Finite Group Databasebeta

← #11787281

Subgroups — #11787281

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63857C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
5C2×#63567C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69931—31nomaximal
9#68879—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×Dic3⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×Dic32—21no—
21#63857—22no—
22#63857C414yescomplemented
23#63841—22no—
24#63841—22no—
25#63643—22no—
26C3×(C2×D3)⋊C8—22no—
27#63567—22no—
28C2×#926—31no—
29C2×#924—31no—
30C2×#897—31no—
31C2×#892—31no—
32C2×C3×C22⋊C8—31no—
33C2×(C2×D3)⋊C8D311yescharacteristic
34C2×#816—31no—
35C2×#816—31no—
36C2×#816—31no—
37C2×#816—61no—
38C2×#810—31no—
39C3×#340—31no—
40#4551—31no—
41#4551D311yescharacteristic, complemented
42#4529—31no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3C2×C412yes—
61C2×C3×C4×D3D412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2×C412yes—
70C3×C4⋊Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74Dic3⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77Dic32—24no—
78#1873—91noSylow
79C23×C3×C4—31no—
80C22×C4×D3C2×D311yescharacteristic
81C22×Dic6—31no—
82C22×Dic6—31no—
83C22×Dic6—61no—
84C22×C3×C8—21no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×#217—61no—
91C2×#217—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94#926—62no—
95#926—62no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102#924—34no—
103#924—62no—
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#897—34no—
109#897—62no—
110#892—62no—
111#892—62no—
112C3×C22⋊C8—62no—
113(C2×D3)⋊C8—22no—
114#816—62no—
115#816—62no—
116#816—64no—
117#816—62no—
118#810—62no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3C22⋊C412yes—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139#634—22no—
140#634—22no—
141#634—41no—
142#634—41no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3C22⋊C412yes—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C32×C8—41no—
157C3×C3⋊C8—41no—
158C2×C22⋊Q8—91no—
159C2×#117—91no—
160C2×#103—91no—
161C2×#103—91no—
162C2×C22⋊C8—31no—
163#340—31no—
164#340—91no—
165C24×C3—31no—
166C23×D3D1211yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—121no—
186C22×Dic3—121no—
187C22×Dic3D1211yescharacteristic
188C2×C4×D3—21no—
189C2×C4×D3—21no—
190C2×C4×D3—21no—
191C2×C4×D3—21no—
192C2×C4×D3C4×D312yes—
193C2×C4×D3#6712yes—
194C2×Dic6—32no—
195C2×Dic6—32no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—121no—
210C2×Dic6—121no—
211C2×Dic6—121no—
212C2×C3×C8—22no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—41no—
220C2×C3×C8—41no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228#217—64no—
229#217—64no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—62no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—64no—
240C4⋊Dic3—121no—
241C4⋊Dic3C4×D312yes—
242C4⋊Dic3D1212yes—
243Dic3⋊C4—64no—
244C4×Dic3—64no—
245C4×Dic3—64no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C22×C32C2×C22⋊C411yescharacteristic
250C22×C32#12011yescharacteristic
251C22×C32#12311yescharacteristic
252C22×C32#13511yescharacteristic
253C22×C32#13511yescharacteristic
254C22×C32#13711yescharacteristic
255C22×C32#13711yescharacteristic
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C32×C4C4×D411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12111yescharacteristic
267C3⋊Dic3—42no—
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—91no—
273C23×C4—31no—
274C22×C8—31no—
275C22×C8D3211yescharacteristic
276C22⋊Q8—94no—
277C22⋊Q8—182no—
278#117—182no—
279#117—182no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—181no—
284C2×C22⋊C4—181no—
285C2×C22⋊C4—181no—
286C2×C42—181no—
287#103—182no—
288#103—182no—
289C22⋊C8—62no—
290C23×C3—21no—
291C23×C3—32no—
292C23×C3—61no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3C2×D1211yescharacteristic
299C23×C3D3×D411yescharacteristic
300C22×D3—21no—
301C22×D3—21no—
302C22×D3—21no—
303C22×D3—21no—
304C22×D3—21no—
305C22×D3—21no—
306C22×D3(C2×D3)⋊C412yes—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—32no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23911yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—241no—
363C2×Dic3—241no—
364C2×Dic3(C2×D3)⋊C412yes—
365C4×D3—22no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3—22no—
369Dic6—64no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—62no—
374Dic6—122no—
375Dic6—122no—
376Dic6—122no—
377Dic6—121no—
378Dic6—121no—
379Dic6—121no—
380Dic6—121no—
381C3×C8—42no—
382C3×C8—41no—
383C3×C8—41no—
384C3×C8—121no—
385C3⋊C8—41no—
386C2×C32#38611yescharacteristic
387C2×C32#41611yescharacteristic
388C2×C32#41911yescharacteristic
389C2×C32#45211yescharacteristic
390C2×C32#45211yescharacteristic
391C2×C32#48511yescharacteristic
392C2×C32#48511yescharacteristic
393C3×D3—42no—
394C24—31no—
395C2×Q8—92no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×Q8—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C22×C4—31no—
402C22×C4—32no—
403C22×C4—32no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4C2×D3211yescharacteristic
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—61no—
419C4⋊C4—32no—
420C4⋊C4—32no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—92no—
424C4⋊C4—184no—
425C4⋊C4—181no—
426C22⋊C4—184no—
427C22⋊C4—184no—
428C42—184no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—62no—
437C22×C3—62no—
438C22×C3—62no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3D3×C22⋊C411yescharacteristic
444C22×C3#88211yescharacteristic
445C22×C3#88211yescharacteristic
446C22×C3#88611yescharacteristic
447C22×C3#89411yescharacteristic
448C22×C3#90411yescharacteristic
449C22×C3#90411yescharacteristic
450C22×C3#90911yescharacteristic
451C22×C3#90911yescharacteristic
452C22×C3#91211yescharacteristic
453C22×C3#91511yescharacteristic
454C22×C3#91611yescharacteristic
455C22×C3#91811yescharacteristic
456C22×C3C2×(C2×D3)⋊C411yescharacteristic
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—41no—
461C2×D3—41no—
462C2×D3—41no—
463C2×D3—41no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—62no—
469C3×C4—122no—
470C3×C4—122no—
471C3×C4C4×D1211yescharacteristic
472C3×C4#67⋊C411yescharacteristic
473C3×C4#67⋊C411yescharacteristic
474C3×C4#88411yescharacteristic
475C3×C4#89311yescharacteristic
476C3×C4#89511yescharacteristic
477C3×C4#93911yescharacteristic
478C3×C4#93911yescharacteristic
479Dic3—22no—
480Dic3—42no—
481Dic3—42no—
482Dic3—124no—
483Dic3—122no—
484Dic3—122no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488C32#187311yescharacteristic, complemented, Sylow
489C23—32no—
490C23—61no—
491C23—61no—
492C23—61no—
493C23—61no—
494C23—61no—
495C23—61no—
496C23D3×D1211yescharacteristic
497Q8—182no—
498Q8—182no—
499Q8—361no—
500Q8—361no—
501C2×C4—32no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—361no—
517C2×C4—361no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4#379611yescharacteristic
521C2×C4C4×D3211yescharacteristic
522C2×C4D3×D1211yescharacteristic
523C2×C4#380411yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C2×C4#381111yescharacteristic
526C8—41no—
527C8—121no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—122no—
536C2×C3#466511yescharacteristic
537C2×C3#472311yescharacteristic
538C2×C3#472311yescharacteristic
539C2×C3#473311yescharacteristic
540C2×C3#473311yescharacteristic
541C2×C3#477211yescharacteristic
542C2×C3#478311yescharacteristic
543C2×C3#480211yescharacteristic
544C2×C3#480811yescharacteristic
545C2×C3#486811yescharacteristic
546C2×C3#488811yescharacteristic
547C2×C3#495811yescharacteristic
548C2×C3#511311yescharacteristic
549C2×C3#512011yescharacteristic
550D3—42no—
551C22—62no—
552C22—62no—
553C22—62no—
554C22—121no—
555C22—121no—
556C22—121no—
557C22—121no—
558C22#6380011yescharacteristic
559C22#6380111yescharacteristic
560C22#6380611yescharacteristic
561C22#6380711yescharacteristic
562C22#6389011yescharacteristic
563C22D3×(C2×D3)⋊C411yescharacteristic
564C22#6392311yescharacteristic
565C4—62no—
566C4—122no—
567C4—122no—
568C4—362no—
569C4—362no—
570C4#6388011yescharacteristic
571C4#6388111yescharacteristic
572C4#6388611yescharacteristic
573C4#6397111yescharacteristic
574C3—21no—
575C3#6887911yescharacteristic, complemented
576C3#6993111yescharacteristic, complemented
577C2—122no—
578C2#1059070811yescharacteristic
579C2#1059070911yescharacteristic
580C2#1059094811yescharacteristic
581C2#1059095411yescharacteristic
582C2#1059096911yescharacteristic
583C2#1059097011yescharacteristic
584C2#1059136411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1873
LCSG ▷ C2×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×#63643C2semidirect
5. C2×#63567C2semidirect
6. C3×#4551C2semidirect
7. #10589164C2semidirect
22. #63857C4semidirect
41. #4551D3semidirect
488. C32#1873semidirect
575. C3#68879semidirect
576. C3#69931semidirect

Maximal subgroups

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

subgroupindex
C2×#638572
C2×#638412
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×#635672
C3×#45512
#105891642
#699313
#688793