Finite Group Databasebeta

← #11791036

Subgroups — #11791036

Order 1152.

833 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
1C22×#3713C211yesmaximal, characteristic
2C2×#63634C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591318C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#70190—31nomaximal
9#69647—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—22no—
19C2×#3713—22no—
20C2×#3713—22no—
21C2×#3713C414yescomplemented
22#63634—22no—
23C3×#809—22no—
24#63563—22no—
25Dic3×C3⋊C8—22no—
26C22×#213—31no—
27C22×#213—31no—
28C2×C3×#102—31no—
29C3×#390—31no—
30#5221—31no—
31C2×#832—31no—
32C2×#821—31no—
33C2×C8×Dic3—31no—
34#4988D311yescharacteristic, complemented
35C2×#809D311yescharacteristic, complemented
36C2×#807—31no—
37C2×#807—31no—
38C2×#807—61no—
39#4939—31no—
40C2×C4×C3⋊C8—31no—
41C23×C3×D3—21no—
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3×Dic3D412yes—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2×C412yes—
58C2×C3×D12C2×C412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C2×C3⋊(C3⋊C8)C2×C412yes—
64C2×C3⋊(C3⋊C8)D412yes—
65C2×C3⋊(C3⋊C8)D412yes—
66C3×(C2×D3)⋊C4—44no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8D412yes—
72(C2×D3)⋊Dic3—44no—
73#3713—28no—
74#1970—91noSylow
75C22×C3×D4—31no—
76C22×C3×D4—31no—
77C22×D12C2×D311yescharacteristic
78C22×D12C2×D311yescharacteristic
79C22×C3×C8—31no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C22⋊C4—62no—
84C2×C3×C42—31no—
85C2×#217—62no—
86C2×#213—34no—
87C2×#213—34no—
88C2×#213—62no—
89C2×#213—62no—
90C2×#213—62no—
91C2×#213—62no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—62no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4×Dic3C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C22×C3⋊C8C2×D311yescharacteristic
102C3×#102—62no—
103#832—62no—
104#821—62no—
105C8×Dic3—62no—
106#809—22no—
107#807—62no—
108#807—62no—
109#807—64no—
110C4×C3⋊C8—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—42no—
119C22×C3×D3—42no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C2×C32×C4—41no—
123C2×C32×C4—42no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—42no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3D814yescomplemented
135C3×D12—22no—
136C3×D12—22no—
137C3×D12—22no—
138C3×D12—22no—
139C3×D12—41no—
140C3×D12—41no—
141C3×D12—41no—
142C3×D12—41no—
143C3⋊(C3⋊C8)C22⋊C414yescomplemented
144C3×C3⋊C8—22no—
145C22×D8—91no—
146C2×#107—91no—
147C2×#102—31no—
148C2×#102—91no—
149C2×C4×C8—91no—
150#390—31no—
151#390—91no—
152C24×C3—61no—
153C24×C3—61no—
154C23×D3—21no—
155C23×D3—21no—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—32no—
172C22×C3×C4—41no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C22×Dic3#6712yes—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12C4×D312yes—
190C2×D12C4×D312yes—
191C2×C3×C8—32no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—41no—
200C3×C22⋊C4—124no—
201C3×C42—61no—
202C3×C42—61no—
203#217—124no—
204#213—68no—
205#213—68no—
206(C2×D3)⋊C4—44no—
207(C2×D3)⋊C4—124no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—121no—
214C4×Dic3—21no—
215C4×Dic3—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8#6712yes—
228C22×C32C4×D411yescharacteristic
229C22×C32#12111yescharacteristic
230C22×C32#12711yescharacteristic
231C22×C32C2×D812yes—
232C22×C32#13512yes—
233C2×C3×D3—42no—
234C2×C3×D3—42no—
235C2×C3×D3—44no—
236C2×C3×D3—44no—
237C2×C3×D3—82no—
238C2×C3×D3—82no—
239C2×C3×D3—81no—
240C2×C3×D3—81no—
241C2×C3×D3—81no—
242C2×C3×D3—81no—
243C32×C4—81no—
244C32×C4C2×C22⋊C411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4#12111yescharacteristic
247C32×C4#12411yescharacteristic
248C3⋊Dic3—81no—
249C3×Dic3—24no—
250C22×D4—31no—
251C22×D4—31no—
252C2×D8—94no—
253C2×D8—182no—
254C2×D8—182no—
255C22×C8—31no—
256C22×C8—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4D3211yescharacteristic
259C2×C22⋊C4—62no—
260C2×C22⋊C4—182no—
261C2×C42—31no—
262#107—182no—
263#102—62no—
264#102—182no—
265C4×C8—182no—
266C23×C3—21no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3—121no—
270C23×C3—122no—
271C23×C3—122no—
272C23×C3—122no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3—122no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—22no—
281C22×D3—41no—
282C22×D3—42no—
283C22×D3—42no—
284C22×D3—42no—
285C22×D3—41no—
286C22×D3—41no—
287C22×D3—41no—
288C22×D3—42no—
289C3×D4—62no—
290C3×D4—62no—
291C3×D4—62no—
292C3×D4—62no—
293C3×D4—121no—
294C3×D4—121no—
295C3×D4—121no—
296C3×D4—121no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—34no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—82no—
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4#23511yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—242no—
332C2×Dic3#21314yescomplemented
333D12—22no—
334D12—22no—
335D12—22no—
336D12—22no—
337D12—41no—
338D12—41no—
339D12—41no—
340D12—41no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—34no—
344C3⋊C8—34no—
345C3⋊C8—64no—
346C2×C32#39011yescharacteristic
347C2×C32C4×D812yes—
348C2×C32#46612yes—
349C2×C32#49311yescharacteristic
350C2×C32#49511yescharacteristic
351C3×D3—82no—
352C3×D3—82no—
353C24—61no—
354C24—61no—
355C2×D4—32no—
356C2×D4—32no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C2×D4—61no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C2×D4—61no—
367C22×C4—21no—
368C22×C4—32no—
369C22×C4—181no—
370C22×C4C2×D3211yescharacteristic
371D8—188no—
372C2×C8—32no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—92no—
376C2×C8—92no—
377C2×C8—92no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C22⋊C4—124no—
383C22⋊C4—364no—
384C42—61no—
385C42—61no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—122no—
392C22×C3—122no—
393C22×C3—124no—
394C22×C3—124no—
395C22×C3—241no—
396C22×C3—241no—
397C22×C3—242no—
398C22×C3—242no—
399C22×C3—241no—
400C22×C3—241no—
401C22×C3#67⋊C411yescharacteristic
402C22×C3#88411yescharacteristic
403C22×C3D3×D812yes—
404C22×C3#91612yes—
405C22×C3C4×#6711yescharacteristic
406C22×C3C2×#21312yes—
407C22×C3#93911yescharacteristic
408C22×C3#94011yescharacteristic
409C22×C3#94011yescharacteristic
410C22×C3#95012yes—
411C2×D3—42no—
412C2×D3—42no—
413C2×D3—44no—
414C2×D3—44no—
415C2×D3—81no—
416C2×D3—81no—
417C2×D3—82no—
418C2×D3—82no—
419C2×D3—81no—
420C2×D3—81no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—64no—
426C3×C4—82no—
427C3×C4—81no—
428C3×C4—81no—
429C3×C4D3×C22⋊C411yescharacteristic
430C3×C4D3×C22⋊C411yescharacteristic
431C3×C4#67⋊C411yescharacteristic
432C3×C4#88411yescharacteristic
433C3×C4#88511yescharacteristic
434C3×C4#88511yescharacteristic
435C3×C4C4×#6711yescharacteristic
436C3×C4#93911yescharacteristic
437Dic3—24no—
438Dic3—242no—
439Dic3—241no—
440Dic3—241no—
441C32#197011yescharacteristic, complemented, Sylow
442C23—62no—
443C23—62no—
444C23—121no—
445C23—121no—
446C23—122no—
447C23—122no—
448C23—122no—
449C23—122no—
450C23—121no—
451C23—121no—
452C23D3×#6711yescharacteristic
453D4—62no—
454D4—62no—
455D4—62no—
456D4—62no—
457D4—121no—
458D4—121no—
459D4—121no—
460D4—121no—
461C2×C4—34no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—362no—
467C2×C4—361no—
468C2×C4#379511yescharacteristic
469C2×C4#379511yescharacteristic
470C2×C4C4×D3211yescharacteristic
471C2×C4#380211yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C2×C4#381111yescharacteristic
474C8—62no—
475C8—94no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—242no—
482C2×C3—242no—
483C2×C3#475612yes—
484C2×C3#477512yes—
485C2×C3#495711yescharacteristic
486C2×C3#495711yescharacteristic
487C2×C3C4×#21312yes—
488C2×C3#503812yes—
489C2×C3#505911yescharacteristic
490C2×C3#507311yescharacteristic
491C2×C3#515111yescharacteristic
492C2×C3#516811yescharacteristic
493D3—82no—
494D3—82no—
495C22—122no—
496C22—122no—
497C22—124no—
498C22—124no—
499C22—242no—
500C22—242no—
501C22—241no—
502C22—241no—
503C22—241no—
504C22—241no—
505C22#6387911yescharacteristic
506C22#6388511yescharacteristic
507C22D3×#21312yes—
508C22#6394712yes—
509C22#6397911yescharacteristic
510C4—64no—
511C4—81no—
512C4—721no—
513C4#6387911yescharacteristic
514C4#6388511yescharacteristic
515C4#6391311yescharacteristic
516C4#6392111yescharacteristic
517C3—21no—
518C3#6964711yescharacteristic, complemented
519C3#7019011yescharacteristic, complemented
520C2—242no—
521C2—242no—
522C2#1059045212yes—
523C2#1059049912yes—
524C2#1059138611yescharacteristic
525C2#1059148211yescharacteristic
526C2#1059160611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1970
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63634C2semidirect
3. C3×#4988C2semidirect
4. C2×C3×#809C2semidirect
5. #10591318C2semidirect
6. C2×#63563C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
21. C2×#3713C4semidirect
34. #4988D3semidirect
35. C2×#809D3semidirect
134. C2×C3×Dic3D8semidirect
143. C3⋊(C3⋊C8)C22⋊C4semidirect
332. C2×Dic3#213semidirect
441. C32#1970semidirect
518. C3#69647semidirect
519. C3#70190semidirect

Maximal subgroups

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

subgroupindex
C22×#37132
C2×#636342
C3×#49882
C2×C3×#8092
#105913182
C2×#635632
C2×Dic3×C3⋊C82
#701903
#696473