Finite Group Databasebeta

← #11895364

Subgroups — #11895364

Order 1152.

772 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
1C3×#5730C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic, complemented
3#10592790C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590533C212yesmaximal, complemented
6#10590530C212yesmaximal, complemented
7#10590467C212yesmaximal, complemented
8#10590452C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83643—31nomaximal
13#81585—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C4×#634C2211yescharacteristic
16C3×#946—22no—
17C3×#897—21no—
18C3×#893C2212yes—
19C3×D3×C4⋊C4—21no—
20C3×#890C2212yes—
21C3×#874C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63898—21no—
25Dic3×D12C2212yes—
26#63884—22no—
27#63863—21no—
28#63860C2212yes—
29C2×#3716C2211yescharacteristic
30C2×#3713C2212yes—
31#63637C2212yes—
32#63634C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5730D311yescharacteristic, complemented
45#5713—31no—
46#5585—31no—
47C3×#486—31no—
48#5091—31no—
49#5091—31no—
50#5091—61no—
51#5088D311yescharacteristic, complemented
52#5072—31no—
53#5068—32no—
54#5066—32no—
55Q8×C3⋊C8—31no—
56C4×#214—31no—
57#5016—32no—
58#5015—31no—
59C4×#213—32no—
60#4787—32no—
61#4768—32no—
62#4763—32no—
63#4756—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6D411yescharacteristic
75C2×D3×Dic3—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96#3716—22no—
97#3713—24no—
98#3361—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×#127—31no—
103C3×#125—32no—
104C3×C22⋊Q8—61no—
105C3×C22⋊Q8—62no—
106C3×C4×Q8—31no—
107C3×C4×D4—32no—
108C3×C4×D4—31no—
109C2×C3×C4⋊C4—61no—
110#947—61no—
111#946—22no—
112#936—32no—
113#936—61no—
114#935—62no—
115D4×Dic3—32no—
116D4×Dic3—61no—
117C2×#214—31no—
118C2×#213—32no—
119C2×#213—32no—
120C2×#204—31no—
121#897—21no—
122#894—62no—
123#893—61no—
124#893C2×D312yes—
125D3×C4⋊C4—21no—
126#890C2×D312yes—
127#875—32no—
128#874C2×D311yescharacteristic
129C4×D12—32no—
130C4×D12C2×D311yescharacteristic
131C4×Dic6—31no—
132C4×Dic6—31no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×#102—32no—
136C3×#102—32no—
137C3×C4×C8—31no—
138#832—32no—
139#832—31no—
140#821—31no—
141#817—31no—
142#816—31no—
143Dic3⋊C8—32no—
144C8×Dic3—32no—
145#810—32no—
146#810—32no—
147#810—31no—
148#810—62no—
149#809—32no—
150#809C2×D312yes—
151#809C2×D312yes—
152#808—31no—
153#807—32no—
154#807—32no—
155#807—62no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C32×Q8—81no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171#634—21no—
172#634—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—42no—
180C3×D12—81no—
181C3×D12#4112yes—
182C3×C4×D3—42no—
183C3×C4×D3—82no—
184C3×Dic6—22no—
185D3×Dic3—82no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—91no—
190#554—31no—
191#488—92no—
192#486—31no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—41no—
204C2×C3×D4—31no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×Dic3—62no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12C22×D312yes—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×C4×D3—62no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6#6711yescharacteristic
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4C22×D312yes—
234C3×C4⋊C4C22×D312yes—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—62no—
242#217—62no—
243#217—62no—
244#214—62no—
245#213—64no—
246#213—64no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—22no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3#6711yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258Dic3⋊C4—22no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—121no—
262Dic3⋊C4#6712yes—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—121no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272#204—62no—
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—21no—
281C32×C4—42no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C3×Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—41no—
290C2×SD16—91no—
291C2×D8—92no—
292C4⋊Q8D3211yescharacteristic
293#127—31no—
294#125—32no—
295#124—92no—
296#124—181no—
297#123—182no—
298C22⋊Q8—61no—
299C22⋊Q8—62no—
300C4×Q8—31no—
301C4×Q8—91no—
302C4×D4—32no—
303C4×D4—31no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C4⋊C4—61no—
307#107—92no—
308#106—91no—
309C4⋊C8—92no—
310C4⋊C8—91no—
311#103—91no—
312#103—92no—
313#102—32no—
314#102—32no—
315#102—92no—
316#102—91no—
317C4×C8—31no—
318C4×C8—92no—
319C23×C3—61no—
320C23×C3—62no—
321C22×D3—21no—
322C22×D3—22no—
323C3×Q8—62no—
324C3×Q8—81no—
325C3×Q8—81no—
326C3×Q8—82no—
327C3×D4—32no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—61no—
331C3×D4—122no—
332C3×D4—241no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—42no—
341C2×C3×C4—61no—
342C2×C3×C4—122no—
343C2×C3×C4—242no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—21no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—242no—
358C2×Dic3C2×#6712yes—
359C2×Dic3C2×#6712yes—
360D12—21no—
361D12—22no—
362D12—22no—
363D12—42no—
364D12—81no—
365D12#23912yes—
366C4×D3—42no—
367C4×D3—82no—
368C4×D3—242no—
369Dic6—22no—
370Dic6—62no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—61no—
375Dic6—121no—
376C3×C8—61no—
377C3×C8—61no—
378C3⋊C8—21no—
379C3⋊C8—21no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C3⋊C8—122no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57611yescharacteristic
386C3×D3—42no—
387C3×D3—82no—
388C2×Q8—21no—
389C2×Q8—31no—
390C2×Q8—91no—
391C2×D4—31no—
392C2×D4—32no—
393C2×D4—61no—
394C2×D4—61no—
395C22×C4—62no—
396C22×C4—61no—
397C22×C4—182no—
398SD16—182no—
399D8—184no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8—92no—
403C4⋊C4—21no—
404C4⋊C4—31no—
405C4⋊C4—32no—
406C4⋊C4—31no—
407C4⋊C4—62no—
408C4⋊C4—62no—
409C4⋊C4—91no—
410C4⋊C4—181no—
411C4⋊C4C2×D3212yes—
412C22⋊C4—62no—
413C22⋊C4—61no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C42—32no—
418C42—181no—
419C42C2×D3211yescharacteristic
420C22×C3—21no—
421C22×C3—62no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C22×#6711yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—62no—
444C3×C4—62no—
445C3×C4—82no—
446C3×C4—121no—
447C3×C4#91612yes—
448C3×C4#95012yes—
449C3×C4C2×#23911yescharacteristic
450C3×C4#100711yescharacteristic
451C3×C4D3×#4111yescharacteristic
452C3×C4#101011yescharacteristic
453Dic3—22no—
454Dic3—22no—
455Dic3—41no—
456Dic3—122no—
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461Dic3—241no—
462C32#336111yescharacteristic, complemented, Sylow
463C23—61no—
464C23—62no—
465Q8—62no—
466Q8—81no—
467Q8—181no—
468Q8—181no—
469D4—32no—
470D4—61no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—22no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—61no—
479C2×C4—122no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—242no—
483C2×C4—722no—
484C2×C4D3×#6711yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—61no—
488C8—61no—
489C8—182no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3—242no—
495C2×C3#567711yescharacteristic
496C2×C3#575711yescharacteristic
497C2×C3C2×#91611yescharacteristic
498C2×C3#581711yescharacteristic
499C2×C3C2×#95011yescharacteristic
500C2×C3#583511yescharacteristic
501D3—42no—
502D3—82no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22C2×D3×#6711yescharacteristic
510C4—21no—
511C4—42no—
512C4—62no—
513C4—62no—
514C4—121no—
515C4—361no—
516C4—361no—
517C4#6394712yes—
518C4#6431511yescharacteristic
519C4D3×#23911yescharacteristic
520C3—21no—
521C3#8158511yescharacteristic, complemented
522C3#8364311yescharacteristic, complemented
523C2—122no—
524C2—242no—
525C2#1059509611yescharacteristic
526C2C2×#6394711yescharacteristic
527C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10590347C2
hypercenterC4⋊Q8D32
hypocenterC32#3361
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×#5730C2semidirect
2. #10593951C2semidirect
3. #10592790C2semidirect
4. C3×#5088C2semidirect
5. #10590533C2semidirect
6. #10590530C2semidirect
7. #10590467C2semidirect
8. #10590452C2semidirect
9. C4×#3716C2semidirect
11. C3⋊C8×Dic6C2semidirect
44. #5730D3semidirect
51. #5088D3semidirect
462. C32#3361semidirect
521. C3#81585semidirect
522. C3#83643semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105939512
#105927902
C3×#50882
#105905332
#105905302
#105904672
#105904522
C4×#37162
#105903472
C3⋊C8×Dic62
#836433
#815853