Finite Group Databasebeta

← #11895253

Subgroups — #11895253

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×#5584C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10590363C211yesmaximal, characteristic, complemented
5C4×#3715C212yesmaximal, complemented
6#10590348C212yesmaximal
7C4×#3713C211yesmaximal, characteristic
8#10590290C211yesmaximal, characteristic, complemented
9#10590286C212yesmaximal, complemented
10#10590278C212yesmaximal, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83667—31nomaximal
13#83637—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C3×#946—21no—
16C3×#946—21no—
17C3×#898—22no—
18C3×#896—22no—
19C3×#892—21no—
20C3×D3×C4⋊C4—21no—
21C3×#875C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2212yes—
25C3×#870C2212yes—
26C3×#869C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3715C2212yes—
30C2×#3713C2211yescharacteristic
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C4⋊(C3⋊(C3⋊C8))C2212yes—
33C4×C3⋊(C3⋊C8)C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63576C2211yescharacteristic
36#63574C2212yes—
37#63565C2212yes—
38#63565C2212yes—
39#63565C2212yes—
40#63562C2212yes—
41#63562C2211yescharacteristic
42#63562C2211yescharacteristic
43C3×#556—31no—
44C3×#554—31no—
45#5584D311yescharacteristic, complemented
46#5579D311yescharacteristic, complemented
47#5093—31no—
48#5084—31no—
49#5083—31no—
50#5079—31no—
51#5068—32no—
52#5063—32no—
53#5057—32no—
54#5056—32no—
55C4×#215—32no—
56Q8×C3⋊C8—31no—
57Q8×C3⋊C8—31no—
58Q8×C3⋊C8—61no—
59#5022—32no—
60#5019—31no—
61C4×#214—32no—
62#5016—32no—
63C4×#213—31no—
64C4×#213—31no—
65#5008—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2312yes—
77C32×C42C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96#3715—24no—
97#3713—22no—
98#3360—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—31no—
101C3×#126—62no—
102C3×#125—32no—
103C3×#124—32no—
104C3×C22⋊Q8—61no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—32no—
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×Q8C2×D311yescharacteristic
111C3×C4×D4—31no—
112C3×C4×D4—31no—
113C3×C4×D4—32no—
114C3×#117—61no—
115C2×C3×C4⋊C4—61no—
116#946—21no—
117#946—21no—
118C2×#215—32no—
119C2×#214—32no—
120C2×#213—31no—
121C2×#213—31no—
122#898—22no—
123#896—22no—
124#892—21no—
125D3×C4⋊C4—21no—
126#875C2×D312yes—
127C4×D12C2×D311yescharacteristic
128C4×D12C2×D311yescharacteristic
129C4×D12C2×D312yes—
130#870C2×D312yes—
131#869C2×D311yescharacteristic
132#869C2×D311yescharacteristic
133C4×Dic6C2×D312yes—
134#835—32no—
135#835—32no—
136#835—32no—
137#832—32no—
138#832—31no—
139#832—31no—
140#810—32no—
141#810—32no—
142#810—32no—
143#809—31no—
144#809—31no—
145#809—32no—
146#808—32no—
147#808—32no—
148#807—31no—
149#807—31no—
150C4⋊(C3⋊C8)—31no—
151C4⋊(C3⋊C8)—32no—
152C4⋊(C3⋊C8)—31no—
153C4⋊(C3⋊C8)—32no—
154C4⋊(C3⋊C8)—61no—
155C4⋊(C3⋊C8)—62no—
156C4×C3⋊C8—31no—
157C4×C3⋊C8—31no—
158C4×C3⋊C8—32no—
159C4×C3⋊C8—32no—
160C4×C3⋊C8—61no—
161C4×C3⋊C8—62no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C32×Q8—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C3×D12—21no—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12#4112yes—
178C3×C4×D3—42no—
179C3×C4×D3—42no—
180C3×C4×D3—82no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—81no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—22no—
187#556—31no—
188#554—31no—
189#488—92no—
190#487—91no—
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—32no—
200C2×C3×Q8—61no—
201C2×C3×Q8#6711yescharacteristic
202C2×C3×Q8#6711yescharacteristic
203C2×C3×D4—31no—
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—62no—
208C2×D12C22×D311yescharacteristic
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—22no—
213C2×Dic6—21no—
214C2×Dic6C22×D312yes—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4#6711yescharacteristic
227C3×C4⋊C4#6711yescharacteristic
228C3×C4⋊C4#6712yes—
229C3×C4⋊C4#6712yes—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—61no—
234C3×C22⋊C4—62no—
235C3×C42—21no—
236C3×C42—22no—
237C3×C42—62no—
238C3×C42C22×D312yes—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D312yes—
242#215—64no—
243#214—64no—
244#213—62no—
245#213—62no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—22no—
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—22no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3C22×D311yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—22no—
258Dic3⋊C4—22no—
259Dic3⋊C4—22no—
260C4×Dic3—22no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—61no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—22no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C32×C4—22no—
278C32×C4—21no—
279C32×C4—22no—
280C32×C4#13512yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3×Dic3—42no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C3×Dic3—42no—
287C2×SD16—92no—
288C2×D8—91no—
289C4⋊Q8—31no—
290C4⋊Q8—31no—
291#126—62no—
292#125—32no—
293#124—32no—
294C22⋊Q8—61no—
295C22⋊Q8—61no—
296C22⋊Q8—62no—
297C4×Q8—32no—
298C4×Q8D3211yescharacteristic
299C4×D4—31no—
300C4×D4—32no—
301C4×D4—31no—
302#117—61no—
303C2×C4⋊C4—61no—
304#107—91no—
305#106—92no—
306C4⋊C8—91no—
307C4⋊C8—92no—
308#103—92no—
309#103—92no—
310#103—92no—
311#102—91no—
312#102—91no—
313#102—92no—
314C4×C8—91no—
315C4×C8—92no—
316C23×C3—61no—
317C23×C3—61no—
318C22×D3—21no—
319C22×D3—21no—
320C3×Q8—24no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×Q8—241no—
326C3×D4—32no—
327C3×D4—61no—
328C3×D4—61no—
329C3×D4—61no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—122no—
340C2×C3×C4—122no—
341C2×C3×C4—242no—
342C2×C3×C4C2×#6712yes—
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C2×#6712yes—
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356D12—21no—
357D12—21no—
358D12—21no—
359D12#23912yes—
360C4×D3—42no—
361C4×D3—42no—
362C4×D3—82no—
363Dic6—22no—
364Dic6—22no—
365Dic6—81no—
366C3⋊C8—62no—
367C3⋊C8—61no—
368C3⋊C8—62no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—62no—
372C3⋊C8—61no—
373C3⋊C8—121no—
374C3⋊C8—122no—
375C2×C32#54811yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C2×C32#57711yescharacteristic
378C3×D3—42no—
379C3×D3—81no—
380C2×Q8—32no—
381C2×Q8—61no—
382C2×Q8#62511yescharacteristic
383C2×D4—31no—
384C2×D4—31no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—62no—
388SD16—184no—
389D8—182no—
390C2×C8—91no—
391C2×C8—92no—
392C2×C8—91no—
393C4⋊C4—32no—
394C4⋊C4—31no—
395C4⋊C4—31no—
396C4⋊C4—62no—
397C4⋊C4—61no—
398C4⋊C4—61no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—61no—
402C4⋊C4#62511yescharacteristic
403C4⋊C4#62512yes—
404C22⋊C4—62no—
405C22⋊C4—61no—
406C22⋊C4—62no—
407C22⋊C4—61no—
408C22⋊C4—62no—
409C42—62no—
410C42C2×D3211yescharacteristic
411C42C2×D3212yes—
412C22×C3—21no—
413C22×C3—62no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C22×#6711yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C3×C4—24no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—42no—
438C3×C4—41no—
439C3×C4—122no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—122no—
443C3×C4#95012yes—
444C3×C4#95012yes—
445C3×C4C2×#23911yescharacteristic
446C3×C4#100711yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4#101011yescharacteristic
449Dic3—41no—
450Dic3—41no—
451Dic3—42no—
452Dic3—42no—
453C32#336011yescharacteristic, complemented, Sylow
454C23—61no—
455C23—61no—
456Q8—22no—
457Q8—62no—
458Q8—62no—
459Q8—241no—
460D4—32no—
461D4—61no—
462D4—61no—
463D4—61no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—62no—
468C2×C4—122no—
469C2×C4—122no—
470C2×C4—242no—
471C2×C4C2×#62512yes—
472C2×C4C2×#62512yes—
473C2×C4C2×#62511yescharacteristic
474C2×C4C2×#62511yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—181no—
477C8—181no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3—241no—
484C2×C3#581711yescharacteristic
485C2×C3C2×#95011yescharacteristic
486C2×C3C2×#95011yescharacteristic
487C2×C3#583111yescharacteristic
488C2×C3#583611yescharacteristic
489C2×C3#583711yescharacteristic
490D3—42no—
491D3—81no—
492C22—62no—
493C22—121no—
494C22—121no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22C22×#62511yescharacteristic
499C4—22no—
500C4—21no—
501C4—22no—
502C4—122no—
503C4—122no—
504C4—121no—
505C4—121no—
506C4#6382212yes—
507C4#6431511yescharacteristic
508C4D3×#23911yescharacteristic
509C3—21no—
510C3#8363711yescharacteristic, complemented
511C3#8366711yescharacteristic, complemented
512C2—122no—
513C2—241no—
514C2C2×#6382211yescharacteristic
515C2#1059540911yescharacteristic
516C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4×Q8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5584C2semidirect
2. C3×#5579C2semidirect
3. Q8×C3⋊(C3⋊C8)C2semidirect
4. #10590363C2semidirect
5. C4×#3715C2semidirect
8. #10590290C2semidirect
9. #10590286C2semidirect
10. #10590278C2semidirect
11. #10590266C2semidirect
45. #5584D3semidirect
46. #5579D3semidirect
453. C32#3360semidirect
510. C3#83637semidirect
511. C3#83667semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×#55792
Q8×C3⋊(C3⋊C8)2
#105903632
C4×#37152
#105903482
C4×#37132
#105902902
#105902862
#105902782
#105902662
#836673
#836373