Finite Group Databasebeta

← #11773380

Subgroups — #11773380

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C2×C32×#95C211yesmaximal, characteristic
3C2×#63658C211yesmaximal, characteristic
4C2×#63658C211yesmaximal, characteristic
5C2×#63658C211yesmaximal, characteristic
6C2×#63658C211yesmaximal, characteristic
7C2×#63658C211yesmaximal, characteristic
8#69413—34nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C2×#3750—22no—
17C2×#3750—22no—
18C2×#3750—22no—
19C32×#95—22no—
20#63658—22no—
21#63658—22no—
22#63658—22no—
23#63658—22no—
24#63658C414yescomplemented
25C22×Dic3⋊C4—34no—
26C2×C3×#95D314yes—
27C2×C3⋊#95—34no—
28C2×C3⋊#95—34no—
29C2×C3⋊#95—34no—
30C2×C3⋊#95—34no—
31C2×C3⋊#95—34no—
32C24×C32C2311yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4—21no—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2×C412yes—
52C22×C32×C4D412yes—
53C22×C32×C4D412yes—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3—21no—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3—21no—
65C22×C3⋊Dic3—21no—
66C22×C3⋊Dic3—21no—
67C22×C3⋊Dic3—21no—
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3—21no—
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3C2×C412yes—
77C22×C3⋊Dic3C2×C412yes—
78C22×C3⋊Dic3D412yes—
79C22×C3⋊Dic3D412yes—
80C22×C3⋊Dic3Q812yes—
81C22×C3⋊Dic3Q812yes—
82#3750—28no—
83#1442—91noSylow
84C23×C3×C4C2×D314yes—
85C23×C3×C4C2×D314yes—
86C23×C3×C4C2×D314yes—
87C23×Dic3—34no—
88C23×Dic3—34no—
89C23×Dic3—34no—
90C23×Dic3—34no—
91C2×Dic3⋊C4—68no—
92C2×Dic3⋊C4—68no—
93C2×Dic3⋊C4—68no—
94C3×#95—28no—
95C3⋊#95—316no—
96C3⋊#95—68no—
97C3⋊#95—68no—
98C3⋊#95—68no—
99C3⋊#95—68no—
100C23×C32C22×C411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D411yescharacteristic
105C23×C32C2×Q811yescharacteristic
106C23×C32C2×Q811yescharacteristic
107C23×C32#4111yescharacteristic
108C23×C32#4111yescharacteristic
109C23×C32#4111yescharacteristic
110C23×C32#4111yescharacteristic
111C23×C32#4111yescharacteristic
112C23×C32#4111yescharacteristic
113C23×C32#4111yescharacteristic
114C23×C32#4111yescharacteristic
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—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—
155C2×C3⋊Dic3—41no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—41no—
159C2×C3⋊Dic3—41no—
160C2×C3⋊Dic3—41no—
161C2×C3⋊Dic3—41no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3C4⋊C414yes—
164C22×C4⋊C4—91no—
165C2×#95—91no—
166C2×#95—91no—
167C2×#95—91no—
168C2×#95—91no—
169C2×#95—91no—
170C2×#95C3⋊D311yescharacteristic
171C24×C3C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4—24no—
176C22×C3×C4—24no—
177C22×C3×C4—24no—
178C22×C3×C4—24no—
179C22×C3×C4—24no—
180C22×C3×C4—24no—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4—24no—
184C22×C3×C4—24no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—24no—
188C22×C3×C4—24no—
189C22×C3×C4—24no—
190C22×C3×C4C4×D318yes—
191C22×C3×C4D1218yes—
192C22×C3×C4#6718yes—
193C22×Dic3—38no—
194C22×Dic3—38no—
195C22×Dic3—38no—
196C22×Dic3—38no—
197C22×Dic3—38no—
198C22×Dic3—38no—
199C22×Dic3—64no—
200C22×Dic3—64no—
201C22×Dic3—64no—
202C22×Dic3—64no—
203C22×Dic3—64no—
204C22×Dic3—64no—
205C22×Dic3—64no—
206C22×Dic3—64no—
207C22×Dic3—64no—
208C22×Dic3—64no—
209C22×Dic3—64no—
210C22×Dic3—64no—
211C22×Dic3—64no—
212C22×Dic3—64no—
213C22×Dic3—64no—
214C22×Dic3—64no—
215C22×Dic3—64no—
216C22×Dic3—64no—
217C22×Dic3—64no—
218C22×Dic3—64no—
219C22×Dic3—64no—
220C22×Dic3—64no—
221Dic3⋊C4—632no—
222C22×C32C2×C4⋊C411yescharacteristic
223C22×C32#11711yescharacteristic
224C22×C32#11711yescharacteristic
225C22×C32C4×D411yescharacteristic
226C22×C32C4×D411yescharacteristic
227C22×C32C4×D411yescharacteristic
228C22×C32C4×Q811yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32#12111yescharacteristic
231C22×C32#12111yescharacteristic
232C22×C32#12111yescharacteristic
233C22×C32C22⋊Q811yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C22×C32C22⋊Q811yescharacteristic
236C22×C32C22⋊Q811yescharacteristic
237C22×C32C22⋊Q811yescharacteristic
238C22×C32#12311yescharacteristic
239C22×C32#12311yescharacteristic
240C22×C32#12311yescharacteristic
241C22×C32#12311yescharacteristic
242C22×C32#12311yescharacteristic
243C22×C32#12411yescharacteristic
244C22×C32#12411yescharacteristic
245C22×C32#12411yescharacteristic
246C22×C32#12411yescharacteristic
247C22×C32#12511yescharacteristic
248C22×C32#12511yescharacteristic
249C22×C32#12511yescharacteristic
250C22×C32#12511yescharacteristic
251C22×C32#12511yescharacteristic
252C22×C32#12611yescharacteristic
253C22×C32#12611yescharacteristic
254C22×C32#12611yescharacteristic
255C22×C32#12611yescharacteristic
256C22×C32C4⋊Q811yescharacteristic
257C32×C4—42no—
258C32×C4—42no—
259C32×C4—42no—
260C3⋊Dic3—24no—
261C3⋊Dic3—42no—
262C3⋊Dic3—42no—
263C3⋊Dic3—42no—
264C23×C4—91no—
265C23×C4—91no—
266C23×C4—91no—
267C23×C4—91no—
268C23×C4C2×C3⋊D311yescharacteristic
269C23×C4C2×C3⋊D311yescharacteristic
270C23×C4C2×C3⋊D311yescharacteristic
271C2×C4⋊C4—182no—
272C2×C4⋊C4—182no—
273C2×C4⋊C4—182no—
274#95—22no—
275#95—94no—
276#95—182no—
277#95—182no—
278#95—182no—
279#95—182no—
280C23×C3C2×C4×D314yes—
281C23×C3C2×D1214yes—
282C23×C3#23514yes—
283C23×C3#23514yes—
284C23×C3#23514yes—
285C23×C3#23514yes—
286C23×C3D3×D414yes—
287C23×C3D3×D414yes—
288C23×C3#23714yes—
289C23×C3#23714yes—
290C23×C3#23714yes—
291C23×C3#23714yes—
292C23×C3D3×Q814yes—
293C23×C3D3×Q814yes—
294C23×C3C2×#6714yes—
295C2×C3×C4—28no—
296C2×C3×C4—28no—
297C2×C3×C4—28no—
298C2×C3×C4—28no—
299C2×C3×C4—28no—
300C2×C3×C4—28no—
301C2×C3×C4—28no—
302C2×C3×C4—28no—
303C2×C3×C4—28no—
304C2×C3×C4—44no—
305C2×C3×C4—44no—
306C2×C3×C4—44no—
307C2×C3×C4—44no—
308C2×C3×C4—44no—
309C2×C3×C4—44no—
310C2×C3×C4—44no—
311C2×C3×C4—44no—
312C2×C3×C4—44no—
313C2×C3×C4—44no—
314C2×C3×C4—44no—
315C2×C3×C4—44no—
316C2×Dic3—316no—
317C2×Dic3—68no—
318C2×Dic3—68no—
319C2×Dic3—68no—
320C2×Dic3—68no—
321C2×Dic3—68no—
322C2×Dic3—68no—
323C2×Dic3—68no—
324C2×Dic3—68no—
325C2×Dic3—68no—
326C2×Dic3—68no—
327C2×Dic3—68no—
328C2×Dic3—68no—
329C2×Dic3—68no—
330C2×Dic3—68no—
331C2×Dic3—68no—
332C2×Dic3—124no—
333C2×Dic3—124no—
334C2×Dic3—124no—
335C2×Dic3—124no—
336C2×Dic3—124no—
337C2×Dic3—124no—
338C2×Dic3—124no—
339C2×Dic3—124no—
340C2×Dic3—124no—
341C2×Dic3—124no—
342C2×Dic3—124no—
343C2×Dic3—124no—
344C2×C32#38211yescharacteristic
345C2×C32#38511yescharacteristic
346C2×C32#38711yescharacteristic
347C2×C32#38711yescharacteristic
348C2×C32#38811yescharacteristic
349C2×C32#38811yescharacteristic
350C2×C32#38911yescharacteristic
351C2×C32#39311yescharacteristic
352C2×C32#39411yescharacteristic
353C2×C32#39711yescharacteristic
354C2×C32#39811yescharacteristic
355C2×C32#39811yescharacteristic
356C2×C32#40011yescharacteristic
357C2×C32#40011yescharacteristic
358C2×C32#40011yescharacteristic
359C24C22×C3⋊D311yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—92no—
379C22×C4—92no—
380C22×C4—92no—
381C22×C4—92no—
382C22×C4—92no—
383C22×C4—92no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4—181no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4—181no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4C4×C3⋊D312yes—
407C22×C4C4⋊(C3⋊D3)12yes—
408C22×C4#63812yes—
409C4⋊C4—188no—
410C22×C3#87214yes—
411C22×C3C4×D1214yes—
412C22×C3#87514yes—
413C22×C3#87614yes—
414C22×C3#87714yes—
415C22×C3#87914yes—
416C22×C3#87914yes—
417C22×C3#87914yes—
418C22×C3#67⋊C414yes—
419C22×C3#88214yes—
420C22×C3#88314yes—
421C22×C3#88314yes—
422C22×C3#88514yes—
423C22×C3#88514yes—
424C22×C3#88514yes—
425C22×C3#88614yes—
426C22×C3#88714yes—
427C22×C3#88914yes—
428C22×C3#88914yes—
429C22×C3#88914yes—
430C22×C3#88914yes—
431C22×C3#88914yes—
432C22×C3D3×C4⋊C414yes—
433C22×C3#89614yes—
434C22×C3#89614yes—
435C22×C3#89614yes—
436C22×C3#89714yes—
437C22×C3#89714yes—
438C22×C3C4×#6714yes—
439C22×C3#92914yes—
440C22×C3#93014yes—
441C22×C3#93514yes—
442C22×C3#93814yes—
443C22×C3#93914yes—
444C22×C3#94414yes—
445C3×C4—48no—
446C3×C4—48no—
447C3×C4—48no—
448Dic3—616no—
449Dic3—128no—
450Dic3—128no—
451Dic3—128no—
452C32#144211yescharacteristic, complemented, Sylow
453C23C2×C4×C3⋊D311yescharacteristic
454C23C2×C4⋊(C3⋊D3)11yescharacteristic
455C23#382811yescharacteristic
456C23#382811yescharacteristic
457C23#382811yescharacteristic
458C23#382811yescharacteristic
459C23D4×C3⋊D311yescharacteristic
460C23D4×C3⋊D311yescharacteristic
461C23#383011yescharacteristic
462C23#383011yescharacteristic
463C23#383011yescharacteristic
464C23#383011yescharacteristic
465C23Q8×C3⋊D311yescharacteristic
466C23Q8×C3⋊D311yescharacteristic
467C23C2×#63811yescharacteristic
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—94no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—361no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4—361no—
509C2×C4—361no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4—361no—
513C2×C4—361no—
514C2×C4—361no—
515C2×C4—361no—
516C2×C4—361no—
517C2×C3#465014yes—
518C2×C3#465214yes—
519C2×C3#465314yes—
520C2×C3#465814yes—
521C2×C3#465814yes—
522C2×C3#465914yes—
523C2×C3#466814yes—
524C2×C3#467314yes—
525C2×C3#494014yes—
526C2×C3#494414yes—
527C2×C3#495214yes—
528C2×C3#496114yes—
529C2×C3#497614yes—
530C2×C3#498114yes—
531C2×C3#498314yes—
532C22#6408111yescharacteristic
533C22C4×C4⋊(C3⋊D3)11yescharacteristic
534C22#6408411yescharacteristic
535C22#6408511yescharacteristic
536C22#6408611yescharacteristic
537C22#6408811yescharacteristic
538C22#6408811yescharacteristic
539C22#6408811yescharacteristic
540C22#6409011yescharacteristic
541C22#6409111yescharacteristic
542C22#6409211yescharacteristic
543C22#6409211yescharacteristic
544C22#6409411yescharacteristic
545C22#6409411yescharacteristic
546C22#6409411yescharacteristic
547C22#6409511yescharacteristic
548C22#6409611yescharacteristic
549C22#6409811yescharacteristic
550C22#6409811yescharacteristic
551C22#6409811yescharacteristic
552C22#6409811yescharacteristic
553C22#6409811yescharacteristic
554C22C4⋊C4×C3⋊D311yescharacteristic
555C22#6410511yescharacteristic
556C22#6410511yescharacteristic
557C22#6410511yescharacteristic
558C22#6410611yescharacteristic
559C22#6410611yescharacteristic
560C22C4×#63811yescharacteristic
561C22#6413811yescharacteristic
562C22#6413911yescharacteristic
563C22#6414411yescharacteristic
564C22#6414711yescharacteristic
565C22#6414811yescharacteristic
566C22#6415311yescharacteristic
567C4—42no—
568C4—42no—
569C4—42no—
570C4—184no—
571C4—362no—
572C4—362no—
573C4—362no—
574C3#6941314yescomplemented
575C2#1059234911yescharacteristic
576C2#1059235111yescharacteristic
577C2#1059235211yescharacteristic
578C2#1059235711yescharacteristic
579C2#1059235711yescharacteristic
580C2#1059235811yescharacteristic
581C2#1059236711yescharacteristic
582C2#1059237211yescharacteristic
583C2#1059263911yescharacteristic
584C2#1059264311yescharacteristic
585C2#1059265111yescharacteristic
586C2#1059266011yescharacteristic
587C2#1059267511yescharacteristic
588C2#1059268011yescharacteristic
589C2#1059268211yescharacteristic
subgroupG/H
center, FrattiniC24C22×C3⋊D3
commutatorC23×C32C22×C4
FittingC2×C32×#95C2
socle, prime radical, cosocleC24×C32C23
hypercenterC2×#95C3⋊D3
hypocenterC32#1442
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C2×#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
24. #63658C4semidirect
452. C32#1442semidirect
574. C3#69413semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C32×#952
C2×#636582
#694133