Finite Group Databasebeta

← #25096136

Subgroups — #25096136

Order 11008.

1482 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D43C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C2×#14582914C212yesmaximal
4#19136999C211yesmaximal, characteristic, complemented
5#19134616C211yesmaximal, characteristic, complemented
6#19134615C211yesmaximal, characteristic, complemented
7#19134614C212yesmaximal, complemented
8#19134613C212yesmaximal, complemented
9#19134612C211yesmaximal, characteristic, complemented
10#19134303C212yesmaximal, complemented
11C43×#1806C211yesmaximal, characteristic, complemented
12C2×#41×D43C2211yescharacteristic
13C2×M16×D43C2212yes—
14#41×Dic43C2211yescharacteristic
15C4×#10621902C411yescharacteristic, complemented
16C4×#10621902C411yescharacteristic, complemented
17C4×#10621898—21no—
18C4×#10621898C2211yescharacteristic
19#14583367—21no—
20#14583367C2211yescharacteristic
21C4×#10621900—21no—
22C4×#10621900—21no—
23C4×#10621900C411yescharacteristic, complemented
24C4×#10621900C411yescharacteristic, complemented
25C4×Q8×D43C411yescharacteristic, complemented
26C4×Q8×D43C411yescharacteristic, complemented
27C4×D4×D43—21no—
28C4×D4×D43—21no—
29C4×D4×D43C411yescharacteristic, complemented
30C4×D4×D43C411yescharacteristic, complemented
31C2×#13063282C2212yes—
32#117×D43—21no—
33#117×D43C2211yescharacteristic
34C2×C42×D43—21no—
35C2×C42×D43C2211yescharacteristic
36#14582923C2211yescharacteristic, complemented
37#14582922C2212yescomplemented
38#14582921—21no—
39#14582921—21no—
40C4⋊C8×D43—21no—
41C4⋊C8×D43—21no—
42#14582914—28no—
43C2×#13063253C2212yes—
44C2×#13063252C2212yes—
45C2×#13063251C2212yes—
46#14582768—21no—
47#14582763—21no—
48#14582758—21no—
49#14582756—21no—
50C4×Dic43⋊C4C2212yescomplemented
51C4×C4⋊Dic43C2211yescharacteristic, complemented
52#14582660C2212yescomplemented
53#14582659C2212yescomplemented
54#14582658C2212yescomplemented
55C4×#41×C43C2211yescharacteristic
56C43×#423C2211yescharacteristic, complemented
57C2×#104×C43C2212yes—
58C4×C4⋊C4×C43C2211yescharacteristic, complemented
59C43×#339C2212yescomplemented
60C2×#10621902C2×C411yescharacteristic
61C2×#10621898—21no—
62C2×#10621898C2311yescharacteristic
63C2×#10621900—21no—
64C2×#10621900C2×C411yescharacteristic
65#41×D43—22no—
66#41×D43—22no—
67#41×D43D414yes—
68#41×D43Q814yes—
69C2×Q8×D43C2×C411yescharacteristic
70C2×D4×D43—21no—
71C2×D4×D43C2×C411yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43D411yescharacteristic
76C22×C4×D43D411yescharacteristic
77C22×C4×D43C2311yescharacteristic
78C2×#10621877C2312yes—
79C2×#10621872—22no—
80M16×D43—24no—
81M16×D43—24no—
82C2×C8×D43—22no—
83Q8×Dic43C2×C411yescharacteristic
84Q8×Dic43C2×C411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86C2×C411yescharacteristic
89#13063290—21no—
90#13063290—21no—
91#13063290C2×C411yescharacteristic
92#13063290C2×C411yescharacteristic
93C4×D172—21no—
94C4×D172—21no—
95C4×D172C2×C411yescharacteristic
96C4×D172C2×C411yescharacteristic
97D4×Dic43—21no—
98D4×Dic43—21no—
99D4×Dic43C2×C411yescharacteristic
100D4×Dic43C2×C411yescharacteristic
101#13063287—21no—
102#13063287—21no—
103#13063287C2×C411yescharacteristic
104#13063287C2×C411yescharacteristic
105C4×C22⋊D43—21no—
106C4×C22⋊D43—21no—
107C4×C22⋊D43—21no—
108C4×C22⋊D43—21no—
109C4×C22⋊D43—21no—
110C4×C22⋊D43—21no—
111(C22⋊D43)⋊C4—21no—
112(C22⋊D43)⋊C4—21no—
113(C22⋊D43)⋊C4—21no—
114(C22⋊D43)⋊C4—21no—
115(C22⋊D43)⋊C4—21no—
116(C22⋊D43)⋊C4—21no—
117#13063284—21no—
118#13063284C2311yescharacteristic
119#13063283—21no—
120#13063283—21no—
121#13063283C2×C411yescharacteristic
122#13063283C2×C411yescharacteristic
123#13063282—21no—
124#13063282—21no—
125#13063282—24no—
126#13063282—24no—
127#13063282—21no—
128#13063281—21no—
129#13063281—21no—
130#13063281—21no—
131C2×C4⋊Dic43—21no—
132C2×Dic43⋊C4—22no—
133C2×Dic43⋊C4—22no—
134C4⋊C4×D43—21no—
135C4⋊C4×D43—21no—
136C4⋊C4×D43C2×C411yescharacteristic
137C4⋊C4×D43C2×C411yescharacteristic
138C2×(C2×D43)⋊C4—22no—
139C22⋊C4×D43—21no—
140C22⋊C4×D43—21no—
141C22⋊C4×D43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43C2312yes—
148C2×C4×Dic43C2311yescharacteristic
149C42×D43—21no—
150C42×D43—21no—
151C42×D43—21no—
152C42×D43—21no—
153C42×D43—21no—
154C42×D43—21no—
155C42×D43—21no—
156C42×D43C2×C411yescharacteristic
157C42×D43C2×C411yescharacteristic
158C42×D43C2×C411yescharacteristic
159C42×D43C2×C411yescharacteristic
160C42×D43D411yescharacteristic
161C42×D43D411yescharacteristic
162C42×D43D411yescharacteristic
163C42×D43D411yescharacteristic
164C4⋊(C43⋊C8)—21no—
165C4⋊(C43⋊C8)—21no—
166Dic43⋊C8—22no—
167Dic43⋊C8—22no—
168#13063253—24no—
169#13063252—24no—
170#13063251—24no—
171C43⋊#95—21no—
172C43⋊#95—22no—
173C2×#41×C43C2311yescharacteristic
174C2×M16×C43C2312yes—
175C4×Q8×C43C2×C411yescharacteristic
176C4×Q8×C43C2×C411yescharacteristic
177C4×D4×C43—21no—
178C4×D4×C43—21no—
179C4×D4×C43C2×C411yescharacteristic
180C4×D4×C43C2×C411yescharacteristic
181#117×C43—21no—
182#117×C43C2311yescharacteristic
183C2×C4⋊C4×C43—21no—
184C2×C42×C43—21no—
185C2×C42×C43C2312yes—
186C2×C42×C43C2311yescharacteristic
187C4⋊C8×C43—21no—
188C4⋊C8×C43—21no—
189#104×C43—24no—
190#95×C43—21no—
191C23×D43—21no—
192C23×D43C2×D411yescharacteristic
193#41×C43—21no—
194#41×C43—21no—
195#41×C43C2×D412yes—
196#41×C43C2×Q812yes—
197C2×Q8×C43C22×C411yescharacteristic
198C2×D4×C43—21no—
199C2×D4×C43C22×C411yescharacteristic
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—22no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—21no—
208C2×C22⋊D43—21no—
209C2×C22⋊D43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—22no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621902—22no—
218#10621902C4⋊C414yescomplemented
219Q8×D43—22no—
220Q8×D43C4⋊C414yescomplemented
221#10621900—24no—
222#10621900—24no—
223#10621900—22no—
224#10621900C4⋊C414yescomplemented
225D4×D43—22no—
226D4×D43—24no—
227D4×D43—24no—
228D4×D43C4⋊C414yescomplemented
229#10621898—21no—
230#10621898—21no—
231#10621898—24no—
232#10621898—24no—
233#10621898C2×D412yes—
234#10621898C2×Q812yes—
235C2×D172—21no—
236C2×D172C22×C411yescharacteristic
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—42no—
249C2×C4×D43—42no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43C22⋊C411yescharacteristic
253C2×C4×D43C22⋊C411yescharacteristic
254C2×C4×D43C22⋊C411yescharacteristic
255C2×C4×D43C22⋊C411yescharacteristic
256C2×C4×D43C22⋊C411yescharacteristic
257C2×C4×D43C22⋊C411yescharacteristic
258C2×C4×D43C22⋊C411yescharacteristic
259C2×C4×D43C22⋊C411yescharacteristic
260C2×C4×D43C22×C411yescharacteristic
261C2×C4×D43C22×C411yescharacteristic
262C2×C4×D43C2×D411yescharacteristic
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D412yes—
265C2×C4×D43C2×Q812yes—
266C2×C4×D43#4112yes—
267C2×C4×D43#4112yes—
268C2×Dic86—21no—
269C2×Dic86C22×C411yescharacteristic
270M16×C43—22no—
271M16×C43—22no—
272C2×C8×C43—22no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—42no—
276C4⋊C4×C43C22×C411yescharacteristic
277C4⋊C4×C43C22×C411yescharacteristic
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C42×C43—21no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43—22no—
285C42×C43—22no—
286C42×C43C22×C411yescharacteristic
287C42×C43C22×C411yescharacteristic
288C42×C43C2×D411yescharacteristic
289C42×C43C2×D411yescharacteristic
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—44no—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—42no—
303C4⋊Dic43C22×C411yescharacteristic
304C4⋊Dic43C22×C411yescharacteristic
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—44no—
312Dic43⋊C4—44no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—22no—
323C4×Dic43—22no—
324C4×Dic43C22⋊C411yescharacteristic
325C4×Dic43C22⋊C411yescharacteristic
326C4×Dic43C22⋊C411yescharacteristic
327C4×Dic43C22⋊C411yescharacteristic
328C4×Dic43C22⋊C411yescharacteristic
329C4×Dic43C22⋊C411yescharacteristic
330C4×Dic43C22⋊C411yescharacteristic
331C4×Dic43C22⋊C411yescharacteristic
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C22×C411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C4×Dic43C2×D411yescharacteristic
336#10621877—22no—
337#10621877—22no—
338C2×C43⋊C8—22no—
339#10621872—44no—
340C8×D43—44no—
341C23×C43—21no—
342C23×C43C22×D411yescharacteristic
343C22×D43—21no—
344C22×D43—24no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43C2×C22⋊C411yescharacteristic
350C22×D43C2×C22⋊C411yescharacteristic
351C22×D43#12112yes—
352C22×D43C22⋊Q812yes—
353Q8×C43—21no—
354Q8×C43C2×C4⋊C412yes—
355D4×C43—22no—
356D4×C43—22no—
357D4×C43—21no—
358D4×C43C2×C4⋊C412yes—
359C2×C4×C43—21no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—41no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—42no—
370C2×C4×C43—42no—
371C2×C4×C43C2×C22⋊C411yescharacteristic
372C2×C4×C43C2×C22⋊C411yescharacteristic
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C23×C411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C22×Q811yescharacteristic
379C2×C4×C43C2×#4111yescharacteristic
380C2×C4×C43C2×#4111yescharacteristic
381C22⋊D43—22no—
382C22⋊D43—22no—
383C22⋊D43—24no—
384C22⋊D43—24no—
385C2×Dic43—21no—
386C2×Dic43—24no—
387C2×Dic43—22no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—41no—
391C2×Dic43—42no—
392C2×Dic43—42no—
393C2×Dic43—42no—
394C2×Dic43—42no—
395C2×Dic43—42no—
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400C2×Dic43C2×C22⋊C411yescharacteristic
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43#12112yes—
403C2×Dic43C22⋊Q812yes—
404D172—24no—
405D172—21no—
406D172C2×C4⋊C412yes—
407C4×D43—24no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—24no—
413C4×D43—22no—
414C4×D43—22no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—41no—
419C4×D43—42no—
420C4×D43—42no—
421C4×D43—42no—
422C4×D43—42no—
423C4×D43—42no—
424C4×D43—42no—
425C4×D43C2×C4⋊C412yes—
426C4×D43C2×C4⋊C412yes—
427C4×D43#11712yes—
428C4×D43#11712yes—
429C4×D43#12112yes—
430C4×D43#12112yes—
431C4×D43C22⋊Q812yes—
432C4×D43C22⋊Q812yes—
433Dic86—21no—
434Dic86—24no—
435Dic86C2×C4⋊C412yes—
436C8×C43—42no—
437C43⋊C8—42no—
438#20654—431nomaximal, Sylow
439C22×C43—21no—
440C22×C43—21no—
441C22×C43—22no—
442C22×C43—41no—
443C22×C43—41no—
444C22×C43C22×C22⋊C411yescharacteristic
445C22×C43C2×#12111yescharacteristic
446C22×C43C2×C22⋊Q811yescharacteristic
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—22no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—48no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43#38012yes—
458C2×D43#38012yes—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—22no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—82no—
466C4×C43#42112yescomplemented
467C4×C43C22×C4⋊C411yescharacteristic
468C4×C43C2×#11711yescharacteristic
469C4×C43C2×#12111yescharacteristic
470C4×C43C2×C22⋊Q811yescharacteristic
471Dic43—21no—
472Dic43—21no—
473Dic43—21no—
474Dic43—22no—
475Dic43—41no—
476Dic43—41no—
477Dic43—82no—
478Dic43#38012yes—
479Dic43#38012yes—
480Dic43#42112yescomplemented
481C2×C4×#41—431no—
482C2×#423—431no—
483C2×#421—432no—
484#2285—431no—
485#1806—431no—
486#1806—432no—
487#1806—431no—
488#1806—432no—
489#1806—431no—
490#1806D4311yescharacteristic, complemented
491#1733—432no—
492C2×C43—21no—
493C2×C43—21no—
494C2×C43—42no—
495C2×C43C2×#38011yescharacteristic
496C2×C43C2×#42111yescharacteristic
497C2×C43C2×#42111yescharacteristic
498D43—22no—
499D43—22no—
500D43—42no—
501C22×#41—431no—
502C22×M16—432no—
503C4×#41—431no—
504C4×#41—431no—
505C4×#41—431no—
506C4×#41—431no—
507C4×#41—431no—
508C4×#41—431no—
509C4×#41—431no—
510C4×#41—861no—
511C4×#41—861no—
512C4×#41—861no—
513C4×#41—861no—
514C4×#41C2×D4311yescharacteristic
515C2×C4×Q8—431no—
516C2×C4×Q8—431no—
517C2×C4×D4—431no—
518C2×C4×D4—431no—
519C2×C4×D4—861no—
520C2×C4×D4—861no—
521C2×#117—432no—
522C2×#117—431no—
523C2×#117—861no—
524C22×C42—431no—
525C22×C42—861no—
526#423—432no—
527#423—431no—
528#423—861no—
529#423—861no—
530#423C2×D4311yescharacteristic, complemented
531C2×C4⋊C8—861no—
532C2×C4⋊C8—861no—
533#421—868no—
534C2×#104—432no—
535C2×#104—432no—
536C2×#104—432no—
537C2×#104C2×D4312yes—
538#384—861no—
539#382—861no—
540#380—861no—
541#380—861no—
542C4×C4⋊C4—432no—
543C4×C4⋊C4—431no—
544C4×C4⋊C4C2×D4311yescharacteristic, complemented
545#339—432no—
546#339—432no—
547#339—432no—
548#339C2×D4312yescomplemented
549C43#2065411yescharacteristic, complemented, Sylow
550C2×#41—434no—
551C2×#41—434no—
552C2×#41—431no—
553C2×#41—431no—
554C2×#41—431no—
555C2×#41—861no—
556C2×#41—861no—
557C2×#41—862no—
558C2×#41—862no—
559C2×#41C22×D4311yescharacteristic
560C22×Q8—431no—
561C22×D4—431no—
562C22×D4—861no—
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—861no—
567C23×C4—861no—
568C23×C4—861no—
569C2×M16—432no—
570C2×M16—862no—
571C2×M16—864no—
572C2×M16—864no—
573C2×M16C22×D4312yes—
574C22×C8—862no—
575C4×Q8—431no—
576C4×Q8—431no—
577C4×Q8—431no—
578C4×Q8—431no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—861no—
582C4×Q8—861no—
583C4×Q8—861no—
584C4×Q8—861no—
585C4×Q8C4×D4311yescharacteristic
586C4×Q8C4×D4311yescharacteristic
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—431no—
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4—861no—
601C4×D4—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4C4×D4311yescharacteristic
614C4×D4C4×D4311yescharacteristic
615#117—21no—
616#117—431no—
617#117—431no—
618#117—431no—
619#117—861no—
620#117—861no—
621#117—864no—
622#117—864no—
623#117—861no—
624#117—861no—
625#117—861no—
626#117—861no—
627#117—861no—
628#117—861no—
629#117—861no—
630#117C22×D4311yescharacteristic
631C2×C4⋊C4—21no—
632C2×C4⋊C4—431no—
633C2×C4⋊C4—431no—
634C2×C4⋊C4—861no—
635C2×C4⋊C4—861no—
636C2×C4⋊C4—862no—
637C2×C4⋊C4—862no—
638C2×C4⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—862no—
643C2×C42—21no—
644C2×C42—431no—
645C2×C42—431no—
646C2×C42—431no—
647C2×C42—431no—
648C2×C42—431no—
649C2×C42—431no—
650C2×C42—431no—
651C2×C42—431no—
652C2×C42—431no—
653C2×C42—431no—
654C2×C42—431no—
655C2×C42—432no—
656C2×C42—861no—
657C2×C42—861no—
658C2×C42—861no—
659C2×C42—861no—
660C2×C42—861no—
661C2×C42—861no—
662C2×C42—861no—
663C2×C42—861no—
664C2×C42—861no—
665C2×C42—861no—
666C2×C42C22×D4312yes—
667C2×C42C22×D4311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670C4⋊C8—862no—
671C4⋊C8—862no—
672C4⋊C8—861no—
673C4⋊C8—861no—
674#104—24no—
675#104—864no—
676#104—864no—
677#104—864no—
678#95—21no—
679#95—862no—
680#95—861no—
681C24—431no—
682C24—861no—
683#41—21no—
684#41—21no—
685#41—434no—
686#41—434no—
687#41—432no—
688#41—432no—
689#41—864no—
690#41—864no—
691#41—864no—
692#41—864no—
693#41—862no—
694#41—862no—
695#41—861no—
696#41—861no—
697#41D4×D4312yes—
698#41Q8×D4312yes—
699C2×Q8—434no—
700C2×Q8—431no—
701C2×Q8—861no—
702C2×Q8—862no—
703C2×Q8C2×C4×D4311yescharacteristic
704C2×D4—21no—
705C2×D4—434no—
706C2×D4—431no—
707C2×D4—861no—
708C2×D4—862no—
709C2×D4—861no—
710C2×D4—864no—
711C2×D4—864no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4C2×C4×D4311yescharacteristic
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—432no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4—432no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—431no—
737C22×C4—431no—
738C22×C4—861no—
739C22×C4—864no—
740C22×C4—864no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—862no—
753C22×C4—1722no—
754C22×C4—1722no—
755C22×C4—1724no—
756C22×C4—1724no—
757C22×C4D4×D4311yescharacteristic
758C22×C4D4×D4311yescharacteristic
759C22×C4C23×D4311yescharacteristic
760M16—22no—
761M16—22no—
762M16—862no—
763M16—862no—
764M16—1724no—
765C2×C8—22no—
766C2×C8—862no—
767C2×C8—1724no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—431no—
772C4⋊C4—431no—
773C4⋊C4—861no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—861no—
777C4⋊C4—861no—
778C4⋊C4—861no—
779C4⋊C4—861no—
780C4⋊C4—861no—
781C4⋊C4—1722no—
782C4⋊C4—1724no—
783C4⋊C4—1724no—
784C4⋊C4C2×C4×D4311yescharacteristic
785C4⋊C4C2×C4×D4311yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—1724no—
799C42—21no—
800C42—21no—
801C42—21no—
802C42—22no—
803C42—22no—
804C42—431no—
805C42—431no—
806C42—431no—
807C42—431no—
808C42—431no—
809C42—431no—
810C42—431no—
811C42—431no—
812C42—431no—
813C42—431no—
814C42—431no—
815C42—431no—
816C42—861no—
817C42—861no—
818C42—861no—
819C42—861no—
820C42—861no—
821C42—861no—
822C42—861no—
823C42—861no—
824C42—861no—
825C42—862no—
826C42—862no—
827C42C2×C4×D4311yescharacteristic
828C42C2×C4×D4311yescharacteristic
829C42D4×D4311yescharacteristic
830C42D4×D4311yescharacteristic
831C23—21no—
832C23—431no—
833C23—431no—
834C23—432no—
835C23—432no—
836C23—864no—
837C23—861no—
838C23—1721no—
839C23—1721no—
840C23—1722no—
841C23—1722no—
842C23C2×D4×D4311yescharacteristic
843Q8—21no—
844Q8—432no—
845Q8—864no—
846Q8—861no—
847Q8C4⋊C4×D4312yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—432no—
852D4—864no—
853D4—864no—
854D4—864no—
855D4—862no—
856D4—862no—
857D4—861no—
858D4C4⋊C4×D4312yes—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—431no—
872C2×C4—431no—
873C2×C4—431no—
874C2×C4—432no—
875C2×C4—432no—
876C2×C4—432no—
877C2×C4—432no—
878C2×C4—432no—
879C2×C4—432no—
880C2×C4—432no—
881C2×C4—432no—
882C2×C4—432no—
883C2×C4—432no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—431no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—864no—
890C2×C4—864no—
891C2×C4—862no—
892C2×C4—864no—
893C2×C4—861no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1722no—
905C2×C4—1722no—
906C2×C4—1722no—
907C2×C4—1722no—
908C2×C4—1722no—
909C2×C4—1722no—
910C2×C4—1721no—
911C2×C4—1722no—
912C2×C4—1722no—
913C2×C4—1722no—
914C2×C4—1722no—
915C2×C4—1722no—
916C2×C4C22⋊C4×D4311yescharacteristic
917C2×C4C22⋊C4×D4311yescharacteristic
918C2×C4C22⋊C4×D4311yescharacteristic
919C2×C4C22⋊C4×D4311yescharacteristic
920C2×C4C22×C4×D4311yescharacteristic
921C2×C4C2×D4×D4311yescharacteristic
922C2×C4C2×D4×D4311yescharacteristic
923C2×C4C2×Q8×D4311yescharacteristic
924C2×C4#41×D4311yescharacteristic
925C2×C4#41×D4311yescharacteristic
926C8—42no—
927C8—1722no—
928C22—21no—
929C22—21no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—432no—
934C22—432no—
935C22—861no—
936C22—861no—
937C22—861no—
938C22—861no—
939C22—862no—
940C22—1722no—
941C22—1722no—
942C22—1728no—
943C22—1721no—
944C22—1721no—
945C22C2×C22⋊C4×D4311yescharacteristic
946C22#121×D4311yescharacteristic
947C22C22⋊Q8×D4311yescharacteristic
948C4—22no—
949C4—21no—
950C4—21no—
951C4—21no—
952C4—41no—
953C4—41no—
954C4—82no—
955C4—432no—
956C4—432no—
957C4—432no—
958C4—862no—
959C4—861no—
960C4—861no—
961C4—861no—
962C4—3442no—
963C4—1721no—
964C4—1721no—
965C4#1458291412yescomplemented
966C4C2×C4⋊C4×D4311yescharacteristic
967C4#117×D4311yescharacteristic
968C4#121×D4311yescharacteristic
969C4C22⋊Q8×D4311yescharacteristic
970C2—21no—
971C2—21no—
972C2—42no—
973C2—862no—
974C2—862no—
975C2—1722no—
976C2#380×D4311yescharacteristic
977C2#421×D4311yescharacteristic
978C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#20654
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
4. #19136999C2semidirect
5. #19134616C2semidirect
6. #19134615C2semidirect
7. #19134614C2semidirect
8. #19134613C2semidirect
9. #19134612C2semidirect
10. #19134303C2semidirect
11. C43×#1806C2semidirect
15. C4×#10621902C4semidirect
16. C4×#10621902C4semidirect
23. C4×#10621900C4semidirect
24. C4×#10621900C4semidirect
25. C4×Q8×D43C4semidirect
26. C4×Q8×D43C4semidirect
29. C4×D4×D43C4semidirect
30. C4×D4×D43C4semidirect
36. #14582923C22semidirect
37. #14582922C22semidirect
50. C4×Dic43⋊C4C22semidirect
51. C4×C4⋊Dic43C22semidirect
52. #14582660C22semidirect
53. #14582659C22semidirect
54. #14582658C22semidirect
56. C43×#423C22semidirect
58. C4×C4⋊C4×C43C22semidirect
59. C43×#339C22semidirect
218. #10621902C4⋊C4semidirect
220. Q8×D43C4⋊C4semidirect
224. #10621900C4⋊C4semidirect
228. D4×D43C4⋊C4semidirect
466. C4×C43#421semidirect
480. Dic43#421semidirect
490. #1806D43semidirect
530. #423C2×D43semidirect
544. C4×C4⋊C4C2×D43semidirect
548. #339C2×D43semidirect
549. C43#20654semidirect
965. C4#14582914semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D432
#423×D432
C2×#145829142
#191369992
#191346162
#191346152
#191346142
#191346132
#191346122
#191343032
C43×#18062
#2065443