Finite Group Databasebeta

← #11791045

Subgroups — #11791045

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2#10592920C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×#63553C211yesmaximal, characteristic, complemented
8#72038—31nomaximal
9#70190—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×#3757—22no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#213—22no—
16C2×C3×#213—22no—
17C2×C3×#213C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—22no—
22C3×#832—22no—
23#63575—22no—
24#63563—22no—
25#63553—22no—
26C22×C3×D8—31no—
27C22×#213D311yescharacteristic
28C2×C3×#102—31no—
29#5221—31no—
30#5221—31no—
31#5221—31no—
32#5221—61no—
33C2×#832—31no—
34C2×#832D311yescharacteristic, complemented
35C2×#821—31no—
36C2×#818—31no—
37C2×C8×Dic3—31no—
38C2×C8×Dic3—31no—
39#4988—31no—
40C2×#807—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⋊Dic3D412yes—
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59#3757—44no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C3×#213—28no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8D412yes—
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—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—31no—
86C2×#217—62no—
87C2×#217—62no—
88C2×#217—62no—
89C2×#217—64no—
90C2×#213—22no—
91C2×#213—22no—
92C2×#213Dic314yescomplemented
93C2×(C2×D3)⋊C4—62no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—61no—
101C22×C3⋊C8C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103C3×#102—62no—
104#832—22no—
105#832—62no—
106#821—62no—
107#818—62no—
108C8×Dic3—62no—
109C8×Dic3—62no—
110#807—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—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—42no—
136C2×C3⋊Dic3D814yescomplemented
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
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—31no—
148C2×#102—91no—
149C2×C4×C8—91no—
150#390—91no—
151#390—91no—
152C24×C3—22no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—61no—
156C23×D3—21no—
157C2×C3×D4—22no—
158C2×C3×D4—21no—
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—22no—
169C2×C3×D4—32no—
170C2×C3×D4—41no—
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—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—62no—
189C22×Dic3—62no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12C2×Dic312yes—
198C3×D8—68no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—32no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207#217—124no—
208#217—124no—
209#217—124no—
210#217—128no—
211#213—28no—
212(C2×D3)⋊C4—124no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220C4⋊Dic3—121no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—121no—
226C4×Dic3—121no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8C2×Dic312yes—
230C2×C3⋊C8#6712yes—
231C2×C3⋊C8#6712yes—
232C2×C3⋊C8#6712yes—
233C22×C32—42no—
234C22×C32—44no—
235C22×C32—82no—
236C22×C32—81no—
237C22×C32—81no—
238C22×C32C4×D411yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12711yescharacteristic
241C22×C32C2×D812yes—
242C22×C32#13512yes—
243C2×C3×D3—42no—
244C2×C3×D3—44no—
245C2×C3×D3—82no—
246C2×C3×D3—81no—
247C2×C3×D3—81no—
248C32×C4C2×C22⋊C411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12411yescharacteristic
252C3⋊Dic3—24no—
253C3⋊Dic3—81no—
254C3×Dic3—81no—
255C22×D4—31no—
256C22×D4D3211yescharacteristic
257C2×D8—34no—
258C2×D8—62no—
259C2×D8—62no—
260C22×C8—31no—
261C22×C8—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—91no—
264C2×C22⋊C4—182no—
265C2×C22⋊C4—182no—
266C2×C42—91no—
267#107—182no—
268#102—62no—
269#102—182no—
270C4×C8—182no—
271C23×C3—24no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—21no—
275C23×C3—44no—
276C23×C3—42no—
277C23×C3—42no—
278C23×C3—44no—
279C23×C3—41no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—62no—
288C23×C3—121no—
289C23×C3—122no—
290C23×C3—122no—
291C23×C3—121no—
292C23×C3D3×D411yescharacteristic
293C23×C3D3×D411yescharacteristic
294C22×D3—22no—
295C22×D3—42no—
296C22×D3—42no—
297C22×D3—41no—
298C22×D3—41no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—62no—
312C3×D4—62no—
313C3×D4—121no—
314C3×D4—121no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—122no—
322C2×C3×C4—121no—
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4#23511yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4#23711yescharacteristic
331C2×C3×C4C22×Dic311yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—42no—
338C2×Dic3—41no—
339C2×Dic3—64no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—124no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352D12—22no—
353D12—22no—
354D12—41no—
355D12—41no—
356C3×C8—34no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8#21714yescomplemented
360C2×C32—82no—
361C2×C32#39011yescharacteristic
362C2×C32C4×D812yes—
363C2×C32#46612yes—
364C2×C32#49311yescharacteristic
365C2×C32#49511yescharacteristic
366C3×D3—82no—
367C24—21no—
368C24—61no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—32no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4D3×Dic312yes—
381C22×C4—61no—
382C22×C4—92no—
383C22×C4—181no—
384C22×C4C2×D3211yescharacteristic
385D8—68no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8—32no—
389C2×C8—32no—
390C2×C8—61no—
391C2×C8—61no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C22⋊C4—364no—
397C22⋊C4—364no—
398C42—181no—
399C42—181no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—44no—
406C22×C3—48no—
407C22×C3—44no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—44no—
411C22×C3—84no—
412C22×C3—82no—
413C22×C3—82no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—82no—
418C22×C3—81no—
419C22×C3—82no—
420C22×C3—122no—
421C22×C3—124no—
422C22×C3—241no—
423C22×C3—241no—
424C22×C3—242no—
425C22×C3#67⋊C411yescharacteristic
426C22×C3#88411yescharacteristic
427C22×C3D3×D812yes—
428C22×C3D3×D812yes—
429C22×C3#91212yes—
430C22×C3#91612yes—
431C22×C3D4×Dic311yescharacteristic
432C22×C3#93811yescharacteristic
433C22×C3#94011yescharacteristic
434C22×C3#94011yescharacteristic
435C2×D3—44no—
436C2×D3—42no—
437C2×D3—81no—
438C2×D3—81no—
439C2×D3—82no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—241no—
445C3×C4D3×C22⋊C411yescharacteristic
446C3×C4#88511yescharacteristic
447C3×C4C4×#6711yescharacteristic
448C3×C4D4×Dic311yescharacteristic
449C3×C4#93611yescharacteristic
450C3×C4#93811yescharacteristic
451C3×C4#93911yescharacteristic
452C3×C4C2×#21711yescharacteristic
453Dic3—64no—
454Dic3—64no—
455Dic3—81no—
456Dic3—124no—
457Dic3—242no—
458Dic3—241no—
459Dic3—241no—
460C32#197011yescharacteristic, complemented, Sylow
461C23—22no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—62no—
467C23—122no—
468C23—122no—
469C23—121no—
470C23—121no—
471C23#381111yescharacteristic
472D4—22no—
473D4—22no—
474D4—41no—
475D4—41no—
476D4—62no—
477D4—62no—
478D4—121no—
479D4—121no—
480C2×C4—94no—
481C2×C4—122no—
482C2×C4—121no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—362no—
486C2×C4—361no—
487C2×C4C2×D3×Dic311yescharacteristic
488C2×C4#380411yescharacteristic
489C2×C4#380511yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C8—34no—
494C8—62no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—84no—
501C2×C3—82no—
502C2×C3—82no—
503C2×C3—242no—
504C2×C3#475612yes—
505C2×C3#477512yes—
506C2×C3#495711yescharacteristic
507C2×C3Dic3×D812yes—
508C2×C3#515111yescharacteristic
509C2×C3#515111yescharacteristic
510C2×C3#515511yescharacteristic
511C2×C3#515712yes—
512C2×C3#516811yescharacteristic
513C2×C3#522111yescharacteristic
514D3—82no—
515C22—44no—
516C22—42no—
517C22—82no—
518C22—81no—
519C22—81no—
520C22—124no—
521C22—122no—
522C22—242no—
523C22—241no—
524C22—241no—
525C22#6392612yes—
526C22#6393612yes—
527C22#6395811yescharacteristic
528C22#67⋊Dic311yescharacteristic
529C22#6397911yescharacteristic
530C4—184no—
531C4—241no—
532C4—721no—
533C4#6395911yescharacteristic
534C4D3×#21711yescharacteristic
535C4#6397011yescharacteristic
536C4Dic3×#6711yescharacteristic
537C3—21no—
538C3#7019011yescharacteristic, complemented
539C3#7203811yescharacteristic, complemented
540C2—82no—
541C2—242no—
542C2#1059143512yes—
543C2#1059145512yes—
544C2#1059147411yescharacteristic
545C2#1059148411yescharacteristic
546C2#1059170711yescharacteristic
subgroupG/H
centerC23#3811
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. #10592920C2semidirect
3. C2×C3×#832C2semidirect
4. #10591323C2semidirect
5. C2×#63575C2semidirect
6. C2×#63563C2semidirect
7. C2×#63553C2semidirect
17. C2×C3×#213C4semidirect
34. C2×#832D3semidirect
92. C2×#213Dic3semidirect
136. C2×C3⋊Dic3D8semidirect
144. C3×C3⋊C8C22⋊C4semidirect
359. C3⋊C8#217semidirect
460. C32#1970semidirect
538. C3#70190semidirect
539. 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
#105929202
C2×C3×#8322
#105913232
C2×#635752
C2×#635632
C2×#635532
#720383
#701903