Finite Group Databasebeta

← #11787285

Subgroups — #11787285

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×#63566C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70269—31nomaximal
9#68879—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3—21no—
16#64101—22no—
17#64101—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C2×#3722—21no—
23#63871—22no—
24#63871C414yescomplemented
25C3×#810—22no—
26#63566—22no—
27#63557—22no—
28C2×#946—31no—
29C2×#897—31no—
30C2×#892—31no—
31C2×#892—31no—
32C2×#892—61no—
33C2×C3×#103—31no—
34C2×#835—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×(C2×D3)⋊C8—31no—
37C2×#816—31no—
38C2×#810D311yescharacteristic, complemented
39C3×#340—31no—
40#4551—31no—
41#4529—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3C2×C412yes—
53C2×C4×C3⋊D3D412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
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—
64#3752—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C4×C3⋊Dic3—24no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2×C412yes—
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—
75C2×C3×C3⋊C8—21no—
76Dic3⋊Dic3—24no—
77#3722—24no—
78#1873—91noSylow
79C22×C3×Q8—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3—61no—
83C22×Dic6C2×D311yescharacteristic
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90#946—34no—
91#946—62no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—62no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—62no—
106C22×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108#897—34no—
109#897—62no—
110#892—62no—
111#892—62no—
112#892—64no—
113#892—64no—
114#892—62no—
115#892—62no—
116C3×#103—62no—
117#835—62no—
118(C2×D3)⋊C8—62no—
119(C2×D3)⋊C8—62no—
120#816—62no—
121#810—22no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3C22⋊C412yes—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3C22⋊C412yes—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C3×C3⋊C8—41no—
160C3×C3⋊C8—41no—
161C2×C22⋊Q8—91no—
162C2×#117—91no—
163C2×#103—31no—
164C2×#103—91no—
165C2×C22⋊C8—91no—
166#340—31no—
167#340—91no—
168C23×D3—31no—
169C23×D3—31no—
170C23×D3—61no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—61no—
190C22×Dic3—62no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6C4×D312yes—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4D1212yes—
230C3×C4⋊C4#6712yes—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—68no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236C4⋊Dic3—21no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—62no—
240C4⋊Dic3—64no—
241C4⋊Dic3—62no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3C4×D312yes—
245Dic3⋊C4—64no—
246C4×Dic3—68no—
247C4×Dic3—64no—
248C4×Dic3—64no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C22×C32C2×C22⋊C411yescharacteristic
256C22×C32#12011yescharacteristic
257C22×C32#12311yescharacteristic
258C22×C32#13511yescharacteristic
259C22×C32#13511yescharacteristic
260C22×C32#13711yescharacteristic
261C22×C32#13711yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C32×C4—42no—
270C32×C4C4×D411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12111yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—42no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C22×Q8—31no—
279C23×C4—91no—
280C22×C8—31no—
281C22×C8—31no—
282C22⋊Q8—94no—
283C22⋊Q8—182no—
284#117—182no—
285#117—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—181no—
289C2×C4⋊C4D3211yescharacteristic
290C2×C22⋊C4—181no—
291C2×C22⋊C4—181no—
292C2×C42—181no—
293#103—62no—
294#103—182no—
295C22⋊C8—182no—
296C23×C3—21no—
297C23×C3D3×D411yescharacteristic
298C23×C3D3×D411yescharacteristic
299C22×D3—32no—
300C22×D3—32no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—62no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—61no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—61no—
316C22×D3—121no—
317C22×D3—121no—
318C22×D3—121no—
319C22×D3—121no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—121no—
323C3×Q8—121no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23911yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C4×D3—64no—
382C4×D3—64no—
383C4×D3—64no—
384C4×D3—64no—
385C4×D3—62no—
386C4×D3—62no—
387C4×D3—62no—
388C4×D3—62no—
389C4×D3—62no—
390C4×D3—62no—
391C4×D3—62no—
392C4×D3—62no—
393Dic6—22no—
394Dic6—22no—
395Dic6—41no—
396Dic6—41no—
397C3×C8—121no—
398C3×C8—121no—
399C3⋊C8—41no—
400C3⋊C8—41no—
401C2×C32#38611yescharacteristic
402C2×C32#41611yescharacteristic
403C2×C32#41911yescharacteristic
404C2×C32#45211yescharacteristic
405C2×C32#45211yescharacteristic
406C2×C32#48511yescharacteristic
407C2×C32#48511yescharacteristic
408C3⋊D3—42no—
409C24—91no—
410C2×Q8—32no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C22×C4—21no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—91no—
420C22×C4—92no—
421C22×C4—92no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428C2×C8—61no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—21no—
435C4⋊C4—32no—
436C4⋊C4—61no—
437C4⋊C4—92no—
438C4⋊C4—184no—
439C4⋊C4—181no—
440C4⋊C4#62612yes—
441C22⋊C4—184no—
442C22⋊C4—184no—
443C42—184no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3D3×C22⋊C411yescharacteristic
452C22×C3D3×C22⋊C411yescharacteristic
453C22×C3#88211yescharacteristic
454C22×C3#88311yescharacteristic
455C22×C3#89411yescharacteristic
456C22×C3#91211yescharacteristic
457C22×C3#91511yescharacteristic
458C22×C3#91511yescharacteristic
459C22×C3#91611yescharacteristic
460C22×C3#91611yescharacteristic
461C22×C3#91811yescharacteristic
462C22×C3#91811yescharacteristic
463C22×C3#91911yescharacteristic
464C22×C3#93711yescharacteristic
465C2×D3—64no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—121no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—121no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—44no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—122no—
494C3×C4—122no—
495C3×C4C4×D1211yescharacteristic
496C3×C4#67⋊C411yescharacteristic
497C3×C4#88411yescharacteristic
498C3×C4#88411yescharacteristic
499C3×C4#89311yescharacteristic
500C3×C4#89511yescharacteristic
501C3×C4C4×#6711yescharacteristic
502C3×C4#93811yescharacteristic
503Dic3—42no—
504Dic3—42no—
505Dic3—64no—
506Dic3—62no—
507Dic3—62no—
508Dic3—124no—
509Dic3—122no—
510Dic3—122no—
511C32#187311yescharacteristic, complemented, Sylow
512C23—92no—
513C23—181no—
514C23—181no—
515C23—181no—
516C23—181no—
517C23—181no—
518C23—181no—
519C23#381111yescharacteristic
520Q8—62no—
521Q8—62no—
522Q8—121no—
523Q8—121no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—92no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—361no—
542C2×C4—361no—
543C2×C4#379611yescharacteristic
544C2×C4#379811yescharacteristic
545C2×C4C4×D3211yescharacteristic
546C2×C4#380211yescharacteristic
547C2×C4C2×#62611yescharacteristic
548C2×C4#381111yescharacteristic
549C8—121no—
550C8—121no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3#466511yescharacteristic
559C2×C3#477211yescharacteristic
560C2×C3#478311yescharacteristic
561C2×C3#480211yescharacteristic
562C2×C3#480211yescharacteristic
563C2×C3#480411yescharacteristic
564C2×C3#480811yescharacteristic
565C2×C3#481411yescharacteristic
566C2×C3#481511yescharacteristic
567C2×C3#486811yescharacteristic
568C2×C3#488811yescharacteristic
569C2×C3#495611yescharacteristic
570C2×C3#517311yescharacteristic
571C2×C3#518711yescharacteristic
572D3—124no—
573D3—122no—
574D3—122no—
575C22—182no—
576C22—182no—
577C22—182no—
578C22—361no—
579C22—361no—
580C22—361no—
581C22—361no—
582C22#6385311yescharacteristic
583C22#6392111yescharacteristic
584C22#6393111yescharacteristic
585C22#6393611yescharacteristic
586C22#6394511yescharacteristic
587C22#6395011yescharacteristic
588C22#6398111yescharacteristic
589C4—42no—
590C4—122no—
591C4—122no—
592C4—182no—
593C4—362no—
594C4#6388111yescharacteristic
595C4C4×#62611yescharacteristic
596C4#6391211yescharacteristic
597C4#6391611yescharacteristic
598C3—21no—
599C3#6887911yescharacteristic, complemented
600C3#7026911yescharacteristic, complemented
601C2—362no—
602C2#1059052611yescharacteristic
603C2#1059052711yescharacteristic
604C2#1059060211yescharacteristic
605C2#1059061111yescharacteristic
606C2#1059138711yescharacteristic
607C2#1059146611yescharacteristic
608C2#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#1873
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
3. C2×C3×#810C2semidirect
4. C2×#63566C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
24. #63871C4semidirect
38. C2×#810D3semidirect
42. #4529D3semidirect
511. C32#1873semidirect
599. C3#68879semidirect
600. C3#70269semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638712
C2×C3×#8102
C2×#635662
C2×#635572
C3×#45292
#105891642
#702693
#688793