Finite Group Databasebeta

← #11895877

Subgroups — #11895877

Order 1152.

798 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590535C212yesmaximal, complemented
6#10590534C212yesmaximal
7#10590489C212yesmaximal, complemented
8#10590478C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic
11#10590258C211yesmaximal, characteristic, complemented
12#83563—31nomaximal
13#81622—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#946—21no—
18C3×#896—22no—
19C3×#893C2212yes—
20C3×#888C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63871—21no—
25#63864C2212yes—
26#63849—21no—
27#63848—22no—
28Dic3×Dic6C2212yes—
29C2×#3715C2212yes—
30C2×#3714C2211yescharacteristic
31#63636C2212yes—
32#63634C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#810C2212yes—
35C3×#810C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63554C2212yes—
43C3×D4×Q8—31no—
44#5732—31no—
45#5727D311yescharacteristic, complemented
46#5584—31no—
47C3×#487—31no—
48#5093D311yescharacteristic, complemented
49#5091—32no—
50#5089—32no—
51#5087—31no—
52#5087—31no—
53#5087—61no—
54#5083—31no—
55#5024—31no—
56#5019—31no—
57#5018—32no—
58#5016—32no—
59C4×#213—31no—
60#4819—32no—
61#4817—32no—
62#4794—32no—
63#4793—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C3×D3×Q8—44no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D411yescharacteristic
75C2×C3×Dic6C2312yes—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C42C2311yescharacteristic
79#3752—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93Dic3⋊Dic3—22no—
94#3722—22no—
95#3722—22no—
96Dic32—22no—
97#3715—24no—
98#3714—22no—
99#3367—91noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C22⋊Q8—62no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112#947—32no—
113#946—21no—
114#946—61no—
115Q8×Dic3—32no—
116C2×#215—32no—
117C2×#214—32no—
118C2×#213—31no—
119C2×D24—31no—
120#898—62no—
121#898—62no—
122#897—61no—
123#896—22no—
124#893C2×D312yes—
125#892—61no—
126#892—61no—
127#888C2×D312yes—
128#875—32no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—61no—
132C4×D12C2×D311yescharacteristic
133#869C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×#103—32no—
137C3×#103—32no—
138C3×C4×C8—31no—
139#835—32no—
140#832—31no—
141#821—31no—
142#821—31no—
143#818—31no—
144#815—32no—
145Dic3⋊C8—32no—
146#810—32no—
147#810C2×D312yes—
148#810C2×D312yes—
149#809—32no—
150#809—32no—
151#809—31no—
152#809—62no—
153#807—32no—
154#807—32no—
155#807—31no—
156#807—62no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—21no—
165C32×Q8—42no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4×C3⋊D3—42no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—44no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—44no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#556—91no—
190D4×Q8—31no—
191#489—92no—
192#487—31no—
193#477—92no—
194#474—91no—
195#463—92no—
196#461—91no—
197#446—91no—
198#440—92no—
199C4×D8—91no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—41no—
205C2×C3×Q8—62no—
206C2×C3×Q8—124no—
207C2×C3×D4—31no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210D3×Q8—44no—
211C2×D12—31no—
212C2×D12—31no—
213C2×D12—61no—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—121no—
220C2×Dic6—22no—
221C2×Dic6#6711yescharacteristic
222C2×Dic6C22×D312yes—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4C22×D312yes—
236C3×C4⋊C4C22×D312yes—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#215—64no—
244#214—64no—
245#213—62no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—22no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—121no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—22no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274D24—62no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3×D3—22no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—21no—
283C32×C4—42no—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—41no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C22×Q8—61no—
293C2×SD16—92no—
294C2×D8—91no—
295C4⋊Q8—32no—
296C4⋊Q8—31no—
297C4⋊Q8D3211yescharacteristic
298#126—182no—
299#124—92no—
300C22⋊Q8—62no—
301C22⋊Q8—61no—
302C22⋊Q8—181no—
303C4×Q8—31no—
304C4×Q8—92no—
305C4×D4—32no—
306C4×D4—31no—
307C4×D4—91no—
308#117—181no—
309#107—91no—
310#107—92no—
311C4⋊C8—92no—
312C4⋊C8—91no—
313#103—32no—
314#103—32no—
315#103—92no—
316#102—91no—
317#102—91no—
318#102—92no—
319#97—92no—
320C4×C8—31no—
321C23×C3—61no—
322C22×D3—21no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—121no—
326C3×Q8—42no—
327C3×Q8—42no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—82no—
332C3×Q8—124no—
333C3×D4—32no—
334C3×D4—61no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—42no—
343C2×C3×C4—61no—
344C2×C3×C4—62no—
345C2×C3×C4—124no—
346C2×C3×C4—122no—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×Dic3—22no—
354C2×Dic3—21no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—121no—
358C2×Dic3C2×#6712yes—
359C2×Dic3C2×#6712yes—
360D12—21no—
361D12—62no—
362D12—61no—
363D12—61no—
364D12—61no—
365D12—61no—
366D12—121no—
367D12#23912yes—
368C4×D3—44no—
369C4×D3—42no—
370C4×D3—122no—
371C4×D3—122no—
372C4×D3—242no—
373Dic6—22no—
374Dic6—22no—
375Dic6—22no—
376Dic6—44no—
377C3×C8—61no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8—21no—
381C3⋊C8—62no—
382C3⋊C8—62no—
383C3⋊C8—122no—
384C2×C32#54811yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C2×C32#57811yescharacteristic
387C3⋊D3—81no—
388C3×D3—42no—
389C2×Q8—21no—
390C2×Q8—31no—
391C2×Q8—32no—
392C2×Q8—62no—
393C2×Q8—124no—
394C2×D4—31no—
395C2×D4—91no—
396C22×C4—62no—
397C22×C4—61no—
398C22×C4—181no—
399SD16—184no—
400D8—182no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8—92no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—91no—
412C4⋊C4—182no—
413C4⋊C4C2×D3212yes—
414C22⋊C4—62no—
415C22⋊C4—61no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C22⋊C4—181no—
419C42—32no—
420C42—182no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3—62no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—122no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—241no—
439C2×D3—241no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—82no—
451C3×C4—121no—
452C3×C4—122no—
453C3×C4#91412yes—
454C3×C4#93212yes—
455C3×C4C2×#23911yescharacteristic
456C3×C4#100711yescharacteristic
457C3×C4D3×#4111yescharacteristic
458C3×C4#101011yescharacteristic
459Dic3—22no—
460Dic3—22no—
461Dic3—42no—
462Dic3—41no—
463Dic3—121no—
464Dic3—121no—
465Dic3—241no—
466C32#336711yescharacteristic, complemented, Sylow
467C23—61no—
468C23—181no—
469Q8—42no—
470Q8—62no—
471Q8—62no—
472Q8—62no—
473Q8—124no—
474D4—32no—
475D4—61no—
476D4—181no—
477D4—181no—
478C2×C4—22no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—124no—
484C2×C4—122no—
485C2×C4—181no—
486C2×C4—362no—
487C2×C4D3×#6711yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—61no—
491C8—61no—
492C8—182no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—122no—
497C2×C3#567711yescharacteristic
498C2×C3C2×#91411yescharacteristic
499C2×C3#576611yescharacteristic
500C2×C3C2×#93211yescharacteristic
501C2×C3#581711yescharacteristic
502C2×C3#583811yescharacteristic
503D3—42no—
504D3—242no—
505D3—241no—
506D3—241no—
507C22—62no—
508C22—121no—
509C22—121no—
510C22—361no—
511C22—361no—
512C22—361no—
513C22C2×D3×#6711yescharacteristic
514C4—21no—
515C4—42no—
516C4—62no—
517C4—62no—
518C4—121no—
519C4—122no—
520C4—361no—
521C4#6393412yes—
522C4#6431511yescharacteristic
523C4D3×#23911yescharacteristic
524C3—21no—
525C3#8162211yescharacteristic, complemented
526C3#8356311yescharacteristic, complemented
527C2—122no—
528C2—721no—
529C2C2×#6393411yescharacteristic
530C2#1059532711yescharacteristic
531C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3367
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. C3×#5727C2semidirect
2. #10593865C2semidirect
3. #10592786C2semidirect
4. C3×#5093C2semidirect
5. #10590535C2semidirect
7. #10590489C2semidirect
8. #10590478C2semidirect
9. #10590363C2semidirect
11. #10590258C2semidirect
45. #5727D3semidirect
48. #5093D3semidirect
466. C32#3367semidirect
525. C3#81622semidirect
526. C3#83563semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105938652
#105927862
C3×#50932
#105905352
#105905342
#105904892
#105904782
#105903632
C4×#37142
#105902582
#835633
#816223