Finite Group Databasebeta

← #11791103

Subgroups — #11791103

Order 1152.

881 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×#3714C211yesmaximal, characteristic
2#10592687C211yesmaximal, characteristic, complemented
3C2×C3×#809C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×#63555C211yesmaximal, characteristic, complemented
8#70576—31nomaximal
9#70191—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—22no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—22no—
19C2×#3714—22no—
20C2×#3714—22no—
21C2×#3714C414yescomplemented
22C3×#809—22no—
23C3×#808—22no—
24#63564—22no—
25#63555—22no—
26C22×#213—31no—
27C22×D24—31no—
28C2×C3×#106—31no—
29C2×C3×#102—31no—
30#5221—31no—
31C2×#821—31no—
32C2×#815—31no—
33C2×#815—31no—
34#4988—31no—
35#4988—31no—
36#4988—31no—
37#4988—61no—
38C2×#809—31no—
39C2×#809D311yescharacteristic, complemented
40C2×#808D311yescharacteristic, complemented
41C23×C3⋊D3—21no—
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D412yes—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
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—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61#3752—44no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8D412yes—
70C2×C3×C3⋊C8D412yes—
71C2×C3×C3⋊C8D412yes—
72(C2×D3)⋊Dic3—44no—
73#3714—28no—
74#1972—91noSylow
75C22×C3×D4—31no—
76C22×D12—31no—
77C22×D12—31no—
78C22×D12—61no—
79C22×D12C2×D311yescharacteristic
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×#217—62no—
87C2×#213—34no—
88C2×#213—62no—
89C2×#213—62no—
90C2×(C2×D3)⋊C4—62no—
91C2×(C2×D3)⋊C4—62no—
92C2×(C2×D3)⋊C4—62no—
93C2×(C2×D3)⋊C4—64no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4×Dic3—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100C2×D24—34no—
101C2×D24—62no—
102C2×D24—62no—
103C3×#106—62no—
104C3×#102—62no—
105#821—62no—
106#815—62no—
107#815—62no—
108#809—22no—
109#809—62no—
110#808—22no—
111C23×C32C2×D411yescharacteristic
112C22×C3⋊D3—22no—
113C22×C3⋊D3—41no—
114C22×C3⋊D3—41no—
115C22×C3⋊D3—42no—
116C22×C3⋊D3—42no—
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
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—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—41no—
136C4⋊(C3⋊D3)—41no—
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—91no—
146C2×#106—31no—
147C2×#102—31no—
148C2×#102—91no—
149C2×#97—91no—
150#390—91no—
151#390—91no—
152C24×C3—61no—
153C23×D3—21no—
154C23×D3—62no—
155C23×D3—61no—
156C23×D3—61no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—32no—
172C22×Dic3—32no—
173C22×Dic3—62no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—32no—
180C2×D12—32no—
181C2×D12—62no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—62no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—121no—
194C2×D12—121no—
195C2×D12—121no—
196C2×D12—121no—
197C2×D12C4×D312yes—
198C2×C3×C8—32no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—32no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—41no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212#217—124no—
213#213—68no—
214(C2×D3)⋊C4—128no—
215(C2×D3)⋊C4—124no—
216(C2×D3)⋊C4—124no—
217(C2×D3)⋊C4—124no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—121no—
225C4×Dic3—121no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8C4×D312yes—
229C2×C3⋊C8D1212yes—
230C2×C3⋊C8#6712yes—
231C2×C3⋊C8#6712yes—
232D24—68no—
233C22×C32C4×D411yescharacteristic
234C22×C32#12111yescharacteristic
235C22×C32#12711yescharacteristic
236C22×C32AGL(1,ℤ/8)12yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C2×C3⋊D3—42no—
239C2×C3⋊D3—44no—
240C2×C3⋊D3—82no—
241C2×C3⋊D3—81no—
242C2×C3⋊D3—81no—
243C2×C3×D3—42no—
244C2×C3×D3—44no—
245C2×C3×D3—82no—
246C2×C3×D3—81no—
247C2×C3×D3—81no—
248C32×C4—81no—
249C32×C4C2×C22⋊C411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12411yescharacteristic
253C3⋊Dic3—42no—
254C3×Dic3—81no—
255C22×D4—31no—
256C22×D4—91no—
257C2×D8—94no—
258C2×D8—182no—
259C2×D8—182no—
260C22×C8—31no—
261C22×C8—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4D3211yescharacteristic
264C2×C22⋊C4—182no—
265C2×C22⋊C4—182no—
266C2×C42—91no—
267#106—62no—
268#102—62no—
269#102—182no—
270#97—182no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3—121no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3—121no—
277C23×C3D3×D411yescharacteristic
278C23×C3D3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—41no—
281C22×D3—42no—
282C22×D3—42no—
283C22×D3—41no—
284C22×D3—64no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—124no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—124no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—121no—
298C22×D3—121no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—44no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—122no—
316C2×C3×C4—121no—
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4#23511yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4#23711yescharacteristic
325C2×C3×C4#23911yescharacteristic
326C2×C3×C4#23911yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×Dic3—42no—
330C2×Dic3—41no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340D12—22no—
341D12—22no—
342D12—41no—
343D12—41no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—122no—
349D12—122no—
350D12—122no—
351D12—122no—
352D12—121no—
353D12—121no—
354D12—121no—
355D12—121no—
356C3×C8—34no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8(C2×D3)⋊C414yescomplemented
360C2×C32#39011yescharacteristic
361C2×C32#44212yes—
362C2×C32#46912yes—
363C2×C32#49611yescharacteristic
364C2×C32#49611yescharacteristic
365C3⋊D3—82no—
366C3×D3—82no—
367C24—61no—
368C24—181no—
369C2×D4—32no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—92no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4—181no—
381C22×C4—21no—
382C22×C4—61no—
383C22×C4—92no—
384C22×C4C2×D3211yescharacteristic
385D8—188no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8—32no—
389C2×C8—32no—
390C2×C8—61no—
391C2×C8—61no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C22⋊C4—364no—
397C22⋊C4—364no—
398C42—181no—
399C42—181no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—124no—
406C22×C3—122no—
407C22×C3—242no—
408C22×C3—241no—
409C22×C3—241no—
410C22×C3#67⋊C411yescharacteristic
411C22×C3#88411yescharacteristic
412C22×C3#89311yescharacteristic
413C22×C3#89511yescharacteristic
414C22×C3#91112yes—
415C22×C3#91412yes—
416C22×C3#91412yes—
417C22×C3#91412yes—
418C22×C3#94011yescharacteristic
419C22×C3#94011yescharacteristic
420C2×D3—42no—
421C2×D3—44no—
422C2×D3—81no—
423C2×D3—81no—
424C2×D3—82no—
425C2×D3—124no—
426C2×D3—128no—
427C2×D3—124no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—124no—
431C2×D3—244no—
432C2×D3—242no—
433C2×D3—242no—
434C2×D3—242no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—241no—
438C2×D3—241no—
439C2×D3—242no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—82no—
445C3×C4—81no—
446C3×C4—81no—
447C3×C4—241no—
448C3×C4D3×C22⋊C411yescharacteristic
449C3×C4#88511yescharacteristic
450C3×C4#89311yescharacteristic
451C3×C4#89511yescharacteristic
452C3×C4C2×(C2×D3)⋊C411yescharacteristic
453C3×C4C4×#6711yescharacteristic
454C3×C4#93911yescharacteristic
455C3×C4#94711yescharacteristic
456Dic3—81no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460C32#197211yescharacteristic, complemented, Sylow
461C23—62no—
462C23—121no—
463C23—122no—
464C23—122no—
465C23—121no—
466C23—182no—
467C23—361no—
468C23—362no—
469C23—362no—
470C23—361no—
471C23#381111yescharacteristic
472D4—62no—
473D4—62no—
474D4—121no—
475D4—121no—
476D4—182no—
477D4—182no—
478D4—361no—
479D4—361no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—122no—
483C2×C4—121no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4#379611yescharacteristic
488C2×C4#379911yescharacteristic
489C2×C4C4×D3211yescharacteristic
490C2×C4D3×D1211yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C8—34no—
494C8—62no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—242no—
501C2×C3#478212yes—
502C2×C3#478512yes—
503C2×C3#486512yes—
504C2×C3#486912yes—
505C2×C3#495711yescharacteristic
506C2×C3#498811yescharacteristic
507C2×C3#515411yescharacteristic
508C2×C3#517611yescharacteristic
509C2×C3#517611yescharacteristic
510C2×C3#517611yescharacteristic
511D3—82no—
512D3—244no—
513D3—242no—
514D3—242no—
515C22—122no—
516C22—124no—
517C22—242no—
518C22—241no—
519C22—241no—
520C22—362no—
521C22—364no—
522C22—722no—
523C22—721no—
524C22—721no—
525C22#6388111yescharacteristic
526C22#6391011yescharacteristic
527C22#6393712yes—
528C22#6394112yes—
529C22#6397911yescharacteristic
530C4—81no—
531C4—241no—
532C4—362no—
533C4#6388611yescharacteristic
534C4#6390411yescharacteristic
535C4#6390711yescharacteristic
536C4D3×(C2×D3)⋊C411yescharacteristic
537C3—21no—
538C3#7019111yescharacteristic, complemented
539C3#7057611yescharacteristic, complemented
540C2—242no—
541C2—722no—
542C2#1059046212yes—
543C2#1059050812yes—
544C2#1059138411yescharacteristic
545C2#1059147511yescharacteristic
546C2#1059162111yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1972
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. #10592687C2semidirect
3. C2×C3×#809C2semidirect
4. C2×C3×#808C2semidirect
5. #10591323C2semidirect
6. C2×#63564C2semidirect
7. C2×#63555C2semidirect
21. C2×#3714C4semidirect
39. C2×#809D3semidirect
40. C2×#808D3semidirect
144. C3×C3⋊C8C22⋊C4semidirect
359. C3⋊C8(C2×D3)⋊C4semidirect
460. C32#1972semidirect
538. C3#70191semidirect
539. C3#70576semidirect

Maximal subgroups

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

subgroupindex
C22×#37142
#105926872
C2×C3×#8092
C2×C3×#8082
#105913232
C2×#635642
C2×#635552
#705763
#701913