Finite Group Databasebeta

← #11773348

Subgroups — #11773348

Order 1152.

1692 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×#3750C211yesmaximal, characteristic
3C2×C32×#95C211yesmaximal, characteristic
4C2×#63658C211yesmaximal, characteristic
5C2×#63658C211yesmaximal, characteristic
6C2×#63658C211yesmaximal, characteristic
7C2×#63658C211yesmaximal, characteristic
8#69409—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—
19C2×#3750—22no—
20C2×#3750—22no—
21C2×#3750C414yescomplemented
22C32×#95—22no—
23#63658—22no—
24#63658—22no—
25#63658—22no—
26#63658—22no—
27C22×Dic3⋊C4—34no—
28C22×Dic3⋊C4—34no—
29C2×C3×#95D314yes—
30C2×C3⋊#95—34no—
31C2×C3⋊#95—34no—
32C2×C3⋊#95—34no—
33C2×C3⋊#95—34no—
34C24×C32C2311yescharacteristic
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×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4C2×C412yes—
54C22×C32×C4D412yes—
55C22×C32×C4Q812yes—
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⋊Dic3D412yes—
81C22×C3⋊Dic3D412yes—
82C22×C3⋊Dic3Q812yes—
83C22×C3⋊Dic3Q812yes—
84#3750—28no—
85#3750—28no—
86#1441—91noSylow
87C23×C3×C4C2×D314yes—
88C23×C3×C4C2×D314yes—
89C23×C3×C4C2×D314yes—
90C23×Dic3—34no—
91C23×Dic3—34no—
92C23×Dic3—34no—
93C23×Dic3—34no—
94C2×Dic3⋊C4—316no—
95C2×Dic3⋊C4—68no—
96C2×Dic3⋊C4—68no—
97C2×Dic3⋊C4—68no—
98C2×Dic3⋊C4—68no—
99C2×Dic3⋊C4—68no—
100C3×#95—28no—
101C3⋊#95—68no—
102C3⋊#95—68no—
103C3⋊#95—68no—
104C3⋊#95—68no—
105C23×C32C22×C411yescharacteristic
106C23×C32C2×D411yescharacteristic
107C23×C32C2×D411yescharacteristic
108C23×C32C2×D411yescharacteristic
109C23×C32C2×D411yescharacteristic
110C23×C32C2×D411yescharacteristic
111C23×C32C2×Q811yescharacteristic
112C23×C32C2×Q811yescharacteristic
113C23×C32C2×Q811yescharacteristic
114C23×C32#4111yescharacteristic
115C23×C32#4111yescharacteristic
116C23×C32#4111yescharacteristic
117C23×C32#4111yescharacteristic
118C23×C32#4111yescharacteristic
119C23×C32#4111yescharacteristic
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
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×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
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—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—41no—
160C2×C3⋊Dic3—41no—
161C2×C3⋊Dic3—41no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3—41no—
164C2×C3⋊Dic3—41no—
165C2×C3⋊Dic3—41no—
166C2×C3⋊Dic3—41no—
167C2×C3⋊Dic3C22⋊C414yes—
168C2×C3⋊Dic3C4⋊C414yescomplemented
169C22×C4⋊C4—91no—
170C22×C4⋊C4—91no—
171C2×#95—91no—
172C2×#95—91no—
173C2×#95—91no—
174C2×#95—91no—
175C2×#95C3⋊D311yescharacteristic
176C24×C3C22×D314yes—
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×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—24no—
193C22×C3×C4—24no—
194C22×C3×C4—24no—
195C22×C3×C4Dic618yes—
196C22×C3×C4C4×D318yes—
197C22×C3×C4#6718yes—
198C22×Dic3—38no—
199C22×Dic3—38no—
200C22×Dic3—38no—
201C22×Dic3—38no—
202C22×Dic3—38no—
203C22×Dic3—38no—
204C22×Dic3—38no—
205C22×Dic3—38no—
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—
221C22×Dic3—64no—
222C22×Dic3—64no—
223C22×Dic3—64no—
224C22×Dic3—64no—
225C22×Dic3—64no—
226Dic3⋊C4—632no—
227Dic3⋊C4—632no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32C2×C4⋊C411yescharacteristic
230C22×C32#11711yescharacteristic
231C22×C32C4×D411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C22×C32C4×Q811yescharacteristic
234C22×C32C4×Q811yescharacteristic
235C22×C32#12011yescharacteristic
236C22×C32#12111yescharacteristic
237C22×C32#12111yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12111yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32C22⋊Q811yescharacteristic
243C22×C32C22⋊Q811yescharacteristic
244C22×C32C22⋊Q811yescharacteristic
245C22×C32C22⋊Q811yescharacteristic
246C22×C32C22⋊Q811yescharacteristic
247C22×C32C22⋊Q811yescharacteristic
248C22×C32C22⋊Q811yescharacteristic
249C22×C32C22⋊Q811yescharacteristic
250C22×C32#12311yescharacteristic
251C22×C32#12311yescharacteristic
252C22×C32#12311yescharacteristic
253C22×C32#12411yescharacteristic
254C22×C32#12511yescharacteristic
255C22×C32#12511yescharacteristic
256C22×C32#12511yescharacteristic
257C22×C32#12511yescharacteristic
258C22×C32#12611yescharacteristic
259C22×C32#12611yescharacteristic
260C22×C32C4⋊Q811yescharacteristic
261C22×C32C4⋊Q811yescharacteristic
262C22×C32C4⋊Q811yescharacteristic
263C32×C4—42no—
264C32×C4—42no—
265C32×C4—42no—
266C3⋊Dic3—24no—
267C3⋊Dic3—24no—
268C3⋊Dic3—42no—
269C3⋊Dic3—42no—
270C23×C4—91no—
271C23×C4—91no—
272C23×C4—91no—
273C23×C4—91no—
274C23×C4C2×C3⋊D311yescharacteristic
275C23×C4C2×C3⋊D311yescharacteristic
276C23×C4C2×C3⋊D311yescharacteristic
277C2×C4⋊C4—94no—
278C2×C4⋊C4—182no—
279C2×C4⋊C4—182no—
280C2×C4⋊C4—182no—
281C2×C4⋊C4—182no—
282C2×C4⋊C4—182no—
283#95—22no—
284#95—182no—
285#95—182no—
286#95—182no—
287#95—182no—
288C23×C3C2×Dic614yes—
289C23×C3C2×C4×D314yes—
290C23×C3#23514yes—
291C23×C3#23514yes—
292C23×C3#23514yes—
293C23×C3#23514yes—
294C23×C3D3×D414yes—
295C23×C3D3×D414yes—
296C23×C3D3×D414yes—
297C23×C3D3×D414yes—
298C23×C3#23714yes—
299C23×C3#23714yes—
300C23×C3D3×Q814yes—
301C23×C3D3×Q814yes—
302C23×C3C2×#6714yes—
303C2×C3×C4—28no—
304C2×C3×C4—28no—
305C2×C3×C4—28no—
306C2×C3×C4—28no—
307C2×C3×C4—28no—
308C2×C3×C4—28no—
309C2×C3×C4—28no—
310C2×C3×C4—28no—
311C2×C3×C4—28no—
312C2×C3×C4—44no—
313C2×C3×C4—44no—
314C2×C3×C4—44no—
315C2×C3×C4—44no—
316C2×C3×C4—44no—
317C2×C3×C4—44no—
318C2×C3×C4—44no—
319C2×C3×C4—44no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—44no—
323C2×C3×C4—44no—
324C2×Dic3—316no—
325C2×Dic3—316no—
326C2×Dic3—68no—
327C2×Dic3—68no—
328C2×Dic3—68no—
329C2×Dic3—68no—
330C2×Dic3—68no—
331C2×Dic3—68no—
332C2×Dic3—68no—
333C2×Dic3—68no—
334C2×Dic3—68no—
335C2×Dic3—68no—
336C2×Dic3—68no—
337C2×Dic3—68no—
338C2×Dic3—68no—
339C2×Dic3—68no—
340C2×Dic3—68no—
341C2×Dic3—68no—
342C2×Dic3—68no—
343C2×Dic3—68no—
344C2×Dic3—124no—
345C2×Dic3—124no—
346C2×Dic3—124no—
347C2×Dic3—124no—
348C2×Dic3—124no—
349C2×Dic3—124no—
350C2×Dic3—124no—
351C2×Dic3—124no—
352C2×C32#38011yescharacteristic
353C2×C32#38611yescharacteristic
354C2×C32#38711yescharacteristic
355C2×C32#38711yescharacteristic
356C2×C32#38911yescharacteristic
357C2×C32#38911yescharacteristic
358C2×C32#39111yescharacteristic
359C2×C32#39411yescharacteristic
360C2×C32#39511yescharacteristic
361C2×C32#39611yescharacteristic
362C2×C32#39611yescharacteristic
363C2×C32#39811yescharacteristic
364C2×C32#39811yescharacteristic
365C2×C32#39811yescharacteristic
366C2×C32#40011yescharacteristic
367C24C22×C3⋊D311yescharacteristic
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—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—92no—
387C22×C4—92no—
388C22×C4—92no—
389C22×C4—92no—
390C22×C4—92no—
391C22×C4—92no—
392C22×C4—92no—
393C22×C4—92no—
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×C4—181no—
407C22×C4—181no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4#63412yes—
415C22×C4C4×C3⋊D312yes—
416C22×C4#63812yes—
417C4⋊C4—188no—
418C4⋊C4—188no—
419C22×C3C4×Dic614yes—
420C22×C3#87014yes—
421C22×C3#87214yes—
422C22×C3#87614yes—
423C22×C3#87814yes—
424C22×C3#87814yes—
425C22×C3#87914yes—
426C22×C3D3×C22⋊C414yes—
427C22×C3#67⋊C414yes—
428C22×C3#88314yes—
429C22×C3#88314yes—
430C22×C3#88414yes—
431C22×C3#88414yes—
432C22×C3#88414yes—
433C22×C3#88414yes—
434C22×C3#88514yes—
435C22×C3#88714yes—
436C22×C3#88814yes—
437C22×C3#88814yes—
438C22×C3#88914yes—
439C22×C3#88914yes—
440C22×C3#88914yes—
441C22×C3D3×C4⋊C414yes—
442C22×C3#89614yes—
443C22×C3#89614yes—
444C22×C3#89614yes—
445C22×C3#89614yes—
446C22×C3#89614yes—
447C22×C3#92414yes—
448C22×C3C4×#6714yes—
449C22×C3#92914yes—
450C22×C3#93714yes—
451C22×C3#93814yes—
452C22×C3#93914yes—
453C22×C3#94414yes—
454C3×C4—48no—
455C3×C4—48no—
456C3×C4—48no—
457Dic3—616no—
458Dic3—616no—
459Dic3—128no—
460Dic3—128no—
461C32#144111yescharacteristic, complemented, Sylow
462C23C2×#63411yescharacteristic
463C23C2×C4×C3⋊D311yescharacteristic
464C23#382811yescharacteristic
465C23#382811yescharacteristic
466C23#382811yescharacteristic
467C23#382811yescharacteristic
468C23D4×C3⋊D311yescharacteristic
469C23D4×C3⋊D311yescharacteristic
470C23D4×C3⋊D311yescharacteristic
471C23D4×C3⋊D311yescharacteristic
472C23#383011yescharacteristic
473C23#383011yescharacteristic
474C23Q8×C3⋊D311yescharacteristic
475C23Q8×C3⋊D311yescharacteristic
476C23C2×#63811yescharacteristic
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—94no—
499C2×C4—94no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4—361no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4—361no—
526C2×C3#464614yes—
527C2×C3#464714yes—
528C2×C3#465214yes—
529C2×C3#465714yes—
530C2×C3#465714yes—
531C2×C3#465814yes—
532C2×C3#466714yes—
533C2×C3#467614yes—
534C2×C3#493314yes—
535C2×C3#494814yes—
536C2×C3#495614yes—
537C2×C3#495914yes—
538C2×C3#497614yes—
539C2×C3#497914yes—
540C2×C3#498314yes—
541C22C4×#63411yescharacteristic
542C22#6407911yescharacteristic
543C22#6408111yescharacteristic
544C22#6408511yescharacteristic
545C22#6408711yescharacteristic
546C22#6408711yescharacteristic
547C22#6408811yescharacteristic
548C22C22⋊C4×C3⋊D311yescharacteristic
549C22#6409011yescharacteristic
550C22#6409211yescharacteristic
551C22#6409211yescharacteristic
552C22#6409311yescharacteristic
553C22#6409311yescharacteristic
554C22#6409311yescharacteristic
555C22#6409311yescharacteristic
556C22#6409411yescharacteristic
557C22#6409611yescharacteristic
558C22#6409711yescharacteristic
559C22#6409711yescharacteristic
560C22#6409811yescharacteristic
561C22#6409811yescharacteristic
562C22#6409811yescharacteristic
563C22C4⋊C4×C3⋊D311yescharacteristic
564C22#6410511yescharacteristic
565C22#6410511yescharacteristic
566C22#6410511yescharacteristic
567C22#6410511yescharacteristic
568C22#6410511yescharacteristic
569C22#6413311yescharacteristic
570C22C4×#63811yescharacteristic
571C22#6413811yescharacteristic
572C22#6414611yescharacteristic
573C22#6414711yescharacteristic
574C22#6414811yescharacteristic
575C22#6415311yescharacteristic
576C4—42no—
577C4—42no—
578C4—42no—
579C4—184no—
580C4—184no—
581C4—362no—
582C4—362no—
583C3#6940914yescomplemented
584C2#1059234511yescharacteristic
585C2#1059234611yescharacteristic
586C2#1059235111yescharacteristic
587C2#1059235611yescharacteristic
588C2#1059235611yescharacteristic
589C2#1059235711yescharacteristic
590C2#1059236611yescharacteristic
591C2#1059237511yescharacteristic
592C2#1059263211yescharacteristic
593C2#1059264711yescharacteristic
594C2#1059265511yescharacteristic
595C2#1059265811yescharacteristic
596C2#1059267511yescharacteristic
597C2#1059267811yescharacteristic
598C2#1059268211yescharacteristic
subgroupG/H
center, FrattiniC24C22×C3⋊D3
commutatorC23×C32C22×C4
FittingC2×C32×#95C2
socle, prime radical, cosocleC24×C32C23
hypercenterC2×#95C3⋊D3
hypocenterC32#1441
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
21. C2×#3750C4semidirect
168. C2×C3⋊Dic3C4⋊C4semidirect
461. C32#1441semidirect
583. C3#69409semidirect

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
#694093