Finite Group Databasebeta

← #25003061

Subgroups — #25003061

Order 11008.

1526 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063239C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
5C2×#14582666C211yesmaximal, characteristic, complemented
6#19132817C211yesmaximal, characteristic, complemented
7C2×C43×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C24×Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C22×(C2×D43)⋊C4C412yescomplemented
13C22×C4×Dic43—21no—
14C2×#13063239—22no—
15C2×#13063239—22no—
16C2×#13063239—22no—
17C2×#13063239—22no—
18C2×#13063239C414yescomplemented
19C2×#13063239C414yescomplemented
20#14582776—21no—
21#14582776—22no—
22#14582776—21no—
23C22⋊C4×Dic43—22no—
24C22⋊C4×Dic43—22no—
25C2×C43⋊#95—21no—
26C2×C43⋊#95—22no—
27C2×C43⋊#95C412yescomplemented
28#14582666—22no—
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C43×#342—22no—
33C24×D43C2×C411yescharacteristic
34C22×C22⋊D43—21no—
35C22×C22⋊D43—21no—
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C22×C22⋊D43—21no—
40C22×C22⋊D43—21no—
41C22×C22⋊D43—21no—
42C22×C22⋊D43—21no—
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C22×C22⋊D43—21no—
46C22×C22⋊D43C2×C412yes—
47C22×C22⋊D43C2×C412yes—
48C23×Dic43—21no—
49C23×Dic43—21no—
50C23×Dic43—21no—
51C23×Dic43—21no—
52C23×Dic43—21no—
53C23×Dic43—21no—
54C23×Dic43—44no—
55C23×Dic43C2×C411yescharacteristic
56C23×Dic43C2×C412yes—
57C23×Dic43D411yescharacteristic
58C23×Dic43D412yes—
59C23×Dic43D411yescharacteristic
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43C2×C412yes—
69C2×C22⋊Dic43C2×C412yes—
70C2×C22⋊Dic43D412yes—
71C2×C22⋊Dic43D412yes—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—44no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—44no—
77#13063239—28no—
78#13063239—28no—
79C43⋊#95—24no—
80C43⋊#95—22no—
81C43⋊#95—22no—
82C43⋊#95—44no—
83C25×C43C2311yescharacteristic
84C23×C4×C43—21no—
85C23×C4×C43—21no—
86C23×C4×C43C2×C412yes—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43C2×C412yes—
102C2×C22⋊C4×C43C2×C412yes—
103C2×C22⋊C4×C43D412yes—
104C2×C22⋊C4×C43D412yes—
105C24×C43—42no—
106C24×C43—42no—
107C24×C43C22×C411yescharacteristic
108C24×C43C22×C411yescharacteristic
109C24×C43C22×C411yescharacteristic
110C24×C43C2×D411yescharacteristic
111C24×C43C2×D411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
115C24×C43C2×D411yescharacteristic
116C24×C43#4111yescharacteristic
117C24×C43#4111yescharacteristic
118C24×C43#4111yescharacteristic
119C24×C43#4111yescharacteristic
120C24×C43#4111yescharacteristic
121C24×C43#4111yescharacteristic
122C23×D43—21no—
123C23×D43—21no—
124C23×D43—21no—
125C23×D43—21no—
126C23×D43—21no—
127C23×D43—21no—
128C23×D43—42no—
129C23×D43—42no—
130C23×D43C4212yescomplemented
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C2×C22⋊D43—22no—
147C2×C22⋊D43—22no—
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C2×C22⋊D43—41no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C22×Dic43—24no—
175C22×Dic43—24no—
176C22×Dic43—24no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—22no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C22×Dic43—44no—
203C22×Dic43—44no—
204C22×Dic43—44no—
205C22×Dic43—44no—
206C22×Dic43—41no—
207C22×Dic43—41no—
208C22×Dic43C4212yescomplemented
209C22×Dic43C22⋊C412yes—
210C22×Dic43C22⋊C412yes—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—41no—
217C22⋊C4×C43—41no—
218C22⋊C4×C43—41no—
219C22⋊C4×C43—41no—
220C22⋊C4×C43—41no—
221C22⋊C4×C43—41no—
222C22⋊C4×C43C22⋊C414yescomplemented
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—41no—
229C22⋊Dic43—41no—
230C22⋊Dic43C22⋊C414yescomplemented
231(C2×D43)⋊C4—44no—
232(C2×D43)⋊C4—44no—
233C4×Dic43—48no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—42no—
245C23×C43—42no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—42no—
249C23×C43—42no—
250C23×C43—41no—
251C23×C43—42no—
252C23×C43—42no—
253C23×C43—42no—
254C23×C43—41no—
255C23×C43—42no—
256C23×C43C2×C4211yescharacteristic
257C23×C43C2×C22⋊C411yescharacteristic
258C23×C43C2×C22⋊C411yescharacteristic
259C23×C43C2×C22⋊C411yescharacteristic
260C23×C43#11711yescharacteristic
261C23×C43#11711yescharacteristic
262C23×C43#11711yescharacteristic
263C23×C43C4×D411yescharacteristic
264C23×C43C4×D411yescharacteristic
265C23×C43C4×D411yescharacteristic
266C23×C43C4×D411yescharacteristic
267C23×C43C4×D411yescharacteristic
268C23×C43C4×D411yescharacteristic
269C23×C43C4×D411yescharacteristic
270C23×C43C4×D411yescharacteristic
271C23×C43C4×D411yescharacteristic
272C23×C43C4×D411yescharacteristic
273C23×C43C4×D411yescharacteristic
274C23×C43C4×D411yescharacteristic
275C23×C43#12011yescharacteristic
276C23×C43#12111yescharacteristic
277C23×C43#12111yescharacteristic
278C23×C43#12111yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12111yescharacteristic
281C23×C43#12111yescharacteristic
282C23×C43#12311yescharacteristic
283C23×C43#12311yescharacteristic
284C23×C43#12311yescharacteristic
285C23×C43#12411yescharacteristic
286C23×C43#12411yescharacteristic
287C23×C43#12411yescharacteristic
288C23×C43#12611yescharacteristic
289C23×C43#12611yescharacteristic
290C23×C43#12711yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—44no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—44no—
302C22×D43—81no—
303C22×D43—81no—
304C22×D43—81no—
305C22×D43—81no—
306C22×D43—82no—
307C22×D43—82no—
308C2×C4×C43—24no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—44no—
312C2×C4×C43—44no—
313C2×C4×C43—44no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—81no—
319C2×C4×C43—81no—
320C2×C4×C43—82no—
321C2×C4×C43—82no—
322C2×C4×C43—82no—
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—24no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—44no—
343C2×Dic43—44no—
344C2×Dic43—44no—
345C2×Dic43—44no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43—44no—
349C2×Dic43—44no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—44no—
357C2×Dic43—42no—
358C2×Dic43—81no—
359C2×Dic43—81no—
360C2×Dic43—82no—
361C2×Dic43#9914yescomplemented
362#10960—431nomaximal, Sylow
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43C4×C22⋊C411yescharacteristic
404C22×C43C4×C22⋊C411yescharacteristic
405C22×C43C4×C22⋊C411yescharacteristic
406C22×C43#38611yescharacteristic
407C22×C43#38611yescharacteristic
408C22×C43#38611yescharacteristic
409C22×C43#38811yescharacteristic
410C22×C43#38811yescharacteristic
411C22×C43#38811yescharacteristic
412C22×C43#38811yescharacteristic
413C22×C43#38811yescharacteristic
414C22×C43#38811yescharacteristic
415C22×C43#39011yescharacteristic
416C22×C43#39011yescharacteristic
417C22×C43#39011yescharacteristic
418C22×C43C2×#9912yes—
419C22×C43#41012yes—
420C2×D43—42no—
421C2×D43—44no—
422C2×D43—82no—
423C2×D43—82no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43—82no—
427C2×D43—82no—
428C2×D43—82no—
429C4×C43—44no—
430C4×C43—82no—
431C4×C43—82no—
432Dic43—24no—
433Dic43—44no—
434Dic43—42no—
435Dic43—42no—
436Dic43—82no—
437C22×#99—431no—
438C22×#99—431no—
439C2×#386—431no—
440C2×C4×C22⋊C4—431no—
441C2×#342—431no—
442C2×#342D4311yescharacteristic, complemented
443C22⋊#95—431no—
444C2×C43—21no—
445C2×C43—21no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—21no—
451C2×C43—21no—
452C2×C43—21no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—21no—
456C2×C43#143711yescharacteristic
457C2×C43C4×#9912yes—
458C2×C43#189811yescharacteristic
459C2×C43#189911yescharacteristic
460C2×C43#196412yes—
461D43—82no—
462C23×D4—431no—
463C24×C4—431no—
464C22×C22⋊C4—431no—
465C22×C22⋊C4—431no—
466C22×C22⋊C4—432no—
467C22×C22⋊C4C2×D4311yescharacteristic
468C22×C22⋊C4C2×D4311yescharacteristic
469C22×C22⋊C4C2×D4311yescharacteristic
470C22×C42—861no—
471C2×#99—434no—
472C2×#99—434no—
473C2×#99—862no—
474C2×#99—862no—
475C2×#99—862no—
476C2×#99—862no—
477#386—861no—
478#386—862no—
479#386—861no—
480C4×C22⋊C4—862no—
481C4×C22⋊C4—862no—
482C2×#95—432no—
483C2×#95—861no—
484C2×#95—862no—
485#342—22no—
486#342—862no—
487C43#1096011yescharacteristic, complemented, Sylow
488C25—431no—
489C25C22×D4311yescharacteristic
490C22×D4—432no—
491C22×D4—432no—
492C22×D4—861no—
493C22×D4—861no—
494C22×D4—861no—
495C22×D4—861no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—861no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—432no—
509C23×C4—432no—
510C23×C4—431no—
511C23×C4—861no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C23×C4—861no—
517C23×C4—1724no—
518C23×C4C4×D4312yes—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—432no—
534C2×C22⋊C4—432no—
535C2×C22⋊C4—432no—
536C2×C22⋊C4—432no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—862no—
545C2×C22⋊C4—862no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—1724no—
548C2×C22⋊C4C4×D4312yes—
549C2×C22⋊C4C4×D4312yes—
550C2×C22⋊C4D17212yes—
551C2×C22⋊C4C22⋊D4312yes—
552C2×C42—864no—
553C2×C42—1724no—
554#99—868no—
555#99—868no—
556#95—862no—
557#95—862no—
558#95—864no—
559#95—1724no—
560C24—42no—
561C24—42no—
562C24—432no—
563C24—861no—
564C24—861no—
565C24—861no—
566C24—861no—
567C24—861no—
568C24—861no—
569C24—1722no—
570C24—1722no—
571C24C2×C4×D4311yescharacteristic
572C24C2×C4×D4311yescharacteristic
573C24C2×C4×D4311yescharacteristic
574C24C2×D17211yescharacteristic
575C24#1062189811yescharacteristic
576C24#1062189811yescharacteristic
577C24D4×D4311yescharacteristic
578C24D4×D4311yescharacteristic
579C24D4×D4311yescharacteristic
580C24D4×D4311yescharacteristic
581C24#1062190011yescharacteristic
582C24#1062190011yescharacteristic
583C24#1062190211yescharacteristic
584C24#1062190211yescharacteristic
585C24C2×C22⋊D4311yescharacteristic
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—862no—
594C2×D4—862no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—1721no—
599C2×D4—1721no—
600C2×D4—1721no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C2×D4—1721no—
605C2×D4—1721no—
606C2×D4—1721no—
607C2×D4—1721no—
608C2×D4—1721no—
609C2×D4—1721no—
610C2×D4—1721no—
611C2×D4—1721no—
612C2×D4—1721no—
613C2×D4—1721no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—432no—
630C22×C4—432no—
631C22×C4—432no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—861no—
644C22×C4—862no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—861no—
652C22×C4—862no—
653C22×C4—1722no—
654C22×C4—1722no—
655C22×C4—1722no—
656C22×C4—1724no—
657C22×C4—1724no—
658C22×C4—1724no—
659C22×C4—1724no—
660C22×C4—1722no—
661C22×C4—1722no—
662C22×C4—1721no—
663C22×C4—1721no—
664C22×C4—1722no—
665C22×C4—1722no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—434no—
678C22⋊C4—862no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—862no—
683C22⋊C4—1724no—
684C22⋊C4—1724no—
685C22⋊C4—1721no—
686C22⋊C4—1721no—
687C22⋊C4(C2×D43)⋊C414yescomplemented
688C42—1728no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—3441no—
715C23—3441no—
716C23—3441no—
717C23—3441no—
718C23—3442no—
719C23—3442no—
720C23—1724no—
721C23—1724no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1722no—
726C23—1722no—
727C23—1721no—
728C23C42×D4311yescharacteristic
729C23C22⋊C4×D4311yescharacteristic
730C23C22⋊C4×D4311yescharacteristic
731C23C2×(C2×D43)⋊C411yescharacteristic
732C23#1306328211yescharacteristic
733C23#1306328311yescharacteristic
734C23#1306328311yescharacteristic
735C23(C22⋊D43)⋊C411yescharacteristic
736C23(C22⋊D43)⋊C411yescharacteristic
737C23(C22⋊D43)⋊C411yescharacteristic
738C23(C22⋊D43)⋊C411yescharacteristic
739C23C4×C22⋊D4311yescharacteristic
740C23C4×C22⋊D4311yescharacteristic
741C23#1306328711yescharacteristic
742C23#1306328711yescharacteristic
743C23#1306328711yescharacteristic
744C23#1306328711yescharacteristic
745C23C4×D17211yescharacteristic
746C23C4×D17211yescharacteristic
747C23#1306329511yescharacteristic
748C23#1306329711yescharacteristic
749C23#1306329711yescharacteristic
750C23#1306329811yescharacteristic
751C23#1306329811yescharacteristic
752C23#1306330011yescharacteristic
753C23#1306330011yescharacteristic
754C23#1306330911yescharacteristic
755C23#1306331011yescharacteristic
756C23#1306331011yescharacteristic
757C23#1306331111yescharacteristic
758C23#1306331111yescharacteristic
759C23#1306331411yescharacteristic
760C23#1306332011yescharacteristic
761C23#1306332011yescharacteristic
762C23#1306332111yescharacteristic
763D4—1722no—
764D4—1722no—
765D4—1722no—
766D4—1722no—
767D4—1722no—
768D4—1722no—
769D4—1722no—
770D4—1722no—
771C2×C4—24no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—434no—
787C2×C4—864no—
788C2×C4—864no—
789C2×C4—862no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—864no—
797C2×C4—862no—
798C2×C4—3441no—
799C2×C4—3441no—
800C2×C4—3442no—
801C2×C4—1724no—
802C2×C4—1724no—
803C2×C4—1724no—
804C2×C4—1724no—
805C2×C4—1724no—
806C2×C4—1722no—
807C2×C4—1722no—
808C2×C4—1722no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1724no—
812C2×C4—1724no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—3442no—
858C22—3442no—
859C22—3442no—
860C22—3442no—
861C22—3441no—
862C22—3441no—
863C22—3442no—
864C22—1722no—
865C22—1724no—
866C22#1458274611yescharacteristic
867C22#1458274611yescharacteristic
868C22C4×(C2×D43)⋊C411yescharacteristic
869C22#1458277611yescharacteristic
870C22#1458277711yescharacteristic
871C22#1458277711yescharacteristic
872C22#1458278811yescharacteristic
873C22#1458278811yescharacteristic
874C22#1458278911yescharacteristic
875C22#1458278911yescharacteristic
876C22#1458279111yescharacteristic
877C22#1458279111yescharacteristic
878C22#1458279911yescharacteristic
879C22#1458279911yescharacteristic
880C22#1458280011yescharacteristic
881C22#99×D4312yes—
882C22#1458287112yes—
883C4—44no—
884C4—82no—
885C4—82no—
886C4—864no—
887C4—3442no—
888C4—1724no—
889C4—1722no—
890C4—1722no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—21no—
895C2—21no—
896C2—21no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—3442no—
904C2#1913283111yescharacteristic
905C2#1913438212yes—
906C2#1913504711yescharacteristic
907C2#1913505211yescharacteristic
908C2#1913542912yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#10960
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic43C2semidirect
5. C2×#14582666C2semidirect
6. #19132817C2semidirect
7. C2×C43×#342C2semidirect
12. C22×(C2×D43)⋊C4C4semidirect
18. C2×#13063239C4semidirect
19. C2×#13063239C4semidirect
27. C2×C43⋊#95C4semidirect
130. C23×D43C42semidirect
208. C22×Dic43C42semidirect
222. C22⋊C4×C43C22⋊C4semidirect
230. C22⋊Dic43C22⋊C4semidirect
361. C2×Dic43#99semidirect
442. C2×#342D43semidirect
487. C43#10960semidirect
687. C22⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632392
C2×#145827762
C2×C22⋊C4×Dic432
C2×#145826662
#191328172
C2×C43×#3422
#1096043