Finite Group Databasebeta

← #11791043

Subgroups — #11791043

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#72038—31nomaximal
9#69647—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—22no—
15C2×C3×#213—22no—
16C2×C3×#213—22no—
17C2×C3×#213C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—22no—
22#63659—22no—
23#63575—22no—
24#63562—22no—
25Dic3×C3⋊C8—22no—
26C22×C3×D8—31no—
27C22×#213D311yescharacteristic
28C3×#390—31no—
29#5221—31no—
30#5221D311yescharacteristic, complemented
31C2×#832—31no—
32C2×#832—31no—
33C2×#832—31no—
34C2×#832—61no—
35C2×#818—31no—
36C2×C8×Dic3—31no—
37C2×#809—31no—
38C2×#807—31no—
39#4939—31no—
40C2×C4×C3⋊C8—31no—
41C24×C32—21no—
42C23×C3×D3—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64C3×#217—44no—
65C3×#213—28no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8C2×C412yes—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73(C2×D3)⋊Dic3—44no—
74#1970—91noSylow
75C22×C3×D4—21no—
76C22×C3×D4—31no—
77C22×C3×D4C2×D311yescharacteristic
78C22×C3×D4C2×D311yescharacteristic
79C22×D12C2×D311yescharacteristic
80C2×C3×D8—34no—
81C2×C3×D8—62no—
82C2×C3×D8—62no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—62no—
86C2×C3×C42—31no—
87C2×#217—22no—
88C2×#217—62no—
89C2×#213—22no—
90C2×#213—22no—
91C2×#213Dic314yescomplemented
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4×Dic3C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C22×C3⋊C8C2×D311yescharacteristic
102#832—62no—
103#832—62no—
104#832—62no—
105#832—64no—
106#818—62no—
107C8×Dic3—62no—
108#809—62no—
109#807—62no—
110C4×C3⋊C8—62no—
111C23×C32—22no—
112C23×C32—41no—
113C23×C32—41no—
114C23×C32—42no—
115C23×C32—42no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4—41no—
125C32×D4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—42no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3D814yescomplemented
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8C22⋊C414yescomplemented
145C22×D8—31no—
146C2×#107—91no—
147C2×#102—91no—
148C2×#102—91no—
149C2×C4×C8—91no—
150#390—31no—
151#390—91no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—41no—
155C24×C3—61no—
156C23×D3—21no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—32no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4C4×D312yes—
180C2×C3×D4C2×Dic312yes—
181C22×C3×C4—21no—
182C22×C3×C4—32no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3#6712yes—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12C2×Dic312yes—
197C3×D8—68no—
198C2×C3×C8—32no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C22⋊C4—124no—
204C3×C42—61no—
205C3×C42—61no—
206#217—44no—
207#217—124no—
208#213—28no—
209(C2×D3)⋊C4—124no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3—62no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—121no—
218C4×Dic3—21no—
219C4×Dic3—21no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—121no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8C2×Dic312yes—
230C2×C3⋊C8#6712yes—
231C2×C3⋊C8#6712yes—
232C22×C32—42no—
233C22×C32—44no—
234C22×C32—82no—
235C22×C32—81no—
236C22×C32—81no—
237C22×C32C4×D411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12711yescharacteristic
240C22×C32C2×D812yes—
241C22×C32#13512yes—
242C2×C3×D3—42no—
243C2×C3×D3—44no—
244C2×C3×D3—82no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C32×C4C2×C22⋊C411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12411yescharacteristic
251C3⋊Dic3—81no—
252C3×Dic3—24no—
253C3×Dic3—81no—
254C22×D4—31no—
255C22×D4D3211yescharacteristic
256C2×D8—34no—
257C2×D8—62no—
258C2×D8—62no—
259C22×C8—31no—
260C22×C8—91no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—62no—
264C2×C22⋊C4—182no—
265C2×C42—31no—
266#107—182no—
267#102—182no—
268#102—182no—
269C4×C8—182no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—21no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—42no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—42no—
284C23×C3—62no—
285C23×C3—82no—
286C23×C3—82no—
287C23×C3—122no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—122no—
291C23×C3D3×D411yescharacteristic
292C23×C3C2×#6711yescharacteristic
293C22×D3—22no—
294C22×D3—42no—
295C22×D3—42no—
296C22×D3—41no—
297C22×D3—41no—
298C3×D4—24no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—41no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—121no—
313C3×D4—121no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—34no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—122no—
324C2×C3×C4—121no—
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4#23711yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4C22×Dic311yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—42no—
340C2×Dic3—41no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—242no—
347C2×Dic3#21314yescomplemented
348D12—22no—
349D12—22no—
350D12—41no—
351D12—41no—
352C3×C8—34no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C3⋊C8#21714yescomplemented
357C2×C32—82no—
358C2×C32#39011yescharacteristic
359C2×C32C4×D812yes—
360C2×C32#46612yes—
361C2×C32#49311yescharacteristic
362C2×C32#49511yescharacteristic
363C3×D3—82no—
364C24—21no—
365C24—61no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4D3×Dic312yes—
378C22×C4—32no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382D8—68no—
383C2×C8—32no—
384C2×C8—32no—
385C2×C8—32no—
386C2×C8—92no—
387C2×C8—181no—
388C2×C8—181no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C22⋊C4—124no—
394C22⋊C4—364no—
395C42—61no—
396C42—61no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—44no—
403C22×C3—44no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—44no—
407C22×C3—84no—
408C22×C3—84no—
409C22×C3—82no—
410C22×C3—82no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—82no—
414C22×C3—82no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—122no—
418C22×C3—124no—
419C22×C3—242no—
420C22×C3—241no—
421C22×C3—241no—
422C22×C3D3×D812yes—
423C22×C3#91212yes—
424C22×C3C4×#6711yescharacteristic
425C22×C3C2×#21312yes—
426C22×C3D4×Dic311yescharacteristic
427C22×C3#93811yescharacteristic
428C22×C3#93911yescharacteristic
429C22×C3#94011yescharacteristic
430C22×C3#94011yescharacteristic
431C22×C3#95012yes—
432C2×D3—44no—
433C2×D3—42no—
434C2×D3—81no—
435C2×D3—81no—
436C2×D3—82no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—64no—
442C3×C4—241no—
443C3×C4D3×C22⋊C411yescharacteristic
444C3×C4#67⋊C411yescharacteristic
445C3×C4#88411yescharacteristic
446C3×C4#88511yescharacteristic
447C3×C4D4×Dic311yescharacteristic
448C3×C4#93611yescharacteristic
449C3×C4#93811yescharacteristic
450C3×C4C2×#21711yescharacteristic
451Dic3—24no—
452Dic3—81no—
453Dic3—242no—
454Dic3—241no—
455Dic3—241no—
456C32#197011yescharacteristic, complemented, Sylow
457C23—22no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—62no—
463C23—122no—
464C23—122no—
465C23—121no—
466C23—121no—
467C23D3×#6711yescharacteristic
468D4—22no—
469D4—22no—
470D4—41no—
471D4—41no—
472D4—62no—
473D4—62no—
474D4—121no—
475D4—121no—
476C2×C4—34no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—122no—
480C2×C4—121no—
481C2×C4—362no—
482C2×C4—361no—
483C2×C4C2×D3×Dic311yescharacteristic
484C2×C4#380411yescharacteristic
485C2×C4#380511yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4D3×#6711yescharacteristic
488C2×C4#381111yescharacteristic
489C8—34no—
490C8—182no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—84no—
497C2×C3—82no—
498C2×C3—82no—
499C2×C3—242no—
500C2×C3#495711yescharacteristic
501C2×C3C4×#21312yes—
502C2×C3#503812yes—
503C2×C3#505911yescharacteristic
504C2×C3#507311yescharacteristic
505C2×C3Dic3×D812yes—
506C2×C3#515111yescharacteristic
507C2×C3#515511yescharacteristic
508C2×C3#515712yes—
509C2×C3#522111yescharacteristic
510D3—82no—
511C22—44no—
512C22—42no—
513C22—82no—
514C22—81no—
515C22—81no—
516C22—124no—
517C22—122no—
518C22—242no—
519C22—241no—
520C22—241no—
521C22D3×#21312yes—
522C22#6393312yes—
523C22#6397011yescharacteristic
524C22Dic3×#6711yescharacteristic
525C22#6397911yescharacteristic
526C4—64no—
527C4—241no—
528C4—721no—
529C4#6395811yescharacteristic
530C4#6395911yescharacteristic
531C4D3×#21711yescharacteristic
532C4#67⋊Dic311yescharacteristic
533C3—21no—
534C3#6964711yescharacteristic, complemented
535C3#7203811yescharacteristic, complemented
536C2—82no—
537C2—242no—
538C2Dic3×#21312yes—
539C2#1059147011yescharacteristic
540C2#1059148211yescharacteristic
541C2#1059149812yes—
542C2#1059170711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1970
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63659C2semidirect
3. C3×#5221C2semidirect
4. #10591318C2semidirect
5. C2×#63575C2semidirect
6. C2×#63562C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
17. C2×C3×#213C4semidirect
30. #5221D3semidirect
91. C2×#213Dic3semidirect
138. C2×C3×Dic3D8semidirect
144. C3×C3⋊C8C22⋊C4semidirect
347. C2×Dic3#213semidirect
356. C3⋊C8#217semidirect
456. C32#1970semidirect
534. C3#69647semidirect
535. C3#72038semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
C2×#636592
C3×#52212
#105913182
C2×#635752
C2×#635622
C2×Dic3×C3⋊C82
#720383
#696473