Finite Group Databasebeta

← #25018093

Subgroups — #25018093

Order 11008.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582776C212yesmaximal
3C2×C22⋊C4×Dic43C212yesmaximal, complemented
4C2×#14582746C211yesmaximal, characteristic, complemented
5C22×C43⋊#95C211yesmaximal, characteristic, complemented
6#19132831C212yesmaximal, complemented
7#19132826C212yesmaximal, complemented
8#19132821C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic43C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C24×Dic43C2212yes—
14C23×C4×D43C2211yescharacteristic
15C2×C4×C22⋊D43—28no—
16C2×C4×C22⋊D43C418yescomplemented
17C22×Dic43⋊C4C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×C4×Dic43C2212yes—
23C22×C4×Dic43C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25#14582776C4116yescomplemented
26C22⋊C4×Dic43—28no—
27#14582746—24no—
28C2×C43⋊#95—24no—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2211yescharacteristic
36C24×C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2212yes—
41C24×D43C2311yescharacteristic
42C22×C22⋊D43—24no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43C2×C414yes—
46C22×C22⋊D43C2×C418yes—
47C23×Dic43—24no—
48C23×Dic43—24no—
49C23×Dic43—24no—
50C23×Dic43—24no—
51C23×Dic43—42no—
52C23×Dic43—42no—
53C23×Dic43C2×C418yescomplemented
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2312yes—
59C22×C4×D43—22no—
60C22×C4×D43—22no—
61C22×C4×D43—24no—
62C22×C4×D43—42no—
63C22×C4×D43C2×C414yescomplemented
64C4×C22⋊D43—232no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4C2×C414yescomplemented
67C2×C22⋊Dic43C2×C414yes—
68C2×C22⋊Dic43D418yes—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—42no—
73C2×(C2×D43)⋊C4—42no—
74C2×(C2×D43)⋊C4C2×C414yescomplemented
75C2×(C2×D43)⋊C4C2×C418yescomplemented
76C2×(C2×D43)⋊C4C2×C418yescomplemented
77C2×C4×Dic43—24no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43—24no—
80C2×C4×Dic43—24no—
81C2×C4×Dic43—24no—
82C2×C4×Dic43—42no—
83C2×C4×Dic43—42no—
84C2×C4×Dic43C2×C414yescomplemented
85C43⋊#95—22no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95C2×C418yescomplemented
90C43⋊#95C2×C418yescomplemented
91C43⋊#95D414yescomplemented
92C25×C43C2311yescharacteristic
93C23×C4×C43—24no—
94C23×C4×C43—22no—
95C23×C4×C43—22no—
96C23×C4×C43—42no—
97C23×C4×C43C2×C414yes—
98C23×C4×C43C2312yes—
99C23×C4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43C2×C418yescomplemented
105#95×C43—22no—
106#95×C43—22no—
107#95×C43—42no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43C22×C412yes—
115C24×C43C22×C414yes—
116C24×C43C2×D414yes—
117C24×C43#4112yes—
118C24×C43#4112yes—
119C24×C43C2411yescharacteristic
120C23×D43—21no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—21no—
124C23×D43—21no—
125C23×D43—21no—
126C23×D43—21no—
127C23×D43—22no—
128C23×D43—21no—
129C23×D43C22×C414yes—
130C23×D43C22×C412yes—
131C22×C4×C43—28no—
132C22×C4×C43—28no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—44no—
152C22×C4×C43—48no—
153C22×C4×C43—48no—
154C22×C4×C43C22×C414yes—
155C22×C4×C43C22×C414yes—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43#4112yes—
160C2×C22⋊D43—28no—
161C2×C22⋊D43—28no—
162C2×C22⋊D43—216no—
163C2×C22⋊D43—216no—
164C2×C22⋊D43C42116yescomplemented
165C22×Dic43—216no—
166C22×Dic43—216no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—21no—
174C22×Dic43—22no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—21no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—21no—
186C22×Dic43—48no—
187C22×Dic43—48no—
188C22×Dic43—48no—
189C22×Dic43—48no—
190C22×Dic43—48no—
191C22×Dic43C22×C414yes—
192C22×Dic43C22×C414yes—
193C22×Dic43C22×C412yes—
194C22×Dic43C22×C412yes—
195C22×Dic43C22×C412yes—
196C22×Dic43C22×C414yes—
197C22×Dic43C2×D414yes—
198C22×Dic43C2×D414yes—
199C22×Dic43C2×D414yes—
200C22×Dic43#4114yes—
201C2×C4×D43—28no—
202C2×C4×D43—28no—
203C2×C4×D43—44no—
204C2×C4×D43—48no—
205C2×C4×D43—48no—
206C22⋊C4×C43—216no—
207C22⋊Dic43C22⋊C4116yescomplemented
208(C2×D43)⋊C4—28no—
209(C2×D43)⋊C4—216no—
210(C2×D43)⋊C4—48no—
211Dic43⋊C4—28no—
212C4×Dic43—28no—
213C4×Dic43—48no—
214C4×Dic43—48no—
215C23×C43—24no—
216C23×C43—22no—
217C23×C43—24no—
218C23×C43—22no—
219C23×C43—24no—
220C23×C43—22no—
221C23×C43—24no—
222C23×C43—22no—
223C23×C43—24no—
224C23×C43—22no—
225C23×C43—24no—
226C23×C43—24no—
227C23×C43—24no—
228C23×C43—22no—
229C23×C43—24no—
230C23×C43—22no—
231C23×C43—24no—
232C23×C43—22no—
233C23×C43C2×C4214yes—
234C23×C43C2×C22⋊C414yes—
235C23×C43#11714yes—
236C23×C43C4×D418yes—
237C23×C43C4×D418yes—
238C23×C43C23×C411yescharacteristic
239C23×C43C23×C412yes—
240C23×C43C22×D412yes—
241C23×C43C22×D411yescharacteristic
242C23×C43C2×#4112yes—
243C23×C43C2×#4111yescharacteristic
244C23×C43C2×#4111yescharacteristic
245C23×C43C2×#4111yescharacteristic
246C23×C43H(5,𝔽2)12yes—
247C23×C43H(5,𝔽2)11yescharacteristic
248C23×C432−1+411yescharacteristic
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—24no—
252C22×D43—22no—
253C22×D43—24no—
254C22×D43—24no—
255C22×D43—24no—
256C22×D43—22no—
257C22×D43—24no—
258C22×D43—22no—
259C22×D43—24no—
260C22×D43—22no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—41no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—41no—
267C22×D43—42no—
268C22×D43—41no—
269C22×D43—42no—
270C22×D43—41no—
271C22×D43C2×C4214yes—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—22no—
277C2×C4×C43—24no—
278C2×C4×C43—24no—
279C2×C4×C43—24no—
280C2×C4×C43—22no—
281C2×C4×C43—24no—
282C2×C4×C43—24no—
283C2×C4×C43—22no—
284C2×C4×C43—24no—
285C2×C4×C43—416no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43C4×D414yes—
297C22⋊D43—232no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—24no—
307C2×Dic43—22no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—24no—
316C2×Dic43—24no—
317C2×Dic43—24no—
318C2×Dic43—24no—
319C2×Dic43—432no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43C2×C4214yes—
325C2×Dic43C2×C22⋊C414yes—
326C2×Dic43C2×C22⋊C414yes—
327C2×Dic43C4×D418yescomplemented
328C4×D43—416no—
329#13813—431nomaximal, Sylow
330C22×C43—24no—
331C22×C43—24no—
332C22×C43—24no—
333C22×C43—24no—
334C22×C43—28no—
335C22×C43—28no—
336C22×C43—28no—
337C22×C43—28no—
338C22×C43—24no—
339C22×C43—24no—
340C22×C43C4×C22⋊C418yescomplemented
341C22×C43C22×C4211yescharacteristic
342C22×C43C22×C22⋊C411yescharacteristic
343C22×C43C2×#11711yescharacteristic
344C22×C43C2×C4×D412yes—
345C22×C43C2×C4×D411yescharacteristic
346C22×C43C2×C4×D412yes—
347C22×C43C2×C4×D412yes—
348C22×C43C4×#4112yes—
349C22×C43C4×#4111yescharacteristic
350C22×C43#51812yes—
351C22×C43#51811yescharacteristic
352C22×C43#52012yes—
353C22×C43#52011yescharacteristic
354C22×C43D4212yes—
355C22×C43#54612yes—
356C22×C43#54611yescharacteristic
357C22×C43#54612yes—
358C22×C43#54712yes—
359C22×C43#54811yescharacteristic
360C22×C43#55112yes—
361C22×C43#55211yescharacteristic
362C22×C43#55312yes—
363C22×C43#55311yescharacteristic
364C2×D43—24no—
365C2×D43—24no—
366C2×D43—24no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—44no—
372C2×D43—44no—
373C2×D43—44no—
374C2×D43—44no—
375C4×C43—24no—
376C4×C43—42no—
377C4×C43—44no—
378C4×C43—44no—
379Dic43—24no—
380Dic43—24no—
381Dic43—28no—
382Dic43—24no—
383Dic43—44no—
384C22×C4×D4—431no—
385C2×#386—432no—
386C2×C4×C22⋊C4—431no—
387C2×C4×C22⋊C4—432no—
388C22×#95—431no—
389#1437—432no—
390#1436—432no—
391#1434—431no—
392C22⋊#95—431no—
393C22⋊#95D4311yescharacteristic, complemented
394C4×#95—431no—
395C2×C43—28no—
396C2×C43C2×C4×C22⋊C411yescharacteristic
397C2×C43C42×D411yescharacteristic
398C2×C43#227511yescharacteristic
399C2×C43D4×C22⋊C411yescharacteristic
400C2×C43#233911yescharacteristic
401C2×C43#235211yescharacteristic
402C2×C43#235311yescharacteristic
403C2×C43#235812yes—
404C2×C43#235912yes—
405C2×C43#236112yes—
406C2×C43#236412yes—
407D43—44no—
408C23×D4—431no—
409C24×C4—432no—
410C24×C4—431no—
411C24×C4C2×D4311yescharacteristic
412C2×C4×D4—438no—
413C2×C4×D4—868no—
414C22×C4⋊C4—431no—
415C22×C22⋊C4—431no—
416C22×C22⋊C4—431no—
417C22×C22⋊C4—432no—
418C22×C22⋊C4—432no—
419C22×C22⋊C4C2×D4312yes—
420C22×C42—431no—
421C22×C42—432no—
422C22×C42—432no—
423#386—4316no—
424C4×C22⋊C4—864no—
425C4×C22⋊C4—868no—
426C2×#95—432no—
427C2×#95—431no—
428C2×#95—432no—
429C2×#95—431no—
430C2×#95—432no—
431C2×#95—432no—
432C2×#95—432no—
433C2×#95—864no—
434C2×#95C2×D4311yescharacteristic
435C2×#95C2×D4311yescharacteristic
436C2×#95C2×D4312yes—
437C43#1381311yescharacteristic, complemented, Sylow
438C25—431no—
439C25C22×D4311yescharacteristic
440C22×D4—434no—
441C22×D4—438no—
442C22×D4—864no—
443C22×D4—862no—
444C22×D4—862no—
445C23×C4—24no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—432no—
452C23×C4—431no—
453C23×C4—432no—
454C23×C4—438no—
455C23×C4—434no—
456C23×C4—864no—
457C23×C4—864no—
458C23×C4—864no—
459C23×C4—864no—
460C23×C4—864no—
461C23×C4—862no—
462C23×C4—862no—
463C23×C4—1722no—
464C23×C4—1722no—
465C23×C4—1722no—
466C23×C4C4×D4314yes—
467C23×C4C22×D4312yes—
468C23×C4C22×D4312yes—
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4311yescharacteristic
471C4×D4—8632no—
472C2×C4⋊C4—434no—
473C2×C4⋊C4—864no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—434no—
477C2×C22⋊C4—438no—
478C2×C22⋊C4—434no—
479C2×C22⋊C4—438no—
480C2×C22⋊C4—438no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—1722no—
485C2×C22⋊C4—1722no—
486C2×C22⋊C4C4×D4318yescomplemented
487C2×C42—434no—
488C2×C42—864no—
489C2×C42—864no—
490C2×C42—864no—
491C2×C42—864no—
492C2×C42—864no—
493C2×C42—1722no—
494C2×C42—1722no—
495#95—22no—
496#95—22no—
497#95—42no—
498#95—438no—
499#95—438no—
500#95—434no—
501#95—864no—
502#95—864no—
503#95—864no—
504#95—862no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—434no—
512C24—432no—
513C24—861no—
514C24—862no—
515C24—862no—
516C24—861no—
517C24—861no—
518C24—861no—
519C24—862no—
520C24—861no—
521C24—861no—
522C24C2×C4×D4312yes—
523C24C2×C4×D4314yes—
524C24D4×D4314yes—
525C24#1062190012yes—
526C24#1062190212yes—
527C24C23×D4311yescharacteristic
528C2×D4—4316no—
529C2×D4—868no—
530C2×D4—868no—
531C2×D4—8616no—
532C2×D4—8616no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—434no—
557C22×C4—434no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—434no—
562C22×C4—434no—
563C22×C4—434no—
564C22×C4—434no—
565C22×C4—434no—
566C22×C4—868no—
567C22×C4—8616no—
568C22×C4—861no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—862no—
575C22×C4—861no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—861no—
579C22×C4—862no—
580C22×C4—861no—
581C22×C4—8616no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—868no—
589C22×C4—1724no—
590C22×C4—1728no—
591C22×C4—1728no—
592C22×C4—1728no—
593C22×C4—1728no—
594C22×C4—1728no—
595C22×C4—1728no—
596C22×C4—1728no—
597C22×C4C2×C4×D4314yes—
598C22×C4C2×C4×D4314yes—
599C22×C4C2×C4×D4312yes—
600C22×C4C2×C4×D4312yes—
601C22×C4D4×D4312yes—
602C22×C4#1062190012yes—
603C4⋊C4—868no—
604C22⋊C4—216no—
605C22⋊C4—4316no—
606C22⋊C4—868no—
607C22⋊C4—8616no—
608C22⋊C4—1728no—
609C42—868no—
610C42—1728no—
611C42—1728no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—434no—
631C23—862no—
632C23—862no—
633C23—864no—
634C23—862no—
635C23—864no—
636C23—864no—
637C23—864no—
638C23—862no—
639C23—864no—
640C23—862no—
641C23—864no—
642C23—862no—
643C23—1721no—
644C23—1722no—
645C23—1721no—
646C23—1722no—
647C23—1721no—
648C23—1722no—
649C23—1722no—
650C23—1721no—
651C23—1722no—
652C23—1722no—
653C23C42×D4314yes—
654C23C22⋊C4×D4314yes—
655C23#1306328314yes—
656C23(C22⋊D43)⋊C418yes—
657C23#1306328718yes—
658C23C22×C4×D4311yescharacteristic
659C23C22×C4×D4312yes—
660C23C2×D4×D4311yescharacteristic
661C23C2×D4×D4312yes—
662C23#41×D4312yes—
663C23C2×#1062190011yescharacteristic
664C23C2×#1062190011yescharacteristic
665C23C2×#1062190211yescharacteristic
666C23#1306337012yes—
667C23#1306337111yescharacteristic
668C23#1306337211yescharacteristic
669D4—8632no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—416no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—434no—
695C2×C4—434no—
696C2×C4—434no—
697C2×C4—438no—
698C2×C4—864no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—864no—
703C2×C4—864no—
704C2×C4—864no—
705C2×C4—862no—
706C2×C4—864no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—864no—
710C2×C4—864no—
711C2×C4—864no—
712C2×C4—864no—
713C2×C4—864no—
714C2×C4—864no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—864no—
718C2×C4—864no—
719C2×C4—17216no—
720C2×C4—17232no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4(C22⋊D43)⋊C414yes—
726C22—24no—
727C22—28no—
728C22—28no—
729C22—28no—
730C22—28no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—864no—
737C22—864no—
738C22—864no—
739C22—1722no—
740C22—1724no—
741C22—1724no—
742C22—1724no—
743C22—1724no—
744C22—1722no—
745C22—1722no—
746C22—1722no—
747C22#1458274618yescomplemented
748C22C2×C42×D4311yescharacteristic
749C22C2×C22⋊C4×D4311yescharacteristic
750C22C2×#1306328311yescharacteristic
751C22C4×D4×D4312yes—
752C22C2×(C22⋊D43)⋊C412yes—
753C22C2×(C22⋊D43)⋊C411yescharacteristic
754C22C2×#1306328712yes—
755C22C4×#1062190012yes—
756C22#1458336711yescharacteristic
757C22#1458337112yes—
758C22#1458337211yescharacteristic
759C22#1458337812yes—
760C22#1458337911yescharacteristic
761C22#1458353112yes—
762C22#1458353612yes—
763C22#1458354011yescharacteristic
764C22#1458354112yes—
765C22#1458354712yes—
766C22#1458355511yescharacteristic
767C22#1458357612yes—
768C22#1458359111yescharacteristic
769C22#1458359212yes—
770C22#1458360111yescharacteristic
771C4—24no—
772C4—44no—
773C4—44no—
774C4—42no—
775C4—868no—
776C4—864no—
777C4—864no—
778C4—864no—
779C4—1724no—
780C2—28no—
781C2—1724no—
782C2C2×#1458274611yescharacteristic
783C2C4×(C22⋊D43)⋊C411yescharacteristic
784C2#1913695411yescharacteristic
785C2#1913741111yescharacteristic
786C2#1913741911yescharacteristic
787C2#1913752611yescharacteristic
788C2#1913753711yescharacteristic
789C2#1913757112yes—
790C2#1913758512yes—
791C2#1913760612yes—
792C2#1913764312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22⋊#95D43
hypocenterC43#13813
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic43C2semidirect
4. C2×#14582746C2semidirect
5. C22×C43⋊#95C2semidirect
6. #19132831C2semidirect
7. #19132826C2semidirect
8. #19132821C2semidirect
9. (C2×D43)⋊#95C2semidirect
10. #95×Dic43C2semidirect
11. C43×C22⋊#95C2semidirect
16. C2×C4×C22⋊D43C4semidirect
25. #14582776C4semidirect
53. C23×Dic43C2×C4semidirect
63. C22×C4×D43C2×C4semidirect
66. C2×Dic43⋊C4C2×C4semidirect
74. C2×(C2×D43)⋊C4C2×C4semidirect
75. C2×(C2×D43)⋊C4C2×C4semidirect
76. C2×(C2×D43)⋊C4C2×C4semidirect
84. C2×C4×Dic43C2×C4semidirect
89. C43⋊#95C2×C4semidirect
90. C43⋊#95C2×C4semidirect
91. C43⋊#95D4semidirect
104. C2×C22⋊C4×C43C2×C4semidirect
164. C2×C22⋊D43C42semidirect
207. C22⋊Dic43C22⋊C4semidirect
327. C2×Dic43C4×D4semidirect
340. C22×C43C4×C22⋊C4semidirect
393. C22⋊#95D43semidirect
437. C43#13813semidirect
486. C2×C22⋊C4C4×D43semidirect
747. C22#14582746semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145827762
C2×C22⋊C4×Dic432
C2×#145827462
C22×C43⋊#952
#191328312
#191328262
#191328212
(C2×D43)⋊#952
#95×Dic432
C43×C22⋊#952
#1381343