Finite Group Databasebeta

← #11897577

Subgroups — #11897577

Order 1152.

802 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#10593903C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590894C212yesmaximal, complemented
7#10590774C212yesmaximal, complemented
8#10590757C212yesmaximal, complemented
9#10590746C212yesmaximal
10C4×#3714C211yesmaximal, characteristic
11#10590303C211yesmaximal, characteristic, complemented
12#80959—31nomaximal
13#79975—31nomaximal
14C2×#3797—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63918C2212yes—
21#63896—22no—
22#63895—22no—
23#63894C2212yes—
24Dic3×D12C2212yes—
25D3×C4⋊Dic3—21no—
26#63871—21no—
27#63869C2212yes—
28#63856—21no—
29C2×#3714C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31#63648C2212yes—
32#63644C2212yes—
33C3×#821C2212yes—
34C3×#818C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63573C2212yes—
40#63573C2212yes—
41#63564C2211yescharacteristic
42#63563C2211yescharacteristic
43#5727—31no—
44#5579—31no—
45Q8×D12—31no—
46#5543—31no—
47C3×#474—31no—
48C3×#446—31no—
49#5080—31no—
50C4×#213—31no—
51#4891—32no—
52#4876—32no—
53#4847—32no—
54#4846D311yescharacteristic, complemented
55#4842—31no—
56#4842—31no—
57#4842—32no—
58#4842—61no—
59#4831D311yescharacteristic, complemented
60#4785—32no—
61#4761—32no—
62#4711—32no—
63#4702—32no—
64C4×D24—31no—
65#4680—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×#624—22no—
75C2×D3×Dic3—22no—
76#3797—44no—
77C2×C32×C8C2312yes—
78C32×C42C2311yescharacteristic
79#3752—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2312yes—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92#3724—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95#3722—22no—
96(C2×D3)⋊Dic3—22no—
97#3714Q814yescomplemented
98#3384—91noSylow
99C2×D3×Q8—61no—
100C2×D3×Q8—61no—
101C3×C4⋊Q8—31no—
102C3×C4×Q8—31no—
103C3×C4×D4—31no—
104#946—61no—
105#946—61no—
106D4×Dic3—32no—
107C2×#213—31no—
108C2×C4⋊Dic3—61no—
109#924—61no—
110C2×D24—31no—
111#897—62no—
112#897—61no—
113#896—62no—
114#896—62no—
115#893—32no—
116D3×C4⋊C4—61no—
117#890—32no—
118#888—32no—
119#878—62no—
120C4×D12—32no—
121C4×D12—31no—
122C4×D12—31no—
123C4×D12—32no—
124C4×D12—61no—
125C4×D12C2×D311yescharacteristic
126#870—32no—
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869C2×D311yescharacteristic
132C4×Dic6C2×D311yescharacteristic
133C3×#107—32no—
134C3×C4⋊C8—21no—
135C3×C4⋊C8—32no—
136C3×C4⋊C8C2×D311yescharacteristic
137C3×C4⋊C8C2×D311yescharacteristic
138C3×#102—32no—
139C3×#97—32no—
140C3×C4×C8—31no—
141#832—31no—
142#821—31no—
143#821—32no—
144#821—32no—
145#821—31no—
146#821—62no—
147#821C2×D312yes—
148#818—31no—
149#818C2×D312yes—
150#817—32no—
151#817—32no—
152#817—32no—
153#817—32no—
154#817—62no—
155#815C2×D312yes—
156Dic3⋊C8C2×D312yes—
157#809—31no—
158#808—32no—
159#808—32no—
160#807—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)C2×Q812yes—
171C4×C3⋊D3—42no—
172#634—81no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12C2×Q812yescomplemented
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—42no—
182#627—44no—
183#624—44no—
184D3×Dic3—82no—
185C32×C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yescomplemented
188#554—91no—
189D4×Q8—91no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—92no—
194#476—91no—
195#474—31no—
196#446—31no—
197#442—92no—
198C4×D8—91no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×C3×D4—31no—
202C22×C3×C4—61no—
203C22×Dic3—62no—
204D3×Q8—124no—
205D3×Q8—124no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—62no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—121no—
217C2×Dic6—21no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—121no—
223C2×Dic6D1211yescharacteristic
224C2×C3×C8—22no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C2×C3×C8C22×D312yes—
228C2×C3×C8C22×D312yes—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—62no—
240#213—34no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—61no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—121no—
248C4⋊Dic3—21no—
249C4⋊Dic3—31no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3D1211yescharacteristic
261C4⋊Dic3C22×D312yes—
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4D1212yes—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271D24—34no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4AGL(1,ℤ/8)12yes—
281C32×C4C22×Q811yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—41no—
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C22×Q8—181no—
290C2×D8—91no—
291C4⋊Q8—31no—
292C4⋊Q8—92no—
293C4⋊Q8—91no—
294#125—92no—
295C22⋊Q8—182no—
296C22⋊Q8—182no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×D4—31no—
301C4×D4—92no—
302C4×D4—92no—
303C4×D4—91no—
304C2×C4⋊C4—181no—
305#107—32no—
306#107—91no—
307#106—92no—
308#106—92no—
309#106—92no—
310C4⋊C8—32no—
311C4⋊C8D3211yescharacteristic
312#102—32no—
313#102—91no—
314#102—91no—
315#102—92no—
316#97—32no—
317C4×C8—31no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—121no—
323C3×Q8—62no—
324C3×Q8—122no—
325C3×D4—32no—
326C3×D4—61no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—122no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—22no—
343C2×Dic3—61no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—122no—
348C2×Dic3—121no—
349C2×Dic3—242no—
350C2×Dic3C2×D1212yes—
351C2×Dic3C2×D1212yes—
352D12—21no—
353D12—32no—
354D12—32no—
355D12—62no—
356D12—61no—
357D12—61no—
358D12—121no—
359D12D3×Q812yescomplemented
360C4×D3—42no—
361C4×D3—124no—
362C4×D3—124no—
363C4×D3—122no—
364C4×D3—122no—
365C4×D3—242no—
366C4×D3—242no—
367Dic6—22no—
368Dic6—42no—
369Dic6—124no—
370Dic6—124no—
371Dic6—241no—
372Dic6—241no—
373Dic6—242no—
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—32no—
377C3×C8—42no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8D3×Q812yescomplemented
381C2×C32D4×Q811yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32#57711yescharacteristic
384C3⋊D3—42no—
385C3×D3—42no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8—182no—
389C2×Q8—181no—
390C2×Q8—364no—
391C2×D4—31no—
392C2×D4—91no—
393C22×C4—61no—
394C22×C4—182no—
395C22×C4—182no—
396C22×C4—181no—
397D8—94no—
398C2×C8—31no—
399C2×C8—31no—
400C2×C8C2×D3212yes—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—32no—
404C4⋊C4—31no—
405C4⋊C4—61no—
406C4⋊C4—92no—
407C4⋊C4—91no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—181no—
412C22⋊C4—61no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C22⋊C4—181no—
416C42—32no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3—62no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3C22×D1211yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
424C2×D3—22no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—122no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—241no—
435C2×D3—241no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—41no—
442C3×C4—62no—
443C3×C4—62no—
444C3×C4—122no—
445C3×C4—121no—
446C3×C4#90812yes—
447C3×C4#91112yes—
448C3×C4C2×D3×Q811yescharacteristic
449C3×C4C2×D3×Q811yescharacteristic
450C3×C4#101011yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—22no—
454Dic3—42no—
455Dic3—41no—
456Dic3—121no—
457Dic3—122no—
458Dic3—121no—
459Dic3—122no—
460Dic3—242no—
461Dic3—241no—
462C32#338411yescharacteristic, complemented, Sylow
463C23—61no—
464C23—181no—
465Q8—62no—
466Q8—122no—
467Q8—364no—
468Q8—721no—
469D4—32no—
470D4—61no—
471D4—92no—
472D4—181no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4—122no—
478C2×C4—182no—
479C2×C4—181no—
480C2×C4—364no—
481C2×C4—362no—
482C2×C4—722no—
483C2×C4D3×D1211yescharacteristic
484C2×C4D3×D1211yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—22no—
487C8—32no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—122no—
493C2×C3Q8×D1211yescharacteristic
494C2×C3#563211yescharacteristic
495C2×C3C2×#90811yescharacteristic
496C2×C3#575111yescharacteristic
497C2×C3C2×#91111yescharacteristic
498C2×C3#577811yescharacteristic
499D3—42no—
500D3—122no—
501D3—122no—
502D3—242no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—182no—
507C22—361no—
508C22—361no—
509C22C2×D3×D1211yescharacteristic
510C4—21no—
511C4—62no—
512C4—62no—
513C4—121no—
514C4—122no—
515C4—361no—
516C4—362no—
517C4#6379512yes—
518C4#6430911yescharacteristic
519C4D32×Q811yescharacteristic
520C3—21no—
521C3#7997511yescharacteristic, complemented
522C3#8095911yescharacteristic, complemented
523C2—122no—
524C2—362no—
525C2#1059438311yescharacteristic
526C2C2×#6379511yescharacteristic
527C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊C8D32
hypocenterC32#3384
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. #10593903C2semidirect
3. #10592541C2semidirect
4. C3×#4846C2semidirect
5. C3×#4831C2semidirect
6. #10590894C2semidirect
7. #10590774C2semidirect
8. #10590757C2semidirect
11. #10590303C2semidirect
54. #4846D3semidirect
59. #4831D3semidirect
97. #3714Q8semidirect
178. C3×D12C2×Q8semidirect
187. C3×C3⋊C8C2×Q8semidirect
359. D12D3×Q8semidirect
380. C3⋊C8D3×Q8semidirect
462. C32#3384semidirect
521. C3#79975semidirect
522. C3#80959semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105939032
#105925412
C3×#48462
C3×#48312
#105908942
#105907742
#105907572
#105907462
C4×#37142
#105903032
#809593
#799753