Finite Group Databasebeta

← #25255992

Subgroups — #25255992

Order 11008.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063281C211yesmaximal, characteristic, complemented
3C2×#117×D43C211yesmaximal, characteristic, complemented
4#19137541C212yesmaximal, complemented
5#19137523C212yesmaximal, complemented
6#19137518C212yesmaximal, complemented
7#19137493C212yesmaximal, complemented
8#19137465C211yesmaximal, characteristic, complemented
9#19137459C211yesmaximal, characteristic, complemented
10#19137447C211yesmaximal, characteristic, complemented
11#19137444C211yesmaximal, characteristic, complemented
12#19137441C211yesmaximal, characteristic, complemented
13C22⋊C4×C22⋊D43C211yesmaximal, characteristic
14#19137411C211yesmaximal, characteristic
15#19137055C212yesmaximal, complemented
16#19137037C212yesmaximal, complemented
17#19137031C212yesmaximal, complemented
18#19136997C211yesmaximal, characteristic, complemented
19#19136975C211yesmaximal, characteristic, complemented
20#19136973C211yesmaximal, characteristic, complemented
21C4×(C22⋊D43)⋊C4C212yesmaximal, complemented
22C4×#13063281C211yesmaximal, characteristic, complemented
23C43×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D43C2211yescharacteristic
25C24×Dic43C2211yescharacteristic
26C23×C4×D43C2211yescharacteristic
27C2×C4×C22⋊D43C2212yes—
28C2×(C22⋊D43)⋊C4C4116yescomplemented
29C2×(C22⋊D43)⋊C4C2212yes—
30C2×(C22⋊D43)⋊C4C2211yescharacteristic
31C2×(C22⋊D43)⋊C4C2211yescharacteristic
32C2×(C22⋊D43)⋊C4C2211yescharacteristic
33C2×(C22⋊D43)⋊C4C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C2×(C22⋊D43)⋊C4C2211yescharacteristic
37C2×(C22⋊D43)⋊C4C2211yescharacteristic
38C2×#13063284C2211yescharacteristic
39C2×#13063283C2212yescomplemented
40C2×#13063282C2212yescomplemented
41C2×#13063281—28no—
42C2×#13063281C2211yescharacteristic
43C2×#13063281C2211yescharacteristic
44C2×#13063281C2211yescharacteristic
45C2×#13063281C2211yescharacteristic
46C2×#13063281C2211yescharacteristic
47C2×#13063281C2211yescharacteristic
48C2×#13063281C2212yescomplemented
49C2×#13063281C2212yescomplemented
50#117×D43—28no—
51C22×Dic43⋊C4C2211yescharacteristic
52C22×Dic43⋊C4C2212yescomplemented
53C2×C4⋊C4×D43C2212yescomplemented
54C22×C22⋊Dic43C2211yescharacteristic
55C22×(C2×D43)⋊C4C2211yescharacteristic
56C2×C22⋊C4×D43C2211yescharacteristic
57C2×C22⋊C4×D43C2211yescharacteristic
58C22×C4×Dic43C2211yescharacteristic
59C22×C4×Dic43C2212yescomplemented
60C2×C42×D43C2212yescomplemented
61#14582799C2212yes—
62#14582799C2212yes—
63#14582796C2212yescomplemented
64#14582794C2212yescomplemented
65#14582792C2212yescomplemented
66#14582792C2212yescomplemented
67#14582791C2212yescomplemented
68#14582790C2212yescomplemented
69#14582789C2212yescomplemented
70#14582788C2212yescomplemented
71#14582786C2212yescomplemented
72#14582783C2212yescomplemented
73#14582781C2212yescomplemented
74#14582780C2212yescomplemented
75#14582778C2212yes—
76#14582776C2212yes—
77#14582775C2212yes—
78#14582775C2212yes—
79#14582774C2212yescomplemented
80#14582773C2212yescomplemented
81#14582770C2212yescomplemented
82#14582768C2212yescomplemented
83#14582763C2212yescomplemented
84#14582762C2211yescharacteristic
85#14582760C2211yescharacteristic
86#14582760C2211yescharacteristic
87#14582759C2211yescharacteristic
88#14582758C2212yescomplemented
89#14582758C2212yescomplemented
90#14582757C2211yescharacteristic
91#14582757C2211yescharacteristic
92#14582757C2212yescomplemented
93#14582757C2212yescomplemented
94#14582755C2211yescharacteristic
95#14582754C2211yescharacteristic
96#14582754C2211yescharacteristic
97C4⋊C4×Dic43C2212yescomplemented
98C4×Dic43⋊C4C2212yescomplemented
99C4×Dic43⋊C4C2212yescomplemented
100#14582750C2212yescomplemented
101#14582750C2212yescomplemented
102#14582750C2212yescomplemented
103C22⋊C4×Dic43C2211yescharacteristic
104C22⋊C4×Dic43C2211yescharacteristic
105C22⋊C4×Dic43C2212yescomplemented
106C22⋊C4×Dic43C2212yescomplemented
107C22⋊C4×Dic43C2212yescomplemented
108C4×(C2×D43)⋊C4C2212yescomplemented
109C4×C22⋊Dic43C2211yescharacteristic
110#14582746C2212yescomplemented
111#14582746C2212yescomplemented
112#14582746C2212yescomplemented
113#14582744C2212yescomplemented
114C42×Dic43C2212yescomplemented
115C2×#117×C43C2211yescharacteristic
116C22×C22⋊C4×C43C2211yescharacteristic
117C22×C22⋊C4×C43C2211yescharacteristic
118C43×#388C2212yescomplemented
119C43×#388C2212yescomplemented
120C43×#385C2212yescomplemented
121C43×#381C2211yescharacteristic
122C43×#380C2211yescharacteristic
123C43×#379C2211yescharacteristic
124C4×C22⋊C4×C43C2211yescharacteristic
125C4×C22⋊C4×C43C2212yescomplemented
126C24×D43C2311yescharacteristic
127C22×C22⋊D43—28no—
128C22×C22⋊D43C2×C418yes—
129C22×C22⋊D43C2311yescharacteristic
130C22×C22⋊D43C2311yescharacteristic
131C22×C22⋊D43C2311yescharacteristic
132C22×C22⋊D43C2311yescharacteristic
133C23×Dic43—24no—
134C23×Dic43—24no—
135C23×Dic43C2×C418yescomplemented
136C23×Dic43C2312yes—
137C23×Dic43C2311yescharacteristic
138C23×Dic43C2311yescharacteristic
139C23×Dic43C2311yescharacteristic
140C23×Dic43C2311yescharacteristic
141C23×Dic43C2311yescharacteristic
142C23×Dic43C2311yescharacteristic
143C23×Dic43C2311yescharacteristic
144C22×C4×D43—24no—
145C22×C4×D43—24no—
146C22×C4×D43C2×C418yescomplemented
147C22×C4×D43C2312yes—
148C22×C4×D43C2312yes—
149C22×C4×D43C2311yescharacteristic
150C22×C4×D43C2311yescharacteristic
151C22×C4×D43C2311yescharacteristic
152C22×C4×D43C2311yescharacteristic
153C4×C22⋊D43—28no—
154(C22⋊D43)⋊C4—28no—
155(C22⋊D43)⋊C4C2×C418yes—
156(C22⋊D43)⋊C4C2×C418yes—
157(C22⋊D43)⋊C4C2×C418yescomplemented
158(C22⋊D43)⋊C4C2×C418yescomplemented
159(C22⋊D43)⋊C4C2×C418yescomplemented
160(C22⋊D43)⋊C4C2×C418yescomplemented
161(C22⋊D43)⋊C4C2×C418yescomplemented
162(C22⋊D43)⋊C4C2×C418yescomplemented
163#13063284—24no—
164#13063283—28no—
165#13063282—28no—
166#13063281—24no—
167#13063281—24no—
168#13063281—24no—
169#13063281—24no—
170#13063281—24no—
171#13063281—28no—
172#13063281—28no—
173#13063281D418yescomplemented
174C2×C4⋊Dic43C2312yes—
175C2×C4⋊Dic43C2312yes—
176C2×Dic43⋊C4—28no—
177C2×Dic43⋊C4C2×C418yescomplemented
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2311yescharacteristic
186C2×Dic43⋊C4C2311yescharacteristic
187C2×Dic43⋊C4C2311yescharacteristic
188C2×Dic43⋊C4C2311yescharacteristic
189C2×Dic43⋊C4C2312yes—
190C4⋊C4×D43—28no—
191C2×C22⋊Dic43—24no—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2311yescharacteristic
194C2×C22⋊Dic43C2311yescharacteristic
195C2×C22⋊Dic43C2311yescharacteristic
196C2×C22⋊Dic43C2312yes—
197C2×C22⋊Dic43C2312yes—
198C2×C22⋊Dic43C2311yescharacteristic
199C2×(C2×D43)⋊C4C2×C418yescomplemented
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2311yescharacteristic
207C2×(C2×D43)⋊C4C2311yescharacteristic
208C2×(C2×D43)⋊C4C2311yescharacteristic
209C2×(C2×D43)⋊C4C2311yescharacteristic
210C22⋊C4×D43—24no—
211C22⋊C4×D43—24no—
212C2×C4×Dic43—28no—
213C2×C4×Dic43C2×C418yescomplemented
214C2×C4×Dic43C2312yes—
215C2×C4×Dic43C2312yes—
216C2×C4×Dic43C2312yes—
217C2×C4×Dic43C2312yes—
218C2×C4×Dic43C2312yes—
219C2×C4×Dic43C2312yes—
220C2×C4×Dic43C2312yes—
221C2×C4×Dic43C2312yes—
222C2×C4×Dic43C2312yes—
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2312yes—
228C42×D43—28no—
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C43⋊#95C2312yes—
236C43⋊#95C2312yes—
237C43⋊#95C2312yes—
238C43⋊#95C2312yes—
239C43⋊#95C2312yes—
240C43⋊#95C2312yes—
241C25×C43C2311yescharacteristic
242C23×C4×C43C2312yes—
243C23×C4×C43C2311yescharacteristic
244C23×C4×C43C2311yescharacteristic
245#117×C43—24no—
246C2×C4⋊C4×C43C2312yes—
247C2×C4⋊C4×C43C2312yes—
248C2×C22⋊C4×C43—24no—
249C2×C22⋊C4×C43C2×C418yescomplemented
250C2×C22⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2311yescharacteristic
252C2×C22⋊C4×C43C2311yescharacteristic
253C2×C22⋊C4×C43C2311yescharacteristic
254C2×C22⋊C4×C43C2312yes—
255C2×C22⋊C4×C43C2312yes—
256C2×C22⋊C4×C43C2311yescharacteristic
257C2×C22⋊C4×C43C2311yescharacteristic
258C2×C22⋊C4×C43C2311yescharacteristic
259C2×C22⋊C4×C43C2311yescharacteristic
260C2×C22⋊C4×C43C2311yescharacteristic
261C2×C42×C43C2312yes—
262C2×C42×C43C2312yes—
263#95×C43C2312yes—
264#95×C43C2312yes—
265#95×C43C2312yes—
266#95×C43C2312yes—
267C24×C43—22no—
268C24×C43—22no—
269C24×C43—24no—
270C24×C43—42no—
271C24×C43C22×C414yes—
272C24×C43C2411yescharacteristic
273C24×C43C2411yescharacteristic
274C24×C43C2411yescharacteristic
275C23×D43—22no—
276C23×D43—22no—
277C23×D43—24no—
278C23×D43—42no—
279C23×D43C22×C414yes—
280C23×D43C2411yescharacteristic
281C23×D43C2411yescharacteristic
282C22×C4×C43—24no—
283C22×C4×C43—22no—
284C22×C4×C43—22no—
285C22×C4×C43—24no—
286C22×C4×C43—42no—
287C22×C4×C43—42no—
288C22×C4×C43C22×C414yes—
289C22×C4×C43C22×C414yes—
290C22×C4×C43C2412yes—
291C22×C4×C43C2412yes—
292C22×C4×C43C2412yes—
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2412yes—
298C2×C22⋊D43—232no—
299C2×C22⋊D43—24no—
300C2×C22⋊D43—24no—
301C2×C22⋊D43—24no—
302C2×C22⋊D43C22×C414yes—
303C2×C22⋊D43C22×C414yes—
304C2×C22⋊D43C22×C414yes—
305C2×C22⋊D43C22×C414yes—
306C2×C22⋊D43#4118yes—
307C22×Dic43—232no—
308C22×Dic43—22no—
309C22×Dic43—22no—
310C22×Dic43—22no—
311C22×Dic43—22no—
312C22×Dic43—22no—
313C22×Dic43—22no—
314C22×Dic43—22no—
315C22×Dic43—22no—
316C22×Dic43—24no—
317C22×Dic43—24no—
318C22×Dic43—22no—
319C22×Dic43—22no—
320C22×Dic43—24no—
321C22×Dic43—42no—
322C22×Dic43C22×C414yes—
323C22×Dic43C22×C414yes—
324C22×Dic43C22×C414yes—
325C22×Dic43C22×C414yes—
326C22×Dic43C22×C414yes—
327C22×Dic43C22×C414yes—
328C22×Dic43C22×C414yes—
329C22×Dic43C2×D414yes—
330C22×Dic43#4114yes—
331C22×Dic43C2412yes—
332C22×Dic43C2412yes—
333C22×Dic43C2412yes—
334C22×Dic43C2411yescharacteristic
335C22×Dic43C2411yescharacteristic
336C22×Dic43C2411yescharacteristic
337C22×Dic43C2412yes—
338C22×Dic43C2411yescharacteristic
339C22×Dic43C2411yescharacteristic
340C22×Dic43C2411yescharacteristic
341C2×C4×D43—232no—
342C2×C4×D43—22no—
343C2×C4×D43—22no—
344C2×C4×D43—22no—
345C2×C4×D43—22no—
346C2×C4×D43—22no—
347C2×C4×D43—22no—
348C2×C4×D43—22no—
349C2×C4×D43—22no—
350C2×C4×D43—24no—
351C2×C4×D43—24no—
352C2×C4×D43—24no—
353C2×C4×D43—24no—
354C2×C4×D43—42no—
355C2×C4×D43—42no—
356C2×C4×D43C22×C414yes—
357C2×C4×D43C22×C414yes—
358C2×C4×D43C22×C414yes—
359C2×C4×D43C22×C414yes—
360C4⋊C4×C43—24no—
361C4⋊C4×C43—42no—
362C22⋊C4×C43—24no—
363C22⋊C4×C43—22no—
364C22⋊C4×C43—22no—
365C22⋊C4×C43—22no—
366C22⋊C4×C43—24no—
367C22⋊C4×C43—42no—
368C22⋊C4×C43C22×C414yes—
369C22⋊C4×C43C22×C414yes—
370C22⋊C4×C43C22×C414yes—
371C22⋊C4×C43C22×C414yes—
372C22⋊C4×C43C2×D414yes—
373C42×C43—24no—
374C42×C43—42no—
375C22⋊Dic43—24no—
376C22⋊Dic43—22no—
377C22⋊Dic43—22no—
378C22⋊Dic43—22no—
379C22⋊Dic43—24no—
380C22⋊Dic43—42no—
381C22⋊Dic43C2×D414yes—
382(C2×D43)⋊C4—24no—
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—24no—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—42no—
387(C2×D43)⋊C4—42no—
388(C2×D43)⋊C4C22×C414yes—
389(C2×D43)⋊C4C22×C414yes—
390(C2×D43)⋊C4C22×C414yes—
391(C2×D43)⋊C4C22×C414yes—
392C4⋊Dic43—24no—
393C4⋊Dic43—42no—
394Dic43⋊C4—24no—
395Dic43⋊C4—24no—
396Dic43⋊C4—24no—
397Dic43⋊C4—24no—
398Dic43⋊C4—24no—
399Dic43⋊C4—24no—
400Dic43⋊C4—24no—
401Dic43⋊C4C22×C414yes—
402Dic43⋊C4C22×C414yes—
403Dic43⋊C4C22×C414yes—
404Dic43⋊C4C22×C414yes—
405Dic43⋊C4C2×D418yescomplemented
406C4×Dic43—24no—
407C4×Dic43—24no—
408C4×Dic43—24no—
409C4×Dic43—24no—
410C4×Dic43—24no—
411C4×Dic43—24no—
412C4×Dic43—24no—
413C4×Dic43—24no—
414C4×Dic43—42no—
415C4×Dic43C22×C414yes—
416C4×Dic43C22×C414yes—
417C4×Dic43C22×C414yes—
418C4×Dic43C22×C414yes—
419C4×Dic43C2×D418yescomplemented
420C23×C43—21no—
421C23×C43—21no—
422C23×C43—22no—
423C23×C43—22no—
424C23×C43—22no—
425C23×C43—28no—
426C23×C43—28no—
427C23×C43—21no—
428C23×C43—21no—
429C23×C43—22no—
430C23×C43—22no—
431C23×C43—44no—
432C23×C43—48no—
433C23×C43—48no—
434C23×C43C23×C412yes—
435C23×C43C23×C412yes—
436C23×C43C23×C412yes—
437C23×C43C22×D412yes—
438C23×C43C2×#4114yes—
439C23×C43C2×#4112yes—
440C23×C43C2511yescharacteristic
441C22×D43—21no—
442C22×D43—21no—
443C22×D43—22no—
444C22×D43—28no—
445C22×D43—21no—
446C22×D43—21no—
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—28no—
450C22×D43—44no—
451C22×D43—48no—
452C22×D43—48no—
453C22×D43C23×C412yes—
454C22×D43C23×C412yes—
455C22×D43C2×#4114yes—
456C2×C4×C43—28no—
457C2×C4×C43—21no—
458C2×C4×C43—21no—
459C2×C4×C43—22no—
460C2×C4×C43—21no—
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—22no—
473C2×C4×C43—22no—
474C2×C4×C43—44no—
475C2×C4×C43—48no—
476C2×C4×C43C23×C412yes—
477C2×C4×C43C23×C412yes—
478C2×C4×C43C23×C412yes—
479C2×C4×C43C23×C412yes—
480C2×C4×C43C22×D414yes—
481C22⋊D43—28no—
482C22⋊D43—28no—
483C22⋊D43—28no—
484C22⋊D43#117116yescomplemented
485C2×Dic43—28no—
486C2×Dic43—21no—
487C2×Dic43—21no—
488C2×Dic43—22no—
489C2×Dic43—21no—
490C2×Dic43—21no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—28no—
494C2×Dic43—28no—
495C2×Dic43—28no—
496C2×Dic43—28no—
497C2×Dic43—28no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—22no—
501C2×Dic43—22no—
502C2×Dic43—22no—
503C2×Dic43—22no—
504C2×Dic43—22no—
505C2×Dic43—22no—
506C2×Dic43—22no—
507C2×Dic43—48no—
508C2×Dic43C4×D4116yescomplemented
509C2×Dic43C23×C412yes—
510C2×Dic43C23×C412yes—
511C2×Dic43C23×C412yes—
512C2×Dic43C23×C412yes—
513C2×Dic43C23×C412yes—
514C2×Dic43C23×C412yes—
515C2×Dic43C22×D414yes—
516C2×Dic43C22×D412yes—
517C2×Dic43C22×D412yes—
518C2×Dic43C2×#4114yes—
519C2×Dic43C2×#4112yes—
520C2×Dic43C2×#4112yes—
521C4×D43—28no—
522C4×D43—28no—
523C4×D43—28no—
524C4×D43—28no—
525C4×D43—48no—
526C4×D43—48no—
527D4×#117—431nomaximal, Sylow
528C22×C43—22no—
529C22×C43—22no—
530C22×C43—22no—
531C22×C43—22no—
532C22×C43—24no—
533C22×C43—24no—
534C22×C43—24no—
535C22×C43—24no—
536C22×C43—22no—
537C22×C43—22no—
538C22×C43—22no—
539C22×C43—416no—
540C22×C43—42no—
541C22×C43—42no—
542C22×C43C2×#11714yescomplemented
543C22×C43C2×C4×D414yes—
544C22×C43C24×C411yescharacteristic
545C22×C43C23×D411yescharacteristic
546C22×C43C22×#4112yes—
547C22×C43C22×#4111yescharacteristic
548C22×C43#58512yes—
549C2×D43—22no—
550C2×D43—22no—
551C2×D43—24no—
552C2×D43—24no—
553C2×D43—22no—
554C2×D43—22no—
555C2×D43—22no—
556C2×D43—416no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43C2×#11714yescomplemented
560C4×C43—22no—
561C4×C43—22no—
562C4×C43—22no—
563C4×C43—22no—
564C4×C43—24no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—42no—
568Dic43—22no—
569Dic43—22no—
570Dic43—22no—
571Dic43—24no—
572Dic43—42no—
573Dic43—42no—
574Dic43—42no—
575Dic43C2×#11714yescomplemented
576Dic43C2×C4×D414yes—
577Dic43C2×C4×D414yes—
578C22×C4×D4—431no—
579C22×#117—431no—
580C22×#117—431no—
581#2354—432no—
582#2352—432no—
583#2352—432no—
584D4×C4⋊C4—432no—
585#2344—431no—
586#2344—431no—
587#2342—431no—
588#2342—431no—
589#2342—431no—
590#2342D4311yescharacteristic, complemented
591D4×C22⋊C4—431no—
592D4×C22⋊C4—431no—
593#2293—432no—
594#2290—432no—
595#2290—432no—
596#2285—431no—
597#2280—431no—
598#2280—431no—
599C42×D4—432no—
600C4×#117—431no—
601C2×C43—24no—
602C2×C43—24no—
603C2×C43—42no—
604C2×C43C22×#11711yescharacteristic
605C2×C43C22×C4×D411yescharacteristic
606C2×C43#342811yescharacteristic
607C2×C43D4×#4112yes—
608C2×C43#347512yes—
609D43—24no—
610D43—42no—
611C23×D4—431no—
612C24×C4—431no—
613C24×C4—431no—
614C2×C4×D4—432no—
615C2×C4×D4—431no—
616C2×C4×D4—431no—
617C2×C4×D4—431no—
618C2×C4×D4—431no—
619C2×C4×D4—431no—
620C2×C4×D4—431no—
621C2×C4×D4—431no—
622C2×C4×D4—431no—
623C2×C4×D4—432no—
624C2×C4×D4—4316no—
625C2×#117—431no—
626C2×#117—432no—
627C2×#117—431no—
628C2×#117—431no—
629C2×#117—431no—
630C2×#117—432no—
631C2×#117—431no—
632C2×#117—431no—
633C2×#117—431no—
634C2×#117—432no—
635C2×#117—432no—
636C2×#117—868no—
637C2×#117—868no—
638C2×#117C2×D4311yescharacteristic
639C22×C4⋊C4—431no—
640C22×C4⋊C4—432no—
641C22×C4⋊C4—432no—
642C22×C22⋊C4—431no—
643C22×C22⋊C4—431no—
644C22×C22⋊C4—431no—
645C22×C22⋊C4—431no—
646C22×C22⋊C4C2×D4311yescharacteristic
647C22×C22⋊C4C2×D4311yescharacteristic
648C22×C42—431no—
649C22×C42—432no—
650C22×C42—432no—
651#390—432no—
652#390—432no—
653#389—432no—
654#389—432no—
655#388—432no—
656#388—432no—
657#388—432no—
658#388—432no—
659#388—432no—
660#388—432no—
661#388C2×D4312yescomplemented
662#388C2×D4312yescomplemented
663#387—432no—
664#387—432no—
665#387—432no—
666#387—432no—
667#386—432no—
668#386—432no—
669#386—432no—
670#386—432no—
671#385—432no—
672#385—432no—
673#385—432no—
674#385C2×D4312yescomplemented
675#384—432no—
676#382—432no—
677#381—431no—
678#381—431no—
679#381—431no—
680#381C2×D4311yescharacteristic
681#380—431no—
682#380—431no—
683#380—431no—
684#380—432no—
685#380—432no—
686#380—432no—
687#380—432no—
688#380C2×D4311yescharacteristic
689#379—431no—
690#379—431no—
691#379—431no—
692#379C2×D4311yescharacteristic
693C4×C4⋊C4—432no—
694C4×C4⋊C4—432no—
695C4×C4⋊C4—432no—
696C4×C4⋊C4—432no—
697C4×C4⋊C4—432no—
698C4×C4⋊C4—432no—
699C4×C22⋊C4—431no—
700C4×C22⋊C4—431no—
701C4×C22⋊C4—431no—
702C4×C22⋊C4—432no—
703C4×C22⋊C4—432no—
704C4×C22⋊C4—432no—
705C4×C22⋊C4—432no—
706C4×C22⋊C4—432no—
707C4×C22⋊C4—432no—
708C4×C22⋊C4—432no—
709C4×C22⋊C4C2×D4311yescharacteristic
710C4×C22⋊C4C2×D4312yescomplemented
711#376—432no—
712C43—432no—
713C43D4×#11711yescharacteristic, complemented, Sylow
714C25—431no—
715C25C22×D4311yescharacteristic
716C22×D4—431no—
717C22×D4—438no—
718C22×D4—431no—
719C22×D4—431no—
720C22×D4—431no—
721C22×D4—868no—
722C23×C4—431no—
723C23×C4—438no—
724C23×C4—431no—
725C23×C4—431no—
726C23×C4—431no—
727C23×C4—431no—
728C23×C4—431no—
729C23×C4—431no—
730C23×C4—438no—
731C23×C4—431no—
732C23×C4—431no—
733C23×C4—431no—
734C23×C4—431no—
735C23×C4—432no—
736C23×C4—432no—
737C23×C4—432no—
738C23×C4—864no—
739C23×C4—864no—
740C23×C4—864no—
741C23×C4—864no—
742C23×C4C22×D4312yes—
743C23×C4C22×D4311yescharacteristic
744C23×C4C22×D4311yescharacteristic
745C4×D4—438no—
746C4×D4—438no—
747C4×D4—438no—
748C4×D4—438no—
749C4×D4—438no—
750C4×D4—438no—
751C4×D4—438no—
752C4×D4—438no—
753C4×D4—868no—
754C4×D4—868no—
755#117—24no—
756#117—438no—
757#117—868no—
758#117—868no—
759#117—868no—
760#117—864no—
761#117—868no—
762#117—864no—
763#117—864no—
764#117—864no—
765#117—864no—
766#117—864no—
767C2×C4⋊C4—438no—
768C2×C4⋊C4—432no—
769C2×C4⋊C4—431no—
770C2×C4⋊C4—431no—
771C2×C4⋊C4—431no—
772C2×C4⋊C4—431no—
773C2×C4⋊C4—432no—
774C2×C4⋊C4—432no—
775C2×C4⋊C4—432no—
776C2×C4⋊C4—432no—
777C2×C4⋊C4—432no—
778C2×C4⋊C4—432no—
779C2×C4⋊C4—432no—
780C2×C4⋊C4—432no—
781C2×C4⋊C4—432no—
782C2×C4⋊C4—868no—
783C2×C4⋊C4—868no—
784C2×C4⋊C4C22×D4312yes—
785C2×C4⋊C4C22×D4312yes—
786C2×C22⋊C4—24no—
787C2×C22⋊C4—431no—
788C2×C22⋊C4—438no—
789C2×C22⋊C4—431no—
790C2×C22⋊C4—431no—
791C2×C22⋊C4—431no—
792C2×C22⋊C4—431no—
793C2×C22⋊C4—431no—
794C2×C22⋊C4—431no—
795C2×C22⋊C4—432no—
796C2×C22⋊C4—431no—
797C2×C22⋊C4—432no—
798C2×C22⋊C4—432no—
799C2×C22⋊C4—432no—
800C2×C22⋊C4—432no—
801C2×C22⋊C4—432no—
802C2×C22⋊C4—432no—
803C2×C22⋊C4—432no—
804C2×C22⋊C4—432no—
805C2×C22⋊C4—864no—
806C2×C22⋊C4—864no—
807C2×C22⋊C4—864no—
808C2×C22⋊C4C4×D4318yescomplemented
809C2×C22⋊C4C22×D4311yescharacteristic
810C2×C22⋊C4C22×D4311yescharacteristic
811C2×C22⋊C4C22×D4312yes—
812C2×C22⋊C4C22×D4311yescharacteristic
813C2×C22⋊C4C22×D4312yes—
814C2×C22⋊C4C22×D4312yes—
815C2×C22⋊C4C22×D4311yescharacteristic
816C2×C22⋊C4C22×D4311yescharacteristic
817C2×C22⋊C4C22×D4311yescharacteristic
818C2×C22⋊C4C22×D4311yescharacteristic
819C2×C22⋊C4C22×D4311yescharacteristic
820C2×C42—438no—
821C2×C42—432no—
822C2×C42—431no—
823C2×C42—431no—
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—432no—
827C2×C42—432no—
828C2×C42—432no—
829C2×C42—432no—
830C2×C42—432no—
831C2×C42—432no—
832C2×C42—432no—
833C2×C42—432no—
834C2×C42—432no—
835C2×C42—868no—
836C2×C42—868no—
837C2×C42C22×D4312yes—
838C2×C42C22×D4312yes—
839#95—432no—
840#95—432no—
841#95—432no—
842#95—432no—
843#95—432no—
844#95—432no—
845#95—432no—
846#95—432no—
847#95—432no—
848#95—432no—
849#95—432no—
850#95—432no—
851#95C22×D4312yes—
852#95C22×D4312yes—
853#95C22×D4312yes—
854#95C22×D4312yes—
855C24—22no—
856C24—22no—
857C24—24no—
858C24—42no—
859C24—431no—
860C24—431no—
861C24—434no—
862C24—864no—
863C24—862no—
864C24—862no—
865C24—1722no—
866C24C2×C4×D4314yes—
867C24C23×D4311yescharacteristic
868C24C23×D4311yescharacteristic
869C24C23×D4311yescharacteristic
870C2×D4—434no—
871C2×D4—438no—
872C2×D4—434no—
873C2×D4—434no—
874C2×D4—434no—
875C2×D4—864no—
876C2×D4—8632no—
877C2×D4—864no—
878C2×D4—864no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—434no—
886C22×C4—434no—
887C22×C4—434no—
888C22×C4—431no—
889C22×C4—431no—
890C22×C4—431no—
891C22×C4—434no—
892C22×C4—434no—
893C22×C4—434no—
894C22×C4—434no—
895C22×C4—434no—
896C22×C4—434no—
897C22×C4—431no—
898C22×C4—431no—
899C22×C4—431no—
900C22×C4—432no—
901C22×C4—434no—
902C22×C4—434no—
903C22×C4—434no—
904C22×C4—434no—
905C22×C4—432no—
906C22×C4—432no—
907C22×C4—432no—
908C22×C4—862no—
909C22×C4—862no—
910C22×C4—862no—
911C22×C4—862no—
912C22×C4—8632no—
913C22×C4—862no—
914C22×C4—862no—
915C22×C4—862no—
916C22×C4—862no—
917C22×C4—864no—
918C22×C4—864no—
919C22×C4—864no—
920C22×C4—862no—
921C22×C4—862no—
922C22×C4—862no—
923C22×C4—862no—
924C22×C4—8632no—
925C22×C4—862no—
926C22×C4—862no—
927C22×C4—862no—
928C22×C4—862no—
929C22×C4—864no—
930C22×C4—864no—
931C22×C4—862no—
932C22×C4—862no—
933C22×C4—864no—
934C22×C4—864no—
935C22×C4—1722no—
936C22×C4—1722no—
937C22×C4—1722no—
938C22×C4C2×C4×D4314yes—
939C22×C4C2×C4×D4314yes—
940C22×C4C23×D4312yes—
941C22×C4C23×D4312yes—
942C22×C4C23×D4312yes—
943C22×C4C23×D4311yescharacteristic
944C22×C4C23×D4311yescharacteristic
945C22×C4C23×D4311yescharacteristic
946C22×C4C23×D4311yescharacteristic
947C22×C4C23×D4312yes—
948C4⋊C4—24no—
949C4⋊C4—42no—
950C4⋊C4—434no—
951C4⋊C4—434no—
952C4⋊C4—434no—
953C4⋊C4—434no—
954C4⋊C4—438no—
955C4⋊C4—864no—
956C4⋊C4—864no—
957C4⋊C4—864no—
958C4⋊C4—864no—
959C4⋊C4—864no—
960C4⋊C4—864no—
961C4⋊C4—864no—
962C4⋊C4—864no—
963C4⋊C4—1722no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—42no—
970C22⋊C4—434no—
971C22⋊C4—434no—
972C22⋊C4—434no—
973C22⋊C4—434no—
974C22⋊C4—434no—
975C22⋊C4—864no—
976C22⋊C4—864no—
977C22⋊C4—864no—
978C22⋊C4—864no—
979C22⋊C4—862no—
980C22⋊C4—862no—
981C22⋊C4—862no—
982C22⋊C4—864no—
983C22⋊C4—864no—
984C22⋊C4—1722no—
985C22⋊C4—1722no—
986C22⋊C4—1722no—
987C22⋊C4C2×C4×D4314yes—
988C22⋊C4C2×C4×D4314yes—
989C22⋊C4C2×C4×D4314yes—
990C22⋊C4C2×C4×D4314yes—
991C22⋊C4D4×D4314yes—
992C42—24no—
993C42—42no—
994C42—434no—
995C42—434no—
996C42—434no—
997C42—434no—
998C42—438no—
999C42—864no—
1000C42—864no—
1001C42—864no—
1002C42—864no—
1003C42—864no—
1004C42—864no—
1005C42—864no—
1006C42—864no—
1007C42—1722no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—28no—
1014C23—28no—
1015C23—21no—
1016C23—21no—
1017C23—22no—
1018C23—22no—
1019C23—44no—
1020C23—48no—
1021C23—48no—
1022C23—432no—
1023C23—434no—
1024C23—432no—
1025C23—868no—
1026C23—861no—
1027C23—861no—
1028C23—862no—
1029C23—868no—
1030C23—861no—
1031C23—861no—
1032C23—862no—
1033C23—862no—
1034C23—1724no—
1035C23—1728no—
1036C23—1728no—
1037C23C22×C4×D4312yes—
1038C23C22×C4×D4312yes—
1039C23C22×C4×D4312yes—
1040C23C2×D4×D4312yes—
1041C23#41×D4314yes—
1042C23#41×D4312yes—
1043C23C24×D4311yescharacteristic
1044D4—4316no—
1045D4—868no—
1046D4—868no—
1047D4—868no—
1048C2×C4—28no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—4316no—
1069C2×C4—432no—
1070C2×C4—432no—
1071C2×C4—432no—
1072C2×C4—432no—
1073C2×C4—432no—
1074C2×C4—434no—
1075C2×C4—432no—
1076C2×C4—432no—
1077C2×C4—432no—
1078C2×C4—432no—
1079C2×C4—432no—
1080C2×C4—434no—
1081C2×C4—868no—
1082C2×C4—868no—
1083C2×C4—868no—
1084C2×C4—868no—
1085C2×C4—868no—
1086C2×C4—868no—
1087C2×C4—868no—
1088C2×C4—868no—
1089C2×C4—868no—
1090C2×C4—868no—
1091C2×C4—861no—
1092C2×C4—861no—
1093C2×C4—862no—
1094C2×C4—861no—
1095C2×C4—861no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—862no—
1102C2×C4—862no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—1728no—
1108C2×C4—1728no—
1109C2×C4—1728no—
1110C2×C4C22×C4×D4312yes—
1111C2×C4C22×C4×D4312yes—
1112C2×C4C22×C4×D4312yes—
1113C2×C4C22×C4×D4312yes—
1114C2×C4C2×D4×D4314yes—
1115C22—22no—
1116C22—22no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—416no—
1127C22—42no—
1128C22—42no—
1129C22—434no—
1130C22—862no—
1131C22—864no—
1132C22—864no—
1133C22—862no—
1134C22—862no—
1135C22—862no—
1136C22—862no—
1137C22—17216no—
1138C22—1722no—
1139C22—1722no—
1140C22#117×D4314yescomplemented
1141C22C4×D4×D4314yes—
1142C22C23×C4×D4311yescharacteristic
1143C22C22×D4×D4311yescharacteristic
1144C22C2×#41×D4312yes—
1145C22C2×#41×D4311yescharacteristic
1146C22#1458373412yes—
1147C4—22no—
1148C4—22no—
1149C4—24no—
1150C4—22no—
1151C4—22no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—434no—
1156C4—434no—
1157C4—434no—
1158C4—864no—
1159C4—862no—
1160C4—862no—
1161C4—862no—
1162C4—1722no—
1163C4—1722no—
1164C4—1722no—
1165C2—24no—
1166C2—24no—
1167C2—42no—
1168C2—864no—
1169C2—1722no—
1170C2C2×#117×D4311yescharacteristic
1171C2C2×C4×D4×D4311yescharacteristic
1172C2#1914779311yescharacteristic
1173C2#1914807912yes—
1174C2#1914815012yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2342C2
socle, cosocleC23×C43C25
prime radicalC23×C22⋊D43C22
hypercenter#2342D43
hypocenterC43D4×#117
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. C22×#13063281C2semidirect
3. C2×#117×D43C2semidirect
4. #19137541C2semidirect
5. #19137523C2semidirect
6. #19137518C2semidirect
7. #19137493C2semidirect
8. #19137465C2semidirect
9. #19137459C2semidirect
10. #19137447C2semidirect
11. #19137444C2semidirect
12. #19137441C2semidirect
15. #19137055C2semidirect
16. #19137037C2semidirect
17. #19137031C2semidirect
18. #19136997C2semidirect
19. #19136975C2semidirect
20. #19136973C2semidirect
21. C4×(C22⋊D43)⋊C4C2semidirect
22. C4×#13063281C2semidirect
23. C43×#2342C2semidirect
28. C2×(C22⋊D43)⋊C4C4semidirect
39. C2×#13063283C22semidirect
40. C2×#13063282C22semidirect
48. C2×#13063281C22semidirect
49. C2×#13063281C22semidirect
52. C22×Dic43⋊C4C22semidirect
53. C2×C4⋊C4×D43C22semidirect
59. C22×C4×Dic43C22semidirect
60. C2×C42×D43C22semidirect
63. #14582796C22semidirect
64. #14582794C22semidirect
65. #14582792C22semidirect
66. #14582792C22semidirect
67. #14582791C22semidirect
68. #14582790C22semidirect
69. #14582789C22semidirect
70. #14582788C22semidirect
71. #14582786C22semidirect
72. #14582783C22semidirect
73. #14582781C22semidirect
74. #14582780C22semidirect
79. #14582774C22semidirect
80. #14582773C22semidirect
81. #14582770C22semidirect
82. #14582768C22semidirect
83. #14582763C22semidirect
88. #14582758C22semidirect
89. #14582758C22semidirect
92. #14582757C22semidirect
93. #14582757C22semidirect
97. C4⋊C4×Dic43C22semidirect
98. C4×Dic43⋊C4C22semidirect
99. C4×Dic43⋊C4C22semidirect
100. #14582750C22semidirect
101. #14582750C22semidirect
102. #14582750C22semidirect
105. C22⋊C4×Dic43C22semidirect
106. C22⋊C4×Dic43C22semidirect
107. C22⋊C4×Dic43C22semidirect
108. C4×(C2×D43)⋊C4C22semidirect
110. #14582746C22semidirect
111. #14582746C22semidirect
112. #14582746C22semidirect
113. #14582744C22semidirect
114. C42×Dic43C22semidirect
118. C43×#388C22semidirect
119. C43×#388C22semidirect
120. C43×#385C22semidirect
125. C4×C22⋊C4×C43C22semidirect
135. C23×Dic43C2×C4semidirect
146. C22×C4×D43C2×C4semidirect
157. (C22⋊D43)⋊C4C2×C4semidirect
158. (C22⋊D43)⋊C4C2×C4semidirect
159. (C22⋊D43)⋊C4C2×C4semidirect
160. (C22⋊D43)⋊C4C2×C4semidirect
161. (C22⋊D43)⋊C4C2×C4semidirect
162. (C22⋊D43)⋊C4C2×C4semidirect
173. #13063281D4semidirect
177. C2×Dic43⋊C4C2×C4semidirect
199. C2×(C2×D43)⋊C4C2×C4semidirect
213. C2×C4×Dic43C2×C4semidirect
249. C2×C22⋊C4×C43C2×C4semidirect
405. Dic43⋊C4C2×D4semidirect
419. C4×Dic43C2×D4semidirect
484. C22⋊D43#117semidirect
508. C2×Dic43C4×D4semidirect
542. C22×C43C2×#117semidirect
559. C2×D43C2×#117semidirect
575. Dic43C2×#117semidirect
590. #2342D43semidirect
661. #388C2×D43semidirect
662. #388C2×D43semidirect
674. #385C2×D43semidirect
710. C4×C22⋊C4C2×D43semidirect
713. C43D4×#117semidirect
808. C2×C22⋊C4C4×D43semidirect
1140. C22#117×D43semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×#130632812
C2×#117×D432
#191375412
#191375232
#191375182
#191374932
#191374652
#191374592
#191374472
#191374442
#191374412
C22⋊C4×C22⋊D432
#191374112
#191370552
#191370372
#191370312
#191369972
#191369752
#191369732
C4×(C22⋊D43)⋊C42
C4×#130632812
C43×#23422
D4×#11743