Finite Group Databasebeta

← #11786507

Subgroups — #11786507

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×C3×#807C211yesmaximal, characteristic, complemented
3#10591325C211yesmaximal, characteristic
4C2×#63573C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70633—31nomaximal
9#68876—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3—21no—
15#64101—22no—
16#64101—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—21no—
22C3×#807—22no—
23#63579—21no—
24#63573—22no—
25#63557C414yescomplemented
26C2×#892—31no—
27C2×#892—31no—
28C2×#892—61no—
29C2×C3×#107—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×(C2×D3)⋊C8—31no—
32C2×#817—31no—
33#4987—31no—
34#4987—31no—
35C2×#808—31no—
36C2×#807D311yescharacteristic, complemented
37C3×#340—31no—
38#4551—31no—
39#4529—31no—
40#4529D311yescharacteristic, complemented
41C23×C3⋊D3D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3C2×C412yes—
51C2×C4×C3⋊D3Q812yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D412yes—
56#3752—24no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D412yes—
59C4×C3⋊Dic3—24no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8C2×C412yes—
70#3722—42no—
71#1854—91noSylow
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—61no—
75C22×C3×C8—31no—
76C22×C3×C8—31no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—62no—
85C2×(C2×D3)⋊C4—61no—
86C2×(C2×D3)⋊C4—61no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3—62no—
95C22×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#892—62no—
98#892—62no—
99#892—64no—
100#892—64no—
101#892—62no—
102#892—62no—
103C3×#107—62no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106(C2×D3)⋊C8—34no—
107(C2×D3)⋊C8—34no—
108#817—62no—
109#808—62no—
110#807—22no—
111C23×C32C2×D411yescharacteristic
112C22×C3⋊D3—21no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3C4⋊C412yes—
119C2×C32×C4—22no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q811yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3C4⋊C412yes—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146C2×#117—91no—
147C2×#107—31no—
148C2×#106—91no—
149C2×C22⋊C8—91no—
150#380—91no—
151#340—31no—
152#340—91no—
153C23×D3—31no—
154C23×D3—31no—
155C23×D3—61no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C2×C4×D3—32no—
173C2×C4×D3—32no—
174C2×C4×D3—32no—
175C2×C4×D3—32no—
176C2×C4×D3—62no—
177C2×C4×D3—62no—
178C2×C4×D3—62no—
179C2×C4×D3—62no—
180C2×C4×D3—62no—
181C2×C4×D3—62no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C3×C8—32no—
191C2×C3×C8—32no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4D1212yes—
205C3×C4⋊C4#6712yes—
206(C2×D3)⋊C4—68no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—122no—
210(C2×D3)⋊C4—122no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4×Dic3—68no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8C4×D312yes—
229C2×C3⋊C8C4×D312yes—
230C22×C32C2×C4⋊C411yescharacteristic
231C22×C32#12011yescharacteristic
232C22×C32#12311yescharacteristic
233C22×C32#13511yescharacteristic
234C22×C32#13511yescharacteristic
235C22×C32AGL(1,ℤ/8)11yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3⋊D3—22no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—22no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3—41no—
244C32×C4—42no—
245C32×C4C4×D411yescharacteristic
246C32×C4C4×D411yescharacteristic
247C32×C4C22⋊Q811yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C3⋊Dic3—22no—
250C3⋊Dic3—42no—
251C3×Dic3—81no—
252C3×Dic3—81no—
253C23×C4—91no—
254C22×C8—31no—
255C22×C8—31no—
256#117—182no—
257#117—182no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—91no—
261C2×C4⋊C4D3211yescharacteristic
262C2×C22⋊C4—181no—
263C2×C22⋊C4—181no—
264C2×C42—181no—
265#107—62no—
266#106—182no—
267C22⋊C8—94no—
268#95—181no—
269C23×C3—21no—
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C22×D3—32no—
273C22×D3—32no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4D3×Q811yescharacteristic
323C2×C3×C4D3×Q811yescharacteristic
324C2×C3×C4#23911yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—64no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C4×D3—64no—
351C4×D3—64no—
352C4×D3—64no—
353C4×D3—64no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—62no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—62no—
360C4×D3—62no—
361C4×D3—62no—
362C3×C8—62no—
363C3×C8—62no—
364C3⋊C8—22no—
365C3⋊C8—22no—
366C2×C32#38511yescharacteristic
367C2×C32#42711yescharacteristic
368C2×C32#42811yescharacteristic
369C2×C32#44911yescharacteristic
370C2×C32#45211yescharacteristic
371C2×C32#48211yescharacteristic
372C2×C32#48511yescharacteristic
373C3⋊D3—42no—
374C24—91no—
375C22×C4—21no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—91no—
379C22×C4—92no—
380C22×C4—92no—
381C22×C4—181no—
382C22×C4—181no—
383C22×C4—181no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4C2×D3211yescharacteristic
387C2×C8—32no—
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C4⋊C4—21no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—92no—
399C4⋊C4—181no—
400C4⋊C4#62612yes—
401C22⋊C4—184no—
402C22⋊C4—362no—
403C42—184no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3#88211yescharacteristic
412C22×C3#88311yescharacteristic
413C22×C3D3×C4⋊C411yescharacteristic
414C22×C3D3×C4⋊C411yescharacteristic
415C22×C3#89411yescharacteristic
416C22×C3#91111yescharacteristic
417C22×C3#91111yescharacteristic
418C22×C3#91211yescharacteristic
419C22×C3#91611yescharacteristic
420C22×C3#91611yescharacteristic
421C22×C3#91811yescharacteristic
422C22×C3#91811yescharacteristic
423C22×C3#91911yescharacteristic
424C22×C3#93711yescharacteristic
425C2×D3—64no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—44no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—241no—
454C3×C4—241no—
455C3×C4C4×D1211yescharacteristic
456C3×C4#67⋊C411yescharacteristic
457C3×C4#89311yescharacteristic
458C3×C4#89611yescharacteristic
459C3×C4#89611yescharacteristic
460C3×C4#89711yescharacteristic
461C3×C4C4×#6711yescharacteristic
462C3×C4#94611yescharacteristic
463Dic3—64no—
464Dic3—62no—
465Dic3—62no—
466Dic3—81no—
467Dic3—81no—
468Dic3—124no—
469Dic3—122no—
470Dic3—122no—
471C32#185411yescharacteristic, complemented, Sylow
472C23—92no—
473C23—181no—
474C23—181no—
475C23—181no—
476C23—181no—
477C23—181no—
478C23—181no—
479C23#381111yescharacteristic
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—92no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—361no—
498C2×C4—361no—
499C2×C4#379611yescharacteristic
500C2×C4#379711yescharacteristic
501C2×C4#379811yescharacteristic
502C2×C4C4×D3211yescharacteristic
503C2×C4C2×#62611yescharacteristic
504C2×C4#381111yescharacteristic
505C8—62no—
506C8—62no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3#466811yescharacteristic
515C2×C3#477911yescharacteristic
516C2×C3#478111yescharacteristic
517C2×C3#480811yescharacteristic
518C2×C3#481511yescharacteristic
519C2×C3#486011yescharacteristic
520C2×C3#488011yescharacteristic
521C2×C3#488111yescharacteristic
522C2×C3#488111yescharacteristic
523C2×C3#488511yescharacteristic
524C2×C3#488811yescharacteristic
525C2×C3#498911yescharacteristic
526C2×C3#515811yescharacteristic
527C2×C3#518711yescharacteristic
528D3—124no—
529D3—122no—
530D3—122no—
531C22—182no—
532C22—182no—
533C22—182no—
534C22—361no—
535C22—361no—
536C22—361no—
537C22—361no—
538C22#6385311yescharacteristic
539C22#6388311yescharacteristic
540C22#6392711yescharacteristic
541C22#6393611yescharacteristic
542C22#6394511yescharacteristic
543C22#6395011yescharacteristic
544C22#6398111yescharacteristic
545C4—42no—
546C4—182no—
547C4—241no—
548C4—241no—
549C4—362no—
550C4#6386511yescharacteristic
551C4#6387111yescharacteristic
552C4#6388111yescharacteristic
553C4C4×#62611yescharacteristic
554C3—21no—
555C3#6887611yescharacteristic, complemented
556C3#7063311yescharacteristic, complemented
557C2—362no—
558C2#1059051211yescharacteristic
559C2#1059052611yescharacteristic
560C2#1059057411yescharacteristic
561C2#1059058211yescharacteristic
562C2#1059129011yescharacteristic
563C2#1059145711yescharacteristic
564C2#1059160211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1854
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
4. C2×#63573C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
25. #63557C4semidirect
36. C2×#807D3semidirect
40. #4529D3semidirect
471. C32#1854semidirect
555. C3#68876semidirect
556. C3#70633semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×C3×#8072
#105913252
C2×#635732
C2×#635572
C3×#45292
#105891642
#706333
#688763