Finite Group Databasebeta

← #11791491

Subgroups — #11791491

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63863C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#70230—31nomaximal
9#70162—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63863—22no—
21#63863C414yescomplemented
22#63658—21no—
23C3×#810—22no—
24C3×#809—22no—
25#63572—22no—
26#63566—22no—
27#63563—22no—
28C2×#947—31no—
29C2×#936—31no—
30C2×C3×#103—31no—
31C2×C3×#102—31no—
32C2×#835—31no—
33C2×#832—31no—
34C2×#821—31no—
35C2×#816—31no—
36C2×Dic3⋊C8—31no—
37C2×Dic3⋊C8—31no—
38Dic3×C4⋊C4—31no—
39Dic3×C4⋊C4—31no—
40Dic3×C4⋊C4—61no—
41C2×#810D311yescharacteristic, complemented
42C2×#809D311yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D412yes—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)D412yes—
66C4×C3⋊Dic3—42no—
67C4×C3⋊Dic3C2×C412yes—
68C4×C3⋊Dic3D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77#1983—91noSylow
78C22×C3×Q8—31no—
79C22×C3×D4—31no—
80C22×D12C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×#217—61no—
88C2×#217—61no—
89#947—34no—
90#947—62no—
91#936—34no—
92#936—62no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—61no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3—62no—
104C22×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C3×#103—62no—
107C3×#102—62no—
108#835—62no—
109#832—62no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—62no—
113#821—62no—
114#816—62no—
115Dic3⋊C8—62no—
116Dic3⋊C8—62no—
117#810—22no—
118#809—22no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4—22no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3C22⋊C412yes—
144C2×C3⋊Dic3C22⋊C412yes—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—41no—
155C3×Dic6—41no—
156C3×C3⋊C8—41no—
157C3×C3⋊C8—41no—
158C2×#124—91no—
159C2×C4⋊C8—91no—
160C2×#103—31no—
161C2×#103—91no—
162C2×#102—31no—
163C2×#102—91no—
164C4×C4⋊C4—91no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12C4×D312yes—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6C4×D312yes—
208C2×C3×C8—61no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4#6712yes—
219C3×C4⋊C4#6712yes—
220#217—64no—
221#217—64no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—64no—
224C4⋊Dic3—32no—
225C4⋊Dic3—32no—
226C4⋊Dic3—62no—
227C4⋊Dic3—62no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—32no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—124no—
237C4×Dic3—122no—
238C4×Dic3—122no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C22×C32C2×C22⋊C411yescharacteristic
246C22×C32#12111yescharacteristic
247C22×C32#12111yescharacteristic
248C22×C32#13511yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32AGL(1,ℤ/8)11yescharacteristic
251C22×C32#13711yescharacteristic
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C32×C4—42no—
260C32×C4C4×D411yescharacteristic
261C32×C4C4×D411yescharacteristic
262C32×C4#12411yescharacteristic
263C32×C4#12711yescharacteristic
264C3⋊Dic3—22no—
265C3⋊Dic3—22no—
266C3⋊Dic3—42no—
267C3×Dic3—42no—
268C22×Q8—31no—
269C22×D4—31no—
270C22×C8—31no—
271C22×C8—31no—
272#124—94no—
273#124—182no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4D3211yescharacteristic
276C2×C22⋊C4—181no—
277C2×C22⋊C4—181no—
278C2×C42—91no—
279C2×C42—181no—
280C4⋊C8—182no—
281#103—62no—
282#103—182no—
283#102—62no—
284#102—182no—
285#95—181no—
286C23×C3—21no—
287C23×C3—62no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3D3×D411yescharacteristic
295C23×C3D3×D411yescharacteristic
296C22×D3—22no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—121no—
306C3×Q8—121no—
307C3×D4—62no—
308C3×D4—62no—
309C3×D4—121no—
310C3×D4—121no—
311C2×C3×C4—24no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—62no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—64no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371D12—22no—
372D12—22no—
373D12—41no—
374D12—41no—
375Dic6—22no—
376Dic6—22no—
377Dic6—41no—
378Dic6—41no—
379C3×C8—121no—
380C3×C8—121no—
381C3⋊C8—41no—
382C3⋊C8—41no—
383C2×C32#39011yescharacteristic
384C2×C32#41611yescharacteristic
385C2×C32#41711yescharacteristic
386C2×C32#46311yescharacteristic
387C2×C32#46311yescharacteristic
388C2×C32#46411yescharacteristic
389C2×C32#46411yescharacteristic
390C3×D3—82no—
391C24—61no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×D4—32no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C22×C4—21no—
405C22×C4—61no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—181no—
409C22×C4C2×D3211yescharacteristic
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—61no—
415C2×C8—61no—
416C4⋊C4—21no—
417C4⋊C4—92no—
418C4⋊C4—181no—
419C4⋊C4#62512yes—
420C22⋊C4—184no—
421C22⋊C4—184no—
422C42—92no—
423C42—92no—
424C42—362no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3D3×C22⋊C411yescharacteristic
441C22×C3#88411yescharacteristic
442C22×C3#88411yescharacteristic
443C22×C3#91111yescharacteristic
444C22×C3#91211yescharacteristic
445C22×C3#91411yescharacteristic
446C22×C3#91511yescharacteristic
447C22×C3#91611yescharacteristic
448C22×C3#91611yescharacteristic
449C22×C3#91811yescharacteristic
450C22×C3#91911yescharacteristic
451C22×C3#93911yescharacteristic
452C22×C3#93911yescharacteristic
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C2×D3—81no—
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#67⋊C411yescharacteristic
469C3×C4#67⋊C411yescharacteristic
470C3×C4#88511yescharacteristic
471C3×C4#88511yescharacteristic
472C3×C4C4×#6711yescharacteristic
473C3×C4C4×#6711yescharacteristic
474C3×C4#94011yescharacteristic
475C3×C4#94011yescharacteristic
476Dic3—42no—
477Dic3—64no—
478Dic3—62no—
479Dic3—62no—
480Dic3—62no—
481Dic3—62no—
482Dic3—122no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#198311yescharacteristic, complemented, Sylow
487C23—62no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23#381111yescharacteristic
495Q8—62no—
496Q8—62no—
497Q8—121no—
498Q8—121no—
499D4—62no—
500D4—62no—
501D4—121no—
502D4—121no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—62no—
507C2×C4—92no—
508C2×C4—92no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—182no—
516C2×C4—361no—
517C2×C4—361no—
518C2×C4#379811yescharacteristic
519C2×C4C4×D3211yescharacteristic
520C2×C4#380211yescharacteristic
521C2×C4#380211yescharacteristic
522C2×C4#380511yescharacteristic
523C2×C4C2×#62511yescharacteristic
524C8—121no—
525C8—121no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—242no—
534C2×C3#476711yescharacteristic
535C2×C3#477111yescharacteristic
536C2×C3#477211yescharacteristic
537C2×C3#478711yescharacteristic
538C2×C3#479811yescharacteristic
539C2×C3#480311yescharacteristic
540C2×C3#480411yescharacteristic
541C2×C3#481911yescharacteristic
542C2×C3#495711yescharacteristic
543C2×C3#495711yescharacteristic
544C2×C3#515311yescharacteristic
545C2×C3#516511yescharacteristic
546C2×C3#516611yescharacteristic
547C2×C3#518511yescharacteristic
548D3—82no—
549C22—122no—
550C22—122no—
551C22—122no—
552C22—241no—
553C22—241no—
554C22—241no—
555C22—241no—
556C22#6391211yescharacteristic
557C22#6392111yescharacteristic
558C22#6393611yescharacteristic
559C22#6393711yescharacteristic
560C22#6395011yescharacteristic
561C22#6395111yescharacteristic
562C22#6398011yescharacteristic
563C4—42no—
564C4—122no—
565C4—182no—
566C4—182no—
567C4—362no—
568C4C4×#62511yescharacteristic
569C4#6390211yescharacteristic
570C4#6391411yescharacteristic
571C4#6391511yescharacteristic
572C3—21no—
573C3#7016211yescharacteristic, complemented
574C3#7023011yescharacteristic, complemented
575C2—242no—
576C2#1059053811yescharacteristic
577C2#1059054011yescharacteristic
578C2#1059061111yescharacteristic
579C2#1059061211yescharacteristic
580C2#1059138511yescharacteristic
581C2#1059147611yescharacteristic
582C2#1059161211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1983
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. C4⋊C4×C3⋊Dic3C2semidirect
3. C2×C3×#810C2semidirect
5. C2×#63572C2semidirect
6. C2×#63566C2semidirect
21. #63863C4semidirect
41. C2×#810D3semidirect
486. C32#1983semidirect
573. C3#70162semidirect
574. C3#70230semidirect

Maximal subgroups

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

subgroupindex
C2×#638632
C4⋊C4×C3⋊Dic32
C2×C3×#8102
C2×C3×#8092
C2×#635722
C2×#635662
C2×#635632
#702303
#701623