Finite Group Databasebeta

← D43×#2405 #25264146

Subgroups — D43×#2405 #25264146

Order 11008.

7822 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D43C211yesmaximal, characteristic
2C2×#123×D43C212yesmaximal, complemented
3C22×C22⋊C4×D43C211yesmaximal, characteristic, complemented
4#19137924C212yesmaximal, complemented
5#19137923C211yesmaximal, characteristic, complemented
6#19137922C211yesmaximal, characteristic, complemented
7#19137921C212yesmaximal, complemented
8#19137920C212yesmaximal, complemented
9#19137919C212yesmaximal, complemented
10#19137918C211yesmaximal, characteristic, complemented
11#19137917C214yesmaximal, complemented
12#394×D43C214yesmaximal, complemented
13#386×D43C212yesmaximal, complemented
14#385×D43C212yesmaximal, complemented
15#379×D43C211yesmaximal, characteristic, complemented
16#379×D43C212yesmaximal, complemented
17C43×#2405C211yesmaximal, characteristic, complemented
18C25×D43C2211yescharacteristic
19C25×D43C2211yescharacteristic
20C23×D172C2211yescharacteristic
21C23×C22⋊D43C2211yescharacteristic
22C23×C22⋊D43C2211yescharacteristic
23C22×D4×D43—28no—
24C22×D4×D43—216no—
25C22×D4×D43C2212yes—
26C22×D4×D43C2212yes—
27C22×D4×D43C2212yes—
28C22×D4×D43C2212yes—
29C23×C4×D43C2211yescharacteristic
30C23×C4×D43C2211yescharacteristic, complemented
31C23×C4×D43C2211yescharacteristic, complemented
32C2×#13063310C2214yescomplemented
33C2×#13063309C2212yescomplemented
34C2×#13063308C2212yescomplemented
35C2×#13063307C2214yescomplemented
36C2×#13063306C2212yescomplemented
37#123×D43—216no—
38C2×C4⋊C4×D43C2214yescomplemented
39C22×C22⋊Dic43C2211yescharacteristic, complemented
40C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
42C2×C22⋊C4×D43—28no—
43C2×C22⋊C4×D43C2212yes—
44C2×C22⋊C4×D43C2212yes—
45C2×C22⋊C4×D43C2212yescomplemented
46C2×C22⋊C4×D43C2212yescomplemented
47C2×C22⋊C4×D43C2212yescomplemented
48C2×C22⋊C4×D43C2214yescomplemented
49C2×C22⋊C4×D43C2212yescomplemented
50C2×C22⋊C4×D43C2212yescomplemented
51C2×C22⋊C4×D43C2214yescomplemented
52#14582817C2214yescomplemented
53#14582816C2214yescomplemented
54#14582815C2214yescomplemented
55#14582815C2214yescomplemented
56#14582814C2214yescomplemented
57#14582814C2214yescomplemented
58#14582813C2214yescomplemented
59#14582779C2212yescomplemented
60#14582778C2212yescomplemented
61#14582777C2214yescomplemented
62#14582776C2212yescomplemented
63#14582775C2214yescomplemented
64#14582774C2212yescomplemented
65#14582773C2214yescomplemented
66#14582772C2212yescomplemented
67#14582771C2212yescomplemented
68#14582770C2214yescomplemented
69#14582755C2212yescomplemented
70#14582755C2211yescharacteristic, complemented
71#14582754C2212yescomplemented
72#14582754C2212yescomplemented
73#14582754C2212yescomplemented
74#14582754C2212yescomplemented
75#14582754C2214yescomplemented
76#14582754C2214yescomplemented
77#14582754C2212yescomplemented
78#95×D43C2214yescomplemented
79C23×D4×C43C2211yescharacteristic
80C2×#123×C43C2212yescomplemented
81C22×C22⋊C4×C43C2211yescharacteristic, complemented
82C43×#394C2214yescomplemented
83C43×#386C2212yescomplemented
84C43×#385C2212yescomplemented
85C43×#379C2212yescomplemented
86C43×#379C2211yescharacteristic, complemented
87C24×D43—28no—
88C24×D43—28no—
89C24×D43—24no—
90C24×D43—28no—
91C24×D43—28no—
92C24×D43—44no—
93C24×D43—44no—
94C24×D43D418yes—
95C24×D43C2311yescharacteristic
96C24×D43C2312yes—
97C24×D43C2312yes—
98C24×D43C2311yescharacteristic
99C24×D43C2311yescharacteristic
100C24×D43C2311yescharacteristic
101C24×D43C2311yescharacteristic
102C24×D43C2311yescharacteristic
103C24×D43C2311yescharacteristic
104C22×D172—24no—
105C22×D172—28no—
106C22×D172C2312yes—
107C22×D172C2312yes—
108C22×C22⋊D43—24no—
109C22×C22⋊D43—24no—
110C22×C22⋊D43—28no—
111C22×C22⋊D43—28no—
112C22×C22⋊D43C2312yes—
113C22×C22⋊D43C2312yes—
114C22×C22⋊D43C2312yes—
115C22×C22⋊D43C2312yes—
116C2×D4×D43—2128no—
117C2×D4×D43—28no—
118C2×D4×D43—28no—
119C2×D4×D43—28no—
120C2×D4×D43—28no—
121C2×D4×D43—28no—
122C2×D4×D43—28no—
123C2×D4×D43—28no—
124C2×D4×D43—28no—
125C2×D4×D43—28no—
126C2×D4×D43—28no—
127C2×D4×D43—28no—
128C2×D4×D43D4116yes—
129C23×Dic43C2311yescharacteristic
130C23×Dic43C2311yescharacteristic, complemented
131C23×Dic43C2311yescharacteristic, complemented
132C22×C4×D43—24no—
133C22×C4×D43—28no—
134C22×C4×D43—24no—
135C22×C4×D43—24no—
136C22×C4×D43—28no—
137C22×C4×D43—44no—
138C22×C4×D43C2314yes—
139C22×C4×D43C2312yes—
140C22×C4×D43C2312yes—
141C22×C4×D43C2312yes—
142C22×C4×D43C2312yes—
143C22×C4×D43C2312yescomplemented
144C22×C4×D43C2312yescomplemented
145#13063310—216no—
146#13063309—28no—
147#13063308—28no—
148#13063307—216no—
149#13063306—28no—
150C2×C4⋊Dic43C2314yescomplemented
151C2×Dic43⋊C4C2314yescomplemented
152C2×Dic43⋊C4C2314yescomplemented
153C4⋊C4×D43—216no—
154C2×C22⋊Dic43—24no—
155C2×C22⋊Dic43C2312yes—
156C2×C22⋊Dic43C2312yes—
157C2×C22⋊Dic43C2312yescomplemented
158C2×C22⋊Dic43C2314yescomplemented
159C2×C22⋊Dic43C2312yescomplemented
160C2×C22⋊Dic43C2312yescomplemented
161C2×C22⋊Dic43C2314yescomplemented
162C2×(C2×D43)⋊C4—24no—
163C2×(C2×D43)⋊C4—24no—
164C2×(C2×D43)⋊C4C2312yes—
165C2×(C2×D43)⋊C4C2312yes—
166C2×(C2×D43)⋊C4C2314yes—
167C2×(C2×D43)⋊C4C2312yescomplemented
168C2×(C2×D43)⋊C4C2314yescomplemented
169C2×(C2×D43)⋊C4C2312yescomplemented
170C2×(C2×D43)⋊C4C2314yescomplemented
171C2×(C2×D43)⋊C4C2314yescomplemented
172C2×(C2×D43)⋊C4C2314yescomplemented
173C2×(C2×D43)⋊C4C2314yescomplemented
174C2×(C2×D43)⋊C4C2314yescomplemented
175C22⋊C4×D43—28no—
176C22⋊C4×D43—28no—
177C22⋊C4×D43—28no—
178C22⋊C4×D43—28no—
179C22⋊C4×D43—28no—
180C22⋊C4×D43—216no—
181C22⋊C4×D43—28no—
182C22⋊C4×D43—44no—
183C22⋊C4×D43—48no—
184C43⋊#95C2314yescomplemented
185C43⋊#95C2314yescomplemented
186C43⋊#95C2314yescomplemented
187C25×C43C2311yescharacteristic
188C25×C43C2311yescharacteristic
189C22×D4×C43—24no—
190C22×D4×C43—28no—
191C22×D4×C43C2312yes—
192C22×D4×C43C2312yes—
193C23×C4×C43C2311yescharacteristic
194C23×C4×C43C2311yescharacteristic, complemented
195C23×C4×C43C2311yescharacteristic, complemented
196#123×C43—28no—
197C2×C4⋊C4×C43C2314yescomplemented
198C2×C22⋊C4×C43—24no—
199C2×C22⋊C4×C43C2312yes—
200C2×C22⋊C4×C43C2312yes—
201C2×C22⋊C4×C43C2312yescomplemented
202C2×C22⋊C4×C43C2314yescomplemented
203C2×C22⋊C4×C43C2312yescomplemented
204C2×C22⋊C4×C43C2312yescomplemented
205C2×C22⋊C4×C43C2314yescomplemented
206#95×C43C2314yescomplemented
207C24×C43—24no—
208C24×C43—24no—
209C24×C43—22no—
210C24×C43—24no—
211C24×C43—24no—
212C24×C43—42no—
213C24×C43—42no—
214C24×C43C2×D414yes—
215C24×C43C2411yescharacteristic
216C24×C43C2412yes—
217C24×C43C2411yescharacteristic
218C24×C43C2411yescharacteristic
219C23×D43—24no—
220C23×D43—24no—
221C23×D43—24no—
222C23×D43—24no—
223C23×D43—232no—
224C23×D43—24no—
225C23×D43—24no—
226C23×D43—22no—
227C23×D43—24no—
228C23×D43—232no—
229C23×D43—232no—
230C23×D43—24no—
231C23×D43—24no—
232C23×D43—24no—
233C23×D43—24no—
234C23×D43—24no—
235C23×D43—24no—
236C23×D43—24no—
237C23×D43—24no—
238C23×D43—24no—
239C23×D43—24no—
240C23×D43—24no—
241C23×D43—28no—
242C23×D43—24no—
243C23×D43—28no—
244C23×D43—24no—
245C23×D43—28no—
246C23×D43—416no—
247C23×D43—42no—
248C23×D43—42no—
249C23×D43—42no—
250C23×D43—44no—
251C23×D43—42no—
252C23×D43—464no—
253C23×D43—464no—
254C23×D43—416no—
255C23×D43—416no—
256C23×D43C2×D414yes—
257C23×D43C2×D418yes—
258C23×D43C2×D414yes—
259C23×D43C2×D414yes—
260C23×D43C2×D414yes—
261C23×D43C2×D418yes—
262C23×D43C2×D414yes—
263C23×D43C2×D414yes—
264C23×D43#4118yes—
265C23×D43C2411yescharacteristic
266C23×D43C2412yes—
267C23×D43C2411yescharacteristic
268C23×D43C2411yescharacteristic
269C23×D43C2411yescharacteristic
270C2×D4×C43—232no—
271C2×D4×C43—24no—
272C2×D4×C43—24no—
273C2×D4×C43—24no—
274C2×D4×C43—24no—
275C2×D4×C43—24no—
276C2×D4×C43C2×D418yes—
277C22×C4×C43—24no—
278C22×C4×C43—22no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—24no—
282C22×C4×C43—42no—
283C22×C4×C43C2412yes—
284C22×C4×C43C2414yes—
285C22×C4×C43C2412yes—
286C22×C4×C43C2412yes—
287C2×C22⋊D43—232no—
288C2×C22⋊D43—232no—
289C2×C22⋊D43—24no—
290C2×C22⋊D43—24no—
291C2×C22⋊D43—24no—
292C2×C22⋊D43—24no—
293C2×C22⋊D43—24no—
294C2×C22⋊D43—24no—
295C2×C22⋊D43—24no—
296C2×C22⋊D43—24no—
297C2×C22⋊D43—24no—
298C2×C22⋊D43—24no—
299C2×C22⋊D43C2×D418yes—
300C2×C22⋊D43C2×D418yes—
301C22×Dic43—24no—
302C22×Dic43—22no—
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—24no—
306C22×Dic43—42no—
307C22×Dic43C2412yes—
308C22×Dic43C2414yes—
309C22×Dic43C2412yes—
310C22×Dic43C2412yes—
311D4×D43—264no—
312D4×D43—264no—
313D4×D43—264no—
314D4×D43—264no—
315C2×D172—232no—
316C2×D172—24no—
317C2×D172—24no—
318C2×D172—24no—
319C2×D172—24no—
320C2×D172—24no—
321C2×D172C2×D418yes—
322C2×C4×D43—232no—
323C2×C4×D43—24no—
324C2×C4×D43—24no—
325C2×C4×D43—24no—
326C2×C4×D43—24no—
327C2×C4×D43—24no—
328C2×C4×D43—28no—
329C2×C4×D43—24no—
330C2×C4×D43—24no—
331C2×C4×D43—24no—
332C2×C4×D43—24no—
333C2×C4×D43—28no—
334C2×C4×D43—28no—
335C2×C4×D43—28no—
336C2×C4×D43—28no—
337C2×C4×D43—28no—
338C2×C4×D43—44no—
339C2×C4×D43—416no—
340C2×C4×D43—416no—
341C2×C4×D43C2×D418yes—
342C4⋊C4×C43—28no—
343C22⋊C4×C43—24no—
344C22⋊C4×C43—24no—
345C22⋊C4×C43—28no—
346C22⋊C4×C43—24no—
347C22⋊C4×C43—24no—
348C22⋊C4×C43—42no—
349C22⋊C4×C43—44no—
350C22⋊Dic43—24no—
351C22⋊Dic43—24no—
352C22⋊Dic43—28no—
353C22⋊Dic43—24no—
354C22⋊Dic43—24no—
355C22⋊Dic43—42no—
356C22⋊Dic43—44no—
357(C2×D43)⋊C4—24no—
358(C2×D43)⋊C4—24no—
359(C2×D43)⋊C4—24no—
360(C2×D43)⋊C4—24no—
361(C2×D43)⋊C4—28no—
362(C2×D43)⋊C4—28no—
363(C2×D43)⋊C4—28no—
364(C2×D43)⋊C4—28no—
365(C2×D43)⋊C4—44no—
366(C2×D43)⋊C4—44no—
367(C2×D43)⋊C4—44no—
368C4⋊Dic43—28no—
369Dic43⋊C4—28no—
370Dic43⋊C4—28no—
371C23×C43—22no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—28no—
376C23×C43—28no—
377C23×C43—28no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—24no—
383C23×C43—22no—
384C23×C43—24no—
385C23×C43—44no—
386C23×C43—416no—
387C23×C43—416no—
388C23×C43—44no—
389C23×C43—44no—
390C23×C43C22×D412yes—
391C23×C43C22×D414yes—
392C23×C43C22×D414yes—
393C23×C43C22×D412yes—
394C23×C43C22×D412yes—
395C23×C43C2×#4114yes—
396C23×C43C2511yescharacteristic
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—28no—
402C22×D43—28no—
403C22×D43—28no—
404C22×D43—28no—
405C22×D43—232no—
406C22×D43—232no—
407C22×D43—28no—
408C22×D43—216no—
409C22×D43—28no—
410C22×D43—28no—
411C22×D43—22no—
412C22×D43—22no—
413C22×D43—22no—
414C22×D43—22no—
415C22×D43—24no—
416C22×D43—22no—
417C22×D43—24no—
418C22×D43—28no—
419C22×D43—28no—
420C22×D43—28no—
421C22×D43—216no—
422C22×D43—28no—
423C22×D43—28no—
424C22×D43—28no—
425C22×D43—28no—
426C22×D43—232no—
427C22×D43—44no—
428C22×D43—44no—
429C22×D43—44no—
430C22×D43—416no—
431C22×D43—416no—
432C22×D43—4128no—
433C22×D43—416no—
434C22×D43—416no—
435C22×D43—416no—
436C22×D43—416no—
437C22×D43—48no—
438C22×D43—4128no—
439C22×D43—44no—
440C22×D43—44no—
441C22×D43—48no—
442C22×D43—48no—
443C22×D43—48no—
444C22×D43—416no—
445C22×D43—416no—
446C22×D43#120116yes—
447C22×D43#123116yescomplemented
448C22×D43C22×D412yes—
449C22×D43C22×D414yes—
450C22×D43C22×D414yes—
451C22×D43C22×D412yes—
452C22×D43C22×D412yes—
453C22×D43C22×D412yes—
454C22×D43C22×D414yes—
455C22×D43C2×#4114yes—
456C22×D43C2×#4114yes—
457C22×D43H(5,𝔽2)14yes—
458D4×C43—216no—
459D4×C43—216no—
460C2×C4×C43—28no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—24no—
464C2×C4×C43—24no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—24no—
468C2×C4×C43—24no—
469C2×C4×C43—24no—
470C2×C4×C43—44no—
471C2×C4×C43—44no—
472C2×C4×C43C22×D414yes—
473C22⋊D43—216no—
474C22⋊D43—216no—
475C22⋊D43—216no—
476C22⋊D43—216no—
477C2×Dic43—28no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—24no—
481C2×Dic43—24no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—24no—
485C2×Dic43—24no—
486C2×Dic43—24no—
487C2×Dic43—44no—
488C2×Dic43—44no—
489C2×Dic43C22×D414yes—
490D172—216no—
491D172—216no—
492C4×D43—216no—
493C4×D43—216no—
494C4×D43—48no—
495C4×D43—48no—
496C4×D43—48no—
497C4×D43—48no—
498C4×D43—416no—
499C2×#2405—431nomaximal, Sylow
500C22×C43—22no—
501C22×C43—22no—
502C22×C43—22no—
503C22×C43—22no—
504C22×C43—28no—
505C22×C43—28no—
506C22×C43—24no—
507C22×C43—22no—
508C22×C43—22no—
509C22×C43—22no—
510C22×C43—28no—
511C22×C43—416no—
512C22×C43—416no—
513C22×C43—42no—
514C22×C43—42no—
515C22×C43—44no—
516C22×C43—44no—
517C22×C43C2×#12014yes—
518C22×C43C2×#12314yescomplemented
519C22×C43C23×D411yescharacteristic
520C22×C43C23×D412yes—
521C22×C43C22×#4112yes—
522C22×C43C2×H(5,𝔽2)12yes—
523C2×D43—22no—
524C2×D43—22no—
525C2×D43—22no—
526C2×D43—22no—
527C2×D43—28no—
528C2×D43—28no—
529C2×D43—232no—
530C2×D43—232no—
531C2×D43—24no—
532C2×D43—22no—
533C2×D43—22no—
534C2×D43—22no—
535C2×D43—28no—
536C2×D43—416no—
537C2×D43—416no—
538C2×D43—416no—
539C2×D43—432no—
540C2×D43—416no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—44no—
544C2×D43—44no—
545C2×D43—416no—
546C2×D43—432no—
547C2×D43C2×#12014yes—
548C2×D43C2×#12014yes—
549C2×D43C2×#12314yes—
550C2×D43C2×#12314yescomplemented
551C2×D43#53414yes—
552C2×D43#546116yes—
553C4×C43—24no—
554C4×C43—42no—
555C4×C43—42no—
556C4×C43—44no—
557Dic43—24no—
558Dic43—42no—
559Dic43—42no—
560Dic43—44no—
561C24×D4—431no—
562C22×#123—432no—
563C23×C22⋊C4—431no—
564#2405—434no—
565#2405—432no—
566#2405—432no—
567#2405—432no—
568#2405—431no—
569#2405—431no—
570#2405—432no—
571#2405—431no—
572#2405D4311yescharacteristic, direct product factor
573C2×#394—434no—
574C2×#386—432no—
575C2×#385—432no—
576C2×#379—432no—
577C2×#379—431no—
578C2×C43—24no—
579C2×C43—24no—
580C2×C43—42no—
581C2×C43—44no—
582C2×C43C22×#12011yescharacteristic
583C2×C43C22×#12311yescharacteristic
584C2×C43C2×#53411yescharacteristic
585C2×C43C2×#54614yes—
586D43—24no—
587D43—24no—
588D43—42no—
589D43—44no—
590D43#240518yesdirect product factor
591C26—431no—
592C26—431no—
593C23×D4—432no—
594C23×D4—431no—
595C23×D4—431no—
596C23×D4—432no—
597C23×D4—432no—
598C23×D4—432no—
599C23×D4—431no—
600C23×D4—8616no—
601C23×D4—868no—
602C23×D4C2×D4311yescharacteristic
603C24×C4—431no—
604C24×C4—431no—
605C24×C4—431no—
606C2×#123—432no—
607C2×#123—432no—
608C2×#123—434no—
609C2×#123—434no—
610C2×#123—432no—
611C2×#123—8616no—
612C2×#123C2×D4312yescomplemented
613C22×C4⋊C4—434no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4—431no—
617C22×C22⋊C4—432no—
618C22×C22⋊C4—432no—
619C22×C22⋊C4—432no—
620C22×C22⋊C4—432no—
621C22×C22⋊C4—434no—
622C22×C22⋊C4—432no—
623C22×C22⋊C4—432no—
624C22×C22⋊C4—432no—
625C22×C22⋊C4—434no—
626C22×C22⋊C4—868no—
627C22×C22⋊C4C2×D4311yescharacteristic, complemented
628#394—434no—
629#394—434no—
630#394—434no—
631#394—434no—
632#394—434no—
633#394—434no—
634#394—434no—
635#394C2×D4314yescomplemented
636#386—432no—
637#386—432no—
638#386—434no—
639#386—432no—
640#386—434no—
641#386C2×D4312yescomplemented
642#385—432no—
643#385—434no—
644#385—432no—
645#385—432no—
646#385—434no—
647#385C2×D4312yescomplemented
648#379—432no—
649#379—431no—
650#379—432no—
651#379—432no—
652#379—432no—
653#379—432no—
654#379—434no—
655#379—434no—
656#379—432no—
657#379C2×D4312yescomplemented
658#379C2×D4311yescharacteristic, complemented
659C2×#95—434no—
660C43C2×#240511yescharacteristic, complemented, Sylow
661C25—431no—
662C25—431no—
663C25—432no—
664C25—431no—
665C25—438no—
666C25—431no—
667C25—431no—
668C25—431no—
669C25—432no—
670C25—431no—
671C25—864no—
672C25—868no—
673C25—868no—
674C25—868no—
675C25—868no—
676C25—1724no—
677C25—1724no—
678C25C22×D4311yescharacteristic
679C25C22×D4311yescharacteristic
680C22×D4—24no—
681C22×D4—28no—
682C22×D4—432no—
683C22×D4—432no—
684C22×D4—4316no—
685C22×D4—432no—
686C22×D4—432no—
687C22×D4—432no—
688C22×D4—432no—
689C22×D4—868no—
690C22×D4—864no—
691C22×D4—868no—
692C22×D4—868no—
693C22×D4—868no—
694C22×D4—868no—
695C22×D4—868no—
696C22×D4—868no—
697C22×D4—868no—
698C22×D4—868no—
699C22×D4—868no—
700C22×D4—868no—
701C22×D4—86128no—
702C22×D4—868no—
703C22×D4—868no—
704C22×D4—864no—
705C22×D4—864no—
706C22×D4—868no—
707C22×D4C22×D4312yes—
708C22×D4C22×D4312yes—
709C23×C4—432no—
710C23×C4—431no—
711C23×C4—431no—
712C23×C4—431no—
713C23×C4—434no—
714C23×C4—432no—
715C23×C4—432no—
716C23×C4—432no—
717C23×C4—432no—
718C23×C4—432no—
719C23×C4—868no—
720C23×C4—864no—
721C23×C4—864no—
722C23×C4—864no—
723C23×C4—868no—
724C23×C4—1724no—
725C23×C4C22×D4311yescharacteristic
726C23×C4C22×D4311yescharacteristic, complemented
727C23×C4C22×D4311yescharacteristic, complemented
728#123—28no—
729#123—8616no—
730#123—868no—
731#123—8616no—
732#123—868no—
733#123—868no—
734C2×C4⋊C4—434no—
735C2×C4⋊C4—434no—
736C2×C4⋊C4—434no—
737C2×C4⋊C4—8616no—
738C2×C4⋊C4C22×D4314yescomplemented
739C2×C22⋊C4—24no—
740C2×C22⋊C4—432no—
741C2×C22⋊C4—432no—
742C2×C22⋊C4—432no—
743C2×C22⋊C4—434no—
744C2×C22⋊C4—432no—
745C2×C22⋊C4—432no—
746C2×C22⋊C4—432no—
747C2×C22⋊C4—432no—
748C2×C22⋊C4—432no—
749C2×C22⋊C4—434no—
750C2×C22⋊C4—434no—
751C2×C22⋊C4—434no—
752C2×C22⋊C4—434no—
753C2×C22⋊C4—434no—
754C2×C22⋊C4—432no—
755C2×C22⋊C4—434no—
756C2×C22⋊C4—434no—
757C2×C22⋊C4—434no—
758C2×C22⋊C4—868no—
759C2×C22⋊C4—868no—
760C2×C22⋊C4—868no—
761C2×C22⋊C4—868no—
762C2×C22⋊C4—868no—
763C2×C22⋊C4—8616no—
764C2×C22⋊C4—868no—
765C2×C22⋊C4—864no—
766C2×C22⋊C4—864no—
767C2×C22⋊C4—864no—
768C2×C22⋊C4—1724no—
769C2×C22⋊C4—1728no—
770C2×C22⋊C4C22×D4312yes—
771C2×C22⋊C4C22×D4312yes—
772C2×C22⋊C4C22×D4312yescomplemented
773C2×C22⋊C4C22×D4312yescomplemented
774C2×C22⋊C4C22×D4314yescomplemented
775C2×C22⋊C4C22×D4314yescomplemented
776C2×C22⋊C4C22×D4312yescomplemented
777#95—434no—
778#95—434no—
779#95—434no—
780#95C22×D4314yescomplemented
781C24—24no—
782C24—24no—
783C24—22no—
784C24—24no—
785C24—24no—
786C24—42no—
787C24—42no—
788C24—431no—
789C24—434no—
790C24—438no—
791C24—434no—
792C24—438no—
793C24—431no—
794C24—431no—
795C24—438no—
796C24—434no—
797C24—432no—
798C24—431no—
799C24—434no—
800C24—434no—
801C24—434no—
802C24—864no—
803C24—864no—
804C24—864no—
805C24—864no—
806C24—868no—
807C24—864no—
808C24—864no—
809C24—864no—
810C24—8632no—
811C24—864no—
812C24—864no—
813C24—864no—
814C24—864no—
815C24—864no—
816C24—864no—
817C24—864no—
818C24—8632no—
819C24—864no—
820C24—868no—
821C24—864no—
822C24—868no—
823C24—8632no—
824C24—864no—
825C24—862no—
826C24—864no—
827C24—864no—
828C24—864no—
829C24—1722no—
830C24—1722no—
831C24—1722no—
832C24—1722no—
833C24—1724no—
834C24—17216no—
835C24—17216no—
836C24—17264no—
837C24—17264no—
838C24—17216no—
839C24D4×D4314yes—
840C24C23×D4311yescharacteristic
841C24C23×D4312yes—
842C24C23×D4311yescharacteristic
843C24C23×D4311yescharacteristic
844C2×D4—232no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—438no—
851C2×D4—438no—
852C2×D4—438no—
853C2×D4—864no—
854C2×D4—864no—
855C2×D4—864no—
856C2×D4—864no—
857C2×D4—8632no—
858C2×D4—864no—
859C2×D4—864no—
860C2×D4—8664no—
861C2×D4—8664no—
862C2×D4—8664no—
863C2×D4—8664no—
864C2×D4—864no—
865C2×D4—864no—
866C2×D4—864no—
867C2×D4—864no—
868C2×D4—8632no—
869C2×D4—8632no—
870C2×D4—864no—
871C2×D4—864no—
872C2×D4—864no—
873C2×D4—864no—
874C2×D4—864no—
875C2×D4D4×D4318yes—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—42no—
882C22×C4—432no—
883C22×C4—438no—
884C22×C4—432no—
885C22×C4—434no—
886C22×C4—432no—
887C22×C4—864no—
888C22×C4—864no—
889C22×C4—864no—
890C22×C4—864no—
891C22×C4—8632no—
892C22×C4—868no—
893C22×C4—864no—
894C22×C4—864no—
895C22×C4—864no—
896C22×C4—864no—
897C22×C4—868no—
898C22×C4—868no—
899C22×C4—868no—
900C22×C4—868no—
901C22×C4—868no—
902C22×C4—864no—
903C22×C4—862no—
904C22×C4—864no—
905C22×C4—862no—
906C22×C4—862no—
907C22×C4—864no—
908C22×C4—1724no—
909C22×C4—17216no—
910C22×C4—17216no—
911C22×C4—1722no—
912C22×C4C23×D4312yes—
913C22×C4C23×D4314yes—
914C22×C4C23×D4312yes—
915C22×C4C23×D4312yes—
916C4⋊C4—28no—
917C4⋊C4—868no—
918C4⋊C4—868no—
919C4⋊C4—868no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—24no—
925C22⋊C4—42no—
926C22⋊C4—44no—
927C22⋊C4—864no—
928C22⋊C4—864no—
929C22⋊C4—864no—
930C22⋊C4—864no—
931C22⋊C4—868no—
932C22⋊C4—868no—
933C22⋊C4—868no—
934C22⋊C4—868no—
935C22⋊C4—864no—
936C22⋊C4—864no—
937C22⋊C4—864no—
938C22⋊C4—868no—
939C22⋊C4—864no—
940C22⋊C4—1724no—
941C22⋊C4—1724no—
942C22⋊C4—1724no—
943C22⋊C4—1722no—
944C22⋊C4—1724no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—28no—
950C23—28no—
951C23—28no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—44no—
960C23—416no—
961C23—416no—
962C23—44no—
963C23—44no—
964C23—434no—
965C23—432no—
966C23—434no—
967C23—434no—
968C23—4316no—
969C23—4316no—
970C23—432no—
971C23—434no—
972C23—432no—
973C23—434no—
974C23—434no—
975C23—432no—
976C23—868no—
977C23—868no—
978C23—868no—
979C23—8632no—
980C23—8632no—
981C23—868no—
982C23—868no—
983C23—8616no—
984C23—868no—
985C23—868no—
986C23—868no—
987C23—868no—
988C23—868no—
989C23—8632no—
990C23—868no—
991C23—868no—
992C23—8616no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—868no—
998C23—868no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—864no—
1003C23—862no—
1004C23—864no—
1005C23—862no—
1006C23—1724no—
1007C23—1724no—
1008C23—1724no—
1009C23—17216no—
1010C23—17216no—
1011C23—17216no—
1012C23—17216no—
1013C23—1724no—
1014C23—17216no—
1015C23—17216no—
1016C23—1728no—
1017C23—1728no—
1018C23—1728no—
1019C23—172128no—
1020C23—17216no—
1021C23—17216no—
1022C23—172128no—
1023C23—1728no—
1024C23—1724no—
1025C23C2×D4×D4312yes—
1026C23C2×D4×D4314yes—
1027C23C2×D4×D4314yes—
1028C23C2×D4×D4312yes—
1029C23C2×D4×D4312yes—
1030C23#41×D4314yes—
1031C23C24×D4311yescharacteristic
1032D4—216no—
1033D4—216no—
1034D4—8616no—
1035D4—8616no—
1036D4—8616no—
1037D4—8616no—
1038D4—8616no—
1039D4—8616no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—434no—
1053C2×C4—8616no—
1054C2×C4—8616no—
1055C2×C4—868no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—864no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—864no—
1062C2×C4—864no—
1063C2×C4—864no—
1064C2×C4—864no—
1065C2×C4—1728no—
1066C2×C4—1728no—
1067C2×C4—1728no—
1068C2×C4—17216no—
1069C2×C4—1728no—
1070C2×C4—1724no—
1071C2×C4—1724no—
1072C2×C4C2×D4×D4314yes—
1073C22—28no—
1074C22—28no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—28no—
1080C22—22no—
1081C22—24no—
1082C22—22no—
1083C22—22no—
1084C22—416no—
1085C22—416no—
1086C22—44no—
1087C22—44no—
1088C22—42no—
1089C22—42no—
1090C22—4316no—
1091C22—434no—
1092C22—434no—
1093C22—434no—
1094C22—434no—
1095C22—434no—
1096C22—8632no—
1097C22—8632no—
1098C22—868no—
1099C22—868no—
1100C22—862no—
1101C22—862no—
1102C22—862no—
1103C22—862no—
1104C22—868no—
1105C22—864no—
1106C22—862no—
1107C22—862no—
1108C22—862no—
1109C22—17216no—
1110C22—17216no—
1111C22—17216no—
1112C22—17216no—
1113C22—17232no—
1114C22—17216no—
1115C22—17232no—
1116C22—1724no—
1117C22—1724no—
1118C22—1722no—
1119C22—1722no—
1120C22#120×D4314yes—
1121C22#123×D4314yescomplemented
1122C22C22×D4×D4312yes—
1123C22C22×D4×D4311yescharacteristic
1124C22C2×#41×D4312yes—
1125C22H(5,𝔽2)×D4312yes—
1126C4—24no—
1127C4—44no—
1128C4—42no—
1129C4—42no—
1130C4—864no—
1131C4—1724no—
1132C4—1722no—
1133C4—1722no—
1134C2—24no—
1135C2—24no—
1136C2—44no—
1137C2—42no—
1138C2—438no—
1139C2—864no—
1140C2—864no—
1141C2—1724no—
1142C2—1722no—
1143C2C2×#120×D4311yescharacteristic
1144C2C2×#123×D4311yescharacteristic
1145C2#534×D4311yescharacteristic
1146C2#546×D4314yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2405C2
prime radicalC23×D4×D43C2
hypercenter#2405D43
hypocenterC43C2×#2405
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. C2×#123×D43C2semidirect
3. C22×C22⋊C4×D43C2semidirect
4. #19137924C2semidirect
5. #19137923C2semidirect
6. #19137922C2semidirect
7. #19137921C2semidirect
8. #19137920C2semidirect
9. #19137919C2semidirect
10. #19137918C2semidirect
11. #19137917C2semidirect
12. #394×D43C2semidirect
13. #386×D43C2semidirect
14. #385×D43C2semidirect
15. #379×D43C2semidirect
16. #379×D43C2semidirect
17. C43×#2405C2semidirect
30. C23×C4×D43C22semidirect
31. C23×C4×D43C22semidirect
32. C2×#13063310C22semidirect
33. C2×#13063309C22semidirect
34. C2×#13063308C22semidirect
35. C2×#13063307C22semidirect
36. C2×#13063306C22semidirect
38. C2×C4⋊C4×D43C22semidirect
39. C22×C22⋊Dic43C22semidirect
40. C22×(C2×D43)⋊C4C22semidirect
41. C22×(C2×D43)⋊C4C22semidirect
45. C2×C22⋊C4×D43C22semidirect
46. C2×C22⋊C4×D43C22semidirect
47. C2×C22⋊C4×D43C22semidirect
48. C2×C22⋊C4×D43C22semidirect
49. C2×C22⋊C4×D43C22semidirect
50. C2×C22⋊C4×D43C22semidirect
51. C2×C22⋊C4×D43C22semidirect
52. #14582817C22semidirect
53. #14582816C22semidirect
54. #14582815C22semidirect
55. #14582815C22semidirect
56. #14582814C22semidirect
57. #14582814C22semidirect
58. #14582813C22semidirect
59. #14582779C22semidirect
60. #14582778C22semidirect
61. #14582777C22semidirect
62. #14582776C22semidirect
63. #14582775C22semidirect
64. #14582774C22semidirect
65. #14582773C22semidirect
66. #14582772C22semidirect
67. #14582771C22semidirect
68. #14582770C22semidirect
69. #14582755C22semidirect
70. #14582755C22semidirect
71. #14582754C22semidirect
72. #14582754C22semidirect
73. #14582754C22semidirect
74. #14582754C22semidirect
75. #14582754C22semidirect
76. #14582754C22semidirect
77. #14582754C22semidirect
78. #95×D43C22semidirect
80. C2×#123×C43C22semidirect
81. C22×C22⋊C4×C43C22semidirect
82. C43×#394C22semidirect
83. C43×#386C22semidirect
84. C43×#385C22semidirect
85. C43×#379C22semidirect
86. C43×#379C22semidirect
130. C23×Dic43C23semidirect
131. C23×Dic43C23semidirect
143. C22×C4×D43C23semidirect
144. C22×C4×D43C23semidirect
150. C2×C4⋊Dic43C23semidirect
151. C2×Dic43⋊C4C23semidirect
152. C2×Dic43⋊C4C23semidirect
157. C2×C22⋊Dic43C23semidirect
158. C2×C22⋊Dic43C23semidirect
159. C2×C22⋊Dic43C23semidirect
160. C2×C22⋊Dic43C23semidirect
161. C2×C22⋊Dic43C23semidirect
167. C2×(C2×D43)⋊C4C23semidirect
168. C2×(C2×D43)⋊C4C23semidirect
169. C2×(C2×D43)⋊C4C23semidirect
170. C2×(C2×D43)⋊C4C23semidirect
171. C2×(C2×D43)⋊C4C23semidirect
172. C2×(C2×D43)⋊C4C23semidirect
173. C2×(C2×D43)⋊C4C23semidirect
174. C2×(C2×D43)⋊C4C23semidirect
184. C43⋊#95C23semidirect
185. C43⋊#95C23semidirect
186. C43⋊#95C23semidirect
194. C23×C4×C43C23semidirect
195. C23×C4×C43C23semidirect
197. C2×C4⋊C4×C43C23semidirect
201. C2×C22⋊C4×C43C23semidirect
202. C2×C22⋊C4×C43C23semidirect
203. C2×C22⋊C4×C43C23semidirect
204. C2×C22⋊C4×C43C23semidirect
205. C2×C22⋊C4×C43C23semidirect
206. #95×C43C23semidirect
447. C22×D43#123semidirect
518. C22×C43C2×#123semidirect
550. C2×D43C2×#123semidirect
572. #2405D43direct (N × H)
590. D43#2405direct (N × H)
612. C2×#123C2×D43semidirect
627. C22×C22⋊C4C2×D43semidirect
635. #394C2×D43semidirect
641. #386C2×D43semidirect
647. #385C2×D43semidirect
657. #379C2×D43semidirect
658. #379C2×D43semidirect
660. C43C2×#2405semidirect
726. C23×C4C22×D43semidirect
727. C23×C4C22×D43semidirect
738. C2×C4⋊C4C22×D43semidirect
772. C2×C22⋊C4C22×D43semidirect
773. C2×C22⋊C4C22×D43semidirect
774. C2×C22⋊C4C22×D43semidirect
775. C2×C22⋊C4C22×D43semidirect
776. C2×C22⋊C4C22×D43semidirect
780. #95C22×D43semidirect
1121. C22#123×D43semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D432
C2×#123×D432
C22×C22⋊C4×D432
#191379242
#191379232
#191379222
#191379212
#191379202
#191379192
#191379182
#191379172
#394×D432
#386×D432
#385×D432
#379×D432
C43×#24052
C2×#240543