Finite Group Databasebeta

← #11810264

Subgroups — #11810264

Order 1152.

1509 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×#63982C211yesmaximal, characteristic, complemented
3C22×#3724C211yesmaximal, characteristic, complemented
4C2×#63865C211yesmaximal, characteristic, complemented
5C3×#4942C212yesmaximal, complemented
6#10591711C212yesmaximal
7#10591396C211yesmaximal, characteristic, complemented
8#10591355C211yesmaximal, characteristic, complemented
9#10591347C212yesmaximal, complemented
10#10591337C211yesmaximal, characteristic, complemented
11#10591198C212yesmaximal, complemented
12#73889—32nomaximal
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×#627C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64090—24no—
23C2×C3×#217C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26#63982—24no—
27C2×#3724—24no—
28C2×#3724C2211yescharacteristic
29C2×#3724C2212yes—
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35#63865—24no—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×Dic3⋊C4—32no—
41C2×#896—32no—
42C2×#67⋊C4—32no—
43C2×#67⋊C4—61no—
44C2×#878—32no—
45C3×#380—32no—
46#5213—32no—
47#4994—32no—
48#4983—32no—
49#4976—32no—
50#4958—32no—
51#4942D312yescomplemented
52#4676—32no—
53#4667—32no—
54#4657—32no—
55#4646—32no—
56C24×C32C2311yescharacteristic
57C23×C3⋊D3C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61C2×#638—22no—
62C2×#638Q814yescomplemented
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3D414yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3—22no—
72C22×C3×Dic3—24no—
73C22×C3×Dic3—24no—
74C22×C3×Dic3—42no—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×#627—22no—
80C2×#627—22no—
81C2×#627—22no—
82C32×C22⋊C4—22no—
83#3752—22no—
84#3750—22no—
85C4×C3⋊Dic3—22no—
86C3×#217—24no—
87C3×Dic3⋊C4—24no—
88C3×Dic3⋊C4—42no—
89#3724—22no—
90#3724—22no—
91#3724—24no—
92#3724D414yescomplemented
93Dic3⋊Dic3—24no—
94#3722—24no—
95#3722—42no—
96#2417—91noSylow
97C23×C3×C4—32no—
98C22×#67—32no—
99C22×#67—61no—
100C23×Dic3—32no—
101C23×Dic3—61no—
102C23×Dic3C2×D312yes—
103C22×C4×D3—32no—
104C22×C4×D3—61no—
105C22×Dic6—32no—
106C2×C3×C4⋊C4—32no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4C2×D312yes—
111C2×#217C2×D312yes—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—61no—
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—61no—
127C2×Dic3⋊C4—68no—
128C2×Dic3⋊C4C2×D312yes—
129C2×Dic3⋊C4C2×D312yes—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132#896—68no—
133#67⋊C4—68no—
134#67⋊C4—68no—
135#878—68no—
136C3×#95—32no—
137C3×#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32C2×D412yes—
149C23×C32C2×Q812yes—
150C23×C32#4112yes—
151C23×C32C2411yescharacteristic
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3C2×Q812yes—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165#638—28no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—28no—
171C2×C3⋊Dic3C2×D412yes—
172C2×C3⋊Dic3C2×D412yes—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×Q812yes—
175C2×C3⋊Dic3#4112yes—
176C4×C3⋊D3—44no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—48no—
189C2×C3×Dic3C2×D414yes—
190#627—44no—
191C2×C22⋊Q8—91no—
192C2×C22⋊Q8—91no—
193C2×C4×D4—91no—
194C22×C4⋊C4—91no—
195#398—92no—
196#396—92no—
197#391—91no—
198#389—91no—
199#386—92no—
200#380—32no—
201#380—91no—
202C24×C3—21no—
203C24×C3C22×D312yes—
204C23×D3—32no—
205C23×D3—61no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—64no—
213C22×C3×C4—64no—
214C22×C3×C4—122no—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D312yes—
217C2×#67—38no—
218C2×#67—64no—
219C2×#67—64no—
220C2×#67—64no—
221C2×#67—64no—
222C2×#67—64no—
223C22×Dic3—24no—
224C22×Dic3—24no—
225C22×Dic3—32no—
226C22×Dic3—38no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—42no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—64no—
233C22×Dic3—61no—
234C22×Dic3—64no—
235C22×Dic3—64no—
236C22×Dic3—122no—
237C22×Dic3—122no—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—64no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×Dic6—64no—
249C2×Dic6—64no—
250C2×Dic6—64no—
251C3×C4⋊C4—64no—
252C3×C4⋊C4—122no—
253C3×C22⋊C4—24no—
254C3×C22⋊C4—24no—
255C3×C22⋊C4—64no—
256#217—24no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—122no—
262(C2×D3)⋊C4—122no—
263C4⋊Dic3—64no—
264Dic3⋊C4—24no—
265Dic3⋊C4—38no—
266Dic3⋊C4—42no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C22×C32—22no—
277C22×C32—22no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—22no—
281C22×C32—22no—
282C22×C32C22⋊Q814yescomplemented
283C22×C32C22×D411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C22×Q811yescharacteristic
286C22×C32C2×#4111yescharacteristic
287C22×C32C2×#4111yescharacteristic
288C22×C32H(5,𝔽2)11yescharacteristic
289C22×C322−1+411yescharacteristic
290C2×C3⋊D3—22no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C32×C4—41no—
298C32×C4—41no—
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3#12114yes—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C3×Dic3—42no—
305C3×Dic3—42no—
306C22×Q8—91no—
307C22×D4—91no—
308C23×C4—32no—
309C23×C4—91no—
310C23×C4—91no—
311C22⋊Q8—184no—
312C22⋊Q8—184no—
313C4×D4—184no—
314C2×C4⋊C4—32no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—92no—
319C2×C4⋊C4—91no—
320C2×C4⋊C4—92no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4—184no—
323C2×C22⋊C4—32no—
324C2×C22⋊C4—92no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—92no—
327C2×C22⋊C4D3211yescharacteristic
328C2×C42—91no—
329#95—32no—
330#95—32no—
331#95—92no—
332#95—92no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—21no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3#23514yes—
346C23×C3D3×D414yes—
347C23×C3D3×Q814yes—
348C23×C3C23×D312yes—
349C22×D3—34no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—62no—
357C22×D3—62no—
358C22×D3—62no—
359C22×D3—121no—
360C22×D3—121no—
361C22×D3—121no—
362C22×D3—121no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—34no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—128no—
388#67—616no—
389#67—616no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—34no—
404C2×Dic3—34no—
405C2×Dic3—34no—
406C2×Dic3—48no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—616no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—128no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3D3×D414yes—
423C4×D3—128no—
424C4×D3—128no—
425Dic6—128no—
426C2×C32—24no—
427C2×C32C2×#12111yescharacteristic
428C2×C32C2×C22⋊Q811yescharacteristic
429C2×C32#53711yescharacteristic
430C2×C32#54611yescharacteristic
431C2×C32D4×Q811yescharacteristic
432C2×C32#55211yescharacteristic
433C2×C32#55411yescharacteristic
434C3⋊D3—42no—
435C24—91no—
436C24C2×D3211yescharacteristic
437C2×Q8—182no—
438C2×Q8—182no—
439C2×Q8—182no—
440C2×D4—94no—
441C2×D4—182no—
442C2×D4—182no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—64no—
448C22×C4—64no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—94no—
453C22×C4—122no—
454C22×C4—182no—
455C22×C4—182no—
456C22×C4—182no—
457C22×C4—182no—
458C22×C4—182no—
459C22×C4C2×D3211yescharacteristic
460C22×C4C2×D3211yescharacteristic
461C4⋊C4—64no—
462C4⋊C4—94no—
463C4⋊C4—122no—
464C4⋊C4—182no—
465C4⋊C4—184no—
466C4⋊C4—182no—
467C4⋊C4—182no—
468C4⋊C4—184no—
469C22⋊C4—22no—
470C22⋊C4—64no—
471C22⋊C4—182no—
472C22⋊C4—184no—
473C22⋊C4—362no—
474C42—182no—
475C22×C3—24no—
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—24no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3#89618yescomplemented
496C22×C3C2×#23512yes—
497C22×C3C2×D3×D412yes—
498C22×C3C2×D3×D412yes—
499C22×C3#100412yes—
500C22×C3C2×D3×Q812yes—
501C22×C3D3×#4112yes—
502C22×C3#101012yes—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C3×C4—42no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—42no—
521C3×C4—64no—
522C3×C4—122no—
523C3×C4—122no—
524C3×C4—122no—
525Dic3—24no—
526Dic3—38no—
527Dic3—42no—
528Dic3—42no—
529Dic3—42no—
530Dic3—64no—
531Dic3—64no—
532Dic3—64no—
533Dic3—64no—
534Dic3—122no—
535C32#241711yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—92no—
541C23—181no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23#379712yes—
548C23#379812yes—
549C23#381112yes—
550C23C22×D3211yescharacteristic
551Q8—364no—
552D4—188no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—34no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—92no—
572C2×C4—92no—
573C2×C4—92no—
574C2×C4—92no—
575C2×C4—92no—
576C2×C4—128no—
577C2×C4—188no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—364no—
583C2×C3—28no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—44no—
592C2×C3#549012yes—
593C2×C3C2×#89612yes—
594C2×C3#553112yes—
595C2×C3#559712yes—
596C2×C3D3×#12112yes—
597C2×C3#563212yes—
598C2×C3#563612yes—
599D3—124no—
600D3—124no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—182no—
608C22—182no—
609C22—182no—
610C22—361no—
611C22—361no—
612C22—361no—
613C22—361no—
614C22#6386514yescomplemented
615C22C2×#379711yescharacteristic
616C22C2×#379811yescharacteristic
617C22#6430911yescharacteristic
618C22D32×D411yescharacteristic
619C22#6431211yescharacteristic
620C22#6431311yescharacteristic
621C22C2×#381111yescharacteristic
622C4—41no—
623C4—41no—
624C4—64no—
625C4—94no—
626C4—122no—
627C4—122no—
628C4—122no—
629C4—182no—
630C4—182no—
631C3—21no—
632C3#7388912yescomplemented
633C2—24no—
634C2—362no—
635C2#1059404611yescharacteristic
636C2#1059407211yescharacteristic
637C2#1059416811yescharacteristic
638C2#1059418311yescharacteristic
639C2C2×#6386511yescharacteristic
640C2#1059516611yescharacteristic
641C2#1059529811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2417
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63982C2semidirect
3. C22×#3724C2semidirect
4. C2×#63865C2semidirect
5. C3×#4942C2semidirect
7. #10591396C2semidirect
8. #10591355C2semidirect
9. #10591347C2semidirect
10. #10591337C2semidirect
11. #10591198C2semidirect
51. #4942D3semidirect
62. C2×#638Q8semidirect
92. #3724D4semidirect
282. C22×C32C22⋊Q8semidirect
495. C22×C3#896semidirect
535. C32#2417semidirect
614. C22#63865semidirect
632. C3#73889semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639822
C22×#37242
C2×#638652
C3×#49422
#105917112
#105913962
#105913552
#105913472
#105913372
#105911982
#738893