Finite Group Databasebeta

← #25256919

Subgroups — #25256919

Order 11008.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3C2×#117×D43C211yesmaximal, characteristic
4#19137625C212yesmaximal, complemented
5#19137619C212yesmaximal, complemented
6#19137603C212yesmaximal, complemented
7#19137597C212yesmaximal, complemented
8#19137463C212yesmaximal, complemented
9#19137461C212yesmaximal, complemented
10#19137443C212yesmaximal
11#19137439C212yesmaximal
12#19137279C211yesmaximal, characteristic, complemented
13#19137277C211yesmaximal, characteristic, complemented
14#19137273C211yesmaximal, characteristic, complemented
15#19137210C211yesmaximal, characteristic, complemented
16#19137178C211yesmaximal, characteristic, complemented
17#19137133C211yesmaximal, characteristic, complemented
18C4×#13063305C211yesmaximal, characteristic, complemented
19#19137125C211yesmaximal, characteristic, complemented
20C4×#13063301C211yesmaximal, characteristic, complemented
21#19136977C211yesmaximal, characteristic
22#19136949C211yesmaximal, characteristic, complemented
23C43×#2323C211yesmaximal, characteristic, complemented
24C22×Q8×D43C2211yescharacteristic
25C23×C4×D43C2211yescharacteristic
26C2×#13063305C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063303C2212yes—
29C2×#13063302C2212yes—
30C2×#13063301C2211yescharacteristic
31C22⋊Q8×D43C4116yescomplemented
32#14583375—28no—
33C2×Q8×Dic43C2211yescharacteristic, complemented
34C2×C4×Dic86C2212yescomplemented
35C2×C4×Dic86C2211yescharacteristic, complemented
36C2×#13063290C2212yescomplemented
37C2×#13063290C2211yescharacteristic, complemented
38C2×#13063284C2211yescharacteristic
39C2×#13063283C2212yes—
40C2×#13063283C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C2×#13063283C2211yescharacteristic
43C2×#13063283C2211yescharacteristic
44C2×#13063282C2212yes—
45C2×#13063282C2211yescharacteristic
46C2×#13063282C2211yescharacteristic
47C2×#13063281C2211yescharacteristic
48C2×#13063281C2211yescharacteristic
49#117×D43—28no—
50C2×C4⋊C4×D43C2211yescharacteristic
51C2×C4⋊C4×D43C2211yescharacteristic
52C2×C4⋊C4×D43C2211yescharacteristic
53C2×C4⋊C4×D43C2212yes—
54C2×C22⋊C4×D43C2211yescharacteristic
55C2×C22⋊C4×D43C2211yescharacteristic
56C2×C22⋊C4×D43C2212yes—
57C2×C42×D43C2211yescharacteristic
58C2×C42×D43C2211yescharacteristic
59#14582806C2211yescharacteristic, complemented
60#14582805C2211yescharacteristic, complemented
61#14582804C2211yescharacteristic, complemented
62#14582803C2212yescomplemented
63#14582803C2212yescomplemented
64#14582798C2212yescomplemented
65#14582798C2211yescharacteristic, complemented
66#14582797C2211yescharacteristic, complemented
67#14582796C2212yescomplemented
68#14582796C2212yescomplemented
69#14582795C2211yescharacteristic, complemented
70#14582794C2212yescomplemented
71#14582794C2212yescomplemented
72#14582793C2212yes—
73#14582793C2212yes—
74#14582792C2212yes—
75#14582792C2212yes—
76#14582787C2212yes—
77#14582787C2212yes—
78#14582786C2212yescomplemented
79#14582786C2212yescomplemented
80#14582785C2212yescomplemented
81#14582784C2212yescomplemented
82#14582782C2212yescomplemented
83#14582780C2212yescomplemented
84#14582780C2212yescomplemented
85#14582773C2212yes—
86#14582773C2212yes—
87#14582770C2212yes—
88#14582770C2212yes—
89#14582761C2212yes—
90#14582761C2212yes—
91#14582761C2212yes—
92#14582759C2211yescharacteristic
93#14582758C2212yes—
94#14582756C2211yescharacteristic
95#14582756C2211yescharacteristic
96#14582756C2212yes—
97#14582754C2212yes—
98C4⋊C4×Dic43C2212yescomplemented
99C4⋊C4×Dic43C2211yescharacteristic, complemented
100C4⋊C4×Dic43C2211yescharacteristic, complemented
101C4×Dic43⋊C4C2212yescomplemented
102C4×Dic43⋊C4C2212yescomplemented
103C4×C4⋊Dic43C2212yescomplemented
104C4×C4⋊Dic43C2211yescharacteristic, complemented
105#14582750C2212yescomplemented
106#14582750C2212yescomplemented
107C22⋊C4×Dic43C2212yes—
108C4×(C2×D43)⋊C4C2212yes—
109C4×(C2×D43)⋊C4C2212yes—
110C4×(C2×D43)⋊C4C2212yes—
111#14582746C2212yes—
112#14582746C2212yes—
113#14582746C2212yes—
114#14582746C2212yes—
115C2×C22⋊Q8×C43C2211yescharacteristic
116C2×C4×Q8×C43C2211yescharacteristic, complemented
117C2×#117×C43C2211yescharacteristic
118C43×#391C2211yescharacteristic, complemented
119C43×#389C2212yescomplemented
120C43×#389C2211yescharacteristic, complemented
121C43×#388C2212yes—
122C43×#388C2212yes—
123C43×#387C2212yescomplemented
124C43×#380C2211yescharacteristic
125C4×C4⋊C4×C43C2211yescharacteristic, complemented
126C24×D43C2311yescharacteristic
127C22×Dic86C2312yes—
128C22×Dic86C2311yescharacteristic
129C2×Q8×D43—24no—
130C2×Q8×D43—24no—
131C2×Q8×D43C2×C418yescomplemented
132C23×Dic43C2311yescharacteristic
133C22×C4×D43—24no—
134C22×C4×D43—24no—
135C22×C4×D43C2×C418yes—
136C22×C4×D43C2311yescharacteristic
137C22×C4×D43C2311yescharacteristic
138C22×C4×D43C2311yescharacteristic
139C22×C4×D43C2311yescharacteristic
140C22×C4×D43C2311yescharacteristic
141C22×C4×D43C2312yes—
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144C22×C4×D43C2312yes—
145C22×C4×D43C2311yescharacteristic
146#13063305C2×C418yes—
147#13063304C2×C418yescomplemented
148#13063303C2×C4116yes—
149#13063302C2×C4116yescomplemented
150#13063301C2×C418yes—
151Q8×Dic43—24no—
152C4×Dic86—24no—
153C4×Dic86—28no—
154#13063290—28no—
155#13063290—24no—
156#13063284—24no—
157#13063283—24no—
158#13063283—24no—
159#13063283—24no—
160#13063283—24no—
161#13063283—28no—
162#13063282—24no—
163#13063282—28no—
164#13063282D418yes—
165#13063281—24no—
166#13063281—24no—
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2311yescharacteristic
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×Dic43⋊C4C2312yes—
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2311yescharacteristic
178C2×Dic43⋊C4C2311yescharacteristic
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2311yescharacteristic
185C2×Dic43⋊C4C2311yescharacteristic
186C4⋊C4×D43—24no—
187C4⋊C4×D43—24no—
188C4⋊C4×D43C2×C4116yescomplemented
189C4⋊C4×D43C2×C418yescomplemented
190C2×C22⋊Dic43C2311yescharacteristic
191C2×C22⋊Dic43C2311yescharacteristic
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2312yes—
194C2×(C2×D43)⋊C4C2311yescharacteristic
195C2×(C2×D43)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
203C2×(C2×D43)⋊C4C2311yescharacteristic
204C22⋊C4×D43—24no—
205C22⋊C4×D43—24no—
206C22⋊C4×D43C2×C4116yes—
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2312yes—
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2312yes—
211C2×C4×Dic43C2312yes—
212C2×C4×Dic43C2312yes—
213C2×C4×Dic43C2311yescharacteristic
214C2×C4×Dic43C2312yes—
215C2×C4×Dic43C2311yescharacteristic
216C2×C4×Dic43C2311yescharacteristic
217C2×C4×Dic43C2312yes—
218C2×C4×Dic43C2312yes—
219C2×C4×Dic43C2312yes—
220C2×C4×Dic43C2311yescharacteristic
221C42×D43—24no—
222C42×D43—24no—
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2312yes—
226C43⋊#95C2312yes—
227C43⋊#95C2312yes—
228C43⋊#95C2312yes—
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C43⋊#95C2312yes—
236C43⋊#95C2312yes—
237C43⋊#95C2312yes—
238C22×Q8×C43C2311yescharacteristic
239C23×C4×C43C2311yescharacteristic
240C22⋊Q8×C43C2×C418yescomplemented
241C4×Q8×C43—24no—
242#117×C43—24no—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C4⋊C4×C43C2312yes—
247C2×C4⋊C4×C43C2311yescharacteristic
248C2×C4⋊C4×C43C2312yes—
249C2×C4⋊C4×C43C2312yes—
250C2×C4⋊C4×C43C2311yescharacteristic
251C2×C22⋊C4×C43C2311yescharacteristic
252C2×C22⋊C4×C43C2311yescharacteristic
253C2×C22⋊C4×C43C2312yes—
254C2×C22⋊C4×C43C2312yes—
255C2×C42×C43C2311yescharacteristic
256C2×C42×C43C2312yes—
257C2×C42×C43C2312yes—
258C2×C42×C43C2311yescharacteristic
259#95×C43C2312yes—
260#95×C43C2312yes—
261#95×C43C2312yes—
262#95×C43C2312yes—
263#95×C43C2312yes—
264C24×C43C2411yescharacteristic
265C23×D43—22no—
266C23×D43—22no—
267C23×D43—22no—
268C23×D43—22no—
269C23×D43—41no—
270C23×D43—41no—
271C23×D43C22×C414yes—
272C23×D43C2411yescharacteristic
273C23×D43C2411yescharacteristic
274C2×Q8×C43—22no—
275C2×Q8×C43—22no—
276C2×Q8×C43C22×C414yes—
277C22×C4×C43—22no—
278C22×C4×C43—22no—
279C22×C4×C43C22×C414yes—
280C22×C4×C43C2412yes—
281C22×C4×C43C2411yescharacteristic
282C22×C4×C43C2411yescharacteristic
283C22×C4×C43C2412yes—
284C22×C4×C43C2412yes—
285C22×C4×C43C2412yes—
286C22×C4×C43C2411yescharacteristic
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C22×Dic43—22no—
291C22×Dic43—22no—
292C22×Dic43C22×C414yes—
293C22×Dic43C2412yes—
294C22×Dic43C2411yescharacteristic
295C22×Dic43C2411yescharacteristic
296C22×Dic43C2412yes—
297C22×Dic43C2411yescharacteristic
298C22×Dic43C2412yes—
299C22×Dic43C2412yes—
300C22×Dic43C2411yescharacteristic
301C22×Dic43C2411yescharacteristic
302C22×Dic43C2411yescharacteristic
303Q8×D43—232no—
304C2×C4×D43—22no—
305C2×C4×D43—22no—
306C2×C4×D43—22no—
307C2×C4×D43—22no—
308C2×C4×D43—232no—
309C2×C4×D43—22no—
310C2×C4×D43—22no—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—24no—
314C2×C4×D43—22no—
315C2×C4×D43—22no—
316C2×C4×D43—24no—
317C2×C4×D43—22no—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—42no—
322C2×C4×D43—42no—
323C2×C4×D43—41no—
324C2×C4×D43—41no—
325C2×C4×D43—41no—
326C2×C4×D43—41no—
327C2×C4×D43C22×C418yes—
328C2×C4×D43C22×C414yes—
329C2×C4×D43C22×C414yes—
330C2×C4×D43C22×C414yes—
331C2×C4×D43C22×C418yes—
332C2×C4×D43C22×C414yes—
333C2×C4×D43C2×D414yes—
334C2×C4×D43#4114yes—
335C2×Dic86—22no—
336C2×Dic86—22no—
337C2×Dic86—24no—
338C2×Dic86—24no—
339C2×Dic86C22×C418yes—
340C2×Dic86C22×C414yes—
341C4⋊C4×C43—22no—
342C4⋊C4×C43—22no—
343C4⋊C4×C43—24no—
344C4⋊C4×C43—22no—
345C4⋊C4×C43—22no—
346C4⋊C4×C43—42no—
347C4⋊C4×C43C22×C418yes—
348C4⋊C4×C43C22×C414yes—
349C22⋊C4×C43—22no—
350C22⋊C4×C43—22no—
351C22⋊C4×C43—42no—
352C22⋊C4×C43C22×C418yes—
353C42×C43—22no—
354C42×C43—24no—
355C42×C43—42no—
356C42×C43C2×D414yes—
357C22⋊Dic43—22no—
358C22⋊Dic43—22no—
359C22⋊Dic43—42no—
360C22⋊Dic43C22×C418yes—
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—24no—
364(C2×D43)⋊C4—24no—
365(C2×D43)⋊C4—24no—
366(C2×D43)⋊C4—24no—
367(C2×D43)⋊C4C22×C418yes—
368(C2×D43)⋊C4C22×C418yes—
369(C2×D43)⋊C4C2×D414yes—
370(C2×D43)⋊C4C2×D414yes—
371C4⋊Dic43—22no—
372C4⋊Dic43—22no—
373C4⋊Dic43—22no—
374C4⋊Dic43—22no—
375C4⋊Dic43—24no—
376C4⋊Dic43—42no—
377C4⋊Dic43C22×C414yes—
378C4⋊Dic43C22×C418yes—
379Dic43⋊C4—24no—
380Dic43⋊C4—22no—
381Dic43⋊C4—22no—
382Dic43⋊C4—24no—
383Dic43⋊C4—42no—
384Dic43⋊C4—42no—
385Dic43⋊C4C22×C418yes—
386Dic43⋊C4C22×C418yes—
387Dic43⋊C4C22×C418yes—
388Dic43⋊C4C2×D414yes—
389Dic43⋊C4C2×D414yes—
390C4×Dic43—22no—
391C4×Dic43—22no—
392C4×Dic43—22no—
393C4×Dic43—24no—
394C4×Dic43—22no—
395C4×Dic43—22no—
396C4×Dic43—24no—
397C4×Dic43—24no—
398C4×Dic43—24no—
399C4×Dic43—24no—
400C4×Dic43—42no—
401C4×Dic43—42no—
402C4×Dic43—42no—
403C4×Dic43C2×D414yes—
404C23×C43—21no—
405C23×C43—21no—
406C23×C43—21no—
407C23×C43—21no—
408C23×C43—21no—
409C23×C43—21no—
410C23×C43C23×C412yes—
411C23×C43C2511yescharacteristic
412C22×D43—21no—
413C22×D43—21no—
414C22×D43—21no—
415C22×D43—21no—
416C22×D43—21no—
417C22×D43—21no—
418C22×D43—21no—
419C22×D43—21no—
420C22×D43—28no—
421C22×D43—28no—
422C22×D43—44no—
423C22×D43—44no—
424C22×D43—44no—
425C22×D43—44no—
426C22×D43—44no—
427C22×D43C23×C412yes—
428C22×D43C23×C412yes—
429C22×D43C22×D412yes—
430C22×D43C2×#4112yes—
431C22×D432−1+412yes—
432C22×D432−1+412yes—
433Q8×C43—28no—
434C2×C4×C43—22no—
435C2×C4×C43—21no—
436C2×C4×C43—22no—
437C2×C4×C43—21no—
438C2×C4×C43—21no—
439C2×C4×C43—21no—
440C2×C4×C43—21no—
441C2×C4×C43—22no—
442C2×C4×C43—21no—
443C2×C4×C43—22no—
444C2×C4×C43—28no—
445C2×C4×C43—22no—
446C2×C4×C43—21no—
447C2×C4×C43—21no—
448C2×C4×C43—22no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—21no—
452C2×C4×C43—21no—
453C2×C4×C43—22no—
454C2×C4×C43—21no—
455C2×C4×C43—22no—
456C2×C4×C43—21no—
457C2×C4×C43C23×C412yes—
458C2×C4×C43C23×C414yes—
459C2×C4×C43C23×C414yes—
460C2×C4×C43C23×C412yes—
461C2×C4×C43C22×D412yes—
462C2×C4×C43C22×D412yes—
463C2×C4×C43C22×D412yes—
464C2×C4×C43C2×#4112yes—
465C2×Dic43—21no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—21no—
469C2×Dic43—21no—
470C2×Dic43—21no—
471C2×Dic43—21no—
472C2×Dic43—21no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—28no—
476C2×Dic43—22no—
477C2×Dic43—21no—
478C2×Dic43—21no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—21no—
483C2×Dic43—21no—
484C2×Dic43—22no—
485C2×Dic43—21no—
486C2×Dic43—22no—
487C2×Dic43—21no—
488C2×Dic43C23×C414yes—
489C2×Dic43C23×C412yes—
490C2×Dic43C23×C414yes—
491C2×Dic43C23×C412yes—
492C2×Dic43C22×D412yes—
493C2×Dic43C22×D412yes—
494C2×Dic43C22×D412yes—
495C2×Dic43C2×#4112yes—
496C4×D43—28no—
497C4×D43—216no—
498C4×D43—28no—
499C4×D43—28no—
500C4×D43—48no—
501C4×D43—44no—
502C4×D43—44no—
503C4×D43—44no—
504C4×D43—44no—
505C4×D43C4×D4116yes—
506Dic86—28no—
507Dic86—216no—
508#34203—431nomaximal, Sylow
509C22×C43—22no—
510C22×C43—22no—
511C22×C43—22no—
512C22×C43—41no—
513C22×C43—41no—
514C22×C43—41no—
515C22×C43—41no—
516C22×C43C24×C411yescharacteristic
517C22×C43C23×D411yescharacteristic
518C22×C43C22×#4111yescharacteristic
519C22×C43C2×2−1+411yescharacteristic
520C22×C43C2×2−1+411yescharacteristic
521C22×C43#58511yescharacteristic
522C22×C43#58511yescharacteristic
523C2×D43—22no—
524C2×D43—22no—
525C2×D43—22no—
526C2×D43—22no—
527C2×D43—22no—
528C2×D43—22no—
529C2×D43—22no—
530C2×D43—22no—
531C2×D43—22no—
532C2×D43—22no—
533C2×D43—22no—
534C2×D43—22no—
535C2×D43—416no—
536C2×D43C2×C4×D414yes—
537C2×D43#51914yescomplemented
538C4×C43—24no—
539C4×C43—22no—
540C4×C43—24no—
541C4×C43—22no—
542C4×C43—22no—
543C4×C43—41no—
544C4×C43—41no—
545C4×C43—42no—
546C4×C43—42no—
547C4×C43C2×C4×D414yes—
548Dic43—24no—
549Dic43—22no—
550Dic43—24no—
551Dic43—22no—
552Dic43—22no—
553Dic43—41no—
554Dic43—41no—
555Dic43—42no—
556Dic43—42no—
557Dic43C2×C4×D414yes—
558C22×C22⋊Q8—431no—
559C2×#519—431no—
560C22×#117—431no—
561#2362—432no—
562#2362—432no—
563#2360—432no—
564#2360—432no—
565#2344—432no—
566#2344—432no—
567#2342—432no—
568#2342—432no—
569#2323—431no—
570#2323—431no—
571#2323—431no—
572#2323D4311yescharacteristic, complemented
573#2316—431no—
574#2310—431no—
575C4×C22⋊Q8—431no—
576C4×C22⋊Q8—431no—
577C4×C22⋊Q8—431no—
578C4×C22⋊Q8—431no—
579#2280—431no—
580#2274—431no—
581C2×C43—42no—
582C2×C43C22×C4×D411yescharacteristic
583C2×C43C2×#51911yescharacteristic
584C2×C43#342811yescharacteristic
585C2×C43#348911yescharacteristic
586C2×C43#348911yescharacteristic
587C2×C43#349511yescharacteristic
588C2×C43#349511yescharacteristic
589D43—24no—
590D43—24no—
591C23×Q8—431no—
592C24×C4—431no—
593C2×C22⋊Q8—431no—
594C2×C22⋊Q8—431no—
595C2×C22⋊Q8—4316no—
596C2×C22⋊Q8—432no—
597C2×C22⋊Q8—431no—
598C2×C22⋊Q8—432no—
599C2×C22⋊Q8C2×D4311yescharacteristic
600#519—868no—
601C2×C4×Q8—431no—
602C2×C4×Q8—431no—
603C2×C4×Q8—432no—
604C2×C4×Q8—431no—
605C2×C4×Q8—432no—
606C2×C4×Q8C2×D4311yescharacteristic, complemented
607C2×#117—431no—
608C2×#117—431no—
609C2×#117—431no—
610C2×#117—432no—
611C2×#117—431no—
612C2×#117—431no—
613C2×#117—431no—
614C2×#117—431no—
615C2×#117—431no—
616C2×#117—431no—
617C2×#117—432no—
618C2×#117—868no—
619C2×#117C2×D4311yescharacteristic
620C22×C4⋊C4—431no—
621C22×C4⋊C4—432no—
622C22×C4⋊C4—431no—
623C22×C4⋊C4—431no—
624C22×C22⋊C4—432no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C42—431no—
628C22×C42—431no—
629#391—431no—
630#391—431no—
631#391—431no—
632#391—432no—
633#391—432no—
634#391C2×D4311yescharacteristic, complemented
635#389—432no—
636#389—432no—
637#389—431no—
638#389—431no—
639#389—432no—
640#389—431no—
641#389—432no—
642#389—432no—
643#389C2×D4311yescharacteristic, complemented
644#389C2×D4312yescomplemented
645#388—432no—
646#388—432no—
647#388—432no—
648#388—432no—
649#388—432no—
650#388—432no—
651#388C2×D4312yes—
652#388C2×D4312yes—
653#387—432no—
654#387—432no—
655#387—432no—
656#387—432no—
657#387—432no—
658#387—432no—
659#387—432no—
660#387C2×D4312yescomplemented
661#385—432no—
662#385—432no—
663#385—432no—
664#385—432no—
665#381—432no—
666#381—432no—
667#381—432no—
668#380—431no—
669#380—432no—
670#380—431no—
671#380—431no—
672#380—432no—
673#380C2×D4311yescharacteristic
674#379—432no—
675C4×C4⋊C4—431no—
676C4×C4⋊C4—431no—
677C4×C4⋊C4—432no—
678C4×C4⋊C4—431no—
679C4×C4⋊C4—432no—
680C4×C4⋊C4—432no—
681C4×C4⋊C4—432no—
682C4×C4⋊C4—432no—
683C4×C4⋊C4—432no—
684C4×C4⋊C4C2×D4311yescharacteristic, complemented
685C4×C22⋊C4—432no—
686C4×C22⋊C4—432no—
687C4×C22⋊C4—432no—
688C4×C22⋊C4—432no—
689C4×C22⋊C4—432no—
690C4×C22⋊C4—432no—
691C4×C22⋊C4—432no—
692C4×C22⋊C4—432no—
693C43#3420311yescharacteristic, complemented, Sylow
694C25—431no—
695C22×Q8—438no—
696C22×Q8—432no—
697C22×Q8—431no—
698C22×Q8—864no—
699C22×Q8—864no—
700C22×Q8C22×D4311yescharacteristic
701C23×C4—431no—
702C23×C4—431no—
703C23×C4—438no—
704C23×C4—432no—
705C23×C4—431no—
706C23×C4—431no—
707C23×C4—431no—
708C23×C4—432no—
709C23×C4—431no—
710C23×C4—431no—
711C23×C4—431no—
712C23×C4—431no—
713C23×C4—864no—
714C23×C4—864no—
715C23×C4C22×D4311yescharacteristic
716C22⋊Q8—438no—
717C22⋊Q8—438no—
718C22⋊Q8—4316no—
719C22⋊Q8—438no—
720C22⋊Q8—4316no—
721C22⋊Q8C4×D4318yescomplemented
722C4×Q8—24no—
723C4×Q8—868no—
724C4×Q8—864no—
725C4×Q8—864no—
726C4×Q8—868no—
727C4×Q8—864no—
728#117—24no—
729#117—438no—
730#117—868no—
731#117—864no—
732#117—864no—
733#117—864no—
734#117—864no—
735#117—864no—
736#117—864no—
737#117—868no—
738#117—864no—
739#117—864no—
740C2×C4⋊C4—431no—
741C2×C4⋊C4—431no—
742C2×C4⋊C4—432no—
743C2×C4⋊C4—432no—
744C2×C4⋊C4—432no—
745C2×C4⋊C4—432no—
746C2×C4⋊C4—431no—
747C2×C4⋊C4—438no—
748C2×C4⋊C4—4316no—
749C2×C4⋊C4—431no—
750C2×C4⋊C4—431no—
751C2×C4⋊C4—431no—
752C2×C4⋊C4—431no—
753C2×C4⋊C4—432no—
754C2×C4⋊C4—432no—
755C2×C4⋊C4—431no—
756C2×C4⋊C4—432no—
757C2×C4⋊C4—431no—
758C2×C4⋊C4—432no—
759C2×C4⋊C4—432no—
760C2×C4⋊C4—432no—
761C2×C4⋊C4—864no—
762C2×C4⋊C4—864no—
763C2×C4⋊C4C22×D4311yescharacteristic
764C2×C4⋊C4C22×D4311yescharacteristic
765C2×C4⋊C4C22×D4311yescharacteristic
766C2×C4⋊C4C22×D4312yes—
767C2×C4⋊C4C22×D4311yescharacteristic
768C2×C4⋊C4C22×D4312yes—
769C2×C4⋊C4C22×D4311yescharacteristic
770C2×C4⋊C4C22×D4312yes—
771C2×C22⋊C4—432no—
772C2×C22⋊C4—431no—
773C2×C22⋊C4—431no—
774C2×C22⋊C4—432no—
775C2×C22⋊C4—432no—
776C2×C22⋊C4—4316no—
777C2×C22⋊C4—431no—
778C2×C22⋊C4—431no—
779C2×C22⋊C4—431no—
780C2×C22⋊C4—431no—
781C2×C22⋊C4—432no—
782C2×C22⋊C4—432no—
783C2×C22⋊C4—432no—
784C2×C22⋊C4—432no—
785C2×C22⋊C4—432no—
786C2×C22⋊C4—864no—
787C2×C22⋊C4—864no—
788C2×C22⋊C4C22×D4311yescharacteristic
789C2×C22⋊C4C22×D4311yescharacteristic
790C2×C22⋊C4C22×D4312yes—
791C2×C22⋊C4C22×D4312yes—
792C2×C42—431no—
793C2×C42—431no—
794C2×C42—431no—
795C2×C42—431no—
796C2×C42—431no—
797C2×C42—431no—
798C2×C42—432no—
799C2×C42—432no—
800C2×C42—432no—
801C2×C42—432no—
802C2×C42—432no—
803C2×C42—432no—
804C2×C42—432no—
805C2×C42—432no—
806C2×C42—864no—
807C2×C42—864no—
808C2×C42C22×D4311yescharacteristic
809C2×C42C22×D4312yes—
810C2×C42C22×D4312yes—
811C2×C42C22×D4311yescharacteristic
812#95—432no—
813#95—432no—
814#95—432no—
815#95—432no—
816#95—432no—
817#95—432no—
818#95—432no—
819#95—432no—
820#95—432no—
821#95—432no—
822#95—432no—
823#95—432no—
824#95—432no—
825#95—432no—
826#95—432no—
827#95C22×D4312yes—
828#95C22×D4312yes—
829#95C22×D4312yes—
830#95C22×D4312yes—
831#95C22×D4312yes—
832C24—431no—
833C24—431no—
834C24—434no—
835C24—862no—
836C24—862no—
837C24—862no—
838C24—862no—
839C24—1721no—
840C24—1721no—
841C24C23×D4311yescharacteristic
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—438no—
845C2×Q8—434no—
846C2×Q8—864no—
847C2×Q8—864no—
848C2×Q8—8632no—
849C2×Q8—862no—
850C2×Q8—862no—
851C2×Q8C2×C4×D4314yes—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—431no—
855C22×C4—434no—
856C22×C4—434no—
857C22×C4—434no—
858C22×C4—434no—
859C22×C4—431no—
860C22×C4—432no—
861C22×C4—432no—
862C22×C4—431no—
863C22×C4—431no—
864C22×C4—438no—
865C22×C4—434no—
866C22×C4—434no—
867C22×C4—434no—
868C22×C4—438no—
869C22×C4—432no—
870C22×C4—431no—
871C22×C4—431no—
872C22×C4—432no—
873C22×C4—862no—
874C22×C4—862no—
875C22×C4—8632no—
876C22×C4—862no—
877C22×C4—862no—
878C22×C4—862no—
879C22×C4—864no—
880C22×C4—862no—
881C22×C4—864no—
882C22×C4—862no—
883C22×C4—862no—
884C22×C4—862no—
885C22×C4—862no—
886C22×C4—862no—
887C22×C4—862no—
888C22×C4—862no—
889C22×C4—862no—
890C22×C4—862no—
891C22×C4—862no—
892C22×C4—1721no—
893C22×C4—1722no—
894C22×C4—1721no—
895C22×C4—1722no—
896C22×C4—1721no—
897C22×C4—1721no—
898C22×C4C2×C4×D4314yes—
899C22×C4C23×D4312yes—
900C22×C4C23×D4311yescharacteristic
901C22×C4C23×D4311yescharacteristic
902C22×C4C23×D4312yes—
903C22×C4C23×D4312yes—
904C22×C4C23×D4312yes—
905C22×C4C23×D4311yescharacteristic
906C22×C4C23×D4311yescharacteristic
907C22×C4C23×D4311yescharacteristic
908C22×C4C23×D4311yescharacteristic
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—24no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—42no—
915C4⋊C4—438no—
916C4⋊C4—438no—
917C4⋊C4—438no—
918C4⋊C4—434no—
919C4⋊C4—438no—
920C4⋊C4—434no—
921C4⋊C4—434no—
922C4⋊C4—862no—
923C4⋊C4—862no—
924C4⋊C4—862no—
925C4⋊C4—862no—
926C4⋊C4—864no—
927C4⋊C4—864no—
928C4⋊C4—864no—
929C4⋊C4—862no—
930C4⋊C4—862no—
931C4⋊C4—1722no—
932C4⋊C4—1722no—
933C4⋊C4—1722no—
934C4⋊C4C2×C4×D4314yes—
935C4⋊C4C2×C4×D4318yes—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—42no—
939C22⋊C4—438no—
940C22⋊C4—438no—
941C22⋊C4—438no—
942C22⋊C4—434no—
943C22⋊C4—434no—
944C22⋊C4—862no—
945C22⋊C4—862no—
946C22⋊C4—864no—
947C22⋊C4—864no—
948C22⋊C4—864no—
949C22⋊C4—864no—
950C22⋊C4—862no—
951C22⋊C4—862no—
952C22⋊C4—1722no—
953C22⋊C4C2×C4×D4318yes—
954C42—22no—
955C42—24no—
956C42—42no—
957C42—434no—
958C42—862no—
959C42—862no—
960C42—864no—
961C42—864no—
962C42—864no—
963C42—864no—
964C42—862no—
965C42—862no—
966C42—862no—
967C42—864no—
968C42—1722no—
969C42—1722no—
970C42—1722no—
971C42D4×D4314yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—432no—
979C23—432no—
980C23—432no—
981C23—432no—
982C23—432no—
983C23—432no—
984C23—868no—
985C23—868no—
986C23—861no—
987C23—861no—
988C23—861no—
989C23—861no—
990C23—861no—
991C23—861no—
992C23—861no—
993C23—861no—
994C23—1724no—
995C23—1724no—
996C23—1724no—
997C23—1724no—
998C23—1724no—
999C23C22×C4×D4312yes—
1000C23C24×D4311yescharacteristic
1001Q8—28no—
1002Q8—8616no—
1003Q8—868no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—28no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—432no—
1028C2×C4—432no—
1029C2×C4—432no—
1030C2×C4—4316no—
1031C2×C4—434no—
1032C2×C4—434no—
1033C2×C4—432no—
1034C2×C4—432no—
1035C2×C4—432no—
1036C2×C4—868no—
1037C2×C4—868no—
1038C2×C4—8616no—
1039C2×C4—868no—
1040C2×C4—861no—
1041C2×C4—862no—
1042C2×C4—861no—
1043C2×C4—862no—
1044C2×C4—861no—
1045C2×C4—861no—
1046C2×C4—861no—
1047C2×C4—862no—
1048C2×C4—861no—
1049C2×C4—862no—
1050C2×C4—868no—
1051C2×C4—862no—
1052C2×C4—861no—
1053C2×C4—861no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—861no—
1058C2×C4—861no—
1059C2×C4—861no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—861no—
1063C2×C4—1728no—
1064C2×C4—1724no—
1065C2×C4—1724no—
1066C2×C4—1724no—
1067C2×C4—1724no—
1068C2×C4C22×C4×D4314yes—
1069C2×C4C22×C4×D4314yes—
1070C2×C4C22×C4×D4312yes—
1071C2×C4C22×C4×D4312yes—
1072C2×C4C2×D4×D4312yes—
1073C2×C4C2×D4×D4312yes—
1074C2×C4C2×D4×D4312yes—
1075C2×C4#41×D4312yes—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—434no—
1084C22—434no—
1085C22—862no—
1086C22—862no—
1087C22—862no—
1088C22—862no—
1089C22—862no—
1090C22—862no—
1091C22—862no—
1092C22—862no—
1093C22—862no—
1094C22—862no—
1095C22—862no—
1096C22—862no—
1097C22—17216no—
1098C22C23×C4×D4311yescharacteristic
1099C22C22×D4×D4311yescharacteristic
1100C22C2×#41×D4311yescharacteristic
1101C222−1+4×D4311yescharacteristic
1102C222−1+4×D4311yescharacteristic
1103C22#1458373411yescharacteristic
1104C22#1458373611yescharacteristic
1105C4—24no—
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—24no—
1110C4—42no—
1111C4—41no—
1112C4—42no—
1113C4—41no—
1114C4—434no—
1115C4—864no—
1116C4—862no—
1117C4—862no—
1118C4—862no—
1119C4—864no—
1120C4—1722no—
1121C4—1721no—
1122C4—1721no—
1123C4—1722no—
1124C4C4×D4×D4314yes—
1125C2—42no—
1126C2—864no—
1127C2—864no—
1128C2C2×C4×D4×D4311yescharacteristic
1129C2#519×D4311yescharacteristic
1130C2#1914779511yescharacteristic
1131C2#1914827011yescharacteristic
1132C2#1914827311yescharacteristic
1133C2#1914833911yescharacteristic
1134C2#1914834511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2323C2
socle, cosocleC23×C43C25
prime radicalC24×D43C23
hypercenter#2323D43
hypocenterC43#34203
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#14583375C2semidirect
4. #19137625C2semidirect
5. #19137619C2semidirect
6. #19137603C2semidirect
7. #19137597C2semidirect
8. #19137463C2semidirect
9. #19137461C2semidirect
12. #19137279C2semidirect
13. #19137277C2semidirect
14. #19137273C2semidirect
15. #19137210C2semidirect
16. #19137178C2semidirect
17. #19137133C2semidirect
18. C4×#13063305C2semidirect
19. #19137125C2semidirect
20. C4×#13063301C2semidirect
22. #19136949C2semidirect
23. C43×#2323C2semidirect
31. C22⋊Q8×D43C4semidirect
33. C2×Q8×Dic43C22semidirect
34. C2×C4×Dic86C22semidirect
35. C2×C4×Dic86C22semidirect
36. C2×#13063290C22semidirect
37. C2×#13063290C22semidirect
59. #14582806C22semidirect
60. #14582805C22semidirect
61. #14582804C22semidirect
62. #14582803C22semidirect
63. #14582803C22semidirect
64. #14582798C22semidirect
65. #14582798C22semidirect
66. #14582797C22semidirect
67. #14582796C22semidirect
68. #14582796C22semidirect
69. #14582795C22semidirect
70. #14582794C22semidirect
71. #14582794C22semidirect
78. #14582786C22semidirect
79. #14582786C22semidirect
80. #14582785C22semidirect
81. #14582784C22semidirect
82. #14582782C22semidirect
83. #14582780C22semidirect
84. #14582780C22semidirect
98. C4⋊C4×Dic43C22semidirect
99. C4⋊C4×Dic43C22semidirect
100. C4⋊C4×Dic43C22semidirect
101. C4×Dic43⋊C4C22semidirect
102. C4×Dic43⋊C4C22semidirect
103. C4×C4⋊Dic43C22semidirect
104. C4×C4⋊Dic43C22semidirect
105. #14582750C22semidirect
106. #14582750C22semidirect
116. C2×C4×Q8×C43C22semidirect
118. C43×#391C22semidirect
119. C43×#389C22semidirect
120. C43×#389C22semidirect
123. C43×#387C22semidirect
125. C4×C4⋊C4×C43C22semidirect
131. C2×Q8×D43C2×C4semidirect
147. #13063304C2×C4semidirect
149. #13063302C2×C4semidirect
188. C4⋊C4×D43C2×C4semidirect
189. C4⋊C4×D43C2×C4semidirect
240. C22⋊Q8×C43C2×C4semidirect
537. C2×D43#519semidirect
572. #2323D43semidirect
606. C2×C4×Q8C2×D43semidirect
634. #391C2×D43semidirect
643. #389C2×D43semidirect
644. #389C2×D43semidirect
660. #387C2×D43semidirect
684. C4×C4⋊C4C2×D43semidirect
693. C43#34203semidirect
721. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145833752
C2×#117×D432
#191376252
#191376192
#191376032
#191375972
#191374632
#191374612
#191374432
#191374392
#191372792
#191372772
#191372732
#191372102
#191371782
#191371332
C4×#130633052
#191371252
C4×#130633012
#191369772
#191369492
C43×#23232
#3420343