Finite Group Databasebeta

← #11783945

Subgroups — #11783945

Order 1152.

893 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×#63648C211yesmaximal, characteristic
3C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
4Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8C4×#821—31nomaximal
9#68780—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#624—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—21no—
19C2×Dic32—21no—
20#63894—22no—
21#63894C414yescomplemented
22#63648C414yescomplemented
23C3×C8×Dic3—22no—
24#63579—21no—
25#63564C414yescomplemented
26C2×#893—31no—
27C2×C4×D12—31no—
28C2×C3×C4×C8—31no—
29C2×#821—31no—
30C2×#821—31no—
31C2×#821—31no—
32C2×#821—61no—
33C2×C8×Dic3D311yescharacteristic, complemented
34Dic3×C4⋊C4—31no—
35C2×#809—31no—
36C4×C4⋊Dic3—31no—
37C3×#340—31no—
38#4551—31no—
39#4551D311yescharacteristic, complemented
40#4529—31no—
41C23×C3⋊D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
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)C2×C412yes—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×#624—24no—
55C2×#624—42no—
56C2×#624—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8C2×C412yescomplemented
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2×C412yescomplemented
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3C2×C412yes—
65C3×C4⋊Dic3C2×C412yescomplemented
66C3×C4×Dic3C2×C412yes—
67C3×C4×Dic3D412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C412yescomplemented
71#3722—24no—
72Dic32—42no—
73C4×#102—91noSylow
74C22×D12—31no—
75C22×D12—31no—
76C22×D12—61no—
77C22×C4×D3—61no—
78C22×C4×D3—61no—
79C22×C3×C8—21no—
80C22×C3×C8—31no—
81C22×C3×C8C2×D311yescharacteristic
82C22×C3×C8C2×D311yescharacteristic
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C42—31no—
86C2×(C2×D3)⋊C4—61no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4×Dic3—61no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#893—34no—
98#893—62no—
99C4×D12—34no—
100C4×D12—62no—
101C3×C4×C8—62no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104#821—34no—
105#821—34no—
106#821—34no—
107#821—64no—
108C8×Dic3—22no—
109#809—34no—
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×C4C22×C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)C4214yescomplemented
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3C22⋊C412yes—
140C2×C3×Dic3C22⋊C412yes—
141C2×C3×Dic3D812yes—
142C2×C3×Dic3SD1612yes—
143#624—48no—
144C32×C8—22no—
145C3×C3⋊C8—22no—
146C2×C4×D4—91no—
147C2×#102—91no—
148C2×#102—91no—
149C2×C4×C8—31no—
150C4×C4⋊C4—91no—
151#340—31no—
152#340—91no—
153C23×D3—61no—
154C23×D3—61no—
155C23×D3—121no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3D1211yescharacteristic
169C22×Dic3D1211yescharacteristic
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—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—22no—
199C2×C3×C8—32no—
200C2×C3×C8—41no—
201C2×C3×C8—41no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8C4×D312yescomplemented
205C2×C3×C8C4×D312yescomplemented
206C3×C4⋊C4—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C42—32no—
211C3×C42—32no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—121no—
222C4⋊Dic3C4×D312yes—
223C4⋊Dic3C4×D312yescomplemented
224C4×Dic3—122no—
225C4×Dic3—122no—
226C4×Dic3C4×D312yes—
227C4×Dic3#6712yes—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8C4×D312yescomplemented
231C22×C32C2×C22⋊C411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C22×C32C2×D811yescharacteristic
235C22×C32C2×SD1611yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13511yescharacteristic
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×C4C2×C4211yescharacteristic
246C32×C4#11711yescharacteristic
247C32×C4C4×D411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C3⋊Dic3—42no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3#10214yescomplemented
254C22×D4—91no—
255C23×C4—181no—
256C22×C8—31no—
257C22×C8D3211yescharacteristic
258C4×D4—94no—
259C4×D4—182no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—181no—
264C2×C42—31no—
265C2×C42—181no—
266#102—94no—
267#102—94no—
268C4×C8—62no—
269#95—181no—
270C23×C3—21no—
271C23×C3C2×D1211yescharacteristic
272C23×C3D3×D411yescharacteristic
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—32no—
302C2×C3×C4—32no—
303C2×C3×C4—32no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4#23911yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—241no—
340C2×Dic3—241no—
341C2×Dic3#20412yes—
342C2×Dic3D2412yes—
343C2×Dic3(C2×D3)⋊C412yes—
344C2×Dic3(C2×D3)⋊C412yes—
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—22no—
360C3×C8—22no—
361C3×C8—42no—
362C3×C8—62no—
363C3⋊C8—22no—
364C2×C32C4×C22⋊C411yescharacteristic
365C2×C32C2×#10211yescharacteristic
366C2×C32#41611yescharacteristic
367C2×C32C4×D811yescharacteristic
368C2×C32C4×D811yescharacteristic
369C2×C32C4×SD1611yescharacteristic
370C2×C32C4×SD1611yescharacteristic
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—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—184no—
384C22×C4—181no—
385C22×C4—362no—
386C22×C4—362no—
387C22×C4C2×D3211yescharacteristic
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—32no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8#62412yescomplemented
394C4⋊C4—32no—
395C4⋊C4—32no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—92no—
399C4⋊C4—181no—
400C22⋊C4—184no—
401C42—32no—
402C42—32no—
403C42—362no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3C4×D1211yescharacteristic
412C22×C3C4×D1211yescharacteristic
413C22×C3D3×C22⋊C411yescharacteristic
414C22×C3#67⋊C411yescharacteristic
415C22×C3#89311yescharacteristic
416C22×C3C2×#20411yescharacteristic
417C22×C3C2×D2411yescharacteristic
418C22×C3#90411yescharacteristic
419C22×C3#90411yescharacteristic
420C22×C3D3×D811yescharacteristic
421C22×C3D3×SD1611yescharacteristic
422C22×C3#91611yescharacteristic
423C22×C3#91911yescharacteristic
424C22×C3C2×(C2×D3)⋊C411yescharacteristic
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—34no—
451C3×C4—62no—
452C3×C4—122no—
453C3×C4—122no—
454C3×C4C42×D311yescharacteristic
455C3×C4C42×D311yescharacteristic
456C3×C4#87211yescharacteristic
457C3×C4#67⋊C411yescharacteristic
458C3×C4#89211yescharacteristic
459C3×C4#89311yescharacteristic
460C3×C4C4×#6711yescharacteristic
461C3×C4C4×#6711yescharacteristic
462Dic3—22no—
463Dic3—42no—
464Dic3—42no—
465Dic3—122no—
466Dic3—122no—
467Dic3—242no—
468Dic3#82114yescomplemented
469C32C4×#10211yescharacteristic, complemented, Sylow
470C23—182no—
471C23—182no—
472C23—182no—
473C23—361no—
474C23—361no—
475C23—361no—
476C23—361no—
477C23D3×D1211yescharacteristic
478D4—94no—
479D4—182no—
480D4—182no—
481D4—182no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—182no—
495C2×C4—368no—
496C2×C4—361no—
497C2×C4—361no—
498C2×C4#379911yescharacteristic
499C2×C4C4×D3211yescharacteristic
500C2×C4C4×D3211yescharacteristic
501C2×C4#380411yescharacteristic
502C2×C4C2×#62411yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C8—22no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3#466611yescharacteristic
514C2×C3C4×#20411yescharacteristic
515C2×C3C4×#20411yescharacteristic
516C2×C3C4×D2411yescharacteristic
517C2×C3C4×D2411yescharacteristic
518C2×C3#475611yescharacteristic
519C2×C3D3×#10211yescharacteristic
520C2×C3#478811yescharacteristic
521C2×C3#480411yescharacteristic
522C2×C3#485211yescharacteristic
523C2×C3#487211yescharacteristic
524C2×C3C4×(C2×D3)⋊C411yescharacteristic
525C2×C3C2×#82111yescharacteristic
526C2×C3#511311yescharacteristic
527D3—124no—
528D3—124no—
529D3—244no—
530C22—184no—
531C22—362no—
532C22—362no—
533C22—362no—
534C22—362no—
535C22—362no—
536C22—362no—
537C22D3×#20411yescharacteristic
538C22D3×D2411yescharacteristic
539C22#6380611yescharacteristic
540C22#6380811yescharacteristic
541C22#6388011yescharacteristic
542C22#6389411yescharacteristic
543C22D3×(C2×D3)⋊C411yescharacteristic
544C4—34no—
545C4—62no—
546C4—122no—
547C4—122no—
548C4—362no—
549C4#6383611yescharacteristic
550C4C4×#62411yescharacteristic
551C4#6390411yescharacteristic
552C4#6395211yescharacteristic
553C3—21no—
554C3#6878011yescharacteristic, complemented
555C3C4×#82111yescharacteristic, complemented
556C2—364no—
557C2#1059069011yescharacteristic
558C2#1059074511yescharacteristic
559C2#1059075811yescharacteristic
560C2#1059076311yescharacteristic
561C2#1059079211yescharacteristic
562C2D3×#82111yescharacteristic
563C2#1059123311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32C4×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×C8×Dic3C2semidirect
4. Dic3×C4⋊Dic3C2semidirect
6. C3×#4551C2semidirect
7. #10589164C2semidirect
21. #63894C4semidirect
22. #63648C4semidirect
25. #63564C4semidirect
33. C2×C8×Dic3D3semidirect
39. #4551D3semidirect
59. C2×C32×C8C2×C4semidirect
61. C4⋊(C3⋊Dic3)C2×C4semidirect
65. C3×C4⋊Dic3C2×C4semidirect
70. C2×C3×C3⋊C8C2×C4semidirect
130. C4⋊(C3⋊D3)C42semidirect
204. C2×C3×C8C4×D3semidirect
205. C2×C3×C8C4×D3semidirect
223. C4⋊Dic3C4×D3semidirect
230. C2×C3⋊C8C4×D3semidirect
253. C3×Dic3#102semidirect
393. C2×C8#624semidirect
468. Dic3#821semidirect
469. C32C4×#102semidirect
554. C3#68780semidirect
555. C3C4×#821semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×#636482
C2×C3×C8×Dic32
Dic3×C4⋊Dic32
C2×#635642
C3×#45512
#105891642
C4×#8213
#687803