—
389C2×D4—31no—
390C2×D4—32no—
391C2×D4—61no—
392C2×D4—61no—
393C22×C4—61no—
394C22×C4—182no—
395C22×C4—182no—
396SD16—62no—
397D8—184no—
398C2×C8—92no—
399C2×C8C2×D3211yescharacteristic
400C2×C8C2×D3211yescharacteristic
401C4⋊C4—32no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—91no—
407C4⋊C4—92no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C22⋊C4—61no—
411C22⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C42—61no—
416C42—92no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3—62no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—22no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—41no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—122no—
443C3×C4#91612yes—
444C3×C4#91612yes—
445C3×C4C2×#23511yescharacteristic
446C3×C4D3×#4111yescharacteristic
447C3×C4#101011yescharacteristic
448C3×C4#101011yescharacteristic
449Dic3—42no—
450Dic3—41no—
451Dic3—41no—
452Dic3—41no—
453Dic3—64no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—122no—
459C32#336111yescharacteristic, complemented, Sylow
460C23—61no—
461C23—62no—
462Q8—61no—
463Q8—61no—
464Q8—182no—
465Q8—241no—
466D4—32no—
467D4—61no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—241no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—122no—
479C2×C4—722no—
480C2×C4—722no—
481C2×C4#380211yescharacteristic
482C2×C4#380211yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—21no—
485C8—21no—
486C8—182no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—242no—
492C2×C3#555211yescharacteristic
493C2×C3#567711yescharacteristic
494C2×C3#575711yescharacteristic
495C2×C3C2×#91611yescharacteristic
496C2×C3C2×#91611yescharacteristic
497C2×C3#576911yescharacteristic
498D3—42no—
499D3—82no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—122no—
504C22—122no—
505C22—122no—
506C22C2×#380211yescharacteristic
507C4—21no—
508C4—121no—
509C4—121no—
510C4—122no—
511C4—121no—
512C4—182no—
513C4—182no—
514C4#6380912yes—
515C4#6429811yescharacteristic
516C4D3×#23511yescharacteristic
517C3—21no—
518C3#7962111yescharacteristic, complemented
519C3#8158511yescharacteristic, complemented
520C2—122no—
521C2—242no—
522C2#1059390511yescharacteristic
523C2#1059468711yescharacteristic
524C2C2×#6380911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590347C2
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. #10593956C2semidirect
2. #10593951C2semidirect
3. C8×#634C2semidirect
4. C3×#4694C2semidirect
5. C3×C4×#204C2semidirect
6. #10590868C2semidirect
7. #10590782C2semidirect
8. #10590750C2semidirect
9. #10590740C2semidirect
11. #10590310C2semidirect
61. #4694D3semidirect
62. C4×#204D3semidirect
459. C32#3361semidirect
518. C3#79621semidirect
519. C3#81585semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105939512
C8×#6342
C3×#46942
C3×C4×#2042
#105908682
#105907822
#105907502
#105907402
#105903472
#105903102
#815853
#796213