Finite Group Databasebeta

← #25004459

Subgroups — #25004459

Order 11008.

1134 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582760C211yesmaximal, characteristic
2C2×#14582760C211yesmaximal, characteristic
3C2×#14582760C211yesmaximal, characteristic
4C2×#14582666C211yesmaximal, characteristic
5C2×#14582665C211yesmaximal, characteristic
6C2×#14582665C211yesmaximal, characteristic
7C2×C43×#342C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12#14582760—22no—
13#14582760—22no—
14#14582760—22no—
15#14582760—22no—
16#14582760—22no—
17#14582760—22no—
18C2×C43⋊#95—22no—
19C2×C43⋊#95—22no—
20C2×C43⋊#95C414yescomplemented
21#14582666—22no—
22#14582665—22no—
23#14582665—22no—
24C22×C22⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C43×#342—22no—
28C23×Dic43—21no—
29C23×Dic43—21no—
30C23×Dic43—21no—
31C23×Dic43—21no—
32C23×Dic43—21no—
33C23×Dic43—21no—
34C23×Dic43—21no—
35C23×Dic43—21no—
36C23×Dic43—21no—
37C23×Dic43—21no—
38C23×Dic43—21no—
39C23×Dic43—21no—
40C23×Dic43—21no—
41C23×Dic43—21no—
42C23×Dic43C2×C412yes—
43C23×Dic43C2×C412yes—
44C23×Dic43D412yes—
45C23×Dic43D412yes—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43D412yes—
63C2×C22⋊Dic43D412yes—
64C43⋊#95—28no—
65C43⋊#95—28no—
66C43⋊#95—28no—
67C25×C43C2311yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43—21no—
70C23×C4×C43C2×C412yes—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43D412yes—
88C2×C22⋊C4×C43D412yes—
89C24×C43—44no—
90C24×C43C22×C411yescharacteristic
91C24×C43C2×D411yescharacteristic
92C24×C43C2×D411yescharacteristic
93C24×C43C2×D411yescharacteristic
94C24×C43C2×D411yescharacteristic
95C24×C43C2×D411yescharacteristic
96C24×C43C2×D411yescharacteristic
97C24×C43#4111yescharacteristic
98C24×C43#4111yescharacteristic
99C24×C43#4111yescharacteristic
100C24×C43#4111yescharacteristic
101C24×C43#4111yescharacteristic
102C24×C43#4111yescharacteristic
103C24×C43#4111yescharacteristic
104C24×C43#4111yescharacteristic
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—44no—
111C22×C4×C43—44no—
112C22×C4×C43—44no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×Dic43—22no—
118C22×Dic43—22no—
119C22×Dic43—22no—
120C22×Dic43—22no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—44no—
141C22×Dic43—44no—
142C22×Dic43—44no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43—41no—
146C22×Dic43—41no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C22×Dic43C22⋊C414yes—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188C23×C43—24no—
189C23×C43—24no—
190C23×C43—24no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43C2×C22⋊C411yescharacteristic
204C23×C43#11711yescharacteristic
205C23×C43#11711yescharacteristic
206C23×C43C4×D411yescharacteristic
207C23×C43C4×D411yescharacteristic
208C23×C43C4×D411yescharacteristic
209C23×C43C4×D411yescharacteristic
210C23×C43#12011yescharacteristic
211C23×C43#12011yescharacteristic
212C23×C43#12111yescharacteristic
213C23×C43#12111yescharacteristic
214C23×C43#12111yescharacteristic
215C23×C43#12111yescharacteristic
216C23×C43#12111yescharacteristic
217C23×C43#12111yescharacteristic
218C23×C43#12111yescharacteristic
219C23×C43#12111yescharacteristic
220C23×C43#12311yescharacteristic
221C23×C43#12311yescharacteristic
222C23×C43#12311yescharacteristic
223C23×C43#12311yescharacteristic
224C23×C43#12311yescharacteristic
225C23×C43#12311yescharacteristic
226C23×C43#12311yescharacteristic
227C23×C43#12311yescharacteristic
228C23×C43#12311yescharacteristic
229C23×C43#12311yescharacteristic
230C23×C43#12411yescharacteristic
231C23×C43#12411yescharacteristic
232C23×C43#12411yescharacteristic
233C23×C43#12411yescharacteristic
234C23×C43#12611yescharacteristic
235C23×C43#12611yescharacteristic
236C23×C43#12611yescharacteristic
237C23×C43#12611yescharacteristic
238C2×C4×C43—44no—
239C2×C4×C43—44no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—44no—
244C2×C4×C43—82no—
245C2×C4×C43—82no—
246C2×C4×C43—82no—
247C2×C4×C43—82no—
248C2×C4×C43—82no—
249C2×C4×C43—82no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—44no—
266C2×Dic43—44no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—44no—
271C2×Dic43—82no—
272C2×Dic43—82no—
273C2×Dic43—82no—
274C2×Dic43—82no—
275C2×Dic43—82no—
276C2×Dic43—82no—
277#11197—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43#38111yescharacteristic
313C22×C43#38611yescharacteristic
314C22×C43#38611yescharacteristic
315C22×C43#38811yescharacteristic
316C22×C43#38811yescharacteristic
317C22×C43#38811yescharacteristic
318C22×C43#38811yescharacteristic
319C22×C43#39411yescharacteristic
320C22×C43#39411yescharacteristic
321C22×C43#39411yescharacteristic
322C22×C43#39411yescharacteristic
323C22×C43#39711yescharacteristic
324C22×C43#39711yescharacteristic
325C22×C43#39711yescharacteristic
326C22×C43#39711yescharacteristic
327C22×C43#41014yes—
328C4×C43—82no—
329C4×C43—82no—
330C4×C43—82no—
331Dic43—44no—
332Dic43—82no—
333Dic43—82no—
334Dic43—82no—
335C2×#381—431no—
336C2×#381—431no—
337C2×#381—431no—
338C2×#342—431no—
339C2×#342—431no—
340C2×#342—431no—
341C2×#342D4311yescharacteristic
342C2×C43—21no—
343C2×C43—21no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—21no—
353C2×C43—21no—
354C2×C43#144011yescharacteristic
355C2×C43#182012yes—
356C2×C43#189912yes—
357C2×C43#189912yes—
358C24×C4—431no—
359C22×C22⋊C4—431no—
360C22×C22⋊C4—431no—
361C22×C22⋊C4—431no—
362C22×C22⋊C4C2×D4311yescharacteristic
363C22×C22⋊C4C2×D4311yescharacteristic
364C22×C22⋊C4C2×D4311yescharacteristic
365#381—862no—
366#381—862no—
367#381—862no—
368#381—862no—
369#381—862no—
370#381—862no—
371C2×#95—434no—
372C2×#95—862no—
373C2×#95—862no—
374#342—22no—
375#342—862no—
376#342—862no—
377#342—862no—
378C43#1119711yescharacteristic, complemented, Sylow
379C25C22×D4311yescharacteristic
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—432no—
383C23×C4—432no—
384C23×C4—432no—
385C23×C4—432no—
386C23×C4—861no—
387C23×C4—861no—
388C23×C4—861no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4—861no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4C4×D4312yes—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—432no—
418C2×C22⋊C4—432no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4D17212yes—
436C2×C22⋊C4C22⋊D4312yes—
437#95—868no—
438#95—868no—
439#95—868no—
440C24—44no—
441C24C2×C4×D4311yescharacteristic
442C24C2×D17211yescharacteristic
443C24#1062189811yescharacteristic
444C24#1062189811yescharacteristic
445C24#1062189811yescharacteristic
446C24#1062189811yescharacteristic
447C24D4×D4311yescharacteristic
448C24D4×D4311yescharacteristic
449C24D4×D4311yescharacteristic
450C24D4×D4311yescharacteristic
451C24#1062190011yescharacteristic
452C24#1062190011yescharacteristic
453C24#1062190211yescharacteristic
454C24#1062190211yescharacteristic
455C24C2×C22⋊D4311yescharacteristic
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—44no—
468C22×C4—434no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—1724no—
493C22×C4—1724no—
494C22×C4—1721no—
495C22×C4—1721no—
496C22×C4—1721no—
497C22×C4—1721no—
498C22×C4—1724no—
499C22×C4—1721no—
500C22×C4—1721no—
501C22×C4—1721no—
502C22×C4—1721no—
503C22×C4—1721no—
504C22×C4—1721no—
505C22×C4—1721no—
506C22×C4—1721no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1721no—
510C22×C4—1721no—
511C22×C4—1721no—
512C22×C4—1721no—
513C22×C4—1721no—
514C22×C4—1721no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—1721no—
532C22⋊C4—1721no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C22⋊C4—1721no—
536C22⋊C4—1721no—
537C22⋊C4—1721no—
538C22⋊C4—1721no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23C22⋊C4×D4311yescharacteristic
555C23#1306328211yescharacteristic
556C23#1306328311yescharacteristic
557C23(C22⋊D43)⋊C411yescharacteristic
558C23C4×C22⋊D4311yescharacteristic
559C23#1306328711yescharacteristic
560C23C4×D17211yescharacteristic
561C23#1306329311yescharacteristic
562C23#1306329511yescharacteristic
563C23#1306329611yescharacteristic
564C23#1306329711yescharacteristic
565C23#1306329811yescharacteristic
566C23#1306329811yescharacteristic
567C23#1306329811yescharacteristic
568C23#1306329911yescharacteristic
569C23#1306330011yescharacteristic
570C23#1306330011yescharacteristic
571C23#1306330711yescharacteristic
572C23#1306330711yescharacteristic
573C23#1306330711yescharacteristic
574C23#1306330811yescharacteristic
575C23#1306330911yescharacteristic
576C23#1306331011yescharacteristic
577C23#1306331011yescharacteristic
578C23#1306331011yescharacteristic
579C23#1306331011yescharacteristic
580C23#1306331011yescharacteristic
581C23#1306331111yescharacteristic
582C23#1306331111yescharacteristic
583C23#1306331311yescharacteristic
584C23#1306331411yescharacteristic
585C23#1306331911yescharacteristic
586C23#1306332011yescharacteristic
587C23#1306332011yescharacteristic
588C23#1306332011yescharacteristic
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—44no—
594C2×C4—42no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—3442no—
605C2×C4—3442no—
606C2×C4—3442no—
607C2×C4—3442no—
608C2×C4—3442no—
609C2×C4—3442no—
610C2×C4—1724no—
611C2×C4—1724no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1724no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#1458276111yescharacteristic
663C22#1458277511yescharacteristic
664C22#1458277711yescharacteristic
665C22#1458278811yescharacteristic
666C22#1458278911yescharacteristic
667C22#1458279011yescharacteristic
668C22#1458279111yescharacteristic
669C22#1458281411yescharacteristic
670C22#1458281511yescharacteristic
671C22#1458281611yescharacteristic
672C22#1458281711yescharacteristic
673C22#1458282511yescharacteristic
674C22#1458282611yescharacteristic
675C22#1458282811yescharacteristic
676C22#1458282811yescharacteristic
677C22#1458287114yes—
678C4—82no—
679C4—82no—
680C4—82no—
681C4—3442no—
682C4—3442no—
683C4—3442no—
684C4—1724no—
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—21no—
690C2—21no—
691C2—21no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—21no—
696C2—21no—
697C2#1913284311yescharacteristic
698C2#1913467112yes—
699C2#1913505012yes—
700C2#1913505212yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43C2×C22⋊C4
prime radical, cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#11197
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
20. C2×C43⋊#95C4semidirect
378. C43#11197semidirect

Maximal subgroups

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

subgroupindex
C2×#145827602
C2×#145826662
C2×#145826652
C2×C43×#3422
#1119743