Finite Group Databasebeta

← #11786834

Subgroups — #11786834

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic
3C3×#4972C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6#10589163C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70638—31nomaximal
9#69625—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#624—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3722—21no—
20#63894—22no—
21#63894—22no—
22#63636—22no—
23C3×C3⋊#95—21no—
24C3×#807—22no—
25#63564C414yescomplemented
26C2×#893—31no—
27C2×C4×D12—31no—
28C2×C3×#107—31no—
29C3×#389—31no—
30C2×#821—31no—
31#4972D311yescharacteristic, complemented
32C2×#809—31no—
33C2×#809—31no—
34C2×#809—31no—
35C2×#809—61no—
36C2×#807D311yescharacteristic, complemented
37#4550—31no—
38#4529—31no—
39#4529—31no—
40#4524—31no—
41C23×C3⋊D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)C2×C412yes—
48C2×C4⋊(C3⋊D3)D412yes—
49C2×C4⋊(C3⋊D3)Q812yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×#624—24no—
55C2×#624—42no—
56C2×#624—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3C2×C412yescomplemented
65C3×C4⋊Dic3D412yes—
66C3×Dic3⋊C4—42no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72#3722—24no—
73#1862—91noSylow
74C22×D12—31no—
75C22×D12—31no—
76C22×D12—61no—
77C22×C4×D3—61no—
78C22×C4×D3—61no—
79C22×C3×C8—31no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—61no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C42—31no—
87C2×(C2×D3)⋊C4—61no—
88C2×(C2×D3)⋊C4—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×Dic3⋊C4—21no—
92C2×C4×Dic3C2×D311yescharacteristic
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—61no—
96C22×C3⋊C8C2×D311yescharacteristic
97#893—62no—
98#893—62no—
99C4×D12—62no—
100C4×D12—62no—
101C3×#107—62no—
102C3×#95—61no—
103C3⋊#95—21no—
104#821—34no—
105#809—34no—
106#809—62no—
107#809—62no—
108#809—64no—
109#807—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3⋊D3—22no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3—41no—
115C22×C3⋊D3—41no—
116C22×C3⋊D3—41no—
117C22×C3⋊D3—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)C4⋊C414yescomplemented
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3D812yes—
143#624—48no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—22no—
146C2×C4×D4—91no—
147C2×#107—31no—
148C2×#102—91no—
149C2×#102—91no—
150#389—31no—
151#340—91no—
152#336—91no—
153C23×D3—61no—
154C23×D3—61no—
155C23×D3—121no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—41no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3#6711yescharacteristic
169C22×Dic3#6711yescharacteristic
170C2×D12—32no—
171C2×D12—32no—
172C2×D12—32no—
173C2×D12—32no—
174C2×D12—32no—
175C2×D12—32no—
176C2×D12—62no—
177C2×D12—62no—
178C2×D12—62no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—121no—
186C2×D12—121no—
187C2×D12—121no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—122no—
191C2×C4×D3—122no—
192C2×C4×D3—122no—
193C2×C4×D3—122no—
194C2×C3×C8—32no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—122no—
208C3×C42—61no—
209C3×C42—61no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3C4×D312yescomplemented
215C4⋊Dic3#6712yes—
216Dic3⋊C4—42no—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8C4×D312yescomplemented
231C22×C32C4×D411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32C22⋊Q811yescharacteristic
234C22×C32C2×D811yescharacteristic
235C22×C32#13511yescharacteristic
236C22×C32AGL(1,ℤ/8)11yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3⋊D3—24no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—42no—
245C32×C4—81no—
246C32×C4C2×C4⋊C411yescharacteristic
247C32×C4C4×D411yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C32×C4#12311yescharacteristic
250C3×Dic3—22no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3—41no—
254C22×D4—91no—
255C23×C4—181no—
256C22×C8—31no—
257C22×C8—91no—
258C4×D4—182no—
259C4×D4—182no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—61no—
263C2×C4⋊C4D3211yescharacteristic
264C2×C22⋊C4—181no—
265C2×C42—31no—
266#107—62no—
267#102—94no—
268#102—182no—
269#95—61no—
270C23×C3—21no—
271C23×C3D3×D411yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C22×D3—62no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—122no—
280C22×D3—122no—
281C22×D3—122no—
282C22×D3—121no—
283C22×D3—121no—
284C22×D3—121no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—121no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—241no—
291C22×D3—241no—
292C22×D3—241no—
293C22×D3—241no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—32no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—62no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—62no—
315C2×C3×C4—81no—
316C2×C3×C4—81no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4#23511yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×Q811yescharacteristic
329C2×C3×C4D3×Q811yescharacteristic
330C2×C3×C4#23911yescharacteristic
331C2×C3×C4#23911yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3#21312yes—
345D12—34no—
346D12—34no—
347D12—64no—
348D12—62no—
349D12—62no—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—122no—
357C4×D3—128no—
358C4×D3—128no—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—122no—
362C3⋊C8—121no—
363C3⋊C8—121no—
364C2×C32#38511yescharacteristic
365C2×C32C4×D811yescharacteristic
366C2×C32#44011yescharacteristic
367C2×C32#44711yescharacteristic
368C2×C32#45211yescharacteristic
369C2×C32#47411yescharacteristic
370C2×C32#47811yescharacteristic
371C3⋊D3—44no—
372C24—181no—
373C2×D4—92no—
374C2×D4—92no—
375C2×D4—92no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—181no—
379C22×C4—21no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—184no—
385C22×C4—362no—
386C22×C4—362no—
387C22×C4C2×D3211yescharacteristic
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—181no—
392C2×C8—181no—
393C2×C8—181no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—122no—
401C22⋊C4—184no—
402C42—61no—
403C42—61no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3#89311yescharacteristic
412C22×C3#89611yescharacteristic
413C22×C3D3×D811yescharacteristic
414C22×C3#91111yescharacteristic
415C22×C3#91811yescharacteristic
416C22×C3#91911yescharacteristic
417C22×C3C4×#6711yescharacteristic
418C22×C3C2×#21311yescharacteristic
419C22×C3#93711yescharacteristic
420C22×C3#93711yescharacteristic
421C22×C3#94211yescharacteristic
422C22×C3#94611yescharacteristic
423C22×C3#94911yescharacteristic
424C22×C3#95011yescharacteristic
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—124no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—242no—
441C2×D3—242no—
442C2×D3—242no—
443C2×D3—242no—
444C2×D3—242no—
445C2×D3—242no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—62no—
451C3×C4—82no—
452C3×C4—81no—
453C3×C4—81no—
454C3×C4—122no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4D3×C4⋊C411yescharacteristic
458C3×C4D3×C4⋊C411yescharacteristic
459C3×C4#89311yescharacteristic
460C3×C4#89411yescharacteristic
461C3×C4#89411yescharacteristic
462C3×C4#89611yescharacteristic
463C3×C4C4×#6711yescharacteristic
464C3×C4#94611yescharacteristic
465Dic3—22no—
466Dic3—42no—
467Dic3—42no—
468Dic3—41no—
469C32#186211yescharacteristic, complemented, Sylow
470C23—182no—
471C23—182no—
472C23—182no—
473C23—361no—
474C23—361no—
475C23—361no—
476C23—361no—
477C23D3×#6711yescharacteristic
478D4—94no—
479D4—182no—
480D4—182no—
481D4—182no—
482C2×C4—32no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—368no—
498C2×C4#379711yescharacteristic
499C2×C4#379911yescharacteristic
500C2×C4#379911yescharacteristic
501C2×C4C4×D3211yescharacteristic
502C2×C4D3×#6711yescharacteristic
503C2×C4#381111yescharacteristic
504C8—62no—
505C8—361no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3#487211yescharacteristic
514C2×C3#488911yescharacteristic
515C2×C3#489011yescharacteristic
516C2×C3#489111yescharacteristic
517C2×C3#498911yescharacteristic
518C2×C3#498911yescharacteristic
519C2×C3C4×#21311yescharacteristic
520C2×C3#502611yescharacteristic
521C2×C3#503611yescharacteristic
522C2×C3#504711yescharacteristic
523C2×C3#506611yescharacteristic
524C2×C3#508711yescharacteristic
525C2×C3#515611yescharacteristic
526C2×C3#518711yescharacteristic
527D3—124no—
528D3—124no—
529D3—244no—
530C22—184no—
531C22—362no—
532C22—362no—
533C22—362no—
534C22—362no—
535C22—362no—
536C22—362no—
537C22#6388811yescharacteristic
538C22#6390411yescharacteristic
539C22D3×#21311yescharacteristic
540C22#6392511yescharacteristic
541C22#6394811yescharacteristic
542C22#6394911yescharacteristic
543C22#6398311yescharacteristic
544C4—62no—
545C4—81no—
546C4—122no—
547C4—121no—
548C4—122no—
549C4#6388311yescharacteristic
550C4#6388811yescharacteristic
551C4#6389711yescharacteristic
552C4#6390411yescharacteristic
553C3—21no—
554C3#6962511yescharacteristic, complemented
555C3#7063811yescharacteristic, complemented
556C2—364no—
557C2#1059045611yescharacteristic
558C2#1059045711yescharacteristic
559C2#1059046411yescharacteristic
560C2#1059046811yescharacteristic
561C2#1059137411yescharacteristic
562C2#1059151511yescharacteristic
563C2#1059165711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1862
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
3. C3×#4972C2semidirect
4. C2×C3×#807C2semidirect
6. #10589163C2semidirect
7. #10589155C2semidirect
25. #63564C4semidirect
31. #4972D3semidirect
36. C2×#807D3semidirect
64. C3×C4⋊Dic3C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
130. C4⋊(C3⋊D3)C4⋊C4semidirect
214. C4⋊Dic3C4×D3semidirect
230. C2×C3⋊C8C4×D3semidirect
469. C32#1862semidirect
554. C3#69625semidirect
555. C3#70638semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×#636362
C3×#49722
C2×C3×#8072
C2×#635642
#105891632
#105891552
#706383
#696253