Finite Group Databasebeta

← #11895367

Subgroups — #11895367

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
3#10592529C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic
6#10590868C212yesmaximal, complemented
7#10590780C212yesmaximal, complemented
8#10590777C212yesmaximal, complemented
9#10590751C212yesmaximal, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic, complemented
12#81134—31nomaximal
13#80319—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×D24C2212yes—
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×#3715C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#818C2212yes—
37C3×#816C2212yes—
38#63574C2211yescharacteristic
39#63565C2211yescharacteristic
40#63562C2212yes—
41#63562C2211yescharacteristic
42#63562C2212yes—
43#5730—31no—
44#5713—31no—
45#5585—31no—
46#5543—31no—
47C3×#477—31no—
48C3×#459—31no—
49#5153—32no—
50Dic3×D8—32no—
51#5088—31no—
52#5070—31no—
53C4×#215—31no—
54C4×#214—31no—
55#4891—32no—
56#4872—32no—
57#4850D311yescharacteristic, complemented
58#4843D311yescharacteristic
59#4830—31no—
60#4830—31no—
61#4830—61no—
62#4819—32no—
63#4800—32no—
64#4768—32no—
65#4766—32no—
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×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×C4⋊Dic3—21no—
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C3×D24—24no—
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#3715—22no—
98#3361—91noSylow
99C2×C3×D8—32no—
100C3×C4⋊Q8—31no—
101C3×#127—31no—
102C3×C4×Q8—31no—
103C3×C4×D4—31no—
104#947—32no—
105#946—62no—
106C2×#215—31no—
107#936—32no—
108#936—61no—
109#935—62no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—61no—
113C2×#214—31no—
114C2×C4⋊Dic3—61no—
115#924—61no—
116C2×D24C2×D312yes—
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×#107—32no—
135C3×C4⋊C8—21no—
136C3×C4⋊C8C2×D311yescharacteristic
137C3×C4⋊C8C2×D311yescharacteristic
138C3×#103—32no—
139C3×#102—32no—
140#835—31no—
141#832—31no—
142#832—32no—
143#832—32no—
144#821C2×D312yes—
145#818C2×D312yes—
146#816C2×D312yes—
147Dic3⋊C8—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—62no—
150C8×Dic3—32no—
151C8×Dic3—32no—
152C8×Dic3—62no—
153#810—31no—
154#809—31no—
155#809—32no—
156#809—32no—
157#808—31no—
158#808—31no—
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—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—31no—
195#463—92no—
196#459—31no—
197C8×Q8—91no—
198C4×SD16—91no—
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×D8—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×C22⋊C4—61no—
231C3×C42—21no—
232C3×C42—61no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—62no—
236#217—62no—
237#217—62no—
238#217—62no—
239#215—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—21no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—61no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3C22×D311yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254C4⋊Dic3C22×D312yes—
255Dic3⋊C4—21no—
256Dic3⋊C4—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261C4×Dic3—21no—
262C4×Dic3—32no—
263C4×Dic3—32no—
264C4×Dic3—62no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271D24—24no—
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—91no—
290C2×D8—32no—
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—32no—
307#106—91no—
308C4⋊C8—92no—
309C4⋊C8D3211yescharacteristic
310#103—32no—
311#103—91no—
312#102—32no—
313#102—91no—
314#102—92no—
315#102—92no—
316C4×C8—92no—
317C4×C8—91no—
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—61no—
327C3×D4—62no—
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#23712yes—
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—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×#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—182no—
397D8—64no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8C2×D3212yes—
401C4⋊C4—31no—
402C4⋊C4—32no—
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—122no—
442C3×C4—121no—
443C3×C4#91212yes—
444C3×C4#91912yes—
445C3×C4C2×#23711yescharacteristic
446C3×C4#100711yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4#101011yescharacteristic
449Dic3—41no—
450Dic3—41no—
451Dic3—42no—
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—62no—
468D4—61no—
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—22no—
485C8—181no—
486C8—181no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—242no—
492C2×C3#559811yescharacteristic
493C2×C3#563311yescharacteristic
494C2×C3C2×#91211yescharacteristic
495C2×C3C2×#91911yescharacteristic
496C2×C3#577411yescharacteristic
497C2×C3#577411yescharacteristic
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#6381012yes—
515C4D3×#23711yescharacteristic
516C4#6431511yescharacteristic
517C3—21no—
518C3#8031911yescharacteristic, complemented
519C3#8113411yescharacteristic, complemented
520C2—122no—
521C2—242no—
522C2#1059452511yescharacteristic
523C2C2×#6381011yescharacteristic
524C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
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. #10593956C2semidirect
2. #10593951C2semidirect
3. #10592529C2semidirect
4. C3×#4850C2semidirect
6. #10590868C2semidirect
7. #10590780C2semidirect
8. #10590777C2semidirect
9. #10590751C2semidirect
10. C4×#3715C2semidirect
11. #10590277C2semidirect
57. #4850D3semidirect
459. C32#3361semidirect
518. C3#80319semidirect
519. C3#81134semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105939512
#105925292
C3×#48502
C3×#48432
#105908682
#105907802
#105907772
#105907512
C4×#37152
#105902772
#811343
#803193