Finite Group Databasebeta

← #11895666

Subgroups — #11895666

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5570C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic
3C4×#3756C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic
5#10591604C212yesmaximal, complemented
6Dic3×#215C212yesmaximal, complemented
7#10590533C212yesmaximal, complemented
8#10590467C212yesmaximal, complemented
9#10590307C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic
11#10590250C211yesmaximal, characteristic, complemented
12#83697—31nomaximal
13#80370—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C2×#3756C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C2×C3×#215C2212yes—
19C3×#890—22no—
20C3×#890C2212yes—
21C3×#874C2211yescharacteristic
22C3×#869—21no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6—21no—
25C3×C4×Dic6C2211yescharacteristic
26#63898—21no—
27Dic3×D12C2212yes—
28#63884—22no—
29#63863—21no—
30#63860C2212yes—
31#63662C2211yescharacteristic
32#63637C2211yescharacteristic
33#63634C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#809C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5713—31no—
45#5585—31no—
46#5570D311yescharacteristic, complemented
47C3×#460—31no—
48#5166—32no—
49Dic3×SD16—32no—
50#5094—31no—
51#5088—31no—
52#5070—31no—
53#5068—32no—
54#5066—32no—
55C4×#216—31no—
56C4×#216—31no—
57C4×#216—61no—
58#5028—32no—
59#5027D311yescharacteristic
60C4×#215—32no—
61Q8×C3⋊C8—31no—
62#4851—31no—
63#4830—31no—
64#4768—32no—
65#4763—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78#3756—22no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#215—24no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3365—91noSylow
99C2×C3×SD16—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—61no—
102C3×#127—31no—
103C3×#125—32no—
104C3×#125—62no—
105C3×C4×Q8—21no—
106C3×C4×Q8—31no—
107C3×C4×Q8—32no—
108C3×C4×Q8—61no—
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×Q8C2×D311yescharacteristic
111#947—61no—
112Q8×Dic3C2×D312yes—
113C2×#216—31no—
114C2×#216—31no—
115C2×#216—61no—
116C2×#215C2×D312yes—
117#936—32no—
118#936—61no—
119#935—62no—
120D4×Dic3—32no—
121D4×Dic3—61no—
122#894—62no—
123#893—61no—
124#890—22no—
125#890C2×D312yes—
126#875—32no—
127#874C2×D311yescharacteristic
128C4×D12—32no—
129#869—21no—
130#869C2×D311yescharacteristic
131C4×Dic6—21no—
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#102—32no—
138#835—31no—
139#835—31no—
140#835—61no—
141#832—32no—
142#832—32no—
143#817—32no—
144#816—32no—
145Dic3⋊C8—32no—
146C8×Dic3—32no—
147#810—31no—
148#810—31no—
149#810—32no—
150#810—61no—
151#809—32no—
152#809—32no—
153#809C2×D312yes—
154#808—32no—
155#807—31no—
156#807—31no—
157#807—61no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)C2×D311yescharacteristic
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—32no—
163C4×C3⋊C8—61no—
164C22×C3×D3—22no—
165C32×Q8—21no—
166C32×Q8#4112yes—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174#634—21no—
175#634—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—22no—
180C3×D12—22no—
181C3×D12—42no—
182C3×D12—81no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185D3×Dic3—82no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#559—91no—
190#557—31no—
191#488—92no—
192#486—91no—
193#478—92no—
194#475—91no—
195#464—92no—
196#460—31no—
197C8×Q8—91no—
198C4×Q16—91no—
199C4×SD16—92no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×Dic3—62no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C22×D312yes—
212C2×C4×D3—62no—
213C2×Dic6—21no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6#6711yescharacteristic
218C3×SD16—64no—
219C2×C3×C8—32no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42—41no—
238C3×C42—62no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—62no—
242#217—62no—
243#217—62no—
244#216—64no—
245#216—62no—
246#216—62no—
247#215—24no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251C4⋊Dic3—21no—
252C4⋊Dic3—22no—
253C4⋊Dic3—22no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—61no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D312yes—
259Dic3⋊C4—22no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—121no—
263Dic3⋊C4#6712yes—
264C4×Dic3—22no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—121no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8C22×D312yes—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—22no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4#13512yes—
284C32×C4C2×#4111yescharacteristic
285C32×C42−1+411yescharacteristic
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C2×Q16—91no—
292C2×SD16—32no—
293C4⋊Q8—31no—
294C4⋊Q8—61no—
295#127—31no—
296#125—32no—
297#125—62no—
298#124—92no—
299#124—181no—
300#123—182no—
301C4×Q8—31no—
302C4×Q8—32no—
303C4×Q8—61no—
304C4×Q8—91no—
305C4×Q8D3211yescharacteristic
306C4×D4—92no—
307C4×D4—181no—
308#107—91no—
309#106—92no—
310C4⋊C8—31no—
311C4⋊C8—92no—
312#103—92no—
313#103—91no—
314#103—91no—
315#102—32no—
316#102—92no—
317#102—92no—
318C4×C8—92no—
319C4×C8—91no—
320C23×C3—62no—
321C22×D3—22no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—22no—
325C3×Q8—41no—
326C3×Q8—62no—
327C3×Q8—122no—
328C3×Q8#23712yes—
329C3×Q8#23912yes—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—122no—
333C3×D4—241no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—62no—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—242no—
360C2×Dic3C2×#6712yes—
361C2×Dic3C2×#6712yes—
362D12—22no—
363D12—22no—
364D12—42no—
365D12—81no—
366C4×D3—242no—
367Dic6—22no—
368Dic6—42no—
369Dic6—62no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—121no—
375C3×C8—62no—
376C3⋊C8—22no—
377C3⋊C8—62no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—61no—
382C3⋊C8—121no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57711yescharacteristic
386C3×D3—82no—
387C2×Q8—31no—
388C2×Q8—61no—
389C2×Q8—91no—
390C2×Q8C2×D3211yescharacteristic
391C2×D4—32no—
392C2×D4—61no—
393C2×D4—61no—
394C22×C4—182no—
395Q16—182no—
396SD16—64no—
397C2×C8—32no—
398C2×C8—91no—
399C2×C8—91no—
400C4⋊C4—21no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—32no—
404C4⋊C4—62no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4—91no—
409C4⋊C4—181no—
410C4⋊C4C2×D3211yescharacteristic
411C22⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C42—21no—
415C42—32no—
416C42—62no—
417C42—181no—
418C42C2×D3211yescharacteristic
419C22×C3—21no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—42no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4—81no—
442C3×C4—122no—
443C3×C4#91612yes—
444C3×C4#95012yes—
445C3×C4C2×#23711yescharacteristic
446C3×C4C2×#23911yescharacteristic
447C3×C4#100711yescharacteristic
448C3×C4#101011yescharacteristic
449Dic3—22no—
450Dic3—22no—
451Dic3—42no—
452Dic3—122no—
453Dic3—121no—
454Dic3—121no—
455Dic3—121no—
456Dic3—121no—
457Dic3—241no—
458C32#336511yescharacteristic, complemented, Sylow
459C23—62no—
460Q8—21no—
461Q8—62no—
462Q8—122no—
463Q8—181no—
464Q8—181no—
465Q8#379612yes—
466D4—62no—
467D4—62no—
468D4—122no—
469D4—241no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—62no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—722no—
478C2×C4D3×#6711yescharacteristic
479C2×C4D3×#6711yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—62no—
482C8—181no—
483C8—181no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—242no—
488C2×C3#559811yescharacteristic
489C2×C3C2×#91611yescharacteristic
490C2×C3#577511yescharacteristic
491C2×C3#581711yescharacteristic
492C2×C3C2×#95011yescharacteristic
493C2×C3#583711yescharacteristic
494D3—82no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22C2×D3×#6711yescharacteristic
499C4—22no—
500C4—21no—
501C4—41no—
502C4—62no—
503C4—62no—
504C4—122no—
505C4—361no—
506C4—361no—
507C4#6394712yes—
508C4C2×#379611yescharacteristic
509C4#6429711yescharacteristic
510C3—21no—
511C3#8037011yescharacteristic, complemented
512C3#8369711yescharacteristic, complemented
513C2—242no—
514C2#1059490011yescharacteristic
515C2C2×#6394711yescharacteristic
516C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4×Q8D32
hypocenterC32#3365
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×#5570C2semidirect
3. C4×#3756C2semidirect
5. #10591604C2semidirect
6. Dic3×#215C2semidirect
7. #10590533C2semidirect
8. #10590467C2semidirect
9. #10590307C2semidirect
11. #10590250C2semidirect
46. #5570D3semidirect
458. C32#3365semidirect
511. C3#80370semidirect
512. C3#83697semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
#105939512
C4×#37562
C3×#50272
#105916042
Dic3×#2152
#105905332
#105904672
#105903072
#105902772
#105902502
#836973
#803703