Finite Group Databasebeta

← D43×#2579 #25266797

Subgroups — D43×#2579 #25266797

Order 11008.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#19139947C211yesmaximal, characteristic, complemented
4#19139946C212yesmaximal, complemented
5#19139945C211yesmaximal, characteristic, complemented
6#19139944C211yesmaximal, characteristic, complemented
7#19139943C212yesmaximal, complemented
8#19139942C211yesmaximal, characteristic, complemented
9#19139941C211yesmaximal, characteristic, complemented
10#19139940C212yesmaximal, complemented
11#19139939C211yesmaximal, characteristic, complemented
12#19139938C211yesmaximal, characteristic, complemented
13#19139937C212yesmaximal, complemented
14#398×D43C212yesmaximal, complemented
15#396×D43C212yesmaximal, complemented
16#387×D43C212yesmaximal, complemented
17#386×D43C211yesmaximal, characteristic
18#386×D43C211yesmaximal, characteristic
19#385×D43C212yesmaximal, complemented
20#385×D43C211yesmaximal, characteristic, complemented
21#385×D43C211yesmaximal, characteristic, complemented
22#380×D43C211yesmaximal, characteristic, complemented
23C43×#2579C211yesmaximal, characteristic, complemented
24C22×D4×D43C2211yescharacteristic
25C23×C4×D43C2211yescharacteristic
26C23×C4×D43C2211yescharacteristic
27C23×C4×D43C2211yescharacteristic
28C23×C4×D43C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30C2×D4×Dic43C2211yescharacteristic
31C2×#13063287C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C4×D4×D43—28no—
37C22×C4⋊Dic43C2211yescharacteristic, complemented
38C22×Dic43⋊C4C2211yescharacteristic, complemented
39C22×Dic43⋊C4C2211yescharacteristic, complemented
40C2×C4⋊C4×D43—28no—
41C2×C4⋊C4×D43C2212yes—
42C2×C4⋊C4×D43C2212yes—
43C2×C4⋊C4×D43C2211yescharacteristic
44C2×C4⋊C4×D43C2212yes—
45C2×C4⋊C4×D43C2212yes—
46C2×C4⋊C4×D43C2212yes—
47C2×C4⋊C4×D43C2212yescomplemented
48C2×C4⋊C4×D43C2212yescomplemented
49C2×C22⋊C4×D43C2211yescharacteristic
50C2×C22⋊C4×D43C2212yes—
51C2×C22⋊C4×D43C2211yescharacteristic
52C2×C22⋊C4×D43C2211yescharacteristic
53C2×C22⋊C4×D43C2211yescharacteristic
54C2×C22⋊C4×D43C2212yes—
55C2×C42×D43C2211yescharacteristic
56#14582833C2212yescomplemented
57#14582833C2212yescomplemented
58#14582832C2212yescomplemented
59#14582832C2212yescomplemented
60#14582831C2212yescomplemented
61#14582830C2212yescomplemented
62#14582829C2212yescomplemented
63#14582823C2212yescomplemented
64#14582822C2212yescomplemented
65#14582822C2212yescomplemented
66#14582822C2212yescomplemented
67#14582821C2212yescomplemented
68#14582821C2212yescomplemented
69#14582821C2212yescomplemented
70#14582786C2212yescomplemented
71#14582785C2212yescomplemented
72#14582784C2212yescomplemented
73#14582783C2212yescomplemented
74#14582782C2212yescomplemented
75#14582781C2212yescomplemented
76#14582780C2212yescomplemented
77#14582779C2211yescharacteristic
78#14582779C2211yescharacteristic
79#14582778C2211yescharacteristic
80#14582778C2211yescharacteristic
81#14582777C2212yes—
82#14582777C2212yes—
83#14582776C2211yescharacteristic
84#14582776C2211yescharacteristic
85#14582775C2212yes—
86#14582775C2212yes—
87#14582774C2212yescomplemented
88#14582774C2211yescharacteristic, complemented
89#14582774C2211yescharacteristic, complemented
90#14582773C2212yescomplemented
91#14582773C2212yescomplemented
92#14582773C2212yescomplemented
93#14582773C2212yescomplemented
94#14582772C2212yescomplemented
95#14582772C2211yescharacteristic, complemented
96#14582772C2211yescharacteristic, complemented
97#14582771C2212yescomplemented
98#14582771C2211yescharacteristic, complemented
99#14582771C2211yescharacteristic, complemented
100#14582770C2212yescomplemented
101#14582770C2212yescomplemented
102#14582770C2212yescomplemented
103#14582770C2212yescomplemented
104#14582759C2211yescharacteristic, complemented
105#14582758C2212yescomplemented
106#14582757C2211yescharacteristic, complemented
107#14582757C2211yescharacteristic, complemented
108#14582756C2212yescomplemented
109#95×D43C2212yes—
110#95×D43C2212yes—
111#95×D43C2212yes—
112#95×D43C2212yes—
113#95×D43C2212yes—
114C2×C4×D4×C43C2211yescharacteristic
115C22×C4⋊C4×C43C2211yescharacteristic, complemented
116C43×#398C2212yescomplemented
117C43×#396C2212yescomplemented
118C43×#387C2212yescomplemented
119C43×#386C2211yescharacteristic
120C43×#386C2211yescharacteristic
121C43×#385C2212yescomplemented
122C43×#385C2211yescharacteristic, complemented
123C43×#385C2211yescharacteristic, complemented
124C43×#380C2211yescharacteristic, complemented
125C24×D43C2311yescharacteristic
126C24×D43C2311yescharacteristic
127C22×D172C2311yescharacteristic
128C22×C22⋊D43C2311yescharacteristic
129C22×C22⋊D43C2311yescharacteristic
130C2×D4×D43—24no—
131C2×D4×D43—24no—
132C2×D4×D43Q818yes—
133C23×Dic43C2311yescharacteristic
134C23×Dic43C2311yescharacteristic
135C23×Dic43C2311yescharacteristic
136C23×Dic43C2311yescharacteristic
137C22×C4×D43—24no—
138C22×C4×D43—28no—
139C22×C4×D43—24no—
140C22×C4×D43—24no—
141C22×C4×D43—44no—
142C22×C4×D43—44no—
143C22×C4×D43—44no—
144C22×C4×D43D418yes—
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2312yes—
147C22×C4×D43C2312yes—
148C22×C4×D43C2311yescharacteristic
149C22×C4×D43C2312yes—
150C22×C4×D43C2312yes—
151C22×C4×D43C2311yescharacteristic
152C22×C4×D43C2311yescharacteristic
153C22×C4×D43C2311yescharacteristic
154C22×C4×D43C2312yes—
155C22×C4×D43C2312yes—
156C22×C4×D43C2311yescharacteristic
157C22×C4×D43C2311yescharacteristic
158C22×C4×D43C2311yescharacteristic
159C22×C4×D43C2311yescharacteristic
160C4×D172—24no—
161D4×Dic43—24no—
162#13063287—24no—
163C4×C22⋊D43—24no—
164C4×C22⋊D43—24no—
165(C22⋊D43)⋊C4—24no—
166(C22⋊D43)⋊C4—24no—
167C2×C4⋊Dic43—24no—
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×Dic43⋊C4—24no—
175C2×Dic43⋊C4—24no—
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2311yescharacteristic
182C2×Dic43⋊C4C2311yescharacteristic
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C4⋊C4×D43—28no—
189C4⋊C4×D43—28no—
190C4⋊C4×D43—28no—
191C4⋊C4×D43—28no—
192C4⋊C4×D43—24no—
193C4⋊C4×D43—28no—
194C4⋊C4×D43—44no—
195C4⋊C4×D43—44no—
196C2×C22⋊Dic43C2311yescharacteristic
197C2×C22⋊Dic43C2312yes—
198C2×C22⋊Dic43C2311yescharacteristic
199C2×C22⋊Dic43C2311yescharacteristic
200C2×C22⋊Dic43C2311yescharacteristic
201C2×C22⋊Dic43C2312yes—
202C2×(C2×D43)⋊C4C2311yescharacteristic
203C2×(C2×D43)⋊C4C2311yescharacteristic
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2311yescharacteristic
207C2×(C2×D43)⋊C4C2311yescharacteristic
208C2×(C2×D43)⋊C4C2312yes—
209C2×(C2×D43)⋊C4C2312yes—
210C2×(C2×D43)⋊C4C2312yes—
211C2×(C2×D43)⋊C4C2312yes—
212C22⋊C4×D43—24no—
213C22⋊C4×D43—24no—
214C22⋊C4×D43—24no—
215C22⋊C4×D43—24no—
216C22⋊C4×D43—28no—
217C22⋊C4×D43—44no—
218C2×C4×Dic43C2311yescharacteristic
219C2×C4×Dic43C2311yescharacteristic
220C2×C4×Dic43C2311yescharacteristic
221C42×D43—24no—
222C43⋊#95C2312yes—
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2312yes—
226C43⋊#95C2312yes—
227C43⋊#95C2312yes—
228C43⋊#95C2312yes—
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C43⋊#95C2312yes—
236C43⋊#95C2312yes—
237C22×D4×C43C2311yescharacteristic
238C23×C4×C43C2311yescharacteristic
239C23×C4×C43C2311yescharacteristic
240C23×C4×C43C2311yescharacteristic
241C23×C4×C43C2311yescharacteristic
242C4×D4×C43—24no—
243C2×C4⋊C4×C43—24no—
244C2×C4⋊C4×C43C2312yes—
245C2×C4⋊C4×C43C2312yes—
246C2×C4⋊C4×C43C2312yes—
247C2×C4⋊C4×C43C2311yescharacteristic
248C2×C4⋊C4×C43C2312yes—
249C2×C4⋊C4×C43C2312yes—
250C2×C22⋊C4×C43C2311yescharacteristic
251C2×C22⋊C4×C43C2311yescharacteristic
252C2×C22⋊C4×C43C2312yes—
253C2×C22⋊C4×C43C2311yescharacteristic
254C2×C22⋊C4×C43C2311yescharacteristic
255C2×C22⋊C4×C43C2312yes—
256C2×C42×C43C2311yescharacteristic
257#95×C43C2312yes—
258#95×C43C2312yes—
259#95×C43C2312yes—
260#95×C43C2312yes—
261#95×C43C2312yes—
262C24×C43C2411yescharacteristic
263C24×C43C2411yescharacteristic
264C23×D43—24no—
265C23×D43—24no—
266C23×D43—22no—
267C23×D43—24no—
268C23×D43—22no—
269C23×D43—24no—
270C23×D43C2×D414yes—
271C23×D43C2×Q814yes—
272C23×D43C2×Q814yes—
273C23×D43#4114yes—
274C23×D43C2411yescharacteristic
275C23×D43C2411yescharacteristic
276C23×D43C2411yescharacteristic
277C2×D4×C43—22no—
278C2×D4×C43—22no—
279C2×D4×C43C2×Q814yes—
280C22×C4×C43—24no—
281C22×C4×C43—22no—
282C22×C4×C43—22no—
283C22×C4×C43—22no—
284C22×C4×C43—42no—
285C22×C4×C43—42no—
286C22×C4×C43—42no—
287C22×C4×C43C2×D414yes—
288C22×C4×C43C2412yes—
289C22×C4×C43C2412yes—
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2412yes—
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C22×C4×C43C2412yes—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—22no—
301C2×C22⋊D43C2×Q814yes—
302C2×C22⋊D43C2×Q814yes—
303C22×Dic43—24no—
304C22×Dic43—22no—
305C22×Dic43—22no—
306C22×Dic43—22no—
307C22×Dic43—42no—
308C22×Dic43—42no—
309C22×Dic43—42no—
310C22×Dic43C2×D414yes—
311C22×Dic43C2412yes—
312C22×Dic43C2412yes—
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2412yes—
315C22×Dic43C2411yescharacteristic
316C22×Dic43C2411yescharacteristic
317C22×Dic43C2411yescharacteristic
318C22×Dic43C2411yescharacteristic
319C22×Dic43C2412yes—
320D4×D43—232no—
321C2×D172—22no—
322C2×D172—22no—
323C2×D172C2×Q814yes—
324C2×C4×D43—232no—
325C2×C4×D43—24no—
326C2×C4×D43—24no—
327C2×C4×D43—22no—
328C2×C4×D43—22no—
329C2×C4×D43—22no—
330C2×C4×D43—24no—
331C2×C4×D43—24no—
332C2×C4×D43—22no—
333C2×C4×D43—22no—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—24no—
337C2×C4×D43—22no—
338C2×C4×D43—24no—
339C2×C4×D43—24no—
340C2×C4×D43—24no—
341C2×C4×D43—24no—
342C2×C4×D43—24no—
343C2×C4×D43—24no—
344C2×C4×D43—24no—
345C2×C4×D43—24no—
346C2×C4×D43—24no—
347C2×C4×D43—24no—
348C2×C4×D43—24no—
349C2×C4×D43—24no—
350C2×C4×D43—416no—
351C2×C4×D43—42no—
352C2×C4×D43—42no—
353C2×C4×D43—42no—
354C2×C4×D43—42no—
355C2×C4×D43—42no—
356C2×C4×D43—42no—
357C2×C4×D43—416no—
358C2×C4×D43—416no—
359C2×C4×D43C2×D414yes—
360C2×C4×D43C2×D414yes—
361C2×C4×D43C2×D414yes—
362C2×C4×D43C2×D414yes—
363C2×C4×D43C2×Q814yes—
364C2×C4×D43#4118yes—
365C4⋊C4×C43—24no—
366C4⋊C4×C43—24no—
367C4⋊C4×C43—22no—
368C4⋊C4×C43—24no—
369C4⋊C4×C43—42no—
370C4⋊C4×C43—42no—
371C22⋊C4×C43—22no—
372C22⋊C4×C43—24no—
373C22⋊C4×C43—22no—
374C22⋊C4×C43—22no—
375C22⋊C4×C43—22no—
376C22⋊C4×C43—42no—
377C42×C43—22no—
378C22⋊Dic43—22no—
379C22⋊Dic43—24no—
380C22⋊Dic43—22no—
381C22⋊Dic43—22no—
382C22⋊Dic43—22no—
383C22⋊Dic43—42no—
384(C2×D43)⋊C4—22no—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—22no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—22no—
389(C2×D43)⋊C4—22no—
390(C2×D43)⋊C4—24no—
391(C2×D43)⋊C4—24no—
392(C2×D43)⋊C4—42no—
393(C2×D43)⋊C4—42no—
394C4⋊Dic43—24no—
395C4⋊Dic43—24no—
396C4⋊Dic43—22no—
397C4⋊Dic43—24no—
398C4⋊Dic43—42no—
399C4⋊Dic43—42no—
400Dic43⋊C4—24no—
401Dic43⋊C4—24no—
402Dic43⋊C4—22no—
403Dic43⋊C4—24no—
404Dic43⋊C4—24no—
405Dic43⋊C4—24no—
406Dic43⋊C4—22no—
407Dic43⋊C4—24no—
408Dic43⋊C4—42no—
409Dic43⋊C4—42no—
410Dic43⋊C4—42no—
411Dic43⋊C4—42no—
412C4×Dic43—22no—
413C4×Dic43—22no—
414C4×Dic43—22no—
415C23×C43—22no—
416C23×C43—22no—
417C23×C43—21no—
418C23×C43—22no—
419C23×C43—21no—
420C23×C43—22no—
421C23×C43C22×D412yes—
422C23×C43C22×Q812yes—
423C23×C43C22×Q812yes—
424C23×C43C2×#4112yes—
425C23×C43C2511yescharacteristic
426C22×D43—22no—
427C22×D43—22no—
428C22×D43—28no—
429C22×D43—28no—
430C22×D43—216no—
431C22×D43—216no—
432C22×D43—21no—
433C22×D43—22no—
434C22×D43—21no—
435C22×D43—22no—
436C22×D43—28no—
437C22×D43—216no—
438C22×D43—44no—
439C22×D43—44no—
440C22×D43—48no—
441C22×D43C22⋊Q8116yes—
442C22×D43C22×D412yes—
443C22×D43C22×D412yes—
444C22×D43C22×Q812yes—
445C22×D43C22×Q812yes—
446C22×D43C22×Q812yes—
447C22×D43C2×#4112yes—
448C22×D43C2×#4112yes—
449C22×D43C2×#4114yes—
450C22×D43H(5,𝔽2)14yes—
451D4×C43—28no—
452C2×C4×C43—28no—
453C2×C4×C43—21no—
454C2×C4×C43—22no—
455C2×C4×C43—22no—
456C2×C4×C43—21no—
457C2×C4×C43—22no—
458C2×C4×C43—22no—
459C2×C4×C43—21no—
460C2×C4×C43—22no—
461C2×C4×C43—21no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
464C2×C4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—22no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—44no—
473C2×C4×C43—44no—
474C2×C4×C43—44no—
475C2×C4×C43C22×D412yes—
476C2×C4×C43C22×D412yes—
477C2×C4×C43C22×Q812yes—
478C2×C4×C43C2×#4114yes—
479C22⋊D43—28no—
480C22⋊D43—28no—
481C2×Dic43—28no—
482C2×Dic43—21no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—21no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—21no—
489C2×Dic43—22no—
490C2×Dic43—21no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—22no—
497C2×Dic43—22no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—22no—
501C2×Dic43—44no—
502C2×Dic43—44no—
503C2×Dic43—44no—
504C2×Dic43C22×D412yes—
505C2×Dic43C22×D412yes—
506C2×Dic43C22×Q812yes—
507C2×Dic43C2×#4114yes—
508D172—28no—
509C4×D43—216no—
510C4×D43—28no—
511C4×D43—216no—
512C4×D43—28no—
513C4×D43—28no—
514C4×D43—44no—
515C4×D43—44no—
516C4×D43—44no—
517C4×D43—44no—
518C4×D43—48no—
519C4×D43—44no—
520C4×D43—44no—
521C4×D43—48no—
522C4×D43—48no—
523C4×D43—48no—
524C2×#2579—431nomaximal, Sylow
525C22×C43—22no—
526C22×C43—22no—
527C22×C43—24no—
528C22×C43—24no—
529C22×C43—22no—
530C22×C43—24no—
531C22×C43—41no—
532C22×C43—41no—
533C22×C43—42no—
534C22×C43C2×C22⋊Q814yes—
535C22×C43C23×D411yescharacteristic
536C22×C43C23×Q811yescharacteristic
537C22×C43C22×#4111yescharacteristic
538C22×C43C22×#4112yes—
539C22×C43C2×H(5,𝔽2)12yes—
540C2×D43—22no—
541C2×D43—22no—
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—232no—
545C2×D43—22no—
546C2×D43—24no—
547C2×D43—41no—
548C2×D43—41no—
549C2×D43—42no—
550C2×D43—416no—
551C2×D43C2×C22⋊Q814yes—
552C2×D43C2×C22⋊Q814yes—
553C2×D43#52514yes—
554C2×D43#53414yes—
555C2×D43#55318yes—
556C2×D43#55418yes—
557C4×C43—22no—
558C4×C43—24no—
559C4×C43—22no—
560C4×C43—22no—
561C4×C43—41no—
562C4×C43—41no—
563C4×C43—42no—
564C4×C43—42no—
565C4×C43—42no—
566Dic43—22no—
567Dic43—24no—
568Dic43—22no—
569Dic43—22no—
570Dic43—41no—
571Dic43—41no—
572Dic43—42no—
573Dic43—42no—
574Dic43—42no—
575C22×C4×D4—431no—
576C23×C4⋊C4—431no—
577#2579—432no—
578#2579—432no—
579#2579—432no—
580#2579—431no—
581#2579—431no—
582#2579—432no—
583#2579—431no—
584#2579—431no—
585#2579—431no—
586#2579—431no—
587#2579—431no—
588#2579D4311yescharacteristic, direct product factor
589C2×#398—432no—
590C2×#396—432no—
591C2×#387—432no—
592C2×#386—431no—
593C2×#386—431no—
594C2×#385—432no—
595C2×#385—431no—
596C2×#385—431no—
597C2×#380—431no—
598C2×C43—24no—
599C2×C43—42no—
600C2×C43C22×C22⋊Q811yescharacteristic
601C2×C43C2×#52511yescharacteristic
602C2×C43C2×#53411yescharacteristic
603C2×C43C2×#55312yes—
604C2×C43C2×#55412yes—
605D43—24no—
606D43—42no—
607D43#257918yesdirect product factor
608C23×D4—431no—
609C24×C4—431no—
610C24×C4—431no—
611C24×C4—431no—
612C24×C4—431no—
613C2×C4×D4—431no—
614C2×C4×D4—431no—
615C2×C4×D4—431no—
616C2×C4×D4—431no—
617C2×C4×D4—431no—
618C2×C4×D4—431no—
619C2×C4×D4—431no—
620C2×C4×D4—868no—
621C2×C4×D4C2×D4311yescharacteristic
622C22×C4⋊C4—431no—
623C22×C4⋊C4—431no—
624C22×C4⋊C4—431no—
625C22×C4⋊C4—432no—
626C22×C4⋊C4—432no—
627C22×C4⋊C4—432no—
628C22×C4⋊C4—432no—
629C22×C4⋊C4—431no—
630C22×C4⋊C4—432no—
631C22×C4⋊C4—432no—
632C22×C4⋊C4—432no—
633C22×C4⋊C4—868no—
634C22×C4⋊C4C2×D4311yescharacteristic, complemented
635C22×C22⋊C4—431no—
636C22×C22⋊C4—432no—
637C22×C22⋊C4—431no—
638C22×C22⋊C4—431no—
639C22×C22⋊C4—431no—
640C22×C22⋊C4—432no—
641C22×C42—431no—
642#398—432no—
643#398—432no—
644#398—432no—
645#398—432no—
646#398—432no—
647#398—432no—
648#398—432no—
649#398C2×D4312yescomplemented
650#396—432no—
651#396—432no—
652#396—432no—
653#396—432no—
654#396—432no—
655#396—432no—
656#396—432no—
657#396C2×D4312yescomplemented
658#387—432no—
659#387—432no—
660#387—432no—
661#387—432no—
662#387—432no—
663#387—432no—
664#387—432no—
665#387C2×D4312yescomplemented
666#386—431no—
667#386—431no—
668#386—431no—
669#386—431no—
670#386—432no—
671#386—432no—
672#386—431no—
673#386—431no—
674#386—432no—
675#386—432no—
676#386C2×D4311yescharacteristic
677#386C2×D4311yescharacteristic
678#385—432no—
679#385—431no—
680#385—431no—
681#385—432no—
682#385—432no—
683#385—432no—
684#385—432no—
685#385—432no—
686#385—431no—
687#385—431no—
688#385—432no—
689#385—431no—
690#385—431no—
691#385—432no—
692#385—432no—
693#385—432no—
694#385—432no—
695#385C2×D4312yescomplemented
696#385C2×D4311yescharacteristic, complemented
697#385C2×D4311yescharacteristic, complemented
698#380—431no—
699#380—432no—
700#380—431no—
701#380—431no—
702#380—432no—
703#380C2×D4311yescharacteristic, complemented
704C2×#95—432no—
705C2×#95—432no—
706C2×#95—432no—
707C2×#95—432no—
708C2×#95—432no—
709C43C2×#257911yescharacteristic, complemented, Sylow
710C25—431no—
711C25—431no—
712C22×D4—431no—
713C22×D4—431no—
714C22×D4—438no—
715C22×D4—431no—
716C22×D4—864no—
717C22×D4—864no—
718C22×D4C22×D4311yescharacteristic
719C23×C4—431no—
720C23×C4—431no—
721C23×C4—432no—
722C23×C4—431no—
723C23×C4—431no—
724C23×C4—438no—
725C23×C4—431no—
726C23×C4—431no—
727C23×C4—431no—
728C23×C4—431no—
729C23×C4—431no—
730C23×C4—432no—
731C23×C4—432no—
732C23×C4—431no—
733C23×C4—431no—
734C23×C4—432no—
735C23×C4—432no—
736C23×C4—432no—
737C23×C4—431no—
738C23×C4—431no—
739C23×C4—868no—
740C23×C4—864no—
741C23×C4—864no—
742C23×C4—864no—
743C23×C4—1724no—
744C23×C4—1724no—
745C23×C4—1724no—
746C23×C4C22×D4311yescharacteristic
747C23×C4C22×D4311yescharacteristic
748C23×C4C22×D4311yescharacteristic
749C23×C4C22×D4311yescharacteristic
750C4×D4—24no—
751C4×D4—864no—
752C4×D4—864no—
753C4×D4—864no—
754C4×D4—864no—
755C4×D4—864no—
756C4×D4—864no—
757C4×D4—864no—
758C2×C4⋊C4—24no—
759C2×C4⋊C4—432no—
760C2×C4⋊C4—432no—
761C2×C4⋊C4—432no—
762C2×C4⋊C4—432no—
763C2×C4⋊C4—432no—
764C2×C4⋊C4—432no—
765C2×C4⋊C4—431no—
766C2×C4⋊C4—431no—
767C2×C4⋊C4—431no—
768C2×C4⋊C4—432no—
769C2×C4⋊C4—432no—
770C2×C4⋊C4—432no—
771C2×C4⋊C4—432no—
772C2×C4⋊C4—432no—
773C2×C4⋊C4—432no—
774C2×C4⋊C4—432no—
775C2×C4⋊C4—432no—
776C2×C4⋊C4—432no—
777C2×C4⋊C4—868no—
778C2×C4⋊C4—868no—
779C2×C4⋊C4—868no—
780C2×C4⋊C4—868no—
781C2×C4⋊C4—864no—
782C2×C4⋊C4—868no—
783C2×C4⋊C4—864no—
784C2×C4⋊C4—864no—
785C2×C4⋊C4—864no—
786C2×C4⋊C4—1724no—
787C2×C4⋊C4—1724no—
788C2×C4⋊C4C22×D4312yes—
789C2×C4⋊C4C22×D4312yes—
790C2×C4⋊C4C22×D4311yescharacteristic
791C2×C4⋊C4C22×D4312yes—
792C2×C4⋊C4C22×D4312yes—
793C2×C4⋊C4C22×D4312yes—
794C2×C22⋊C4—431no—
795C2×C22⋊C4—431no—
796C2×C22⋊C4—431no—
797C2×C22⋊C4—431no—
798C2×C22⋊C4—432no—
799C2×C22⋊C4—431no—
800C2×C22⋊C4—431no—
801C2×C22⋊C4—431no—
802C2×C22⋊C4—431no—
803C2×C22⋊C4—432no—
804C2×C22⋊C4—432no—
805C2×C22⋊C4—432no—
806C2×C22⋊C4—432no—
807C2×C22⋊C4—432no—
808C2×C22⋊C4—432no—
809C2×C22⋊C4—432no—
810C2×C22⋊C4—864no—
811C2×C22⋊C4—868no—
812C2×C22⋊C4—864no—
813C2×C22⋊C4—864no—
814C2×C22⋊C4—864no—
815C2×C22⋊C4—1724no—
816C2×C22⋊C4C22×D4311yescharacteristic
817C2×C22⋊C4C22×D4311yescharacteristic
818C2×C22⋊C4C22×D4311yescharacteristic
819C2×C22⋊C4C22×D4311yescharacteristic
820C2×C22⋊C4C22×D4312yes—
821C2×C22⋊C4C22×D4312yes—
822C2×C42—431no—
823C2×C42—431no—
824C2×C42—431no—
825C2×C42—864no—
826C2×C42C22×D4311yescharacteristic
827#95—432no—
828#95—432no—
829#95—432no—
830#95—432no—
831#95—432no—
832#95—432no—
833#95—432no—
834#95—432no—
835#95—432no—
836#95—432no—
837#95—432no—
838#95—432no—
839#95—432no—
840#95—432no—
841#95—432no—
842#95C22×D4312yes—
843#95C22×D4312yes—
844#95C22×D4312yes—
845#95C22×D4312yes—
846#95C22×D4312yes—
847C24—431no—
848C24—434no—
849C24—434no—
850C24—434no—
851C24—431no—
852C24—434no—
853C24—431no—
854C24—864no—
855C24—864no—
856C24—862no—
857C24—864no—
858C24—864no—
859C24—862no—
860C24C23×D4311yescharacteristic
861C24C23×D4311yescharacteristic
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—434no—
865C2×D4—434no—
866C2×D4—434no—
867C2×D4—862no—
868C2×D4—862no—
869C2×D4—8632no—
870C2×D4—862no—
871C2×D4—862no—
872C2×D4—862no—
873C2×D4—862no—
874C2×D4Q8×D4314yes—
875C22×C4—22no—
876C22×C4—24no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—431no—
883C22×C4—431no—
884C22×C4—432no—
885C22×C4—431no—
886C22×C4—434no—
887C22×C4—434no—
888C22×C4—434no—
889C22×C4—434no—
890C22×C4—438no—
891C22×C4—434no—
892C22×C4—434no—
893C22×C4—432no—
894C22×C4—432no—
895C22×C4—431no—
896C22×C4—431no—
897C22×C4—432no—
898C22×C4—864no—
899C22×C4—862no—
900C22×C4—862no—
901C22×C4—864no—
902C22×C4—864no—
903C22×C4—864no—
904C22×C4—864no—
905C22×C4—864no—
906C22×C4—862no—
907C22×C4—8632no—
908C22×C4—862no—
909C22×C4—862no—
910C22×C4—864no—
911C22×C4—864no—
912C22×C4—864no—
913C22×C4—864no—
914C22×C4—864no—
915C22×C4—864no—
916C22×C4—864no—
917C22×C4—864no—
918C22×C4—864no—
919C22×C4—864no—
920C22×C4—864no—
921C22×C4—864no—
922C22×C4—864no—
923C22×C4—862no—
924C22×C4—862no—
925C22×C4—864no—
926C22×C4—862no—
927C22×C4—862no—
928C22×C4—1722no—
929C22×C4—1722no—
930C22×C4—1722no—
931C22×C4—1722no—
932C22×C4—1722no—
933C22×C4—1722no—
934C22×C4—17216no—
935C22×C4—17216no—
936C22×C4—17216no—
937C22×C4—1722no—
938C22×C4—1722no—
939C22×C4—1722no—
940C22×C4D4×D4314yes—
941C22×C4C23×D4312yes—
942C22×C4C23×D4312yes—
943C22×C4C23×D4311yescharacteristic
944C22×C4C23×D4311yescharacteristic
945C22×C4C23×D4312yes—
946C22×C4C23×D4311yescharacteristic
947C22×C4C23×D4311yescharacteristic
948C22×C4C23×D4311yescharacteristic
949C22×C4C23×D4312yes—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—24no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—864no—
957C4⋊C4—864no—
958C4⋊C4—864no—
959C4⋊C4—864no—
960C4⋊C4—862no—
961C4⋊C4—862no—
962C4⋊C4—864no—
963C4⋊C4—864no—
964C4⋊C4—864no—
965C4⋊C4—864no—
966C4⋊C4—862no—
967C4⋊C4—864no—
968C4⋊C4—1722no—
969C4⋊C4—1722no—
970C4⋊C4—1722no—
971C4⋊C4—1722no—
972C4⋊C4—1722no—
973C4⋊C4—1722no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—24no—
979C22⋊C4—42no—
980C22⋊C4—862no—
981C22⋊C4—864no—
982C22⋊C4—862no—
983C22⋊C4—862no—
984C22⋊C4—864no—
985C22⋊C4—864no—
986C22⋊C4—862no—
987C22⋊C4—864no—
988C22⋊C4—862no—
989C22⋊C4—862no—
990C22⋊C4—862no—
991C22⋊C4—862no—
992C22⋊C4—864no—
993C22⋊C4—1722no—
994C22⋊C4—1722no—
995C22⋊C4—1722no—
996C42—22no—
997C42—862no—
998C42—862no—
999C42—862no—
1000C23—22no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—21no—
1005C23—22no—
1006C23—432no—
1007C23—432no—
1008C23—434no—
1009C23—432no—
1010C23—434no—
1011C23—4316no—
1012C23—432no—
1013C23—432no—
1014C23—432no—
1015C23—432no—
1016C23—868no—
1017C23—868no—
1018C23—8616no—
1019C23—8616no—
1020C23—868no—
1021C23—8616no—
1022C23—862no—
1023C23—862no—
1024C23—861no—
1025C23—862no—
1026C23—861no—
1027C23—862no—
1028C23—1724no—
1029C23—1724no—
1030C23—1728no—
1031C23C2×D4×D4312yes—
1032C23C2×Q8×D4312yes—
1033C23C2×Q8×D4312yes—
1034C23#41×D4312yes—
1035C23C24×D4311yescharacteristic
1036D4—28no—
1037D4—868no—
1038D4—868no—
1039D4—868no—
1040C2×C4—28no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—432no—
1064C2×C4—432no—
1065C2×C4—432no—
1066C2×C4—434no—
1067C2×C4—8616no—
1068C2×C4—868no—
1069C2×C4—868no—
1070C2×C4—868no—
1071C2×C4—8616no—
1072C2×C4—868no—
1073C2×C4—861no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—861no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—861no—
1080C2×C4—861no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—1724no—
1093C2×C4—1724no—
1094C2×C4—1724no—
1095C2×C4—1724no—
1096C2×C4—1724no—
1097C2×C4—1728no—
1098C2×C4—1724no—
1099C2×C4—1728no—
1100C2×C4—1728no—
1101C2×C4—1728no—
1102C2×C4—1724no—
1103C2×C4—1724no—
1104C2×C4—1724no—
1105C2×C4C2×D4×D4312yes—
1106C2×C4C2×D4×D4312yes—
1107C2×C4C2×Q8×D4312yes—
1108C2×C4#41×D4314yes—
1109C22—22no—
1110C22—24no—
1111C22—24no—
1112C22—22no—
1113C22—22no—
1114C22—24no—
1115C22—41no—
1116C22—42no—
1117C22—41no—
1118C22—434no—
1119C22—434no—
1120C22—438no—
1121C22—438no—
1122C22—434no—
1123C22—434no—
1124C22—8632no—
1125C22—862no—
1126C22—864no—
1127C22—864no—
1128C22—862no—
1129C22—862no—
1130C22—864no—
1131C22—17216no—
1132C22—1721no—
1133C22—1722no—
1134C22—1721no—
1135C22C22⋊Q8×D4314yes—
1136C22C22×D4×D4311yescharacteristic
1137C22C22×Q8×D4311yescharacteristic
1138C22C2×#41×D4311yescharacteristic
1139C22C2×#41×D4312yes—
1140C22H(5,𝔽2)×D4312yes—
1141C4—22no—
1142C4—24no—
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—42no—
1147C4—42no—
1148C4—41no—
1149C4—42no—
1150C4—862no—
1151C4—864no—
1152C4—862no—
1153C4—862no—
1154C4—1721no—
1155C4—1722no—
1156C4—1722no—
1157C4—1721no—
1158C4—1722no—
1159C2—24no—
1160C2—42no—
1161C2—438no—
1162C2—864no—
1163C2—1722no—
1164C2C2×C22⋊Q8×D4311yescharacteristic
1165C2#525×D4311yescharacteristic
1166C2#534×D4311yescharacteristic
1167C2#553×D4312yes—
1168C2#554×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2579C2
prime radicalC22×D4×D43C22
hypercenter#2579D43
hypocenterC43C2×#2579
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. #19139947C2semidirect
4. #19139946C2semidirect
5. #19139945C2semidirect
6. #19139944C2semidirect
7. #19139943C2semidirect
8. #19139942C2semidirect
9. #19139941C2semidirect
10. #19139940C2semidirect
11. #19139939C2semidirect
12. #19139938C2semidirect
13. #19139937C2semidirect
14. #398×D43C2semidirect
15. #396×D43C2semidirect
16. #387×D43C2semidirect
19. #385×D43C2semidirect
20. #385×D43C2semidirect
21. #385×D43C2semidirect
22. #380×D43C2semidirect
23. C43×#2579C2semidirect
37. C22×C4⋊Dic43C22semidirect
38. C22×Dic43⋊C4C22semidirect
39. C22×Dic43⋊C4C22semidirect
47. C2×C4⋊C4×D43C22semidirect
48. C2×C4⋊C4×D43C22semidirect
56. #14582833C22semidirect
57. #14582833C22semidirect
58. #14582832C22semidirect
59. #14582832C22semidirect
60. #14582831C22semidirect
61. #14582830C22semidirect
62. #14582829C22semidirect
63. #14582823C22semidirect
64. #14582822C22semidirect
65. #14582822C22semidirect
66. #14582822C22semidirect
67. #14582821C22semidirect
68. #14582821C22semidirect
69. #14582821C22semidirect
70. #14582786C22semidirect
71. #14582785C22semidirect
72. #14582784C22semidirect
73. #14582783C22semidirect
74. #14582782C22semidirect
75. #14582781C22semidirect
76. #14582780C22semidirect
87. #14582774C22semidirect
88. #14582774C22semidirect
89. #14582774C22semidirect
90. #14582773C22semidirect
91. #14582773C22semidirect
92. #14582773C22semidirect
93. #14582773C22semidirect
94. #14582772C22semidirect
95. #14582772C22semidirect
96. #14582772C22semidirect
97. #14582771C22semidirect
98. #14582771C22semidirect
99. #14582771C22semidirect
100. #14582770C22semidirect
101. #14582770C22semidirect
102. #14582770C22semidirect
103. #14582770C22semidirect
104. #14582759C22semidirect
105. #14582758C22semidirect
106. #14582757C22semidirect
107. #14582757C22semidirect
108. #14582756C22semidirect
115. C22×C4⋊C4×C43C22semidirect
116. C43×#398C22semidirect
117. C43×#396C22semidirect
118. C43×#387C22semidirect
121. C43×#385C22semidirect
122. C43×#385C22semidirect
123. C43×#385C22semidirect
124. C43×#380C22semidirect
588. #2579D43direct (N × H)
607. D43#2579direct (N × H)
634. C22×C4⋊C4C2×D43semidirect
649. #398C2×D43semidirect
657. #396C2×D43semidirect
665. #387C2×D43semidirect
695. #385C2×D43semidirect
696. #385C2×D43semidirect
697. #385C2×D43semidirect
703. #380C2×D43semidirect
709. C43C2×#2579semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C22×C4⋊C4×D432
#191399472
#191399462
#191399452
#191399442
#191399432
#191399422
#191399412
#191399402
#191399392
#191399382
#191399372
#398×D432
#396×D432
#387×D432
#386×D432
#385×D432
#380×D432
C43×#25792
C2×#257943