Finite Group Databasebeta

← #11896080

Subgroups — #11896080

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic
5#10590541C212yesmaximal
6#10590538C212yesmaximal
7#10590497C212yesmaximal, complemented
8#10590485C212yesmaximal, complemented
9#10590388C211yesmaximal, characteristic, complemented
10C4×#3716C211yesmaximal, characteristic
11#10590296C211yesmaximal, characteristic, complemented
12#81626—31nomaximal
13#81091—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64153—22no—
16#64097—21no—
17#64097C2212yes—
18#64096—21no—
19#64096C2212yes—
20C4×#634C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63863C2212yes—
25#63858—22no—
26#63857—21no—
27#63843C2212yes—
28#63841—21no—
29C2×#3719C2212yes—
30C2×#3716C2211yescharacteristic
31C3×#810C2212yes—
32C3×#810C2212yes—
33C3×#809C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63567C2211yescharacteristic
40#63566C2212yes—
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5732—31no—
44#5722—31no—
45#5722—31no—
46#5722—61no—
47#5542—31no—
48C3×#487—31no—
49C3×#476—31no—
50#5093D311yescharacteristic, complemented
51#5090—31no—
52#5084D311yescharacteristic
53C4×#214—31no—
54#4854—32no—
55#4853—32no—
56#4849—31no—
57#4831—31no—
58#4798—32no—
59#4794—32no—
60#4791—32no—
61#4789—32no—
62#4767—32no—
63#4765—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×#634—22no—
68C2×#634D411yescharacteristic
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79#3750—22no—
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3—21no—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3719—24no—
97#3716—22no—
98#3369—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×C4×D4—31no—
104#947—32no—
105Q8×Dic3—32no—
106#944—62no—
107#944—62no—
108#944—64no—
109C2×#216—32no—
110#936—32no—
111C2×#214—31no—
112#926—61no—
113#924—61no—
114C2×Dic12—32no—
115C2×#204—31no—
116#898—62no—
117#897—61no—
118#892—61no—
119#888—32no—
120#888—32no—
121#888—62no—
122#888—61no—
123#888—61no—
124#888—62no—
125#887—32no—
126#887—32no—
127#887—32no—
128#887—62no—
129#887—61no—
130#887—61no—
131#887—62no—
132#879—62no—
133C4×D12C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6—31no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C3×#106—32no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—32no—
148#832—31no—
149#821—31no—
150#817—31no—
151#816—32no—
152#816—31no—
153#815—32no—
154#815—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157#810—31no—
158#810C2×D312yes—
159#810C2×D312yes—
160#809C2×D312yes—
161#808—31no—
162#808C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3—21no—
166C32×Q8—81no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175#634—22no—
176#634—21no—
177#634—82no—
178#634#4112yes—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189Q82—91no—
190#556—91no—
191#489—92no—
192#487—31no—
193#476—31no—
194#475—92no—
195#464—92no—
196#462—91no—
197#446—91no—
198#441—92no—
199C4×SD16—91no—
200C2×C3×Q8—22no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—32no—
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—64no—
217C2×Dic6C22×D312yes—
218C2×C3×C8—31no—
219C2×C3×C8—32no—
220C2×C3×C8—31no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4C22×D312yes—
229C3×C4⋊C4C22×D312yes—
230C3×C22⋊C4—61no—
231C3×C42—21no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#217—62no—
236#216—64no—
237#214—62no—
238(C2×D3)⋊C4—21no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3C22×D311yescharacteristic
251Dic3⋊C4—32no—
252Dic3⋊C4—32no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264C4×Dic3—32no—
265C4×Dic3—32no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—64no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C2×C3⋊C8C22×D311yescharacteristic
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D312yes—
278Dic12—64no—
279#204—62no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4—21no—
285C32×C4—42no—
286C32×C4#13712yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3—22no—
292C3⋊Dic3—41no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C2×Q16—92no—
296C2×SD16—91no—
297C4⋊Q8—31no—
298C4⋊Q8—92no—
299C4⋊Q8—181no—
300C4⋊Q8—182no—
301C4⋊Q8D3211yescharacteristic
302#126—182no—
303#124—92no—
304C22⋊Q8—181no—
305C4×Q8—91no—
306C4×Q8—92no—
307C4×Q8—92no—
308C4×Q8—91no—
309C4×Q8—181no—
310C4×D4—31no—
311#117—181no—
312#106—32no—
313#106—91no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—32no—
317#103—32no—
318#103—91no—
319#103—92no—
320#102—32no—
321#102—91no—
322#97—92no—
323C4×C8—31no—
324C23×C3—61no—
325C22×D3—21no—
326C3×Q8—62no—
327C3×Q8—62no—
328C3×Q8—81no—
329C3×Q8—81no—
330C3×Q8—82no—
331C3×D4—61no—
332C3×D4—61no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—61no—
340C2×C3×C4—62no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
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—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—62no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362D12—21no—
363D12—21no—
364C4×D3—42no—
365Dic6—22no—
366Dic6—22no—
367Dic6—32no—
368Dic6—32no—
369Dic6—62no—
370Dic6—62no—
371Dic6—64no—
372Dic6—62no—
373Dic6—62no—
374Dic6—61no—
375Dic6—61no—
376Dic6—242no—
377Dic6—242no—
378Dic6—244no—
379C3×C8—61no—
380C3×C8—61no—
381C3×C8—62no—
382C3⋊C8—21no—
383C3⋊C8—22no—
384C3⋊C8—21no—
385C2×C32#54811yescharacteristic
386C2×C32C2×#13711yescharacteristic
387C2×C32#57711yescharacteristic
388C3×D3—81no—
389C2×Q8—21no—
390C2×Q8—32no—
391C2×Q8—91no—
392C2×Q8—91no—
393C2×Q8—182no—
394C2×D4—31no—
395C22×C4—61no—
396Q16—184no—
397SD16—182no—
398C2×C8—31no—
399C2×C8—31no—
400C2×C8—32no—
401C4⋊C4—21no—
402C4⋊C4—31no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4—91no—
406C4⋊C4—92no—
407C4⋊C4—91no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—181no—
412C4⋊C4C2×D3212yes—
413C22⋊C4—61no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C42—92no—
417C42—182no—
418C42—182no—
419C42—181no—
420C42C2×D3211yescharacteristic
421C22×C3—21no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—44no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—122no—
440C3×C4—121no—
441C3×C4#91512yes—
442C3×C4#91812yes—
443C3×C4#100711yescharacteristic
444C3×C4D3×#4111yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4#101011yescharacteristic
447Dic3—42no—
448Dic3—41no—
449Dic3—64no—
450Dic3—64no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—122no—
458Dic3—122no—
459Dic3—121no—
460Dic3—121no—
461C32#336911yescharacteristic, complemented, Sylow
462C23—61no—
463Q8—62no—
464Q8—62no—
465Q8—81no—
466Q8—92no—
467Q8—181no—
468Q8—182no—
469Q8—722no—
470D4—61no—
471D4—61no—
472C2×C4—22no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—122no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4#381111yescharacteristic
481C2×C4#381111yescharacteristic
482C2×C4C22×D3211yescharacteristic
483C8—61no—
484C8—61no—
485C8—62no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—241no—
490C2×C3#563311yescharacteristic
491C2×C3#567711yescharacteristic
492C2×C3C2×#91511yescharacteristic
493C2×C3#576211yescharacteristic
494C2×C3C2×#91811yescharacteristic
495C2×C3#577511yescharacteristic
496D3—81no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22C2×#381111yescharacteristic
501C4—21no—
502C4—42no—
503C4—121no—
504C4—122no—
505C4—182no—
506C4—182no—
507C4—182no—
508C4—361no—
509C4#6395112yes—
510C4#6431511yescharacteristic
511C4#6431911yescharacteristic
512C3—21no—
513C3#8109111yescharacteristic, complemented
514C3#8162611yescharacteristic, complemented
515C2—241no—
516C2#1059511511yescharacteristic
517C2C2×#6395111yescharacteristic
518C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊Q8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596193C2semidirect
3. C3×#5093C2semidirect
7. #10590497C2semidirect
8. #10590485C2semidirect
9. #10590388C2semidirect
11. #10590296C2semidirect
50. #5093D3semidirect
461. C32#3369semidirect
513. C3#81091semidirect
514. C3#81626semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105938632
C3×#50932
C3×#50842
#105905412
#105905382
#105904972
#105904852
#105903882
C4×#37162
#105902962
#816263
#810913