Finite Group Databasebeta

← D43×#2603 #25267233

Subgroups — D43×#2603 #25267233

Order 11008.

3330 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×#126×D43C211yesmaximal, characteristic, complemented
2C2×C4×D4×D43C211yesmaximal, characteristic, complemented
3#19140225C211yesmaximal, characteristic, complemented
4#19140224C211yesmaximal, characteristic, complemented
5#19140223C211yesmaximal, characteristic, complemented
6#19140222C211yesmaximal, characteristic, complemented
7#19140221C212yesmaximal, complemented
8#19140220C212yesmaximal, complemented
9#19140219C212yesmaximal, complemented
10#19140218C212yesmaximal, complemented
11#19140217C211yesmaximal, characteristic, complemented
12#19140216C211yesmaximal, characteristic, complemented
13#19140215C211yesmaximal, characteristic, complemented
14#398×D43C211yesmaximal, characteristic, complemented
15#397×D43C211yesmaximal, characteristic, complemented
16#394×D43C211yesmaximal, characteristic, complemented
17#392×D43C211yesmaximal, characteristic
18#390×D43C212yesmaximal, complemented
19#388×D43C212yesmaximal, complemented
20#386×D43C212yesmaximal, complemented
21#385×D43C212yesmaximal, complemented
22#376×D43C211yesmaximal, characteristic, complemented
23C43×#2603C211yesmaximal, characteristic, complemented
24C22×D4×D43C2211yescharacteristic
25C22×D4×D43C2212yes—
26C23×C4×D43C2212yes—
27C2×#13063320C2211yescharacteristic, complemented
28C2×#13063320C2211yescharacteristic, complemented
29C2×#13063320C2211yescharacteristic, complemented
30C2×#13063319C2211yescharacteristic, complemented
31C2×#13063318C2211yescharacteristic, complemented
32C2×#13063318C2211yescharacteristic, complemented
33C2×#13063318C2211yescharacteristic, complemented
34#126×D43—28no—
35C2×C4×D172C2211yescharacteristic, complemented
36C2×D4×Dic43C2211yescharacteristic, complemented
37C2×#13063287C2211yescharacteristic, complemented
38C2×C4×C22⋊D43C2212yescomplemented
39C2×(C22⋊D43)⋊C4C2212yescomplemented
40C4×D4×D43—28no—
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic
45C2×C4⋊C4×D43C2212yes—
46C2×C22⋊C4×D43C2212yes—
47C2×C22⋊C4×D43C2211yescharacteristic
48C2×C22⋊C4×D43C2212yes—
49C2×C22⋊C4×D43C2211yescharacteristic
50C2×C22⋊C4×D43C2211yescharacteristic
51C2×C22⋊C4×D43C2212yes—
52C2×C22⋊C4×D43C2212yes—
53C2×C22⋊C4×D43C2212yes—
54C2×C42×D43C2212yes—
55C2×C42×D43C2211yescharacteristic
56#14582833C2212yescomplemented
57#14582832C2212yescomplemented
58#14582831C2211yescharacteristic, complemented
59#14582830C2211yescharacteristic, complemented
60#14582829C2211yescharacteristic, complemented
61#14582828C2212yescomplemented
62#14582827C2212yescomplemented
63#14582826C2211yescharacteristic, complemented
64#14582825C2211yescharacteristic, complemented
65#14582824C2211yescharacteristic, complemented
66#14582817C2211yescharacteristic, complemented
67#14582816C2211yescharacteristic, complemented
68#14582815C2212yescomplemented
69#14582814C2212yescomplemented
70#14582813C2211yescharacteristic, complemented
71#14582809C2211yescharacteristic
72#14582808C2212yes—
73#14582808C2211yescharacteristic
74#14582807C2211yescharacteristic
75#14582807C2212yes—
76#14582802C2212yescomplemented
77#14582801C2212yescomplemented
78#14582800C2212yescomplemented
79#14582799C2212yescomplemented
80#14582799C2212yescomplemented
81#14582799C2212yescomplemented
82#14582799C2212yescomplemented
83#14582793C2212yescomplemented
84#14582792C2212yescomplemented
85#14582791C2212yescomplemented
86#14582790C2212yescomplemented
87#14582789C2212yescomplemented
88#14582788C2212yescomplemented
89#14582787C2212yescomplemented
90#14582779C2212yescomplemented
91#14582778C2212yescomplemented
92#14582777C2212yescomplemented
93#14582777C2212yescomplemented
94#14582776C2212yescomplemented
95#14582775C2212yescomplemented
96#14582775C2212yescomplemented
97#14582774C2212yescomplemented
98#14582773C2212yescomplemented
99#14582773C2212yescomplemented
100#14582772C2212yescomplemented
101#14582771C2212yescomplemented
102#14582770C2212yescomplemented
103#14582770C2212yescomplemented
104#14582745C2211yescharacteristic, complemented
105#14582745C2212yescomplemented
106#14582744C2211yescharacteristic, complemented
107#14582744C2211yescharacteristic, complemented
108#14582744C2212yescomplemented
109#95×D43C2211yescharacteristic
110#95×D43C2212yes—
111#95×D43C2211yescharacteristic
112#95×D43C2212yes—
113#95×D43C2212yes—
114C2×#126×C43C2211yescharacteristic, complemented
115C2×C4×D4×C43C2211yescharacteristic, complemented
116C43×#398C2211yescharacteristic, complemented
117C43×#397C2211yescharacteristic, complemented
118C43×#394C2211yescharacteristic, complemented
119C43×#392C2211yescharacteristic
120C43×#390C2212yescomplemented
121C43×#388C2212yescomplemented
122C43×#386C2212yescomplemented
123C43×#385C2212yescomplemented
124C43×#376C2211yescharacteristic, complemented
125C24×D43C2311yescharacteristic
126C24×D43C2312yes—
127C22×D172C2311yescharacteristic
128C22×D172C2312yes—
129C22×C22⋊D43C2312yes—
130C22×C22⋊D43C2312yes—
131C22×C22⋊D43C2312yes—
132C2×D4×D43—28no—
133C2×D4×D43—28no—
134C2×D4×D43—24no—
135C2×D4×D43—28no—
136C2×D4×D43—44no—
137C23×Dic43C2312yes—
138C22×C4×D43—28no—
139C22×C4×D43—44no—
140C22×C4×D43—44no—
141C22×C4×D43C2312yes—
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144C22×C4×D43C2311yescharacteristic
145C22×C4×D43C2312yes—
146C22×C4×D43C2311yescharacteristic
147C22×C4×D43C2311yescharacteristic
148C22×C4×D43C2311yescharacteristic
149C22×C4×D43C2312yes—
150C22×C4×D43C2312yes—
151C22×C4×D43C2312yes—
152#13063320—24no—
153#13063320—24no—
154#13063320—24no—
155#13063319—24no—
156#13063318—24no—
157#13063318—24no—
158#13063318—24no—
159C4×D172—24no—
160D4×Dic43—24no—
161#13063287—24no—
162C4×C22⋊D43—28no—
163(C22⋊D43)⋊C4—28no—
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2311yescharacteristic
166C2×C4⋊Dic43C2311yescharacteristic
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2312yes—
169C2×Dic43⋊C4C2311yescharacteristic
170C2×Dic43⋊C4C2311yescharacteristic
171C2×Dic43⋊C4C2311yescharacteristic
172C2×Dic43⋊C4C2311yescharacteristic
173C2×Dic43⋊C4C2312yes—
174C2×Dic43⋊C4C2311yescharacteristic
175C2×Dic43⋊C4C2311yescharacteristic
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2312yes—
178C4⋊C4×D43—24no—
179C4⋊C4×D43—24no—
180C4⋊C4×D43—24no—
181C4⋊C4×D43—24no—
182C4⋊C4×D43—44no—
183C2×C22⋊Dic43C2312yes—
184C2×C22⋊Dic43C2312yes—
185C2×C22⋊Dic43C2312yes—
186C2×C22⋊Dic43C2311yescharacteristic
187C2×C22⋊Dic43C2311yescharacteristic
188C2×C22⋊Dic43C2311yescharacteristic
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2311yescharacteristic
198C2×(C2×D43)⋊C4C2311yescharacteristic
199C2×(C2×D43)⋊C4C2311yescharacteristic
200C2×(C2×D43)⋊C4C2311yescharacteristic
201C2×(C2×D43)⋊C4C2311yescharacteristic
202C2×(C2×D43)⋊C4C2311yescharacteristic
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2312yes—
207C22⋊C4×D43—28no—
208C22⋊C4×D43—28no—
209C22⋊C4×D43—24no—
210C22⋊C4×D43—24no—
211C22⋊C4×D43—24no—
212C22⋊C4×D43—28no—
213C22⋊C4×D43—44no—
214C22⋊C4×D43—44no—
215C2×C4×Dic43C2312yes—
216C2×C4×Dic43C2312yes—
217C2×C4×Dic43C2312yes—
218C2×C4×Dic43C2311yescharacteristic
219C2×C4×Dic43C2311yescharacteristic
220C2×C4×Dic43C2311yescharacteristic
221C42×D43—28no—
222C42×D43D418yescomplemented
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2312yes—
226C43⋊#95C2312yes—
227C43⋊#95C2312yes—
228C43⋊#95C2312yes—
229C43⋊#95C2311yescharacteristic
230C43⋊#95C2312yes—
231C43⋊#95C2311yescharacteristic
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C43⋊#95C2312yes—
236C22×D4×C43C2311yescharacteristic
237C22×D4×C43C2312yes—
238C23×C4×C43C2312yes—
239#126×C43—24no—
240C4×D4×C43—24no—
241C2×C4⋊C4×C43C2311yescharacteristic
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2312yes—
246C2×C22⋊C4×C43C2312yes—
247C2×C22⋊C4×C43C2312yes—
248C2×C22⋊C4×C43C2312yes—
249C2×C22⋊C4×C43C2311yescharacteristic
250C2×C22⋊C4×C43C2311yescharacteristic
251C2×C22⋊C4×C43C2311yescharacteristic
252C2×C22⋊C4×C43C2312yes—
253C2×C22⋊C4×C43C2312yes—
254C2×C42×C43C2312yes—
255C2×C42×C43C2311yescharacteristic
256#95×C43C2312yes—
257#95×C43C2312yes—
258#95×C43C2311yescharacteristic
259#95×C43C2311yescharacteristic
260#95×C43C2312yes—
261C24×C43C2411yescharacteristic
262C24×C43C2412yes—
263C23×D43—24no—
264C23×D43—24no—
265C23×D43—24no—
266C23×D43—24no—
267C23×D43—24no—
268C23×D43—24no—
269C23×D43—22no—
270C23×D43—24no—
271C23×D43—24no—
272C23×D43—22no—
273C23×D43—22no—
274C23×D43#4118yes—
275C23×D43C2411yescharacteristic
276C23×D43C2412yes—
277C23×D43C2411yescharacteristic
278C2×D4×C43—22no—
279C2×D4×C43—24no—
280C2×D4×C43—24no—
281C2×D4×C43—24no—
282C2×D4×C43—42no—
283C22×C4×C43—24no—
284C22×C4×C43—42no—
285C22×C4×C43—42no—
286C22×C4×C43C2412yes—
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2412yes—
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2412yes—
295C2×C22⋊D43—24no—
296C2×C22⋊D43—24no—
297C2×C22⋊D43—24no—
298C2×C22⋊D43—24no—
299C2×C22⋊D43—24no—
300C2×C22⋊D43—24no—
301C2×C22⋊D43—24no—
302C2×C22⋊D43—42no—
303C2×C22⋊D43—42no—
304C22×Dic43—24no—
305C22×Dic43—42no—
306C22×Dic43—42no—
307C22×Dic43C2412yes—
308C22×Dic43C2411yescharacteristic
309C22×Dic43C2411yescharacteristic
310C22×Dic43C2412yes—
311C22×Dic43C2411yescharacteristic
312C22×Dic43C2411yescharacteristic
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2412yes—
316D4×D43—232no—
317D4×D43—432no—
318C2×D172—22no—
319C2×D172—24no—
320C2×D172—24no—
321C2×D172—24no—
322C2×D172—42no—
323C2×C4×D43—24no—
324C2×C4×D43—24no—
325C2×C4×D43—22no—
326C2×C4×D43—22no—
327C2×C4×D43—22no—
328C2×C4×D43—24no—
329C2×C4×D43—24no—
330C2×C4×D43—24no—
331C2×C4×D43—24no—
332C2×C4×D43—24no—
333C2×C4×D43—24no—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—24no—
337C2×C4×D43—22no—
338C2×C4×D43—22no—
339C2×C4×D43—22no—
340C2×C4×D43—24no—
341C2×C4×D43—24no—
342C2×C4×D43—22no—
343C2×C4×D43—24no—
344C2×C4×D43—42no—
345C2×C4×D43—42no—
346C2×C4×D43—42no—
347C2×C4×D43—42no—
348C2×C4×D43—432no—
349C2×C4×D43C2×D414yes—
350C2×C4×D43C2×D414yes—
351C2×C4×D43C2×D414yes—
352C2×C4×D43#4118yes—
353C4⋊C4×C43—22no—
354C4⋊C4×C43—22no—
355C4⋊C4×C43—22no—
356C4⋊C4×C43—22no—
357C4⋊C4×C43—42no—
358C22⋊C4×C43—24no—
359C22⋊C4×C43—22no—
360C22⋊C4×C43—22no—
361C22⋊C4×C43—22no—
362C22⋊C4×C43—24no—
363C22⋊C4×C43—24no—
364C22⋊C4×C43—42no—
365C22⋊C4×C43—42no—
366C42×C43—24no—
367C42×C43C2×D414yescomplemented
368C22⋊Dic43—24no—
369C22⋊Dic43—22no—
370C22⋊Dic43—22no—
371C22⋊Dic43—22no—
372C22⋊Dic43—24no—
373C22⋊Dic43—24no—
374C22⋊Dic43—42no—
375C22⋊Dic43—42no—
376(C2×D43)⋊C4—24no—
377(C2×D43)⋊C4—22no—
378(C2×D43)⋊C4—22no—
379(C2×D43)⋊C4—22no—
380(C2×D43)⋊C4—24no—
381(C2×D43)⋊C4—24no—
382(C2×D43)⋊C4—22no—
383(C2×D43)⋊C4—22no—
384(C2×D43)⋊C4—22no—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—24no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—42no—
389(C2×D43)⋊C4—42no—
390(C2×D43)⋊C4—42no—
391(C2×D43)⋊C4—42no—
392C4⋊Dic43—22no—
393C4⋊Dic43—22no—
394C4⋊Dic43—22no—
395C4⋊Dic43—22no—
396C4⋊Dic43—42no—
397Dic43⋊C4—22no—
398Dic43⋊C4—22no—
399Dic43⋊C4—22no—
400Dic43⋊C4—24no—
401Dic43⋊C4—22no—
402Dic43⋊C4—22no—
403Dic43⋊C4—22no—
404Dic43⋊C4—42no—
405Dic43⋊C4—42no—
406C4×Dic43—24no—
407C4×Dic43—24no—
408C4×Dic43—24no—
409C4×Dic43C2×D414yescomplemented
410C4×Dic43C2×D414yescomplemented
411C4×Dic43C2×D414yescomplemented
412C23×C43—22no—
413C23×C43—22no—
414C23×C43—22no—
415C23×C43—22no—
416C23×C43—22no—
417C23×C43—22no—
418C23×C43—21no—
419C23×C43—22no—
420C23×C43—22no—
421C23×C43—21no—
422C23×C43—21no—
423C23×C43C2×#4114yes—
424C23×C43C2511yescharacteristic
425C22×D43—22no—
426C22×D43—22no—
427C22×D43—22no—
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—216no—
432C22×D43—216no—
433C22×D43—216no—
434C22×D43—21no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—21no—
438C22×D43—21no—
439C22×D43—48no—
440C22×D43—48no—
441C22×D43—48no—
442C22×D43—48no—
443C22×D43—44no—
444C22×D43—44no—
445C22×D43—44no—
446C22×D43—48no—
447C22×D43—48no—
448C22×D43C22×D412yes—
449C22×D43C2×#4114yes—
450C22×D43C2×#4114yes—
451C22×D43C2×#4114yes—
452C22×D43H(5,𝔽2)12yes—
453C22×D43H(5,𝔽2)12yes—
454D4×C43—28no—
455D4×C43—48no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—21no—
461C2×C4×C43—21no—
462C2×C4×C43—21no—
463C2×C4×C43—21no—
464C2×C4×C43—21no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—22no—
470C2×C4×C43—21no—
471C2×C4×C43—22no—
472C2×C4×C43—21no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—48no—
476C2×C4×C43C22×D412yes—
477C2×C4×C43C22×D412yes—
478C2×C4×C43C22×D412yes—
479C2×C4×C43C2×#4114yes—
480C22⋊D43—216no—
481C22⋊D43—48no—
482C22⋊D43—48no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—21no—
488C2×Dic43—21no—
489C2×Dic43—21no—
490C2×Dic43—21no—
491C2×Dic43—21no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—22no—
497C2×Dic43—21no—
498C2×Dic43—22no—
499C2×Dic43—21no—
500C2×Dic43—22no—
501C2×Dic43—22no—
502C2×Dic43—48no—
503C2×Dic43C22×D412yes—
504C2×Dic43C22×D412yes—
505C2×Dic43C22×D412yes—
506C2×Dic43C2×#4114yes—
507D172—28no—
508D172—48no—
509C4×D43—28no—
510C4×D43—28no—
511C4×D43—28no—
512C4×D43—216no—
513C4×D43—48no—
514C4×D43—48no—
515C4×D43—44no—
516C4×D43—44no—
517C4×D43—44no—
518C4×D43—48no—
519C4×D43—48no—
520C2×#2603—431nomaximal, Sylow
521C22×C43—24no—
522C22×C43—24no—
523C22×C43—24no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—41no—
529C22×C43—41no—
530C22×C43—41no—
531C22×C43—42no—
532C22×C43—42no—
533C22×C43C23×D411yescharacteristic
534C22×C43C22×#4112yes—
535C22×C43C22×#4112yes—
536C22×C43C2×H(5,𝔽2)11yescharacteristic
537C22×C43C2×H(5,𝔽2)11yescharacteristic
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—24no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—432no—
546C2×D43—41no—
547C2×D43—41no—
548C2×D43—41no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—88no—
552C2×D43#52514yes—
553C2×D43#53214yes—
554C2×D43#53514yes—
555C2×D43#55118yes—
556C2×D43#55318yes—
557C4×C43—22no—
558C4×C43—22no—
559C4×C43—22no—
560C4×C43—24no—
561C4×C43—41no—
562C4×C43—41no—
563C4×C43—42no—
564C4×C43—41no—
565C4×C43—42no—
566Dic43—22no—
567Dic43—22no—
568Dic43—22no—
569Dic43—24no—
570Dic43—41no—
571Dic43—41no—
572Dic43—42no—
573Dic43—41no—
574Dic43—42no—
575C22×#126—431no—
576C22×C4×D4—431no—
577#2603—431no—
578#2603—431no—
579#2603—431no—
580#2603—431no—
581#2603—432no—
582#2603—432no—
583#2603—432no—
584#2603—432no—
585#2603—431no—
586#2603—431no—
587#2603—431no—
588#2603D4311yescharacteristic, direct product factor
589C2×#398—431no—
590C2×#397—431no—
591C2×#394—431no—
592C2×#392—431no—
593C2×#390—432no—
594C2×#388—432no—
595C2×#386—432no—
596C2×#385—432no—
597C2×#376—431no—
598C2×C43—44no—
599C2×C43—81no—
600C2×C43C2×#52511yescharacteristic
601C2×C43C2×#53211yescharacteristic
602C2×C43C2×#53511yescharacteristic
603C2×C43C2×#55112yes—
604C2×C43C2×#55312yes—
605D43—44no—
606D43—81no—
607D43#260318yesdirect product factor
608C23×D4—431no—
609C23×D4—432no—
610C24×C4—432no—
611C2×#126—431no—
612C2×#126—431no—
613C2×#126—431no—
614C2×#126—431no—
615C2×#126—431no—
616C2×#126—431no—
617C2×#126—431no—
618C2×#126—868no—
619C2×#126C2×D4311yescharacteristic, complemented
620C2×C4×D4—431no—
621C2×C4×D4—432no—
622C2×C4×D4—431no—
623C2×C4×D4—432no—
624C2×C4×D4—431no—
625C2×C4×D4—868no—
626C2×C4×D4C2×D4311yescharacteristic, complemented
627C22×C4⋊C4—431no—
628C22×C4⋊C4—431no—
629C22×C4⋊C4—431no—
630C22×C4⋊C4—431no—
631C22×C4⋊C4—432no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4—432no—
634C22×C22⋊C4—432no—
635C22×C22⋊C4—432no—
636C22×C22⋊C4—431no—
637C22×C22⋊C4—431no—
638C22×C22⋊C4—432no—
639C22×C22⋊C4—432no—
640C22×C42—431no—
641C22×C42—432no—
642#398—431no—
643#398—431no—
644#398—432no—
645#398—431no—
646#398—432no—
647#398C2×D4311yescharacteristic, complemented
648#397—431no—
649#397—431no—
650#397—432no—
651#397—431no—
652#397—432no—
653#397C2×D4311yescharacteristic, complemented
654#394—431no—
655#394—431no—
656#394—432no—
657#394—432no—
658#394—431no—
659#394C2×D4311yescharacteristic, complemented
660#392—432no—
661#392—431no—
662#392—432no—
663#392—431no—
664#392—431no—
665#392C2×D4311yescharacteristic
666#390—432no—
667#390—432no—
668#390—432no—
669#390—432no—
670#390—432no—
671#390—432no—
672#390—432no—
673#390C2×D4312yescomplemented
674#388—432no—
675#388—432no—
676#388—432no—
677#388—432no—
678#388—432no—
679#388—432no—
680#388—432no—
681#388C2×D4312yescomplemented
682#386—432no—
683#386—432no—
684#386—432no—
685#386—432no—
686#386—432no—
687#386—432no—
688#386—432no—
689#386C2×D4312yescomplemented
690#385—432no—
691#385—432no—
692#385—432no—
693#385—432no—
694#385—432no—
695#385—432no—
696#385—432no—
697#385C2×D4312yescomplemented
698#376—432no—
699#376—431no—
700#376—431no—
701#376—431no—
702#376—432no—
703#376C2×D4311yescharacteristic, complemented
704C2×#95—431no—
705C2×#95—431no—
706C2×#95—432no—
707C2×#95—432no—
708C2×#95—432no—
709C43C2×#260311yescharacteristic, complemented, Sylow
710C25—432no—
711C25—431no—
712C22×D4—432no—
713C22×D4—432no—
714C22×D4—432no—
715C22×D4—431no—
716C22×D4—432no—
717C22×D4—864no—
718C22×D4—868no—
719C22×D4—868no—
720C22×D4—868no—
721C22×D4—1724no—
722C22×D4C22×D4311yescharacteristic
723C22×D4C22×D4312yes—
724C23×C4—431no—
725C23×C4—431no—
726C23×C4—431no—
727C23×C4—432no—
728C23×C4—432no—
729C23×C4—431no—
730C23×C4—431no—
731C23×C4—431no—
732C23×C4—432no—
733C23×C4—432no—
734C23×C4—432no—
735C23×C4—432no—
736C23×C4—868no—
737C23×C4—1724no—
738C23×C4—1724no—
739C23×C4C22×D4312yes—
740#126—24no—
741#126—864no—
742#126—864no—
743#126—864no—
744#126—864no—
745#126—864no—
746#126—864no—
747#126—864no—
748C4×D4—24no—
749C4×D4—868no—
750C4×D4—864no—
751C4×D4—868no—
752C4×D4—864no—
753C4×D4—864no—
754C2×C4⋊C4—432no—
755C2×C4⋊C4—431no—
756C2×C4⋊C4—431no—
757C2×C4⋊C4—431no—
758C2×C4⋊C4—431no—
759C2×C4⋊C4—431no—
760C2×C4⋊C4—431no—
761C2×C4⋊C4—431no—
762C2×C4⋊C4—431no—
763C2×C4⋊C4—431no—
764C2×C4⋊C4—431no—
765C2×C4⋊C4—432no—
766C2×C4⋊C4—432no—
767C2×C4⋊C4—432no—
768C2×C4⋊C4—864no—
769C2×C4⋊C4—864no—
770C2×C4⋊C4—864no—
771C2×C4⋊C4—864no—
772C2×C4⋊C4—1724no—
773C2×C4⋊C4C22×D4311yescharacteristic
774C2×C4⋊C4C22×D4311yescharacteristic
775C2×C4⋊C4C22×D4311yescharacteristic
776C2×C4⋊C4C22×D4311yescharacteristic
777C2×C4⋊C4C22×D4312yes—
778C2×C22⋊C4—432no—
779C2×C22⋊C4—431no—
780C2×C22⋊C4—431no—
781C2×C22⋊C4—431no—
782C2×C22⋊C4—432no—
783C2×C22⋊C4—432no—
784C2×C22⋊C4—432no—
785C2×C22⋊C4—432no—
786C2×C22⋊C4—431no—
787C2×C22⋊C4—431no—
788C2×C22⋊C4—431no—
789C2×C22⋊C4—431no—
790C2×C22⋊C4—431no—
791C2×C22⋊C4—431no—
792C2×C22⋊C4—432no—
793C2×C22⋊C4—432no—
794C2×C22⋊C4—432no—
795C2×C22⋊C4—432no—
796C2×C22⋊C4—432no—
797C2×C22⋊C4—432no—
798C2×C22⋊C4—432no—
799C2×C22⋊C4—432no—
800C2×C22⋊C4—432no—
801C2×C22⋊C4—432no—
802C2×C22⋊C4—868no—
803C2×C22⋊C4—864no—
804C2×C22⋊C4—864no—
805C2×C22⋊C4—864no—
806C2×C22⋊C4—868no—
807C2×C22⋊C4—868no—
808C2×C22⋊C4—1724no—
809C2×C22⋊C4—1724no—
810C2×C22⋊C4C22×D4312yes—
811C2×C22⋊C4C22×D4311yescharacteristic
812C2×C22⋊C4C22×D4311yescharacteristic
813C2×C22⋊C4C22×D4311yescharacteristic
814C2×C22⋊C4C22×D4312yes—
815C2×C22⋊C4C22×D4312yes—
816C2×C22⋊C4C22×D4312yes—
817C2×C22⋊C4C22×D4312yes—
818C2×C42—431no—
819C2×C42—431no—
820C2×C42—431no—
821C2×C42—438no—
822C2×C42—432no—
823C2×C42—432no—
824C2×C42—432no—
825C2×C42—868no—
826C2×C42C22×D4312yes—
827C2×C42C22×D4311yescharacteristic
828#95—432no—
829#95—432no—
830#95—432no—
831#95—431no—
832#95—432no—
833#95—432no—
834#95—431no—
835#95—432no—
836#95—432no—
837#95—432no—
838#95—432no—
839#95—432no—
840#95—432no—
841#95C22×D4312yes—
842#95C22×D4311yescharacteristic
843#95C22×D4311yescharacteristic
844#95C22×D4312yes—
845#95C22×D4312yes—
846C24—431no—
847C24—438no—
848C24—432no—
849C24—431no—
850C24—864no—
851C24—864no—
852C24—864no—
853C24—864no—
854C24—864no—
855C24—864no—
856C24—862no—
857C24—862no—
858C24—864no—
859C24—864no—
860C24—862no—
861C24C23×D4311yescharacteristic
862C24C23×D4312yes—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—24no—
867C2×D4—42no—
868C2×D4—864no—
869C2×D4—864no—
870C2×D4—864no—
871C2×D4—864no—
872C2×D4—864no—
873C2×D4—8632no—
874C2×D4—864no—
875C2×D4—864no—
876C2×D4—864no—
877C2×D4—864no—
878C2×D4—862no—
879C2×D4—864no—
880C2×D4—1722no—
881C2×D4—17232no—
882C2×D4—1722no—
883C2×D4—1722no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—432no—
888C22×C4—431no—
889C22×C4—431no—
890C22×C4—431no—
891C22×C4—434no—
892C22×C4—434no—
893C22×C4—434no—
894C22×C4—438no—
895C22×C4—432no—
896C22×C4—431no—
897C22×C4—431no—
898C22×C4—432no—
899C22×C4—431no—
900C22×C4—864no—
901C22×C4—864no—
902C22×C4—864no—
903C22×C4—862no—
904C22×C4—862no—
905C22×C4—864no—
906C22×C4—864no—
907C22×C4—864no—
908C22×C4—862no—
909C22×C4—862no—
910C22×C4—862no—
911C22×C4—864no—
912C22×C4—864no—
913C22×C4—864no—
914C22×C4—864no—
915C22×C4—862no—
916C22×C4—864no—
917C22×C4—864no—
918C22×C4—862no—
919C22×C4—864no—
920C22×C4—864no—
921C22×C4—864no—
922C22×C4—1722no—
923C22×C4—1722no—
924C22×C4—1722no—
925C22×C4—1722no—
926C22×C4—17232no—
927C22×C4—1722no—
928C22×C4—1722no—
929C22×C4C23×D4312yes—
930C22×C4C23×D4311yescharacteristic
931C22×C4C23×D4311yescharacteristic
932C22×C4C23×D4312yes—
933C22×C4C23×D4311yescharacteristic
934C22×C4C23×D4311yescharacteristic
935C22×C4C23×D4311yescharacteristic
936C22×C4C23×D4311yescharacteristic
937C22×C4C23×D4312yes—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—864no—
944C4⋊C4—862no—
945C4⋊C4—862no—
946C4⋊C4—862no—
947C4⋊C4—862no—
948C4⋊C4—862no—
949C4⋊C4—862no—
950C4⋊C4—862no—
951C4⋊C4—862no—
952C4⋊C4—862no—
953C4⋊C4—862no—
954C4⋊C4—1722no—
955C4⋊C4—1722no—
956C4⋊C4—1722no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—24no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—864no—
966C22⋊C4—862no—
967C22⋊C4—862no—
968C22⋊C4—862no—
969C22⋊C4—864no—
970C22⋊C4—864no—
971C22⋊C4—864no—
972C22⋊C4—864no—
973C22⋊C4—862no—
974C22⋊C4—862no—
975C22⋊C4—862no—
976C22⋊C4—864no—
977C22⋊C4—864no—
978C22⋊C4—864no—
979C22⋊C4—862no—
980C22⋊C4—862no—
981C22⋊C4—862no—
982C22⋊C4—864no—
983C22⋊C4—1722no—
984C22⋊C4—1722no—
985C22⋊C4—1722no—
986C22⋊C4—1722no—
987C22⋊C4—1722no—
988C22⋊C4—1722no—
989C42—24no—
990C42—434no—
991C42—434no—
992C42—434no—
993C42—864no—
994C42—864no—
995C42—864no—
996C42D4×D4314yescomplemented
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—21no—
1008C23—432no—
1009C23—434no—
1010C23—434no—
1011C23—432no—
1012C23—432no—
1013C23—434no—
1014C23—8616no—
1015C23—8616no—
1016C23—8616no—
1017C23—862no—
1018C23—862no—
1019C23—862no—
1020C23—862no—
1021C23—862no—
1022C23—862no—
1023C23—861no—
1024C23—862no—
1025C23—862no—
1026C23—861no—
1027C23—861no—
1028C23—1728no—
1029C23—1724no—
1030C23—1728no—
1031C23—1724no—
1032C23—1724no—
1033C23—1728no—
1034C23—1728no—
1035C23—1728no—
1036C23—1728no—
1037C23#41×D4314yes—
1038C23C24×D4311yescharacteristic
1039D4—28no—
1040D4—48no—
1041D4—868no—
1042D4—8616no—
1043D4—1728no—
1044D4—1728no—
1045D4—1728no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—48no—
1066C2×C4—432no—
1067C2×C4—432no—
1068C2×C4—432no—
1069C2×C4—434no—
1070C2×C4—868no—
1071C2×C4—868no—
1072C2×C4—8616no—
1073C2×C4—868no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—861no—
1079C2×C4—861no—
1080C2×C4—861no—
1081C2×C4—861no—
1082C2×C4—861no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—861no—
1090C2×C4—862no—
1091C2×C4—861no—
1092C2×C4—862no—
1093C2×C4—1728no—
1094C2×C4—1728no—
1095C2×C4—1728no—
1096C2×C4—1724no—
1097C2×C4—1728no—
1098C2×C4—1724no—
1099C2×C4—1724no—
1100C2×C4—1728no—
1101C2×C4C2×D4×D4312yes—
1102C2×C4C2×D4×D4312yes—
1103C2×C4C2×D4×D4312yes—
1104C2×C4#41×D4314yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—42no—
1114C22—42no—
1115C22—41no—
1116C22—41no—
1117C22—434no—
1118C22—438no—
1119C22—438no—
1120C22—434no—
1121C22—434no—
1122C22—864no—
1123C22—864no—
1124C22—864no—
1125C22—3448no—
1126C22—17232no—
1127C22—1721no—
1128C22—1722no—
1129C22—1722no—
1130C22—1721no—
1131C22—1721no—
1132C22—1722no—
1133C22—1722no—
1134C22—1722no—
1135C22—1722no—
1136C22C22×D4×D4311yescharacteristic
1137C22C2×#41×D4312yes—
1138C22C2×#41×D4312yes—
1139C22H(5,𝔽2)×D4311yescharacteristic
1140C22H(5,𝔽2)×D4311yescharacteristic
1141C4—22no—
1142C4—24no—
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—42no—
1147C4—41no—
1148C4—42no—
1149C4—41no—
1150C4—862no—
1151C4—864no—
1152C4—862no—
1153C4—862no—
1154C4—1721no—
1155C4—1722no—
1156C4—1721no—
1157C4—1722no—
1158C4—1721no—
1159C2—44no—
1160C2—81no—
1161C2—438no—
1162C2—3441no—
1163C2—1724no—
1164C2#525×D4311yescharacteristic
1165C2#532×D4311yescharacteristic
1166C2#535×D4311yescharacteristic
1167C2#551×D4312yes—
1168C2#553×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2603C2
prime radical#392×D43C2
hypercenter#2603D43
hypocenterC43C2×#2603
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2603

Complements

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

NH ≅ G/Ntype
1. C2×#126×D43C2semidirect
2. C2×C4×D4×D43C2semidirect
3. #19140225C2semidirect
4. #19140224C2semidirect
5. #19140223C2semidirect
6. #19140222C2semidirect
7. #19140221C2semidirect
8. #19140220C2semidirect
9. #19140219C2semidirect
10. #19140218C2semidirect
11. #19140217C2semidirect
12. #19140216C2semidirect
13. #19140215C2semidirect
14. #398×D43C2semidirect
15. #397×D43C2semidirect
16. #394×D43C2semidirect
18. #390×D43C2semidirect
19. #388×D43C2semidirect
20. #386×D43C2semidirect
21. #385×D43C2semidirect
22. #376×D43C2semidirect
23. C43×#2603C2semidirect
27. C2×#13063320C22semidirect
28. C2×#13063320C22semidirect
29. C2×#13063320C22semidirect
30. C2×#13063319C22semidirect
31. C2×#13063318C22semidirect
32. C2×#13063318C22semidirect
33. C2×#13063318C22semidirect
35. C2×C4×D172C22semidirect
36. C2×D4×Dic43C22semidirect
37. C2×#13063287C22semidirect
38. C2×C4×C22⋊D43C22semidirect
39. C2×(C22⋊D43)⋊C4C22semidirect
56. #14582833C22semidirect
57. #14582832C22semidirect
58. #14582831C22semidirect
59. #14582830C22semidirect
60. #14582829C22semidirect
61. #14582828C22semidirect
62. #14582827C22semidirect
63. #14582826C22semidirect
64. #14582825C22semidirect
65. #14582824C22semidirect
66. #14582817C22semidirect
67. #14582816C22semidirect
68. #14582815C22semidirect
69. #14582814C22semidirect
70. #14582813C22semidirect
76. #14582802C22semidirect
77. #14582801C22semidirect
78. #14582800C22semidirect
79. #14582799C22semidirect
80. #14582799C22semidirect
81. #14582799C22semidirect
82. #14582799C22semidirect
83. #14582793C22semidirect
84. #14582792C22semidirect
85. #14582791C22semidirect
86. #14582790C22semidirect
87. #14582789C22semidirect
88. #14582788C22semidirect
89. #14582787C22semidirect
90. #14582779C22semidirect
91. #14582778C22semidirect
92. #14582777C22semidirect
93. #14582777C22semidirect
94. #14582776C22semidirect
95. #14582775C22semidirect
96. #14582775C22semidirect
97. #14582774C22semidirect
98. #14582773C22semidirect
99. #14582773C22semidirect
100. #14582772C22semidirect
101. #14582771C22semidirect
102. #14582770C22semidirect
103. #14582770C22semidirect
104. #14582745C22semidirect
105. #14582745C22semidirect
106. #14582744C22semidirect
107. #14582744C22semidirect
108. #14582744C22semidirect
114. C2×#126×C43C22semidirect
115. C2×C4×D4×C43C22semidirect
116. C43×#398C22semidirect
117. C43×#397C22semidirect
118. C43×#394C22semidirect
120. C43×#390C22semidirect
121. C43×#388C22semidirect
122. C43×#386C22semidirect
123. C43×#385C22semidirect
124. C43×#376C22semidirect
222. C42×D43D4semidirect
367. C42×C43C2×D4semidirect
409. C4×Dic43C2×D4semidirect
410. C4×Dic43C2×D4semidirect
411. C4×Dic43C2×D4semidirect
588. #2603D43direct (N × H)
607. D43#2603direct (N × H)
619. C2×#126C2×D43semidirect
626. C2×C4×D4C2×D43semidirect
647. #398C2×D43semidirect
653. #397C2×D43semidirect
659. #394C2×D43semidirect
673. #390C2×D43semidirect
681. #388C2×D43semidirect
689. #386C2×D43semidirect
697. #385C2×D43semidirect
703. #376C2×D43semidirect
709. C43C2×#2603semidirect
996. C42D4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D432
C2×C4×D4×D432
#191402252
#191402242
#191402232
#191402222
#191402212
#191402202
#191402192
#191402182
#191402172
#191402162
#191402152
#398×D432
#397×D432
#394×D432
#392×D432
#390×D432
#388×D432
#386×D432
#385×D432
#376×D432
C43×#26032
C2×#260343