Finite Group Databasebeta

← #25266452

Subgroups — #25266452

Order 11008.

2926 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3#19138910C211yesmaximal, characteristic, complemented
4#19138908C211yesmaximal, characteristic, complemented
5#19138901C211yesmaximal, characteristic, complemented
6#19138899C211yesmaximal, characteristic, complemented
7#19138893C211yesmaximal, characteristic, complemented
8#19138892C211yesmaximal, characteristic, complemented
9#19138886C211yesmaximal, characteristic, complemented
10#19138880C212yesmaximal, complemented
11#19138872C212yesmaximal, complemented
12#19138867C212yesmaximal, complemented
13#19137917C212yesmaximal
14#19137853C212yesmaximal, complemented
15#19137851C212yesmaximal, complemented
16#19137122C212yesmaximal, complemented
17#19137116C212yesmaximal, complemented
18#19137076C211yesmaximal, characteristic, complemented
19#19137076C211yesmaximal, characteristic, complemented
20#19136977C211yesmaximal, characteristic, complemented
21#19136977C211yesmaximal, characteristic, complemented
22#19136977C211yesmaximal, characteristic, complemented
23C43×#2485C211yesmaximal, characteristic, complemented
24C22×D4×D43C2211yescharacteristic
25C23×C4×D43C2211yescharacteristic
26C23×C4×D43C2211yescharacteristic
27C2×#13063310C2212yes—
28C2×#13063307C2212yes—
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—
37C2×#13063284C2211yescharacteristic, complemented
38C2×#13063283C2211yescharacteristic
39C2×#13063283C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C2×#13063282C2212yes—
43C2×#13063281C2212yescomplemented
44#117×D43—28no—
45C2×C4⋊C4×D43C2211yescharacteristic
46C2×C4⋊C4×D43C2211yescharacteristic, complemented
47C2×C4⋊C4×D43C2211yescharacteristic, complemented
48C2×C22⋊C4×D43C2211yescharacteristic
49C2×C22⋊C4×D43C2211yescharacteristic
50C2×C22⋊C4×D43C2212yes—
51C2×C42×D43C2211yescharacteristic
52C2×C42×D43C2212yescomplemented
53#14582841C2212yescomplemented
54#14582840C2212yescomplemented
55#14582835C2212yescomplemented
56#14582834C2212yescomplemented
57#14582833C2212yescomplemented
58#14582832C2212yescomplemented
59#14582828C2212yescomplemented
60#14582827C2212yescomplemented
61#14582827C2212yescomplemented
62#14582827C2212yescomplemented
63#14582824C2212yescomplemented
64#14582815C2212yes—
65#14582814C2212yes—
66#14582813C2212yes—
67#14582798C2211yescharacteristic, complemented
68#14582798C2211yescharacteristic, complemented
69#14582797C2211yescharacteristic, complemented
70#14582797C2211yescharacteristic, complemented
71#14582795C2211yescharacteristic, complemented
72#14582795C2211yescharacteristic, complemented
73#14582791C2212yescomplemented
74#14582790C2212yescomplemented
75#14582787C2212yescomplemented
76#14582784C2212yescomplemented
77#14582783C2212yescomplemented
78#14582780C2212yescomplemented
79#14582777C2212yes—
80#14582775C2212yes—
81#14582773C2212yes—
82#14582773C2212yes—
83#14582773C2212yescomplemented
84#14582770C2212yes—
85#14582770C2212yes—
86#14582770C2212yescomplemented
87#14582761C2212yes—
88#14582761C2212yes—
89#14582761C2212yes—
90#14582761C2212yescomplemented
91#14582761C2212yescomplemented
92#14582759C2211yescharacteristic, complemented
93#14582759C2211yescharacteristic, complemented
94#14582759C2211yescharacteristic, complemented
95#14582756C2211yescharacteristic, complemented
96#14582756C2211yescharacteristic, complemented
97#14582756C2211yescharacteristic, complemented
98#14582756C2211yescharacteristic, complemented
99#14582756C2211yescharacteristic, complemented
100#14582756C2211yescharacteristic, complemented
101#14582754C2212yes—
102#14582754C2212yes—
103#14582754C2212yes—
104C4⋊C4×Dic43C2212yescomplemented
105C4⋊C4×Dic43C2212yescomplemented
106#14582750C2212yescomplemented
107#14582750C2212yescomplemented
108C22⋊C4×Dic43C2212yescomplemented
109C22⋊C4×Dic43C2212yescomplemented
110C22⋊C4×Dic43C2212yescomplemented
111#14582746C2212yescomplemented
112#14582746C2212yescomplemented
113#14582746C2212yescomplemented
114C2×C4×D4×C43C2211yescharacteristic
115C2×#117×C43C2211yescharacteristic, complemented
116C43×#397C2212yescomplemented
117C43×#394C2212yes—
118C43×#389C2211yescharacteristic, complemented
119C43×#389C2211yescharacteristic, complemented
120C43×#388C2212yescomplemented
121C43×#387C2212yescomplemented
122C43×#380C2211yescharacteristic, complemented
123C43×#380C2211yescharacteristic, 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×D43—24no—
133C23×Dic43C2311yescharacteristic
134C23×Dic43C2311yescharacteristic
135C22×C4×D43—24no—
136C22×C4×D43—24no—
137C22×C4×D43—24no—
138C22×C4×D43—24no—
139C22×C4×D43—24no—
140C22×C4×D43D418yes—
141C22×C4×D43C2311yescharacteristic
142C22×C4×D43C2312yes—
143C22×C4×D43C2311yescharacteristic
144C22×C4×D43C2311yescharacteristic
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2311yescharacteristic
147C22×C4×D43C2311yescharacteristic
148C22×C4×D43C2311yescharacteristic
149C22×C4×D43C2311yescharacteristic
150C22×C4×D43C2312yes—
151C22×C4×D43C2311yescharacteristic
152#13063310—28no—
153#13063307—28no—
154C4×D172—24no—
155D4×Dic43—24no—
156#13063287—24no—
157C4×C22⋊D43—24no—
158C4×C22⋊D43—24no—
159(C22⋊D43)⋊C4—24no—
160(C22⋊D43)⋊C4—24no—
161#13063284—24no—
162#13063283—24no—
163#13063283—24no—
164#13063283—24no—
165#13063283—24no—
166#13063282—28no—
167#13063281—28no—
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C2311yescharacteristic
174C2×C4⋊Dic43C2312yes—
175C2×Dic43⋊C4C2311yescharacteristic
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2311yescharacteristic
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C4⋊C4×D43—24no—
184C4⋊C4×D43—24no—
185C4⋊C4×D43—24no—
186C2×C22⋊Dic43C2312yes—
187C2×C22⋊Dic43C2312yes—
188C2×C22⋊Dic43C2311yescharacteristic
189C2×C22⋊Dic43C2311yescharacteristic
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2312yes—
192C2×(C2×D43)⋊C4C2311yescharacteristic
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2311yescharacteristic
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2311yescharacteristic
199C2×(C2×D43)⋊C4C2311yescharacteristic
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C22⋊C4×D43—28no—
207C22⋊C4×D43—24no—
208C22⋊C4×D43—24no—
209C2×C4×Dic43C2312yes—
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C2×C4×Dic43C2312yes—
214C2×C4×Dic43C2312yes—
215C2×C4×Dic43C2312yes—
216C2×C4×Dic43C2312yes—
217C42×D43—24no—
218C42×D43—28no—
219C43⋊#95C2312yes—
220C43⋊#95C2312yes—
221C43⋊#95C2312yes—
222C43⋊#95C2312yes—
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2312yes—
226C43⋊#95C2312yes—
227C43⋊#95C2312yes—
228C43⋊#95C2312yes—
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C22×D4×C43C2311yescharacteristic
235C23×C4×C43C2311yescharacteristic
236C23×C4×C43C2311yescharacteristic
237C4×D4×C43—24no—
238#117×C43—24no—
239C2×C4⋊C4×C43C2311yescharacteristic
240C2×C4⋊C4×C43C2311yescharacteristic
241C2×C4⋊C4×C43C2311yescharacteristic
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2312yes—
245C2×C4⋊C4×C43C2312yes—
246C2×C22⋊C4×C43C2311yescharacteristic
247C2×C22⋊C4×C43C2312yes—
248C2×C22⋊C4×C43C2311yescharacteristic
249C2×C22⋊C4×C43C2312yes—
250C2×C22⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2312yes—
252C2×C42×C43C2312yes—
253C2×C42×C43C2311yescharacteristic
254#95×C43C2312yes—
255#95×C43C2312yes—
256#95×C43C2312yes—
257#95×C43C2312yes—
258#95×C43C2312yes—
259C24×C43C2411yescharacteristic
260C24×C43C2411yescharacteristic
261C23×D43—22no—
262C23×D43—22no—
263C23×D43—22no—
264C23×D43—22no—
265C23×D43—22no—
266C23×D43—22no—
267C23×D43—22no—
268C23×D43—22no—
269C23×D43—22no—
270C23×D43—41no—
271C23×D43—41no—
272C23×D43—41no—
273C23×D43—41no—
274C23×D43C2×D414yes—
275C23×D43C2411yescharacteristic
276C23×D43C2411yescharacteristic
277C23×D43C2411yescharacteristic
278C2×D4×C43—22no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C22×C4×C43—22no—
282C22×C4×C43—22no—
283C22×C4×C43—22no—
284C22×C4×C43—22no—
285C22×C4×C43—22no—
286C22×C4×C43C2×D414yes—
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2412yes—
289C22×C4×C43C2412yes—
290C22×C4×C43C2412yes—
291C22×C4×C43C2412yes—
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—22no—
301C2×C22⋊D43#4114yes—
302C22×Dic43—22no—
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—22no—
306C22×Dic43—22no—
307C22×Dic43C2×D414yes—
308C22×Dic43C2411yescharacteristic
309C22×Dic43C2412yes—
310C22×Dic43C2412yes—
311C22×Dic43C2412yes—
312C22×Dic43C2412yes—
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2411yescharacteristic
316C22×Dic43C2411yescharacteristic
317D4×D43—232no—
318C2×D172—22no—
319C2×D172—22no—
320C2×D172#4114yes—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—22no—
324C2×C4×D43—22no—
325C2×C4×D43—22no—
326C2×C4×D43—22no—
327C2×C4×D43—232no—
328C2×C4×D43—22no—
329C2×C4×D43—22no—
330C2×C4×D43—22no—
331C2×C4×D43—22no—
332C2×C4×D43—22no—
333C2×C4×D43—22no—
334C2×C4×D43—22no—
335C2×C4×D43—22no—
336C2×C4×D43—24no—
337C2×C4×D43—24no—
338C2×C4×D43—22no—
339C2×C4×D43—22no—
340C2×C4×D43—22no—
341C2×C4×D43—24no—
342C2×C4×D43—24no—
343C2×C4×D43—22no—
344C2×C4×D43—22no—
345C2×C4×D43—42no—
346C2×C4×D43—42no—
347C2×C4×D43—41no—
348C2×C4×D43—41no—
349C2×C4×D43—416no—
350C2×C4×D43C2×D414yes—
351C2×C4×D43C2×D414yes—
352C2×C4×D43C2×D414yes—
353C2×C4×D43C2×D414yes—
354C2×C4×D43#4114yes—
355C2×C4×D43#4114yes—
356C4⋊C4×C43—22no—
357C4⋊C4×C43—22no—
358C4⋊C4×C43—22no—
359C4⋊C4×C43—22no—
360C4⋊C4×C43—22no—
361C4⋊C4×C43—24no—
362C4⋊C4×C43—42no—
363C22⋊C4×C43—22no—
364C22⋊C4×C43—24no—
365C22⋊C4×C43—22no—
366C22⋊C4×C43—24no—
367C22⋊C4×C43—42no—
368C22⋊C4×C43—42no—
369C42×C43—24no—
370C42×C43—22no—
371C22⋊Dic43—22no—
372C22⋊Dic43—24no—
373C22⋊Dic43—22no—
374C22⋊Dic43—24no—
375C22⋊Dic43—42no—
376C22⋊Dic43—42no—
377(C2×D43)⋊C4—22no—
378(C2×D43)⋊C4—22no—
379(C2×D43)⋊C4—24no—
380(C2×D43)⋊C4—24no—
381(C2×D43)⋊C4—22no—
382(C2×D43)⋊C4—22no—
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—24no—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—24no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—24no—
389(C2×D43)⋊C4—42no—
390(C2×D43)⋊C4—42no—
391C4⋊Dic43—22no—
392C4⋊Dic43—22no—
393C4⋊Dic43—22no—
394C4⋊Dic43—22no—
395C4⋊Dic43—22no—
396C4⋊Dic43—24no—
397C4⋊Dic43—42no—
398Dic43⋊C4—22no—
399Dic43⋊C4—24no—
400Dic43⋊C4—24no—
401Dic43⋊C4—24no—
402Dic43⋊C4—22no—
403Dic43⋊C4—24no—
404Dic43⋊C4—42no—
405Dic43⋊C4—42no—
406C4×Dic43—24no—
407C4×Dic43—22no—
408C4×Dic43—24no—
409C4×Dic43—24no—
410C4×Dic43—22no—
411C4×Dic43—22no—
412C4×Dic43—24no—
413C4×Dic43—24no—
414C23×C43—21no—
415C23×C43—21no—
416C23×C43—21no—
417C23×C43—21no—
418C23×C43—21no—
419C23×C43—21no—
420C23×C43—21no—
421C23×C43—21no—
422C23×C43—21no—
423C23×C43—21no—
424C23×C43—21no—
425C23×C43—21no—
426C23×C43C22×D412yes—
427C23×C43C2×#4112yes—
428C23×C43C2511yescharacteristic
429C22×D43—21no—
430C22×D43—21no—
431C22×D43—21no—
432C22×D43—21no—
433C22×D43—21no—
434C22×D43—21no—
435C22×D43—21no—
436C22×D43—21no—
437C22×D43—28no—
438C22×D43—21no—
439C22×D43—21no—
440C22×D43—21no—
441C22×D43—21no—
442C22×D43—21no—
443C22×D43—21no—
444C22×D43—28no—
445C22×D43—28no—
446C22×D43—44no—
447C22×D43—44no—
448C22×D43—44no—
449C22×D43—44no—
450C22×D43—44no—
451C22×D43—44no—
452C22×D43—44no—
453C22×D43—44no—
454C22×D43—44no—
455C22×D43—44no—
456C22×D43—44no—
457C22×D43C22×D412yes—
458C22×D43C22×D412yes—
459C22×D43C2×#4112yes—
460C22×D43C2×#4112yes—
461C22×D43C2×#4112yes—
462C22×D43C2×#4112yes—
463C22×D43C2×#4112yes—
464D4×C43—28no—
465C2×C4×C43—21no—
466C2×C4×C43—21no—
467C2×C4×C43—21no—
468C2×C4×C43—21no—
469C2×C4×C43—28no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—21no—
473C2×C4×C43—21no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—22no—
477C2×C4×C43—22no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—21no—
481C2×C4×C43—21no—
482C2×C4×C43—21no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—21no—
488C2×C4×C43—44no—
489C2×C4×C43C22×D412yes—
490C2×C4×C43C22×D412yes—
491C2×C4×C43C2×#4112yes—
492C2×C4×C43C2×#4112yes—
493C2×C4×C43C2×#4112yes—
494C22⋊D43—28no—
495C22⋊D43—28no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—21no—
499C2×Dic43—21no—
500C2×Dic43—28no—
501C2×Dic43—22no—
502C2×Dic43—22no—
503C2×Dic43—21no—
504C2×Dic43—21no—
505C2×Dic43—22no—
506C2×Dic43—22no—
507C2×Dic43—22no—
508C2×Dic43—22no—
509C2×Dic43—22no—
510C2×Dic43—22no—
511C2×Dic43—21no—
512C2×Dic43—21no—
513C2×Dic43—21no—
514C2×Dic43—22no—
515C2×Dic43—22no—
516C2×Dic43—22no—
517C2×Dic43—21no—
518C2×Dic43—22no—
519C2×Dic43—44no—
520C2×Dic43C22×D412yes—
521C2×Dic43C22×D412yes—
522C2×Dic43C2×#4112yes—
523C2×Dic43C2×#4112yes—
524C2×Dic43C2×#4112yes—
525D172—28no—
526C4×D43—28no—
527C4×D43—28no—
528C4×D43—28no—
529C4×D43—28no—
530C4×D43—44no—
531C4×D43—48no—
532C4×D43—44no—
533C4×D43—48no—
534C4×D43—44no—
535C4×D43—44no—
536C4×D43#123116yescomplemented
537#34809—431nomaximal, Sylow
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—22no—
541C22×C43—22no—
542C22×C43—22no—
543C22×C43—22no—
544C22×C43—41no—
545C22×C43—41no—
546C22×C43—41no—
547C22×C43—41no—
548C22×C43—41no—
549C22×C43—41no—
550C22×C43—41no—
551C22×C43—41no—
552C22×C43C23×D411yescharacteristic
553C22×C43C22×#4111yescharacteristic
554C22×C43C22×#4111yescharacteristic
555C22×C43C22×#4111yescharacteristic
556C22×C43C22×#4111yescharacteristic
557C22×C43#58511yescharacteristic
558C22×C43#58511yescharacteristic
559C2×D43—22no—
560C2×D43—22no—
561C2×D43—22no—
562C2×D43—22no—
563C2×D43—22no—
564C2×D43—22no—
565C2×D43—22no—
566C2×D43—22no—
567C2×D43—22no—
568C2×D43—22no—
569C2×D43—22no—
570C2×D43—22no—
571C2×D43—22no—
572C2×D43—22no—
573C2×D43—22no—
574C2×D43—416no—
575C2×D43—416no—
576C2×D43—41no—
577C2×D43—41no—
578C2×D43—41no—
579C2×D43—41no—
580C2×D43C2×#12314yes—
581C2×D43#52514yes—
582C4×C43—22no—
583C4×C43—22no—
584C4×C43—41no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43—41no—
588C4×C43—42no—
589C4×C43—42no—
590C4×C43C2×#12314yes—
591Dic43—22no—
592Dic43—22no—
593Dic43—41no—
594Dic43—42no—
595Dic43—42no—
596Dic43—41no—
597Dic43—42no—
598Dic43—42no—
599Dic43C2×#12314yes—
600C22×C4×D4—431no—
601C22×#117—431no—
602#2487—431no—
603#2487—431no—
604#2486—431no—
605#2486—431no—
606#2485—431no—
607#2485—431no—
608#2485—431no—
609#2485D4311yescharacteristic, complemented
610#2484—432no—
611#2483—432no—
612#2482—432no—
613#2405—432no—
614#2395—432no—
615#2395—432no—
616C4×#123—432no—
617C4×#123—432no—
618#2296—431no—
619#2296—431no—
620#2280—431no—
621#2280—431no—
622#2280—431no—
623C2×C43—42no—
624C2×C43—42no—
625C2×C43C22×#12311yescharacteristic
626C2×C43C2×#52511yescharacteristic
627C2×C43#344911yescharacteristic
628C2×C43#347511yescharacteristic
629C2×C43#347511yescharacteristic
630C2×C43#347511yescharacteristic
631C2×C43#347511yescharacteristic
632D43—24no—
633D43—24no—
634D43—42no—
635C23×D4—431no—
636C24×C4—431no—
637C24×C4—431no—
638C2×#123—432no—
639C2×#123—432no—
640C2×C4×D4—431no—
641C2×C4×D4—431no—
642C2×C4×D4—431no—
643C2×C4×D4—431no—
644C2×C4×D4—431no—
645C2×C4×D4—431no—
646C2×C4×D4—431no—
647C2×C4×D4—868no—
648C2×C4×D4C2×D4311yescharacteristic
649C2×#117—431no—
650C2×#117—431no—
651C2×#117—431no—
652C2×#117—431no—
653C2×#117—431no—
654C2×#117—432no—
655C2×#117—432no—
656C2×#117—868no—
657C2×#117C2×D4311yescharacteristic, complemented
658C22×C4⋊C4—431no—
659C22×C4⋊C4—431no—
660C22×C4⋊C4—431no—
661C22×C22⋊C4—432no—
662C22×C22⋊C4—431no—
663C22×C22⋊C4—431no—
664C22×C42—431no—
665C22×C42—432no—
666#400—432no—
667#400—432no—
668#399—432no—
669#399—432no—
670#398—432no—
671#398—432no—
672#397—432no—
673#397—432no—
674#397—432no—
675#397—432no—
676#397—432no—
677#397C2×D4312yescomplemented
678#394—432no—
679#394—432no—
680#394—432no—
681#394C2×D4312yes—
682#389—431no—
683#389—431no—
684#389—431no—
685#389—431no—
686#389—431no—
687#389—431no—
688#389C2×D4311yescharacteristic, complemented
689#389C2×D4311yescharacteristic, complemented
690#388—432no—
691#388—432no—
692#388—432no—
693#388C2×D4312yescomplemented
694#387—432no—
695#387—432no—
696#387—432no—
697#387C2×D4312yescomplemented
698#386—432no—
699#386—432no—
700#385—432no—
701#385—432no—
702#385—432no—
703#385—432no—
704#385—432no—
705#385—432no—
706#381—432no—
707#381—432no—
708#381—432no—
709#381—432no—
710#381—432no—
711#380—431no—
712#380—431no—
713#380—431no—
714#380—431no—
715#380—431no—
716#380—431no—
717#380—431no—
718#380—431no—
719#380—431no—
720#380C2×D4311yescharacteristic, complemented
721#380C2×D4311yescharacteristic, complemented
722#380C2×D4311yescharacteristic, complemented
723#379—432no—
724#379—432no—
725#379—432no—
726C4×C4⋊C4—432no—
727C4×C4⋊C4—432no—
728C4×C4⋊C4—432no—
729C4×C4⋊C4—432no—
730C4×C22⋊C4—432no—
731C4×C22⋊C4—432no—
732C4×C22⋊C4—432no—
733C4×C22⋊C4—432no—
734C4×C22⋊C4—432no—
735C4×C22⋊C4—432no—
736C43#3480911yescharacteristic, complemented, Sylow
737C25—431no—
738C25—431no—
739C22×D4—431no—
740C22×D4—431no—
741C22×D4—431no—
742C22×D4—864no—
743C22×D4—864no—
744C22×D4—864no—
745C22×D4C22×D4311yescharacteristic
746C23×C4—431no—
747C23×C4—431no—
748C23×C4—438no—
749C23×C4—431no—
750C23×C4—431no—
751C23×C4—431no—
752C23×C4—431no—
753C23×C4—432no—
754C23×C4—431no—
755C23×C4—431no—
756C23×C4—431no—
757C23×C4—431no—
758C23×C4—431no—
759C23×C4—432no—
760C23×C4—864no—
761C23×C4—864no—
762C23×C4—864no—
763C23×C4—864no—
764C23×C4—864no—
765C23×C4C22×D4311yescharacteristic
766C23×C4C22×D4311yescharacteristic
767#123—868no—
768#123—868no—
769C4×D4—24no—
770C4×D4—864no—
771C4×D4—864no—
772C4×D4—864no—
773C4×D4—864no—
774C4×D4—864no—
775C4×D4—864no—
776C4×D4—864no—
777#117—24no—
778#117—868no—
779#117—868no—
780#117—864no—
781#117—864no—
782#117—864no—
783#117—864no—
784#117—864no—
785C2×C4⋊C4—432no—
786C2×C4⋊C4—432no—
787C2×C4⋊C4—431no—
788C2×C4⋊C4—431no—
789C2×C4⋊C4—431no—
790C2×C4⋊C4—431no—
791C2×C4⋊C4—431no—
792C2×C4⋊C4—431no—
793C2×C4⋊C4—431no—
794C2×C4⋊C4—432no—
795C2×C4⋊C4—432no—
796C2×C4⋊C4—432no—
797C2×C4⋊C4—432no—
798C2×C4⋊C4—432no—
799C2×C4⋊C4—432no—
800C2×C4⋊C4—864no—
801C2×C4⋊C4—864no—
802C2×C4⋊C4—864no—
803C2×C4⋊C4C22×D4311yescharacteristic
804C2×C4⋊C4C22×D4311yescharacteristic
805C2×C4⋊C4C22×D4311yescharacteristic
806C2×C4⋊C4C22×D4311yescharacteristic
807C2×C4⋊C4C22×D4311yescharacteristic
808C2×C4⋊C4C22×D4312yes—
809C2×C4⋊C4C22×D4312yes—
810C2×C22⋊C4—432no—
811C2×C22⋊C4—431no—
812C2×C22⋊C4—431no—
813C2×C22⋊C4—432no—
814C2×C22⋊C4—432no—
815C2×C22⋊C4—432no—
816C2×C22⋊C4—431no—
817C2×C22⋊C4—431no—
818C2×C22⋊C4—431no—
819C2×C22⋊C4—431no—
820C2×C22⋊C4—432no—
821C2×C22⋊C4—432no—
822C2×C22⋊C4—432no—
823C2×C22⋊C4—432no—
824C2×C22⋊C4—432no—
825C2×C22⋊C4—432no—
826C2×C22⋊C4—432no—
827C2×C22⋊C4—432no—
828C2×C22⋊C4—432no—
829C2×C22⋊C4—432no—
830C2×C22⋊C4—864no—
831C2×C22⋊C4—868no—
832C2×C22⋊C4—864no—
833C2×C22⋊C4C22×D4312yes—
834C2×C22⋊C4C22×D4311yescharacteristic
835C2×C22⋊C4C22×D4311yescharacteristic
836C2×C22⋊C4C22×D4312yes—
837C2×C22⋊C4C22×D4312yes—
838C2×C22⋊C4C22×D4312yes—
839C2×C42—432no—
840C2×C42—432no—
841C2×C42—432no—
842C2×C42—432no—
843C2×C42—432no—
844C2×C42—431no—
845C2×C42—431no—
846C2×C42—431no—
847C2×C42—868no—
848C2×C42—864no—
849C2×C42C22×D4312yes—
850C2×C42C22×D4311yescharacteristic
851#95—432no—
852#95—432no—
853#95—432no—
854#95—432no—
855#95—432no—
856#95—432no—
857#95—432no—
858#95—432no—
859#95—432no—
860#95—432no—
861#95—432no—
862#95—432no—
863#95—432no—
864#95—432no—
865#95—432no—
866#95C22×D4312yes—
867#95C22×D4312yes—
868#95C22×D4312yes—
869#95C22×D4312yes—
870#95C22×D4312yes—
871C24—431no—
872C24—431no—
873C24—431no—
874C24—434no—
875C24—862no—
876C24—862no—
877C24—862no—
878C24—862no—
879C24—862no—
880C24—862no—
881C24—862no—
882C24—862no—
883C24—862no—
884C24—1721no—
885C24—1721no—
886C24—1721no—
887C24—1721no—
888C24C23×D4311yescharacteristic
889C24C23×D4311yescharacteristic
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—434no—
894C2×D4—434no—
895C2×D4—862no—
896C2×D4—862no—
897C2×D4—862no—
898C2×D4—8632no—
899C2×D4—862no—
900C2×D4—862no—
901C2×D4—862no—
902C2×D4—862no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—431no—
909C22×C4—434no—
910C22×C4—434no—
911C22×C4—434no—
912C22×C4—434no—
913C22×C4—431no—
914C22×C4—431no—
915C22×C4—434no—
916C22×C4—434no—
917C22×C4—434no—
918C22×C4—431no—
919C22×C4—432no—
920C22×C4—432no—
921C22×C4—431no—
922C22×C4—432no—
923C22×C4—432no—
924C22×C4—862no—
925C22×C4—862no—
926C22×C4—8632no—
927C22×C4—862no—
928C22×C4—862no—
929C22×C4—862no—
930C22×C4—862no—
931C22×C4—862no—
932C22×C4—862no—
933C22×C4—862no—
934C22×C4—862no—
935C22×C4—864no—
936C22×C4—864no—
937C22×C4—862no—
938C22×C4—864no—
939C22×C4—864no—
940C22×C4—862no—
941C22×C4—862no—
942C22×C4—862no—
943C22×C4—862no—
944C22×C4—862no—
945C22×C4—862no—
946C22×C4—862no—
947C22×C4—862no—
948C22×C4—862no—
949C22×C4—862no—
950C22×C4—862no—
951C22×C4—862no—
952C22×C4—862no—
953C22×C4—1722no—
954C22×C4—1721no—
955C22×C4—1722no—
956C22×C4—1721no—
957C22×C4—17216no—
958C22×C4D4×D4314yes—
959C22×C4C23×D4311yescharacteristic
960C22×C4C23×D4312yes—
961C22×C4C23×D4312yes—
962C22×C4C23×D4311yescharacteristic
963C22×C4C23×D4312yes—
964C22×C4C23×D4312yes—
965C22×C4C23×D4311yescharacteristic
966C22×C4C23×D4311yescharacteristic
967C22×C4C23×D4311yescharacteristic
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—24no—
974C4⋊C4—42no—
975C4⋊C4—864no—
976C4⋊C4—864no—
977C4⋊C4—862no—
978C4⋊C4—862no—
979C4⋊C4—864no—
980C4⋊C4—864no—
981C4⋊C4—862no—
982C4⋊C4—862no—
983C4⋊C4—862no—
984C4⋊C4—862no—
985C4⋊C4—862no—
986C4⋊C4—864no—
987C4⋊C4—1722no—
988C4⋊C4—1722no—
989C4⋊C4—1722no—
990C22⋊C4—24no—
991C22⋊C4—22no—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—862no—
997C22⋊C4—864no—
998C22⋊C4—864no—
999C22⋊C4—862no—
1000C22⋊C4—862no—
1001C22⋊C4—864no—
1002C22⋊C4—864no—
1003C22⋊C4—864no—
1004C22⋊C4—864no—
1005C22⋊C4—864no—
1006C22⋊C4—864no—
1007C22⋊C4—862no—
1008C22⋊C4—864no—
1009C22⋊C4—862no—
1010C22⋊C4—864no—
1011C22⋊C4—862no—
1012C22⋊C4—1722no—
1013C22⋊C4—1722no—
1014C22⋊C4—1722no—
1015C22⋊C4—1722no—
1016C42—24no—
1017C42—22no—
1018C42—864no—
1019C42—864no—
1020C42—862no—
1021C42—862no—
1022C42—864no—
1023C42—864no—
1024C42—864no—
1025C42—862no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—432no—
1039C23—432no—
1040C23—432no—
1041C23—432no—
1042C23—432no—
1043C23—432no—
1044C23—432no—
1045C23—868no—
1046C23—868no—
1047C23—868no—
1048C23—861no—
1049C23—861no—
1050C23—861no—
1051C23—861no—
1052C23—861no—
1053C23—861no—
1054C23—861no—
1055C23—861no—
1056C23—861no—
1057C23—861no—
1058C23—861no—
1059C23—861no—
1060C23—861no—
1061C23—861no—
1062C23—1724no—
1063C23—1724no—
1064C23—1724no—
1065C23—1724no—
1066C23—1724no—
1067C23—1724no—
1068C23—1724no—
1069C23—1724no—
1070C23—1724no—
1071C23—1724no—
1072C23—1724no—
1073C23C2×D4×D4312yes—
1074C23#41×D4312yes—
1075C23C24×D4311yescharacteristic
1076D4—28no—
1077D4—868no—
1078D4—868no—
1079D4—868no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—28no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—44no—
1104C2×C4—432no—
1105C2×C4—432no—
1106C2×C4—432no—
1107C2×C4—4316no—
1108C2×C4—432no—
1109C2×C4—432no—
1110C2×C4—868no—
1111C2×C4—868no—
1112C2×C4—868no—
1113C2×C4—868no—
1114C2×C4—861no—
1115C2×C4—861no—
1116C2×C4—861no—
1117C2×C4—861no—
1118C2×C4—868no—
1119C2×C4—861no—
1120C2×C4—862no—
1121C2×C4—862no—
1122C2×C4—861no—
1123C2×C4—862no—
1124C2×C4—862no—
1125C2×C4—862no—
1126C2×C4—862no—
1127C2×C4—862no—
1128C2×C4—862no—
1129C2×C4—861no—
1130C2×C4—861no—
1131C2×C4—862no—
1132C2×C4—861no—
1133C2×C4—862no—
1134C2×C4—862no—
1135C2×C4—862no—
1136C2×C4—861no—
1137C2×C4—1724no—
1138C2×C4—1724no—
1139C2×C4—1728no—
1140C2×C4—1728no—
1141C2×C4—1724no—
1142C2×C4—1724no—
1143C2×C4—1724no—
1144C2×C4C2×D4×D4312yes—
1145C2×C4C2×D4×D4312yes—
1146C2×C4#41×D4312yes—
1147C2×C4#41×D4312yes—
1148C2×C4#41×D4312yes—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—434no—
1164C22—434no—
1165C22—862no—
1166C22—862no—
1167C22—862no—
1168C22—862no—
1169C22—862no—
1170C22—862no—
1171C22—862no—
1172C22—862no—
1173C22—862no—
1174C22—862no—
1175C22—862no—
1176C22—862no—
1177C22—862no—
1178C22—862no—
1179C22—862no—
1180C22—17216no—
1181C22—17216no—
1182C22—1721no—
1183C22—1721no—
1184C22—1721no—
1185C22—1721no—
1186C22C22×D4×D4311yescharacteristic
1187C22C2×#41×D4311yescharacteristic
1188C22C2×#41×D4311yescharacteristic
1189C22C2×#41×D4311yescharacteristic
1190C22C2×#41×D4311yescharacteristic
1191C22#1458373411yescharacteristic
1192C22#1458373611yescharacteristic
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—41no—
1200C4—42no—
1201C4—434no—
1202C4—862no—
1203C4—862no—
1204C4—1721no—
1205C4—1722no—
1206C4—1722no—
1207C4—1722no—
1208C4—1721no—
1209C4—1722no—
1210C4#123×D4314yes—
1211C2—42no—
1212C2—42no—
1213C2—864no—
1214C2—864no—
1215C2—1722no—
1216C2C2×#123×D4311yescharacteristic
1217C2#525×D4311yescharacteristic
1218C2#1914792311yescharacteristic
1219C2#1914814811yescharacteristic
1220C2#1914815211yescharacteristic
1221C2#1914815411yescharacteristic
1222C2#1914815611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2485C2
prime radicalC22×D4×D43C22
hypercenter#2485D43
hypocenterC43#34809
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2485

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. #19138910C2semidirect
4. #19138908C2semidirect
5. #19138901C2semidirect
6. #19138899C2semidirect
7. #19138893C2semidirect
8. #19138892C2semidirect
9. #19138886C2semidirect
10. #19138880C2semidirect
11. #19138872C2semidirect
12. #19138867C2semidirect
14. #19137853C2semidirect
15. #19137851C2semidirect
16. #19137122C2semidirect
17. #19137116C2semidirect
18. #19137076C2semidirect
19. #19137076C2semidirect
20. #19136977C2semidirect
21. #19136977C2semidirect
22. #19136977C2semidirect
23. C43×#2485C2semidirect
37. C2×#13063284C22semidirect
43. C2×#13063281C22semidirect
46. C2×C4⋊C4×D43C22semidirect
47. C2×C4⋊C4×D43C22semidirect
52. C2×C42×D43C22semidirect
53. #14582841C22semidirect
54. #14582840C22semidirect
55. #14582835C22semidirect
56. #14582834C22semidirect
57. #14582833C22semidirect
58. #14582832C22semidirect
59. #14582828C22semidirect
60. #14582827C22semidirect
61. #14582827C22semidirect
62. #14582827C22semidirect
63. #14582824C22semidirect
67. #14582798C22semidirect
68. #14582798C22semidirect
69. #14582797C22semidirect
70. #14582797C22semidirect
71. #14582795C22semidirect
72. #14582795C22semidirect
73. #14582791C22semidirect
74. #14582790C22semidirect
75. #14582787C22semidirect
76. #14582784C22semidirect
77. #14582783C22semidirect
78. #14582780C22semidirect
83. #14582773C22semidirect
86. #14582770C22semidirect
90. #14582761C22semidirect
91. #14582761C22semidirect
92. #14582759C22semidirect
93. #14582759C22semidirect
94. #14582759C22semidirect
95. #14582756C22semidirect
96. #14582756C22semidirect
97. #14582756C22semidirect
98. #14582756C22semidirect
99. #14582756C22semidirect
100. #14582756C22semidirect
104. C4⋊C4×Dic43C22semidirect
105. C4⋊C4×Dic43C22semidirect
106. #14582750C22semidirect
107. #14582750C22semidirect
108. C22⋊C4×Dic43C22semidirect
109. C22⋊C4×Dic43C22semidirect
110. C22⋊C4×Dic43C22semidirect
111. #14582746C22semidirect
112. #14582746C22semidirect
113. #14582746C22semidirect
115. C2×#117×C43C22semidirect
116. C43×#397C22semidirect
118. C43×#389C22semidirect
119. C43×#389C22semidirect
120. C43×#388C22semidirect
121. C43×#387C22semidirect
122. C43×#380C22semidirect
123. C43×#380C22semidirect
124. C43×#380C22semidirect
536. C4×D43#123semidirect
609. #2485D43semidirect
657. C2×#117C2×D43semidirect
677. #397C2×D43semidirect
688. #389C2×D43semidirect
689. #389C2×D43semidirect
693. #388C2×D43semidirect
697. #387C2×D43semidirect
720. #380C2×D43semidirect
721. #380C2×D43semidirect
722. #380C2×D43semidirect
736. C43#34809semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#117×D432
#191389102
#191389082
#191389012
#191388992
#191388932
#191388922
#191388862
#191388802
#191388722
#191388672
#191379172
#191378532
#191378512
#191371222
#191371162
#191370762
#191369772
C43×#24852
#3480943