Finite Group Databasebeta

← #11895263

Subgroups — #11895263

Order 1152.

754 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3#10592783C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590537C212yesmaximal, complemented
6#10590534C212yesmaximal
7#10590491C212yesmaximal, complemented
8#10590475C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83637—31nomaximal
13#81621—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C3×#946—22no—
17C3×#897—21no—
18C3×#893C2212yes—
19C3×D3×C4⋊C4—21no—
20C3×#890C2212yes—
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#63635C2212yes—
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
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5732—31no—
45#5730D311yescharacteristic, complemented
46#5584—31no—
47C3×#487—31no—
48#5093D311yescharacteristic, complemented
49#5084—31no—
50#5084—31no—
51#5084—61no—
52#5083—31no—
53#5068—32no—
54#5063—32no—
55Q8×C3⋊C8—31no—
56#5019—31no—
57C4×#214—32no—
58#5016—32no—
59C4×#213—31no—
60#4819—32no—
61#4800—32no—
62#4796—32no—
63#4788—32no—
64C4×D24—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77#3752—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×(C2×D3)⋊C4—21no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95Dic32—22no—
96#3715—24no—
97#3714—22no—
98#3360—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
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—32no—
111#946—22no—
112#946—61no—
113Q8×Dic3—32no—
114C2×#215—32no—
115C2×#214—32no—
116C2×#213—31no—
117C2×D24—31no—
118#898—62no—
119#898—62no—
120#897—21no—
121#897—61no—
122#893C2×D312yes—
123#892—61no—
124#892—61no—
125D3×C4⋊C4—21no—
126#890C2×D312yes—
127#875—32no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—61no—
131C4×D12C2×D311yescharacteristic
132#869C2×D311yescharacteristic
133C4×Dic6—32no—
134C4×Dic6C2×D311yescharacteristic
135C3×#103—32no—
136C3×#103—32no—
137C3×C4×C8—31no—
138#835—32no—
139#832—31no—
140#821—31no—
141#821—31no—
142#818—31no—
143Dic3⋊C8—32no—
144C8×Dic3—32no—
145#810—32no—
146#810C2×D312yes—
147#810C2×D312yes—
148#809—32no—
149#809—32no—
150#809—31no—
151#809—62no—
152#808—32no—
153#808—32no—
154#808—62no—
155#807—31no—
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—21no—
164C32×Q8—81no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—21no—
171C4⋊(C3⋊D3)—21no—
172C4×C3⋊D3—42no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×C4×D3—82no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#556—91no—
188#554—31no—
189#488—92no—
190#487—31no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—91no—
195C8×Q8—91no—
196C4×SD16—92no—
197C4×D8—91no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—41no—
203C2×C3×D4—31no—
204C22×C3×C4—62no—
205C22×C3×C4—61no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—22no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—121no—
215C2×Dic6#6711yescharacteristic
216C2×Dic6C22×D312yes—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—41no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C22×D312yes—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—61no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#215—64no—
239#214—64no—
240#213—62no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—22no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—121no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—22no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—22no—
260Dic3⋊C4—62no—
261Dic3⋊C4#6712yes—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270D24—62no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—42no—
280C32×C4#13512yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—41no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C2×SD16—92no—
289C2×D8—91no—
290C4⋊Q8—31no—
291C4⋊Q8D3211yescharacteristic
292#126—182no—
293#125—32no—
294#124—92no—
295C22⋊Q8—61no—
296C22⋊Q8—62no—
297C22⋊Q8—181no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4—91no—
303#117—181no—
304C2×C4⋊C4—61no—
305#107—91no—
306#106—92no—
307C4⋊C8—92no—
308C4⋊C8—91no—
309#103—32no—
310#103—32no—
311#103—92no—
312#102—91no—
313#102—91no—
314#102—92no—
315C4×C8—31no—
316C4×C8—92no—
317C23×C3—61no—
318C22×D3—21no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×Q8—81no—
326C3×Q8—81no—
327C3×Q8—82no—
328C3×D4—32no—
329C3×D4—61no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—42no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—122no—
341C2×C3×C4—242no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—21no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3C2×#6712yes—
354C2×Dic3C2×#6712yes—
355D12—21no—
356D12—62no—
357D12—61no—
358D12—61no—
359D12—61no—
360D12—61no—
361D12—121no—
362D12#23912yes—
363C4×D3—42no—
364C4×D3—82no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—242no—
368Dic6—22no—
369Dic6—22no—
370Dic6—22no—
371C3×C8—61no—
372C3×C8—61no—
373C3⋊C8—21no—
374C3⋊C8—21no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—122no—
378C2×C32#54811yescharacteristic
379C2×C32C2×#13511yescharacteristic
380C2×C32#57711yescharacteristic
381C3⋊D3—81no—
382C3×D3—42no—
383C2×Q8—21no—
384C2×Q8—31no—
385C2×Q8—32no—
386C2×D4—31no—
387C2×D4—91no—
388C22×C4—62no—
389C22×C4—61no—
390C22×C4—181no—
391SD16—184no—
392D8—182no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8—92no—
396C4⋊C4—21no—
397C4⋊C4—31no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—62no—
401C4⋊C4—62no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—91no—
405C4⋊C4—182no—
406C4⋊C4C2×D3212yes—
407C22⋊C4—62no—
408C22⋊C4—61no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C22⋊C4—181no—
412C42—32no—
413C42—182no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—122no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—241no—
432C2×D3—241no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4—62no—
443C3×C4—82no—
444C3×C4—121no—
445C3×C4—122no—
446C3×C4#91912yes—
447C3×C4#95012yes—
448C3×C4C2×#23911yescharacteristic
449C3×C4#100711yescharacteristic
450C3×C4D3×#4111yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—22no—
454Dic3—42no—
455Dic3—41no—
456Dic3—121no—
457Dic3—121no—
458Dic3—241no—
459C32#336011yescharacteristic, complemented, Sylow
460C23—61no—
461C23—181no—
462Q8—62no—
463Q8—62no—
464Q8—62no—
465Q8—81no—
466D4—32no—
467D4—61no—
468D4—181no—
469D4—181no—
470C2×C4—22no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—62no—
474C2×C4—61no—
475C2×C4—122no—
476C2×C4—181no—
477C2×C4—242no—
478C2×C4—362no—
479C2×C4D3×#6711yescharacteristic
480C2×C4D3×#6711yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—61no—
483C8—61no—
484C8—182no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—122no—
489C2×C3#567711yescharacteristic
490C2×C3#576211yescharacteristic
491C2×C3C2×#91911yescharacteristic
492C2×C3#581711yescharacteristic
493C2×C3C2×#95011yescharacteristic
494C2×C3#583611yescharacteristic
495D3—42no—
496D3—242no—
497D3—241no—
498D3—241no—
499C22—62no—
500C22—121no—
501C22—121no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22C2×D3×#6711yescharacteristic
506C4—21no—
507C4—42no—
508C4—62no—
509C4—62no—
510C4—121no—
511C4—122no—
512C4—361no—
513C4#6394912yes—
514C4#6431511yescharacteristic
515C4D3×#23911yescharacteristic
516C3—21no—
517C3#8162111yescharacteristic, complemented
518C3#8363711yescharacteristic, complemented
519C2—122no—
520C2—721no—
521C2#1059510511yescharacteristic
522C2C2×#6394911yescharacteristic
523C2#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#3360
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. #10593865C2semidirect
3. #10592783C2semidirect
4. C3×#5093C2semidirect
5. #10590537C2semidirect
7. #10590491C2semidirect
8. #10590475C2semidirect
9. #10590363C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5730D3semidirect
48. #5093D3semidirect
459. C32#3360semidirect
517. C3#81621semidirect
518. C3#83637semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105938652
#105927832
C3×#50932
#105905372
#105905342
#105904912
#105904752
#105903632
C4×#37142
C3⋊C8×Dic62
#836373
#816213