Finite Group Databasebeta

← #25256215

Subgroups — #25256215

Order 11008.

3298 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2C2×C4×#10621898C211yesmaximal, characteristic, complemented
3C2×#14583367C211yesmaximal, characteristic, complemented
4#19137669C212yesmaximal, complemented
5#19137663C212yesmaximal, complemented
6#19137658C212yesmaximal, complemented
7#19137650C212yesmaximal, complemented
8#19137644C212yesmaximal, complemented
9#19137641C212yesmaximal, complemented
10#19137614C212yesmaximal, complemented
11#19137608C212yesmaximal, complemented
12#19137081C211yesmaximal, characteristic, complemented
13#19137081C211yesmaximal, characteristic, complemented
14#19137058C211yesmaximal, characteristic, complemented
15#19137054C211yesmaximal, characteristic, complemented
16#19137040C211yesmaximal, characteristic, complemented
17#19137039C211yesmaximal, characteristic, complemented
18#19137036C211yesmaximal, characteristic, complemented
19C42×C22⋊D43C211yesmaximal, characteristic, complemented
20C4×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
21#19136934C211yesmaximal, characteristic, complemented
22C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
23C43×#2290C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26#14583446C4116yescomplemented
27C2×#13063324C2211yescharacteristic
28C2×#13063321C2211yescharacteristic
29C2×#13063311C2211yescharacteristic
30C2×#13063311C2211yescharacteristic
31C2×#13063300C2211yescharacteristic
32C2×#13063298C2211yescharacteristic
33C2×#13063298C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C4×#10621898—28no—
36#14583367—28no—
37C2×C4×Dic86C2212yes—
38C2×#13063290C2212yes—
39C2×C4×D172C2212yes—
40C2×C4×D172C2211yescharacteristic
41C2×#13063287C2212yes—
42C2×C4×C22⋊D43C2212yes—
43C2×C4×C22⋊D43C2212yes—
44C2×C4×C22⋊D43C2212yes—
45C2×C4×C22⋊D43C2211yescharacteristic
46C2×C4×C22⋊D43C2211yescharacteristic
47C2×(C22⋊D43)⋊C4C2212yes—
48C2×(C22⋊D43)⋊C4C2212yes—
49C2×(C22⋊D43)⋊C4C2212yes—
50C2×#13063284C2211yescharacteristic
51C2×#13063282C2211yescharacteristic
52C2×#13063282C2211yescharacteristic
53C2×#13063282C2211yescharacteristic
54C2×#13063282C2211yescharacteristic
55C2×C4⋊C4×D43C2212yes—
56C22×C4×Dic43C2211yescharacteristic
57C2×C42×D43C2211yescharacteristic
58C2×C42×D43C2211yescharacteristic
59C2×C42×D43C2211yescharacteristic
60C2×C42×D43C2211yescharacteristic
61C2×C42×D43C2211yescharacteristic
62#14582803C2212yes—
63#14582803C2212yes—
64#14582799C2212yes—
65#14582799C2212yes—
66#14582799C2212yes—
67#14582799C2212yes—
68#14582796C2212yes—
69#14582794C2212yes—
70#14582793C2212yes—
71#14582792C2212yes—
72#14582791C2212yes—
73#14582791C2212yes—
74#14582789C2212yes—
75#14582789C2212yes—
76#14582787C2212yes—
77#14582785C2212yes—
78#14582784C2212yes—
79#14582782C2212yes—
80#14582779C2212yes—
81#14582777C2212yes—
82#14582777C2212yes—
83#14582777C2212yes—
84#14582777C2212yes—
85#14582775C2212yes—
86#14582775C2212yes—
87#14582774C2212yes—
88#14582773C2212yes—
89#14582770C2212yes—
90C4⋊C4×Dic43C2212yes—
91C4×Dic43⋊C4C2211yescharacteristic
92C4×Dic43⋊C4C2212yes—
93C4×Dic43⋊C4C2211yescharacteristic
94C4×C4⋊Dic43C2211yescharacteristic
95#14582750C2212yes—
96#14582750C2212yes—
97#14582750C2212yes—
98#14582750C2212yes—
99C22⋊C4×Dic43C2212yes—
100C4×(C2×D43)⋊C4C2211yescharacteristic
101C4×(C2×D43)⋊C4C2211yescharacteristic
102C4×(C2×D43)⋊C4C2211yescharacteristic
103C4×(C2×D43)⋊C4C2211yescharacteristic
104C4×(C2×D43)⋊C4C2212yes—
105C4×C22⋊Dic43C2211yescharacteristic
106C4×C22⋊Dic43C2211yescharacteristic
107C4×C22⋊Dic43C2212yes—
108#14582746C2212yes—
109#14582746C2212yes—
110#14582746C2212yes—
111#14582745C2211yescharacteristic
112#95×D43C2212yes—
113C42×Dic43C2211yescharacteristic
114C42×Dic43C2211yescharacteristic
115C2×C4×D4×C43C2211yescharacteristic
116C2×#117×C43C2211yescharacteristic
117C22×C42×C43C2211yescharacteristic
118C43×#388C2212yes—
119C43×#387C2212yes—
120C43×#386C2212yes—
121C43×#385C2212yes—
122C4×C4⋊C4×C43C2211yescharacteristic
123C4×C22⋊C4×C43C2211yescharacteristic
124C4×C22⋊C4×C43C2211yescharacteristic
125C43×#376C2211yescharacteristic
126C2×#10621898—24no—
127C2×#10621898—24no—
128C2×#10621898—24no—
129C2×#10621898—24no—
130C2×#10621898C2×C418yescomplemented
131C2×#10621898C2×C418yescomplemented
132C22×Dic86C2311yescharacteristic
133C22×Dic86C2311yescharacteristic
134C22×D172C2311yescharacteristic
135C22×D172C2311yescharacteristic
136C22×D172C2311yescharacteristic
137C22×C22⋊D43C2311yescharacteristic
138C22×C22⋊D43C2311yescharacteristic
139C22×C22⋊D43C2311yescharacteristic
140C22×C22⋊D43C2311yescharacteristic
141C22×C22⋊D43C2311yescharacteristic
142C22×C22⋊D43C2311yescharacteristic
143C23×Dic43C2312yes—
144C22×C4×D43C2312yes—
145C22×C4×D43C2312yes—
146C22×C4×D43C2312yes—
147C22×C4×D43C2312yes—
148C22×C4×D43C2311yescharacteristic
149C22×C4×D43C2311yescharacteristic
150C22×C4×D43C2311yescharacteristic
151C22×C4×D43C2311yescharacteristic
152C22×C4×D43C2311yescharacteristic
153#13063324C2×C418yescomplemented
154#13063321C2×C418yescomplemented
155#13063311C2×C418yescomplemented
156#13063311C2×C418yescomplemented
157#13063300C2×C418yescomplemented
158#13063298C2×C418yescomplemented
159#13063298C2×C418yescomplemented
160#13063296C2×C418yescomplemented
161C4×Dic86—28no—
162#13063290—28no—
163C4×D172—28no—
164C4×D172C2×C418yescomplemented
165#13063287—28no—
166C4×C22⋊D43—28no—
167C4×C22⋊D43—28no—
168C4×C22⋊D43—28no—
169C4×C22⋊D43C2×C418yescomplemented
170C4×C22⋊D43C2×C418yescomplemented
171(C22⋊D43)⋊C4—28no—
172(C22⋊D43)⋊C4—28no—
173(C22⋊D43)⋊C4—28no—
174#13063284—24no—
175#13063282—24no—
176#13063282—24no—
177#13063282—24no—
178#13063282D418yescomplemented
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2312yes—
181C2×C4⋊Dic43C2311yescharacteristic
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2311yescharacteristic
187C2×Dic43⋊C4C2311yescharacteristic
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2312yes—
190C4⋊C4×D43—28no—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2312yes—
194C2×C22⋊Dic43C2311yescharacteristic
195C2×C22⋊Dic43C2311yescharacteristic
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2311yescharacteristic
204C2×(C2×D43)⋊C4C2311yescharacteristic
205C2×(C2×D43)⋊C4C2311yescharacteristic
206C2×(C2×D43)⋊C4C2311yescharacteristic
207C2×(C2×D43)⋊C4C2312yes—
208C2×C4×Dic43—24no—
209C2×C4×Dic43C2312yes—
210C2×C4×Dic43C2312yes—
211C2×C4×Dic43C2312yes—
212C2×C4×Dic43C2312yes—
213C2×C4×Dic43C2312yes—
214C2×C4×Dic43C2312yes—
215C2×C4×Dic43C2312yes—
216C2×C4×Dic43C2311yescharacteristic
217C2×C4×Dic43C2311yescharacteristic
218C2×C4×Dic43C2311yescharacteristic
219C2×C4×Dic43C2312yes—
220C2×C4×Dic43C2312yes—
221C2×C4×Dic43C2311yescharacteristic
222C2×C4×Dic43C2311yescharacteristic
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C42×D43—24no—
226C42×D43—24no—
227C42×D43—24no—
228C42×D43—24no—
229C42×D43C2×C418yescomplemented
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C43⋊#95C2312yes—
236C43⋊#95C2312yes—
237C43⋊#95C2312yes—
238C43⋊#95C2312yes—
239C43⋊#95C2312yes—
240C43⋊#95C2312yes—
241C22×D4×C43C2311yescharacteristic
242C23×C4×C43C2312yes—
243C23×C4×C43C2311yescharacteristic
244C23×C4×C43C2311yescharacteristic
245C4×D4×C43C2×C418yescomplemented
246#117×C43—24no—
247C2×C4⋊C4×C43C2312yes—
248C2×C4⋊C4×C43C2312yes—
249C2×C4⋊C4×C43C2311yescharacteristic
250C2×C22⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2312yes—
252C2×C22⋊C4×C43C2312yes—
253C2×C22⋊C4×C43C2311yescharacteristic
254C2×C22⋊C4×C43C2311yescharacteristic
255C2×C42×C43—24no—
256C2×C42×C43C2311yescharacteristic
257C2×C42×C43C2312yes—
258C2×C42×C43C2311yescharacteristic
259C2×C42×C43C2311yescharacteristic
260C2×C42×C43C2311yescharacteristic
261C2×C42×C43C2311yescharacteristic
262#95×C43C2312yes—
263#95×C43C2312yes—
264#95×C43C2312yes—
265#95×C43C2312yes—
266#95×C43C2312yes—
267C24×C43C2411yescharacteristic
268C24×C43C2411yescharacteristic
269C23×D43C2411yescharacteristic
270C23×D43C2411yescharacteristic
271C23×D43C2411yescharacteristic
272C2×D4×C43—42no—
273C2×D4×C43C22×C414yes—
274C22×C4×C43—22no—
275C22×C4×C43—22no—
276C22×C4×C43—22no—
277C22×C4×C43—22no—
278C22×C4×C43—24no—
279C22×C4×C43—24no—
280C22×C4×C43—42no—
281C22×C4×C43C22×C414yes—
282C22×C4×C43C22×C414yes—
283C22×C4×C43C2412yes—
284C22×C4×C43C2412yes—
285C22×C4×C43C2411yescharacteristic
286C22×C4×C43C2411yescharacteristic
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2412yes—
290C22×C4×C43C2412yes—
291C22×C4×C43C2411yescharacteristic
292C2×C22⋊D43—22no—
293C2×C22⋊D43—22no—
294C2×C22⋊D43—24no—
295C2×C22⋊D43—24no—
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—22no—
301C2×C22⋊D43—22no—
302C2×C22⋊D43C22×C414yes—
303C2×C22⋊D43C22×C414yes—
304C2×C22⋊D43C22×C414yes—
305C2×C22⋊D43C22×C414yes—
306C2×C22⋊D43C22×C414yes—
307C2×C22⋊D43C22×C414yes—
308C22×Dic43—24no—
309C22×Dic43—24no—
310C22×Dic43—42no—
311C22×Dic43C2412yes—
312C22×Dic43C2412yes—
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2411yescharacteristic
316C22×Dic43C2412yes—
317C22×Dic43C2412yes—
318C22×Dic43C2411yescharacteristic
319C22×Dic43C2411yescharacteristic
320#10621898—232no—
321#10621898—232no—
322C2×D172—22no—
323C2×D172—22no—
324C2×D172—22no—
325C2×D172—22no—
326C2×D172—42no—
327C2×D172C22×C414yes—
328C2×D172C22×C414yes—
329C2×D172C22×C414yes—
330C2×C4×D43—22no—
331C2×C4×D43—22no—
332C2×C4×D43—22no—
333C2×C4×D43—22no—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—24no—
337C2×C4×D43—24no—
338C2×C4×D43—24no—
339C2×C4×D43—24no—
340C2×C4×D43—24no—
341C2×C4×D43—24no—
342C2×C4×D43—24no—
343C2×C4×D43—42no—
344C2×C4×D43—42no—
345C2×C4×D43—42no—
346C2×C4×D43—42no—
347C2×C4×D43—42no—
348C2×C4×D43C22×C414yes—
349C2×C4×D43C22×C414yes—
350C2×C4×D43C22×C414yes—
351C2×C4×D43C22×C414yes—
352C2×C4×D43C22×C414yes—
353C2×C4×D43C2×D414yes—
354C2×C4×D43#4114yes—
355C2×Dic86—22no—
356C2×Dic86—22no—
357C2×Dic86—22no—
358C2×Dic86—22no—
359C2×Dic86C22×C414yes—
360C2×Dic86C22×C414yes—
361C4⋊C4×C43—24no—
362C4⋊C4×C43—24no—
363C4⋊C4×C43C22×C414yes—
364C22⋊C4×C43—24no—
365C22⋊C4×C43—24no—
366C22⋊C4×C43—42no—
367C22⋊C4×C43C22×C414yes—
368C22⋊C4×C43C22×C414yes—
369C42×C43—22no—
370C42×C43—24no—
371C42×C43—22no—
372C42×C43—22no—
373C42×C43C22×C414yes—
374C42×C43C2×D414yes—
375C22⋊Dic43—24no—
376C22⋊Dic43—24no—
377C22⋊Dic43—42no—
378C22⋊Dic43C22×C414yes—
379C22⋊Dic43C22×C414yes—
380(C2×D43)⋊C4—24no—
381(C2×D43)⋊C4—24no—
382(C2×D43)⋊C4—24no—
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—24no—
385(C2×D43)⋊C4—42no—
386(C2×D43)⋊C4—42no—
387(C2×D43)⋊C4C22×C414yes—
388(C2×D43)⋊C4C22×C414yes—
389(C2×D43)⋊C4C22×C414yes—
390(C2×D43)⋊C4C22×C414yes—
391(C2×D43)⋊C4C2×D418yes—
392C4⋊Dic43—24no—
393C4⋊Dic43—24no—
394C4⋊Dic43C22×C414yes—
395Dic43⋊C4—24no—
396Dic43⋊C4—24no—
397Dic43⋊C4—24no—
398Dic43⋊C4—24no—
399Dic43⋊C4C22×C414yes—
400Dic43⋊C4C22×C414yes—
401Dic43⋊C4C2×D418yes—
402Dic43⋊C4#4118yescomplemented
403C4×Dic43—22no—
404C4×Dic43—22no—
405C4×Dic43—24no—
406C4×Dic43—22no—
407C4×Dic43—24no—
408C4×Dic43—24no—
409C4×Dic43—24no—
410C4×Dic43—24no—
411C4×Dic43—24no—
412C4×Dic43—24no—
413C4×Dic43—42no—
414C4×Dic43—42no—
415C4×Dic43C22×C414yes—
416C4×Dic43C22×C414yes—
417C4×Dic43C22×C414yes—
418C4×Dic43C2×D414yes—
419C23×C43—21no—
420C23×C43—21no—
421C23×C43—22no—
422C23×C43—22no—
423C23×C43—21no—
424C23×C43—21no—
425C23×C43—22no—
426C23×C43—22no—
427C23×C43C23×C412yes—
428C23×C43C23×C412yes—
429C23×C43C2511yescharacteristic
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—21no—
433C22×D43—21no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—21no—
437C22×D43—21no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43C23×C412yes—
441C22×D43C23×C412yes—
442C22×D43C23×C412yes—
443C22×D43C22×D412yes—
444C22×D43C2×#4112yes—
445D4×C43—44no—
446C2×C4×C43—22no—
447C2×C4×C43—21no—
448C2×C4×C43—21no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—21no—
452C2×C4×C43—21no—
453C2×C4×C43—22no—
454C2×C4×C43—22no—
455C2×C4×C43—22no—
456C2×C4×C43—28no—
457C2×C4×C43—28no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
464C2×C4×C43—48no—
465C2×C4×C43C23×C412yes—
466C2×C4×C43C23×C412yes—
467C2×C4×C43C23×C412yes—
468C2×C4×C43C23×C412yes—
469C2×C4×C43C23×C412yes—
470C2×C4×C43C22×D414yes—
471C2×C4×C43C22×D412yes—
472C2×C4×C43C2×#4114yes—
473C2×C4×C43C2×#4112yes—
474C22⋊D43—28no—
475C22⋊D43—28no—
476C22⋊D43—28no—
477C22⋊D43—28no—
478C22⋊D43—28no—
479C22⋊D43—28no—
480C2×Dic43—22no—
481C2×Dic43—21no—
482C2×Dic43—21no—
483C2×Dic43—22no—
484C2×Dic43—21no—
485C2×Dic43—21no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—22no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—48no—
496C2×Dic43C23×C412yes—
497C2×Dic43C23×C412yes—
498C2×Dic43C23×C412yes—
499C2×Dic43C23×C412yes—
500C2×Dic43C23×C412yes—
501C2×Dic43C22×D414yes—
502C2×Dic43C22×D412yes—
503C2×Dic43C2×#4114yes—
504C2×Dic43C2×#4112yes—
505C2×Dic43C2×#4114yes—
506D172—28no—
507D172—28no—
508D172—44no—
509C4×D43—28no—
510C4×D43—28no—
511C4×D43—28no—
512C4×D43—44no—
513C4×D43—48no—
514C4×D43—48no—
515C4×D43—48no—
516C4×D43—48no—
517C4×D43C4×D4116yescomplemented
518Dic86—28no—
519Dic86—28no—
520#34141—431nomaximal, Sylow
521C22×C43—22no—
522C22×C43—22no—
523C22×C43—22no—
524C22×C43—22no—
525C22×C43—22no—
526C22×C43—22no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43—42no—
530C22×C43—42no—
531C22×C43C24×C411yescharacteristic
532C22×C43C23×D411yescharacteristic
533C22×C43C22×#4111yescharacteristic
534C22×C43C22×#4112yes—
535C22×C43#58512yes—
536C2×D43—22no—
537C2×D43—22no—
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—22no—
541C2×D43—22no—
542C2×D43—22no—
543C2×D43—22no—
544C2×D43—22no—
545C2×D43—22no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43C2×C4×D414yes—
551C4×C43—22no—
552C4×C43—22no—
553C4×C43—22no—
554C4×C43—22no—
555C4×C43—24no—
556C4×C43—24no—
557C4×C43—42no—
558C4×C43—42no—
559C4×C43C2×C4×D414yes—
560Dic43—22no—
561Dic43—22no—
562Dic43—22no—
563Dic43—24no—
564Dic43—24no—
565Dic43—42no—
566Dic43—42no—
567Dic43C2×C4×D414yes—
568Dic43C4×#4114yescomplemented
569C2×#532—431no—
570C2×C4×#41—431no—
571C2×C4×#41—431no—
572#2367—432no—
573#2367—432no—
574#2366—432no—
575#2365—432no—
576#2364—432no—
577#2364—432no—
578#2361—432no—
579#2361—432no—
580#2297—431no—
581#2297—431no—
582#2293—431no—
583#2293—431no—
584#2290—431no—
585#2290—431no—
586#2290—431no—
587#2290D4311yescharacteristic, complemented
588C42×D4—431no—
589C42×D4—431no—
590C4×#117—431no—
591C2×C4×C4⋊C4—431no—
592C2×C43—42no—
593C2×C43—42no—
594C2×C43C22×C4×D411yescharacteristic
595C2×C43C2×C4×#4111yescharacteristic
596C2×C43#342811yescharacteristic
597C2×C43D4×#4112yes—
598C2×C43#348012yes—
599D43—24no—
600D43—42no—
601D43—42no—
602C22×#41—431no—
603C22×#41—431no—
604#532—4316no—
605C2×C4⋊Q8—431no—
606C2×#127—431no—
607C2×#124—431no—
608C2×#124—431no—
609C2×#121—431no—
610C2×#121—431no—
611C2×#121—431no—
612C2×#121—431no—
613C4×#41—868no—
614C4×#41—868no—
615C2×C4×Q8—432no—
616C2×C4×Q8—432no—
617C2×C4×D4—431no—
618C2×C4×D4—431no—
619C2×C4×D4—432no—
620C2×C4×D4—432no—
621C2×C4×D4—432no—
622C2×C4×D4—432no—
623C2×C4×D4—432no—
624C2×C4×D4—432no—
625C2×C4×D4—432no—
626C2×C4×D4—431no—
627C2×C4×D4—432no—
628C2×C4×D4C2×D4311yescharacteristic
629C2×#117—431no—
630C2×#117—431no—
631C2×#117—431no—
632C2×#117—431no—
633C2×#117—431no—
634C2×#117C2×D4311yescharacteristic
635C22×C4⋊C4—432no—
636C22×C42—431no—
637C22×C42—431no—
638C22×C42—431no—
639C22×C42—431no—
640C22×C42—431no—
641C22×C42—431no—
642C22×C42C2×D4311yescharacteristic
643#391—432no—
644#391—432no—
645#390—432no—
646#390—432no—
647#390—432no—
648#390—432no—
649#389—432no—
650#389—432no—
651#388—432no—
652#388—432no—
653#388—432no—
654#388—432no—
655#388—432no—
656#388—432no—
657#388—432no—
658#388C2×D4312yes—
659#387—432no—
660#387—432no—
661#387—432no—
662#387C2×D4312yes—
663#386—432no—
664#386—432no—
665#386—432no—
666#386—432no—
667#386—432no—
668#386—432no—
669#386—432no—
670#386C2×D4312yes—
671#385—432no—
672#385—432no—
673#385—432no—
674#385C2×D4312yes—
675C4×C4⋊C4—432no—
676C4×C4⋊C4—432no—
677C4×C4⋊C4—431no—
678C4×C4⋊C4—431no—
679C4×C4⋊C4—431no—
680C4×C4⋊C4—432no—
681C4×C4⋊C4—432no—
682C4×C4⋊C4—432no—
683C4×C4⋊C4—432no—
684C4×C4⋊C4C2×D4311yescharacteristic
685C4×C22⋊C4—432no—
686C4×C22⋊C4—431no—
687C4×C22⋊C4—431no—
688C4×C22⋊C4—432no—
689C4×C22⋊C4—432no—
690C4×C22⋊C4—431no—
691C4×C22⋊C4—431no—
692C4×C22⋊C4—431no—
693C4×C22⋊C4—431no—
694C4×C22⋊C4—432no—
695C4×C22⋊C4—432no—
696C4×C22⋊C4—432no—
697C4×C22⋊C4C2×D4311yescharacteristic
698C4×C22⋊C4C2×D4311yescharacteristic
699#376—431no—
700#376C2×D4311yescharacteristic
701C2×#95—432no—
702C43—431no—
703C43—431no—
704C43#3414111yescharacteristic, complemented, Sylow
705C2×#41—438no—
706C2×#41—438no—
707C2×#41—864no—
708C2×#41—864no—
709C2×#41—864no—
710C2×#41—864no—
711C22×Q8—431no—
712C22×Q8—431no—
713C22×D4—431no—
714C22×D4—431no—
715C22×D4—431no—
716C22×D4—431no—
717C22×D4—431no—
718C22×D4—431no—
719C22×D4—431no—
720C22×D4—431no—
721C22×D4—431no—
722C22×D4C22×D4311yescharacteristic
723C23×C4—431no—
724C23×C4—431no—
725C23×C4—431no—
726C23×C4—431no—
727C23×C4—431no—
728C23×C4—432no—
729C23×C4—432no—
730C23×C4—432no—
731C23×C4—432no—
732C23×C4—432no—
733C23×C4C22×D4312yes—
734C23×C4C22×D4311yescharacteristic
735C23×C4C22×D4311yescharacteristic
736C4⋊Q8—438no—
737#127—438no—
738#124—438no—
739#124—438no—
740#121—438no—
741#121—438no—
742#121—438no—
743#121—438no—
744C4×Q8—868no—
745C4×Q8—868no—
746C4×D4—438no—
747C4×D4—438no—
748C4×D4—438no—
749C4×D4—868no—
750C4×D4—868no—
751C4×D4—868no—
752C4×D4—868no—
753C4×D4—868no—
754C4×D4—868no—
755C4×D4—868no—
756C4×D4—868no—
757C4×D4C4×D4318yescomplemented
758#117—24no—
759#117—438no—
760#117—864no—
761#117—864no—
762#117—864no—
763#117—864no—
764C2×C4⋊C4—432no—
765C2×C4⋊C4—432no—
766C2×C4⋊C4—431no—
767C2×C4⋊C4—431no—
768C2×C4⋊C4—431no—
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—868no—
776C2×C4⋊C4C22×D4312yes—
777C2×C4⋊C4C22×D4312yes—
778C2×C4⋊C4C22×D4311yescharacteristic
779C2×C22⋊C4—431no—
780C2×C22⋊C4—431no—
781C2×C22⋊C4—432no—
782C2×C22⋊C4—431no—
783C2×C22⋊C4—431no—
784C2×C22⋊C4—431no—
785C2×C22⋊C4—431no—
786C2×C22⋊C4—432no—
787C2×C22⋊C4—432no—
788C2×C22⋊C4—432no—
789C2×C22⋊C4—432no—
790C2×C22⋊C4—432no—
791C2×C22⋊C4—432no—
792C2×C22⋊C4—432no—
793C2×C22⋊C4—432no—
794C2×C22⋊C4—432no—
795C2×C22⋊C4—432no—
796C2×C22⋊C4C22×D4312yes—
797C2×C22⋊C4C22×D4312yes—
798C2×C22⋊C4C22×D4312yes—
799C2×C22⋊C4C22×D4311yescharacteristic
800C2×C22⋊C4C22×D4311yescharacteristic
801C2×C42—24no—
802C2×C42—431no—
803C2×C42—431no—
804C2×C42—431no—
805C2×C42—431no—
806C2×C42—438no—
807C2×C42—432no—
808C2×C42—432no—
809C2×C42—432no—
810C2×C42—432no—
811C2×C42—432no—
812C2×C42—432no—
813C2×C42—432no—
814C2×C42—431no—
815C2×C42—431no—
816C2×C42—431no—
817C2×C42—432no—
818C2×C42—432no—
819C2×C42—864no—
820C2×C42—864no—
821C2×C42—864no—
822C2×C42—864no—
823C2×C42—864no—
824C2×C42C22×D4312yes—
825C2×C42C22×D4311yescharacteristic
826C2×C42C22×D4311yescharacteristic
827C2×C42C22×D4311yescharacteristic
828C2×C42C22×D4311yescharacteristic
829C2×C42C22×D4311yescharacteristic
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#95C22×D4312yes—
842#95C22×D4312yes—
843#95C22×D4312yes—
844#95C22×D4312yes—
845#95C22×D4312yes—
846C24—431no—
847C24—431no—
848C24—431no—
849C24C23×D4311yescharacteristic
850C24C23×D4311yescharacteristic
851#41—8632no—
852#41—8632no—
853C2×Q8—434no—
854C2×Q8—434no—
855C2×Q8—862no—
856C2×Q8—862no—
857C2×Q8—862no—
858C2×Q8—862no—
859C2×D4—42no—
860C2×D4—434no—
861C2×D4—434no—
862C2×D4—434no—
863C2×D4—434no—
864C2×D4—434no—
865C2×D4—434no—
866C2×D4—434no—
867C2×D4—434no—
868C2×D4—434no—
869C2×D4—862no—
870C2×D4—862no—
871C2×D4—862no—
872C2×D4—862no—
873C2×D4—862no—
874C2×D4—862no—
875C2×D4—864no—
876C2×D4—864no—
877C2×D4—862no—
878C2×D4—862no—
879C2×D4—862no—
880C2×D4—862no—
881C2×D4—862no—
882C2×D4—862no—
883C2×D4—1722no—
884C2×D4C2×C4×D4314yes—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—42no—
892C22×C4—431no—
893C22×C4—431no—
894C22×C4—434no—
895C22×C4—434no—
896C22×C4—434no—
897C22×C4—431no—
898C22×C4—432no—
899C22×C4—431no—
900C22×C4—431no—
901C22×C4—432no—
902C22×C4—434no—
903C22×C4—434no—
904C22×C4—434no—
905C22×C4—434no—
906C22×C4—432no—
907C22×C4—432no—
908C22×C4—864no—
909C22×C4—864no—
910C22×C4—864no—
911C22×C4—864no—
912C22×C4—864no—
913C22×C4—864no—
914C22×C4—864no—
915C22×C4—864no—
916C22×C4—862no—
917C22×C4—862no—
918C22×C4—862no—
919C22×C4—862no—
920C22×C4—864no—
921C22×C4—864no—
922C22×C4—864no—
923C22×C4—1722no—
924C22×C4—1722no—
925C22×C4—1722no—
926C22×C4—1722no—
927C22×C4—1722no—
928C22×C4—1722no—
929C22×C4C2×C4×D4314yes—
930C22×C4C2×C4×D4314yes—
931C22×C4C23×D4312yes—
932C22×C4C23×D4312yes—
933C22×C4C23×D4311yescharacteristic
934C22×C4C23×D4311yescharacteristic
935C22×C4C23×D4311yescharacteristic
936C22×C4C23×D4311yescharacteristic
937C22×C4C23×D4312yes—
938C22×C4C23×D4312yes—
939C22×C4C23×D4311yescharacteristic
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—434no—
943C4⋊C4—434no—
944C4⋊C4—434no—
945C4⋊C4—438no—
946C4⋊C4—438no—
947C4⋊C4—864no—
948C4⋊C4—864no—
949C4⋊C4—864no—
950C4⋊C4—864no—
951C4⋊C4—864no—
952C4⋊C4—864no—
953C4⋊C4C2×C4×D4314yes—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—42no—
957C22⋊C4—434no—
958C22⋊C4—434no—
959C22⋊C4—434no—
960C22⋊C4—434no—
961C22⋊C4—434no—
962C22⋊C4—434no—
963C22⋊C4—438no—
964C22⋊C4—864no—
965C22⋊C4—864no—
966C22⋊C4—864no—
967C22⋊C4—864no—
968C22⋊C4—864no—
969C22⋊C4—864no—
970C22⋊C4—864no—
971C22⋊C4—1722no—
972C22⋊C4—1722no—
973C22⋊C4—1722no—
974C22⋊C4C2×C4×D4314yes—
975C22⋊C4C2×C4×D4314yes—
976C42—22no—
977C42—24no—
978C42—22no—
979C42—22no—
980C42—434no—
981C42—434no—
982C42—434no—
983C42—434no—
984C42—864no—
985C42—864no—
986C42—864no—
987C42—864no—
988C42—864no—
989C42—864no—
990C42—862no—
991C42—862no—
992C42—864no—
993C42—862no—
994C42—1722no—
995C42—1722no—
996C42C2×C4×D4314yes—
997C42D4×D4314yes—
998C23—21no—
999C23—21no—
1000C23—22no—
1001C23—22no—
1002C23—21no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—432no—
1007C23—432no—
1008C23—432no—
1009C23—432no—
1010C23—432no—
1011C23—862no—
1012C23—862no—
1013C23—861no—
1014C23—861no—
1015C23—862no—
1016C23—862no—
1017C23—861no—
1018C23—861no—
1019C23—862no—
1020C23—862no—
1021C23C22×C4×D4312yes—
1022C23C22×C4×D4312yes—
1023C23C24×D4311yescharacteristic
1024Q8—868no—
1025Q8—868no—
1026D4—44no—
1027D4—868no—
1028D4—868no—
1029D4—868no—
1030D4—868no—
1031D4—868no—
1032D4—868no—
1033D4—868no—
1034D4—868no—
1035D4—1724no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—28no—
1047C2×C4—28no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—48no—
1055C2×C4—432no—
1056C2×C4—432no—
1057C2×C4—432no—
1058C2×C4—434no—
1059C2×C4—432no—
1060C2×C4—4316no—
1061C2×C4—432no—
1062C2×C4—432no—
1063C2×C4—432no—
1064C2×C4—434no—
1065C2×C4—434no—
1066C2×C4—868no—
1067C2×C4—862no—
1068C2×C4—861no—
1069C2×C4—861no—
1070C2×C4—862no—
1071C2×C4—861no—
1072C2×C4—861no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—868no—
1077C2×C4—868no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—1724no—
1085C2×C4—1728no—
1086C2×C4—1728no—
1087C2×C4—1728no—
1088C2×C4—1728no—
1089C2×C4—1728no—
1090C2×C4C22×C4×D4312yes—
1091C2×C4C22×C4×D4312yes—
1092C2×C4C22×C4×D4312yes—
1093C2×C4C22×C4×D4312yes—
1094C2×C4C22×C4×D4312yes—
1095C2×C4C2×D4×D4314yes—
1096C2×C4C2×D4×D4312yes—
1097C2×C4#41×D4314yes—
1098C2×C4#41×D4312yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—434no—
1110C22—862no—
1111C22—864no—
1112C22—864no—
1113C22—862no—
1114C22—862no—
1115C22—862no—
1116C22—862no—
1117C22—862no—
1118C22—862no—
1119C22—862no—
1120C22—1722no—
1121C22—1722no—
1122C22—1722no—
1123C22—1722no—
1124C22C23×C4×D4311yescharacteristic
1125C22C22×D4×D4311yescharacteristic
1126C22C2×#41×D4312yes—
1127C22C2×#41×D4311yescharacteristic
1128C22#1458373512yes—
1129C4—22no—
1130C4—24no—
1131C4—24no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—42no—
1136C4—42no—
1137C4—434no—
1138C4—434no—
1139C4—862no—
1140C4—864no—
1141C4—864no—
1142C4—862no—
1143C4—862no—
1144C4—1722no—
1145C4—1722no—
1146C4C4×D4×D4314yes—
1147C2—42no—
1148C2—42no—
1149C2—864no—
1150C2—1722no—
1151C2—1722no—
1152C2C2×C4×D4×D4311yescharacteristic
1153C2C4×#41×D4311yescharacteristic
1154C2#1914779611yescharacteristic
1155C2#1914807812yes—
1156C2#1914818612yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC43×#2290C2
socle, cosocleC23×C43C25
prime radicalC2×#14583446C2
hypercenter#2290D43
hypocenterC43#34141
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621898C2semidirect
3. C2×#14583367C2semidirect
4. #19137669C2semidirect
5. #19137663C2semidirect
6. #19137658C2semidirect
7. #19137650C2semidirect
8. #19137644C2semidirect
9. #19137641C2semidirect
10. #19137614C2semidirect
11. #19137608C2semidirect
12. #19137081C2semidirect
13. #19137081C2semidirect
14. #19137058C2semidirect
15. #19137054C2semidirect
16. #19137040C2semidirect
17. #19137039C2semidirect
18. #19137036C2semidirect
19. C42×C22⋊D43C2semidirect
20. C4×(C22⋊D43)⋊C4C2semidirect
21. #19136934C2semidirect
22. C4×C4⋊C4×D43C2semidirect
23. C43×#2290C2semidirect
26. #14583446C4semidirect
130. C2×#10621898C2×C4semidirect
131. C2×#10621898C2×C4semidirect
153. #13063324C2×C4semidirect
154. #13063321C2×C4semidirect
155. #13063311C2×C4semidirect
156. #13063311C2×C4semidirect
157. #13063300C2×C4semidirect
158. #13063298C2×C4semidirect
159. #13063298C2×C4semidirect
160. #13063296C2×C4semidirect
164. C4×D172C2×C4semidirect
169. C4×C22⋊D43C2×C4semidirect
170. C4×C22⋊D43C2×C4semidirect
178. #13063282D4semidirect
229. C42×D43C2×C4semidirect
245. C4×D4×C43C2×C4semidirect
402. Dic43⋊C4#41semidirect
517. C4×D43C4×D4semidirect
568. Dic43C4×#41semidirect
587. #2290D43semidirect
704. C43#34141semidirect
757. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×C4×#106218982
C2×#145833672
#191376692
#191376632
#191376582
#191376502
#191376442
#191376412
#191376142
#191376082
#191370812
#191370582
#191370542
#191370402
#191370392
#191370362
C42×C22⋊D432
C4×(C22⋊D43)⋊C42
#191369342
C4×C4⋊C4×D432
C43×#22902
#3414143