Finite Group Databasebeta

← #11895879

Subgroups — #11895879

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592792C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590590C212yesmaximal, complemented
6#10590531C212yesmaximal, complemented
7#10590530C212yesmaximal
8#10590488C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10C4×#3713C211yesmaximal, characteristic
11#10590259C211yesmaximal, characteristic, complemented
12#83563—31nomaximal
13#80993—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#946—21no—
18C3×#896—22no—
19C3×#893C2212yes—
20C3×#888C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63861—22no—
25#63860C2212yes—
26#63856—21no—
27#63844C2212yes—
28#63841—21no—
29C2×#3716C2212yes—
30C2×#3713C2211yescharacteristic
31#63637C2212yes—
32#63637C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#809C2212yes—
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×D4×Q8—31no—
44#5727D311yescharacteristic, complemented
45#5584—31no—
46#5542—31no—
47C3×#474—31no—
48#5093—31no—
49#5093—31no—
50#5093—61no—
51#5091—32no—
52#5089—32no—
53#5087D311yescharacteristic, complemented
54#5024—31no—
55#5019—31no—
56#5018—32no—
57#5016—32no—
58C4×#213—31no—
59C4×#213—31no—
60#4889—32no—
61#4875—32no—
62#4841—31no—
63#4831—31no—
64#4787—32no—
65#4765—32no—
66C2×C32×Q8—21no—
67C2×#634C2312yes—
68C3×D3×Q8—44no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D411yescharacteristic
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3716—24no—
98#3713—22no—
99#3367—91noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C22⋊Q8—62no—
107C3×C22⋊Q8—61no—
108C3×C4×Q8—31no—
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×C4×D4—31no—
112#946—21no—
113#946—61no—
114#936—32no—
115C2×#214—32no—
116C2×#213—31no—
117C2×#213—31no—
118#926—61no—
119#924—61no—
120C2×#204—32no—
121#898—62no—
122#896—22no—
123#893C2×D312yes—
124#892—61no—
125#888C2×D312yes—
126#887—32no—
127#879—62no—
128#875—32no—
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D311yescharacteristic
131#869—31no—
132#869—31no—
133#869—61no—
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×#107—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#832—31no—
140#832—31no—
141#816—32no—
142#815—32no—
143Dic3⋊C8—32no—
144#810—32no—
145#810—32no—
146#810—32no—
147#810—32no—
148#810—32no—
149#810—62no—
150#810—62no—
151#809—31no—
152#809—31no—
153#809C2×D312yes—
154#807—31no—
155#807—31no—
156#807C2×D312yes—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
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—22no—
171#634—22no—
172#634—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—21no—
180C3×D12#4112yes—
181C3×C4×D3—44no—
182C3×C4×D3—42no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—44no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#556—91no—
190D4×Q8—31no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—31no—
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—41no—
204C2×C3×Q8—62no—
205C2×C3×Q8—124no—
206C2×C3×D4—31no—
207C2×C3×D4—31no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211D3×Q8—44no—
212C2×D12C22×D311yescharacteristic
213C2×D12C22×D311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×Dic6—22no—
218C2×Dic6—32no—
219C2×Dic6—32no—
220C2×Dic6—62no—
221C2×Dic6#6711yescharacteristic
222C2×C3×C8—32no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4C22×D312yes—
233C3×C4⋊C4C22×D312yes—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—62no—
242#217—62no—
243#214—64no—
244#213—62no—
245#213—62no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—121no—
256C4⋊Dic3—121no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260Dic3⋊C4—22no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8C22×D312yes—
274#204—64no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
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—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C22×Q8—61no—
293C2×SD16—92no—
294C2×D8—91no—
295C4⋊Q8—32no—
296C4⋊Q8—91no—
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—31no—
308#117—181no—
309#107—32no—
310#107—91no—
311C4⋊C8—31no—
312C4⋊C8—92no—
313#103—92no—
314#103—92no—
315#103—92no—
316#102—32no—
317#102—91no—
318#102—91no—
319#97—92no—
320C4×C8—91no—
321C23×C3—61no—
322C23×C3—61no—
323C22×D3—21no—
324C22×D3—21no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—62no—
328C3×Q8—82no—
329C3×Q8—124no—
330C3×D4—32no—
331C3×D4—61no—
332C3×D4—61no—
333C3×D4—61no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—42no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—124no—
345C2×C3×C4—122no—
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—21no—
354C2×Dic3—21no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—122no—
358C2×Dic3C2×#6712yes—
359C2×Dic3C2×#6712yes—
360D12—21no—
361D12—21no—
362D12—21no—
363D12#23912yes—
364C4×D3—44no—
365C4×D3—42no—
366C4×D3—42no—
367Dic6—22no—
368Dic6—44no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—122no—
374Dic6—122no—
375C3×C8—62no—
376C3⋊C8—22no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—121no—
382C3⋊C8—121no—
383C2×C32#54811yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C2×C32#57811yescharacteristic
386C3×D3—42no—
387C3×D3—81no—
388C2×Q8—21no—
389C2×Q8—31no—
390C2×Q8—62no—
391C2×Q8—92no—
392C2×Q8—124no—
393C2×D4—31no—
394C2×D4—31no—
395C22×C4—62no—
396C22×C4—61no—
397C22×C4—61no—
398SD16—184no—
399D8—182no—
400C2×C8—32no—
401C2×C8—91no—
402C2×C8—91no—
403C4⋊C4—21no—
404C4⋊C4—31no—
405C4⋊C4—32no—
406C4⋊C4—31no—
407C4⋊C4—31no—
408C4⋊C4—62no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4C2×D3212yes—
413C22⋊C4—62no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C42—32no—
419C42—182no—
420C42C2×D3211yescharacteristic
421C22×C3—21no—
422C22×C3—62no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—22no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—82no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4#91112yes—
450C3×C4#93212yes—
451C3×C4C2×#23911yescharacteristic
452C3×C4#100711yescharacteristic
453C3×C4#100711yescharacteristic
454C3×C4D3×#4111yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—41no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462C32#336711yescharacteristic, complemented, Sylow
463C23—61no—
464C23—61no—
465Q8—42no—
466Q8—62no—
467Q8—124no—
468Q8—182no—
469Q8—182no—
470D4—32no—
471D4—61no—
472D4—61no—
473D4—61no—
474C2×C4—22no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—124no—
480C2×C4—122no—
481C2×C4—122no—
482C2×C4—182no—
483C2×C4D3×#6711yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—181no—
488C8—181no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—122no—
493C2×C3—241no—
494C2×C3#563311yescharacteristic
495C2×C3C2×#91111yescharacteristic
496C2×C3#577911yescharacteristic
497C2×C3C2×#93211yescharacteristic
498C2×C3#581711yescharacteristic
499C2×C3#583811yescharacteristic
500D3—42no—
501D3—81no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22C2×D3×#6711yescharacteristic
509C4—21no—
510C4—42no—
511C4—62no—
512C4—62no—
513C4—121no—
514C4—121no—
515C4—362no—
516C4#6393212yes—
517C4#6431611yescharacteristic
518C4D3×#23911yescharacteristic
519C3—21no—
520C3#8099311yescharacteristic, complemented
521C3#8356311yescharacteristic, complemented
522C2—122no—
523C2—241no—
524C2C2×#6393211yescharacteristic
525C2#1059532811yescharacteristic
526C2#1059540211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
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. #10593879C2semidirect
3. #10592792C2semidirect
4. C3×#5087C2semidirect
5. #10590590C2semidirect
6. #10590531C2semidirect
8. #10590488C2semidirect
9. #10590365C2semidirect
11. #10590259C2semidirect
44. #5727D3semidirect
53. #5087D3semidirect
462. C32#3367semidirect
520. C3#80993semidirect
521. C3#83563semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105938792
#105927922
C3×#50872
#105905902
#105905312
#105905302
#105904882
#105903652
C4×#37132
#105902592
#835633
#809933