Finite Group Databasebeta

← #25018827

Subgroups — #25018827

Order 11008.

2278 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D43C211yesmaximal, characteristic
2C2×#14582761C214yesmaximal
3C2×#14582756C211yesmaximal, characteristic
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19132861C214yesmaximal, complemented
6#19132825C211yesmaximal, characteristic, complemented
7#19132824C211yesmaximal, characteristic, complemented
8#19132824C211yesmaximal, characteristic, complemented
9C43×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D43C2212yes—
11C23×C4×D43C2211yescharacteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C2×C4⋊C4×D43—24no—
16C2×C4⋊C4×D43—24no—
17C2×C4⋊C4×D43C418yescomplemented
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21#14582761—216no—
22#14582756—24no—
23C4×(C2×D43)⋊C4—24no—
24C2×C43⋊#95C2214yes—
25C2×C43⋊#95C2214yes—
26C2×C43⋊#95C2214yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C22×C4⋊C4×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C2×#95×C43C2214yes—
33C24×D43C2311yescharacteristic
34C23×Dic43C2312yes—
35C23×Dic43C2312yes—
36C23×Dic43C2312yes—
37C23×Dic43C2311yescharacteristic
38C22×C4×D43—22no—
39C22×C4×D43—22no—
40C22×C4×D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—24no—
43C22×C4×D43—24no—
44C22×C4×D43—28no—
45C22×C4×D43—28no—
46C22×C4×D43C2×C418yes—
47C22×C4×D43C2×C414yes—
48C22×C4×D43D414yes—
49C22×C4×D43D414yes—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43C2×C414yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4C2×C418yes—
59C4⋊C4×D43—232no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—28no—
64C2×(C2×D43)⋊C4D418yes—
65C2×C4×Dic43—22no—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—22no—
68C43⋊#95—28no—
69C43⋊#95—24no—
70C43⋊#95—24no—
71C43⋊#95—28no—
72C43⋊#95—28no—
73C23×C4×C43C2312yes—
74C23×C4×C43C2312yes—
75C23×C4×C43C2312yes—
76C23×C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43—22no—
78C2×C4⋊C4×C43—22no—
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43C2×C414yes—
83C2×C42×C43—22no—
84C2×C42×C43—22no—
85C2×C42×C43—22no—
86#95×C43—28no—
87C24×C43C2411yescharacteristic
88C23×D43—21no—
89C23×D43—21no—
90C23×D43—21no—
91C23×D43—21no—
92C23×D43—22no—
93C23×D43—22no—
94C23×D43C22×C412yes—
95C23×D43C2×D412yes—
96C23×D43C2×D412yes—
97C23×D43C2×D414yes—
98C23×D43#4114yes—
99C22×C4×C43—24no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—24no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—24no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—24no—
114C22×C4×C43C22×C414yes—
115C22×C4×C43C22×C412yes—
116C22×C4×C43C2×D414yes—
117C22×C4×C43C2×D412yes—
118C22×C4×C43C2×D412yes—
119C22×C4×C43#4112yes—
120C22×C4×C43#4112yes—
121C22×C4×C43#4112yes—
122C22×C4×C43#4112yes—
123C22×Dic43—24no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—24no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—24no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—24no—
142C22×Dic43C22×C414yes—
143C22×Dic43C22×C412yes—
144C22×Dic43C2×D414yes—
145C22×Dic43C2×D412yes—
146C22×Dic43C2×D412yes—
147C2×C4×D43—28no—
148C2×C4×D43—28no—
149C2×C4×D43—28no—
150C2×C4×D43—28no—
151C2×C4×D43—28no—
152C2×C4×D43—28no—
153C2×C4×D43—216no—
154C2×C4×D43—232no—
155C2×C4×D43—416no—
156C2×C4×D43—48no—
157C2×C4×D43—48no—
158C2×C4×D43C22⋊C4116yes—
159C4⋊C4×C43—28no—
160C4⋊C4×C43—44no—
161C42×C43—44no—
162(C2×D43)⋊C4—216no—
163(C2×D43)⋊C4—48no—
164C4⋊Dic43—28no—
165C4⋊Dic43—44no—
166Dic43⋊C4—216no—
167C4×Dic43—44no—
168C23×C43C23×C411yescharacteristic
169C23×C43C22×D411yescharacteristic
170C23×C43C22×D411yescharacteristic
171C23×C43C22×D412yes—
172C23×C43C2×#4112yes—
173C23×C43C2×#4111yescharacteristic
174C23×C43C2×#4111yescharacteristic
175C23×C43C2×#4111yescharacteristic
176C23×C43C2×#4111yescharacteristic
177C23×C432−1+412yes—
178C23×C432−1+412yes—
179C22×D43—22no—
180C22×D43—22no—
181C22×D43—24no—
182C22×D43—22no—
183C22×D43—22no—
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—22no—
187C22×D43—24no—
188C22×D43—22no—
189C22×D43—24no—
190C22×D43—24no—
191C22×D43—24no—
192C22×D43—24no—
193C22×D43—24no—
194C22×D43—24no—
195C22×D43—24no—
196C22×D43—24no—
197C22×D43C2×C22⋊C414yes—
198C22×D43C4×D418yes—
199C22×D43#12118yes—
200C22×D43#12414yes—
201C22×D43#12714yes—
202C2×C4×C43—24no—
203C2×C4×C43—28no—
204C2×C4×C43—24no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—44no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—44no—
218C2×C4×C43—44no—
219C2×C4×C43C2×C22⋊C414yes—
220C2×C4×C43#11714yes—
221C2×C4×C43#11714yes—
222C2×C4×C43#12314yes—
223C2×C4×C43#12314yes—
224C2×C4×C43#12314yes—
225C2×C4×C43#12314yes—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—24no—
233C2×Dic43—28no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—44no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43C2×C22⋊C414yes—
250C4×D43—232no—
251C4×D43—432no—
252#13904—431nomaximal, Sylow
253C22×C43C22×C22⋊C411yescharacteristic
254C22×C43C2×#11711yescharacteristic
255C22×C43C2×#11711yescharacteristic
256C22×C43C2×C4×D412yes—
257C22×C43#51912yes—
258C22×C43C2×#12112yes—
259C22×C43C2×#12311yescharacteristic
260C22×C43C2×#12311yescharacteristic
261C22×C43C2×#12311yescharacteristic
262C22×C43C2×#12311yescharacteristic
263C22×C43C2×#12411yescharacteristic
264C22×C43C2×#12711yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43#53612yes—
267C22×C43#53611yescharacteristic
268C22×C43#54712yes—
269C22×C43#54712yes—
270C22×C43#54712yes—
271C22×C43#54712yes—
272C22×C43#55212yes—
273C22×C43#55212yes—
274C22×C43#55212yes—
275C22×C43#55212yes—
276C2×D43—24no—
277C2×D43—28no—
278C2×D43—28no—
279C2×D43—28no—
280C2×D43—28no—
281C2×D43—24no—
282C2×D43—24no—
283C2×D43—24no—
284C2×D43—24no—
285C2×D43—24no—
286C2×D43#39018yes—
287C4×C43—44no—
288C4×C43—44no—
289C4×C43—82no—
290C4×C43#38118yescomplemented
291Dic43—24no—
292Dic43—44no—
293Dic43—44no—
294Dic43—82no—
295C23×C4⋊C4—431no—
296C2×#381—434no—
297C2×#380—431no—
298C2×C4×C22⋊C4—431no—
299#1445—434no—
300C4⋊#95—431no—
301C4⋊#95—431no—
302C4⋊#95—431no—
303C4⋊#95D4311yescharacteristic, complemented
304C2×C43C2×#38111yescharacteristic
305C2×C43C2×#39011yescharacteristic
306C2×C43#231011yescharacteristic
307C2×C43#234412yes—
308C2×C43#234412yes—
309C2×C43#248612yes—
310C2×C43#248612yes—
311C2×C43#250111yescharacteristic
312C2×C43#250111yescharacteristic
313C2×C43#250311yescharacteristic
314C2×C43#250311yescharacteristic
315D43—28no—
316C24×C4—431no—
317C24×C4—432no—
318C22×C4⋊C4—432no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4—438no—
321C22×C4⋊C4—431no—
322C22×C4⋊C4—864no—
323C22×C4⋊C4—864no—
324C22×C4⋊C4C2×D4311yescharacteristic
325C22×C4⋊C4C2×D4311yescharacteristic
326C22×C22⋊C4—432no—
327C22×C22⋊C4—432no—
328C22×C42—431no—
329C22×C42C2×D4311yescharacteristic
330#381—8616no—
331#380—864no—
332C4×C22⋊C4—864no—
333C2×#95—434no—
334C2×#95—434no—
335C2×#95—434no—
336C2×#95—432no—
337C2×#95—432no—
338C2×#95C2×D4314yes—
339C43#1390411yescharacteristic, complemented, Sylow
340C25—431no—
341C23×C4—431no—
342C23×C4—434no—
343C23×C4—434no—
344C23×C4—434no—
345C23×C4—432no—
346C23×C4—432no—
347C23×C4—438no—
348C23×C4—432no—
349C23×C4—864no—
350C23×C4—864no—
351C23×C4—868no—
352C23×C4—868no—
353C23×C4—862no—
354C23×C4—862no—
355C23×C4—862no—
356C23×C4—862no—
357C23×C4C22×D4312yes—
358C23×C4C22×D4312yes—
359C23×C4C22×D4312yes—
360C23×C4C22×D4311yescharacteristic
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—438no—
367C2×C4⋊C4—434no—
368C2×C4⋊C4—8632no—
369C2×C4⋊C4—864no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4C4×D4314yes—
377C2×C22⋊C4—438no—
378C2×C22⋊C4—864no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—868no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—862no—
386C2×C42—862no—
387C2×C42—862no—
388#95—28no—
389#95—864no—
390#95—864no—
391#95—868no—
392#95—868no—
393#95—868no—
394C24—432no—
395C24—434no—
396C24—432no—
397C24—432no—
398C24—434no—
399C24—861no—
400C24—861no—
401C24—861no—
402C24—861no—
403C24—862no—
404C24—862no—
405C24C23×D4311yescharacteristic
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—432no—
422C22×C4—432no—
423C22×C4—432no—
424C22×C4—4316no—
425C22×C4—434no—
426C22×C4—434no—
427C22×C4—8616no—
428C22×C4—8632no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—868no—
434C22×C4—868no—
435C22×C4—868no—
436C22×C4—868no—
437C22×C4—868no—
438C22×C4—868no—
439C22×C4—864no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—864no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—864no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—864no—
454C22×C4—17216no—
455C22×C4—1728no—
456C22×C4—1728no—
457C22×C4C2×C4×D4314yes—
458C22×C4C2×C4×D4312yes—
459C22×C4#1062189812yes—
460C22×C4#1062189812yes—
461C22×C4D4×D4314yes—
462C22×C4D4×D4312yes—
463C22×C4D4×D4312yes—
464C22×C4#1062190012yes—
465C22×C4#1062190212yes—
466C4⋊C4—28no—
467C4⋊C4—44no—
468C4⋊C4—8616no—
469C4⋊C4—868no—
470C4⋊C4—1724no—
471C22⋊C4—8616no—
472C22⋊C4—1728no—
473C42—44no—
474C42—1724no—
475C23—434no—
476C23—438no—
477C23—438no—
478C23—434no—
479C23—434no—
480C23—864no—
481C23—864no—
482C23—864no—
483C23—864no—
484C23—864no—
485C23—864no—
486C23—862no—
487C23—862no—
488C23—864no—
489C23—862no—
490C23—862no—
491C23—862no—
492C23—862no—
493C23—862no—
494C23—864no—
495C23—862no—
496C23—864no—
497C23—864no—
498C23C22×C4×D4311yescharacteristic
499C23C2×D4×D4312yes—
500C23C2×D4×D4311yescharacteristic
501C23C2×D4×D4311yescharacteristic
502C23#41×D4312yes—
503C23C2×#1062190011yescharacteristic
504C23C2×#1062189811yescharacteristic
505C23C2×#1062189811yescharacteristic
506C23C2×#1062190211yescharacteristic
507C23#1306337212yes—
508C23#1306337312yes—
509C2×C4—24no—
510C2×C4—28no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—434no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—8632no—
534C2×C4—864no—
535C2×C4—864no—
536C2×C4—864no—
537C2×C4—868no—
538C2×C4—864no—
539C2×C4—17232no—
540C2×C4—1724no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1724no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1724no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4C22⋊C4×D4314yes—
553C2×C4#1306328214yes—
554C2×C4#1306328314yes—
555C2×C4#1306330714yes—
556C2×C4#1306330714yes—
557C2×C4#1306331014yes—
558C2×C4#1306331014yes—
559C22—438no—
560C22—864no—
561C22—864no—
562C22—868no—
563C22—868no—
564C22—864no—
565C22—868no—
566C22—868no—
567C22—864no—
568C22—864no—
569C22—864no—
570C22C2×C22⋊C4×D4311yescharacteristic
571C22C2×#1306328211yescharacteristic
572C22C2×#1306328311yescharacteristic
573C22C4×D4×D4312yes—
574C22#1458337512yes—
575C22#121×D4312yes—
576C22C2×#1306330711yescharacteristic
577C22C2×#1306330711yescharacteristic
578C22C2×#1306331011yescharacteristic
579C22C2×#1306331011yescharacteristic
580C22#124×D4311yescharacteristic
581C22#127×D4311yescharacteristic
582C22#1458346911yescharacteristic
583C22#1458347212yes—
584C22#1458347411yescharacteristic
585C22#1458354912yes—
586C22#1458355012yes—
587C22#1458355212yes—
588C22#1458355412yes—
589C22#1458358312yes—
590C22#1458358712yes—
591C22#1458358812yes—
592C22#1458359012yes—
593C4—44no—
594C4—44no—
595C4—82no—
596C4—864no—
597C4—3442no—
598C4—1724no—
599C4—1724no—
600C4#1458276118yescomplemented
601C2—868no—
602C2C2×#1458276111yescharacteristic
603C2#390×D4311yescharacteristic
604C2#1913717811yescharacteristic
605C2#1913746012yes—
606C2#1913746312yes—
607C2#1913889912yes—
608C2#1913890112yes—
609C2#1913906311yescharacteristic
610C2#1913906511yescharacteristic
611C2#1913907711yescharacteristic
612C2#1913907911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4⋊#95D43
hypocenterC43#13904
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. #19132861C2semidirect
6. #19132825C2semidirect
7. #19132824C2semidirect
8. #19132824C2semidirect
9. C43×C4⋊#95C2semidirect
17. C2×C4⋊C4×D43C4semidirect
290. C4×C43#381semidirect
303. C4⋊#95D43semidirect
339. C43#13904semidirect
600. C4#14582761semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
C2×#145827612
C2×#145827562
C2×C4×(C2×D43)⋊C42
#191328612
#191328252
#191328242
C43×C4⋊#952
#1390443