Finite Group Databasebeta

← #11786837

Subgroups — #11786837

Order 1152.

937 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C2×C3×#807C211yesmaximal, characteristic, complemented
3#10591357C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic
5C2×#63564C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70638—31nomaximal
9#68894—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64102—22no—
16#64102—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C3×#807—22no—
23#63579—21no—
24#63564—22no—
25#63564C414yescomplemented
26C2×#893—31no—
27C2×#893—31no—
28C2×#893—61no—
29C2×C3×#107—31no—
30C2×#821—31no—
31C2×#821—31no—
32#4984—31no—
33#4972—31no—
34C2×#809—31no—
35C2×#809—31no—
36C2×#807D311yescharacteristic, complemented
37C3×#340—31no—
38#4550—31no—
39#4550—31no—
40#4529D311yescharacteristic, complemented
41C23×C3⋊D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4⋊(C3⋊D3)D412yes—
51C2×C4⋊(C3⋊D3)Q812yes—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—42no—
54C2×C4×C3⋊D3—42no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4D412yes—
59#3752—24no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C412yescomplemented
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72Dic3⋊Dic3—42no—
73#1862—91noSylow
74C22×D12—31no—
75C22×D12—31no—
76C22×D12—61no—
77C22×C4×D3—61no—
78C22×C4×D3—61no—
79C22×C4×D3—62no—
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×(C2×D3)⋊C4—61no—
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4—62no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×Dic3⋊C4—61no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—61no—
97C22×C3⋊C8C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99#893—62no—
100#893—62no—
101#893—64no—
102#893—64no—
103#893—62no—
104#893—62no—
105C3×#107—62no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108#821—34no—
109#821—62no—
110#809—34no—
111#809—62no—
112#807—22no—
113C23×C32C2×D411yescharacteristic
114C22×C3⋊D3—22no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—41no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3D812yes—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—22no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)C4⋊C414yescomplemented
140C4×C3⋊D3—48no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149C2×C4×D4—91no—
150C2×#107—31no—
151C2×#102—91no—
152C2×#102—91no—
153#389—91no—
154#340—31no—
155#336—91no—
156C23×D3—62no—
157C23×D3—61no—
158C23×D3—61no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C2×D12—32no—
176C2×D12—32no—
177C2×D12—32no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—32no—
181C2×D12—62no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×C4×D3—68no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—122no—
197C2×C4×D3—122no—
198C2×C4×D3—124no—
199C2×C4×D3—124no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4D1212yes—
217C3×C4⋊C4#6712yes—
218(C2×D3)⋊C4—68no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—122no—
225C4⋊Dic3C4×D312yescomplemented
226Dic3⋊C4—122no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8C4×D312yescomplemented
239C22×C32C4×D411yescharacteristic
240C22×C32#12011yescharacteristic
241C22×C32C22⋊Q811yescharacteristic
242C22×C32C2×D811yescharacteristic
243C22×C32#13511yescharacteristic
244C22×C32AGL(1,ℤ/8)11yescharacteristic
245C22×C32#13711yescharacteristic
246C2×C3⋊D3—24no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—42no—
252C2×C3⋊D3—42no—
253C32×C4—42no—
254C32×C4C2×C4⋊C411yescharacteristic
255C32×C4C4×D411yescharacteristic
256C32×C4C22⋊Q811yescharacteristic
257C32×C4#12311yescharacteristic
258C3⋊Dic3—22no—
259C3⋊Dic3—41no—
260C3×Dic3—42no—
261C3×Dic3—81no—
262C22×D4—91no—
263C23×C4—181no—
264C22×C8—31no—
265C22×C8—31no—
266C4×D4—182no—
267C4×D4—182no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—181no—
271C2×C4⋊C4D3211yescharacteristic
272C2×C22⋊C4—181no—
273C2×C42—91no—
274#107—62no—
275#102—94no—
276#102—182no—
277#95—181no—
278C23×C3—21no—
279C23×C3D3×D411yescharacteristic
280C23×C3D3×D411yescharacteristic
281C22×D3—64no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—62no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4#23711yescharacteristic
331C2×C3×C4D3×Q811yescharacteristic
332C2×C3×C4D3×Q811yescharacteristic
333C2×C3×C4#23911yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—62no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359D12—34no—
360D12—34no—
361D12—64no—
362D12—64no—
363D12—64no—
364D12—64no—
365D12—62no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—62no—
371C4×D3—1216no—
372C4×D3—128no—
373C4×D3—128no—
374C3×C8—62no—
375C3×C8—121no—
376C3⋊C8—22no—
377C3⋊C8—41no—
378C2×C32#38511yescharacteristic
379C2×C32C4×D811yescharacteristic
380C2×C32#44011yescharacteristic
381C2×C32#44711yescharacteristic
382C2×C32#45211yescharacteristic
383C2×C32#47411yescharacteristic
384C2×C32#47811yescharacteristic
385C3⋊D3—44no—
386C24—181no—
387C2×D4—92no—
388C2×D4—92no—
389C2×D4—92no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—181no—
393C22×C4—21no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—184no—
399C22×C4—362no—
400C22×C4—362no—
401C22×C4C2×D3211yescharacteristic
402C2×C8—32no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C4⋊C4—21no—
409C4⋊C4—32no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—362no—
414C4⋊C4#62612yes—
415C22⋊C4—184no—
416C42—181no—
417C42—181no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3#67⋊C411yescharacteristic
426C22×C3#88211yescharacteristic
427C22×C3#89311yescharacteristic
428C22×C3#89611yescharacteristic
429C22×C3#89611yescharacteristic
430C22×C3D3×D811yescharacteristic
431C22×C3D3×D811yescharacteristic
432C22×C3#91111yescharacteristic
433C22×C3#91411yescharacteristic
434C22×C3#91611yescharacteristic
435C22×C3#91811yescharacteristic
436C22×C3#91811yescharacteristic
437C22×C3#91911yescharacteristic
438C22×C3#93711yescharacteristic
439C2×D3—68no—
440C2×D3—64no—
441C2×D3—64no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—44no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—122no—
468C3×C4—241no—
469C3×C4C4×D1211yescharacteristic
470C3×C4#88311yescharacteristic
471C3×C4D3×C4⋊C411yescharacteristic
472C3×C4D3×C4⋊C411yescharacteristic
473C3×C4#89411yescharacteristic
474C3×C4#89711yescharacteristic
475C3×C4C4×#6711yescharacteristic
476C3×C4#94611yescharacteristic
477Dic3—42no—
478Dic3—64no—
479Dic3—62no—
480Dic3—62no—
481Dic3—81no—
482Dic3—122no—
483Dic3—121no—
484Dic3—121no—
485C32#186211yescharacteristic, complemented, Sylow
486C23—182no—
487C23—182no—
488C23—182no—
489C23—361no—
490C23—361no—
491C23—361no—
492C23—361no—
493C23#381111yescharacteristic
494D4—94no—
495D4—182no—
496D4—182no—
497D4—182no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—368no—
514C2×C4#379611yescharacteristic
515C2×C4#379711yescharacteristic
516C2×C4#379811yescharacteristic
517C2×C4C4×D3211yescharacteristic
518C2×C4C2×#62611yescharacteristic
519C2×C4#381111yescharacteristic
520C8—62no—
521C8—121no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3#466811yescharacteristic
530C2×C3#475611yescharacteristic
531C2×C3#477311yescharacteristic
532C2×C3#480811yescharacteristic
533C2×C3#481711yescharacteristic
534C2×C3#487111yescharacteristic
535C2×C3#487211yescharacteristic
536C2×C3#488911yescharacteristic
537C2×C3#489011yescharacteristic
538C2×C3#489011yescharacteristic
539C2×C3#489111yescharacteristic
540C2×C3#498911yescharacteristic
541C2×C3#515611yescharacteristic
542C2×C3#518711yescharacteristic
543D3—128no—
544D3—124no—
545D3—124no—
546C22—184no—
547C22—362no—
548C22—362no—
549C22—362no—
550C22—362no—
551C22—362no—
552C22—362no—
553C22#6386511yescharacteristic
554C22#6388111yescharacteristic
555C22#6392611yescharacteristic
556C22#6393711yescharacteristic
557C22#6394511yescharacteristic
558C22#6395011yescharacteristic
559C22#6398111yescharacteristic
560C4—42no—
561C4—122no—
562C4—182no—
563C4—241no—
564C4—361no—
565C4#6385311yescharacteristic
566C4#6387111yescharacteristic
567C4#6388311yescharacteristic
568C4C4×#62611yescharacteristic
569C3—21no—
570C3#6889411yescharacteristic, complemented
571C3#7063811yescharacteristic, complemented
572C2—364no—
573C2#1059043011yescharacteristic
574C2#1059043511yescharacteristic
575C2#1059045911yescharacteristic
576C2#1059048411yescharacteristic
577C2#1059129011yescharacteristic
578C2#1059145611yescharacteristic
579C2#1059160211yescharacteristic
subgroupG/H
centerC23#3811
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
2. C2×C3×#807C2semidirect
3. #10591357C2semidirect
6. C3×#4529C2semidirect
7. #10589156C2semidirect
25. #63564C4semidirect
36. C2×#807D3semidirect
40. #4529D3semidirect
65. C3×C4⋊Dic3C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
139. C4⋊(C3⋊D3)C4⋊C4semidirect
225. C4⋊Dic3C4×D3semidirect
238. C2×C3⋊C8C4×D3semidirect
485. C32#1862semidirect
570. C3#68894semidirect
571. C3#70638semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C3×#8072
#105913572
C2×#635642
C3×#45292
#105891562
#706383
#688943