Finite Group Databasebeta

← #25063795

Subgroups — #25063795

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148621C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19136954C211yesmaximal, characteristic, complemented
4#19133117C211yesmaximal, characteristic, complemented
5#19133109C211yesmaximal, characteristic, complemented
6#19133101C211yesmaximal, characteristic, complemented
7#19133100C211yesmaximal, characteristic, complemented
8#19133096C211yesmaximal, characteristic, complemented
9#19133088C211yesmaximal, characteristic, complemented
10#19133084C211yesmaximal, characteristic, complemented
11#19133083C211yesmaximal, characteristic, complemented
12#19133078C211yesmaximal, characteristic, complemented
13C2×#14582633C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1507C211yesmaximal, characteristic, complemented
16#14583613C411yescharacteristic, complemented
17#14583604C411yescharacteristic, complemented
18#14583597C411yescharacteristic, complemented
19#14583596C411yescharacteristic, complemented
20#14583592—21no—
21#14583567C411yescharacteristic, complemented
22#14583546C411yescharacteristic, complemented
23#14583543—21no—
24#14583543C411yescharacteristic, complemented
25#14583538—21no—
26D4×C22⋊D43—21no—
27D4×C22⋊D43C411yescharacteristic, complemented
28#14583499—21no—
29#14583487—21no—
30#14583481—21no—
31#14583444C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583409C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583372—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39#14582975—21no—
40#14582968—21no—
41#14582967—21no—
42(C22⋊D43)⋊C8—21no—
43#14582953C2211yescharacteristic, complemented
44#14582949C2211yescharacteristic, complemented
45#14582861C2211yescharacteristic, complemented
46C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C22⋊C8×D43C2211yescharacteristic, complemented
48C4×Dic43⋊C4—21no—
49#14582750C2211yescharacteristic, complemented
50C22⋊C4×Dic43—21no—
51C4×(C2×D43)⋊C4—21no—
52#14582746C2211yescharacteristic, complemented
53#14582744C2211yescharacteristic, complemented
54C2×C43⋊#95C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582633C2211yescharacteristic, complemented
65#14582633C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C4×C22⋊C4×C43C2211yescharacteristic, complemented
71C43×#327C2211yescharacteristic
72C43×#327C2211yescharacteristic
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621898C2×C411yescharacteristic, complemented
76C2×#10621900—21no—
77C2×#10621900C2×C411yescharacteristic, complemented
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic, complemented
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88#13063324C2×C411yescharacteristic, complemented
89#13063321—21no—
90#13063321C2×C411yescharacteristic, complemented
91#13063320—21no—
92#13063318—21no—
93#13063318—21no—
94#13063316C2×C411yescharacteristic, complemented
95#13063315—21no—
96#13063312—21no—
97#13063312C2×C411yescharacteristic, complemented
98#13063311—21no—
99#13063311—21no—
100#13063310—21no—
101#13063308—21no—
102#13063307—21no—
103#13063307—21no—
104#13063306—21no—
105#13063306—21no—
106#13063306—21no—
107#13063305C2×C411yescharacteristic, complemented
108#13063304—21no—
109#13063304C2×C411yescharacteristic, complemented
110#13063304C2311yescharacteristic
111#13063303—21no—
112#13063300C2×C411yescharacteristic, complemented
113#13063299—21no—
114#13063299C2×C411yescharacteristic, complemented
115#13063299C2311yescharacteristic
116#13063298—21no—
117#13063298—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063297—21no—
123#13063297—21no—
124#13063296—21no—
125#13063296—21no—
126#13063296C2×C411yescharacteristic, complemented
127#13063296C2×C411yescharacteristic, complemented
128#13063294—21no—
129#13063294—21no—
130#13063294—21no—
131#13063293—21no—
132#13063293—21no—
133#13063293—21no—
134#13063290C2×C411yescharacteristic, complemented
135D4×Dic43—21no—
136D4×Dic43—21no—
137D4×Dic43C2×C411yescharacteristic, complemented
138D4×Dic43C2×C411yescharacteristic, complemented
139#13063287C2×C411yescharacteristic, complemented
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152(C22⋊D43)⋊C4—28no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156(C22⋊D43)⋊C4—21no—
157#13063284C2×C411yescharacteristic, complemented
158#13063283C2×C411yescharacteristic, complemented
159#13063281—21no—
160#13063281—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4D411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic, complemented
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43D411yescharacteristic
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C22×D4×C43—21no—
189C22×D4×C43C2×C411yescharacteristic, complemented
190C23×C4×C43C2311yescharacteristic
191C2×M16×C43—21no—
192#121×C43—21no—
193#121×C43—21no—
194#121×C43C2×C411yescharacteristic, complemented
195#121×C43C2×C411yescharacteristic, complemented
196#121×C43C2311yescharacteristic
197#121×C43C2311yescharacteristic
198C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C43—21no—
200C2×C22⋊C4×C43—21no—
201C2×C42×C43—21no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43—21no—
208C24×C43C2×D411yescharacteristic
209C23×D43—21no—
210C23×D43C2×D411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43—81no—
219C2×D4×C43C22×C411yescharacteristic
220C2×D4×C43C22×C411yescharacteristic
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—81no—
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C22×C411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—24no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—21no—
241C2×C22⋊D43—44no—
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C2×C22⋊D43C22⋊C411yescharacteristic
245C2×C22⋊D43C22⋊C411yescharacteristic
246C22×Dic43—24no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—81no—
253C22×Dic43—81no—
254C22×Dic43C2×D411yescharacteristic
255C22×Dic43C2×D411yescharacteristic
256C22×Dic43C2×D411yescharacteristic
257#10621900—81no—
258#10621900—81no—
259#10621900—81no—
260D4×D43—81no—
261D4×D43—81no—
262D4×D43—81no—
263#10621898—81no—
264C2×D172—21no—
265C2×D172C22×C411yescharacteristic
266C2×C4×D43—24no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—81no—
271C2×C4×D43—81no—
272C2×C4×D43—81no—
273C2×C4×D43C22×C411yescharacteristic
274C2×C4×D43C22×C411yescharacteristic
275C2×C4×D43C2×D411yescharacteristic
276C2×C4×D43C2×D411yescharacteristic
277C2×Dic86—21no—
278C2×Dic86C22×C411yescharacteristic
279M16×C43—81no—
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43C22×C411yescharacteristic
284C4⋊C4×C43C22×C411yescharacteristic
285C22⋊C4×C43—24no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C42×C43—81no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43—21no—
300C22⋊Dic43C22⋊C411yescharacteristic
301C22⋊Dic43C22⋊C411yescharacteristic
302C22⋊Dic43C22⋊C411yescharacteristic
303C22⋊Dic43C22⋊C411yescharacteristic
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315C4⋊Dic43—21no—
316C4⋊Dic43—21no—
317C4⋊Dic43C22×C411yescharacteristic
318C4⋊Dic43C22×C411yescharacteristic
319Dic43⋊C4—24no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328Dic43⋊C4C22⋊C411yescharacteristic
329Dic43⋊C4C22⋊C411yescharacteristic
330C4×Dic43—24no—
331C4×Dic43—21no—
332C4×Dic43—21no—
333C4×Dic43—21no—
334C4×Dic43—81no—
335C4×Dic43—81no—
336C4×Dic43C22×C411yescharacteristic
337C4×Dic43C22×C411yescharacteristic
338C4×Dic43C2×D411yescharacteristic
339C4×Dic43C2×D411yescharacteristic
340C2×C43⋊C8—21no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—81no—
343#10621872—81no—
344C8×D43—81no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—21no—
349C23×C43—21no—
350C23×C43—41no—
351C23×C43—42no—
352C23×C43—81no—
353C23×C43—81no—
354C23×C43C2×C22⋊C411yescharacteristic
355C23×C43C2×C22⋊C411yescharacteristic
356C23×C43C22×D411yescharacteristic
357C22×D43—21no—
358C22×D43—21no—
359C22×D43—22no—
360C22×D43—21no—
361C22×D43—41no—
362C22×D43—42no—
363C22×D43—81no—
364C22×D43—81no—
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43C2×C22⋊C411yescharacteristic
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43—81no—
374D4×C43—81no—
375D4×C43—81no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—81no—
391C2×C4×C43C2×C22⋊C411yescharacteristic
392C2×C4×C43C2×C22⋊C411yescharacteristic
393C2×C4×C43C23×C411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C22⋊D43—22no—
396C22⋊D43—22no—
397C22⋊D43—22no—
398C22⋊D43—41no—
399C22⋊D43—41no—
400C22⋊D43—42no—
401C22⋊D43—42no—
402C22⋊D43—42no—
403C22⋊D43—81no—
404C22⋊D43—81no—
405C22⋊D43—81no—
406C22⋊D43—81no—
407C22⋊D43—81no—
408C22⋊D43#10414yes—
409C2×Dic43—21no—
410C2×Dic43—21no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—21no—
415C2×Dic43—21no—
416C2×Dic43—21no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—42no—
423C2×Dic43—81no—
424C2×Dic43—81no—
425C2×Dic43—84no—
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428C2×Dic43C2×C22⋊C411yescharacteristic
429C2×Dic43C2×C22⋊C411yescharacteristic
430C2×Dic43C2×C22⋊C411yescharacteristic
431C2×Dic43C2×C22⋊C411yescharacteristic
432D172—41no—
433D172—81no—
434C4×D43—41no—
435C4×D43—41no—
436C4×D43—41no—
437C4×D43—41no—
438C4×D43—81no—
439C4×D43—81no—
440C4×D43—81no—
441C4×D43—84no—
442Dic86—41no—
443Dic86—81no—
444C8×C43—41no—
445C8×C43—41no—
446C43⋊C8—41no—
447C43⋊C8—41no—
448#17547—431nomaximal, Sylow
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43—41no—
461C22×C43—41no—
462C22×C43—41no—
463C22×C43—41no—
464C22×C43—162no—
465C22×C43C2×#10412yes—
466C22×C43C22×C22⋊C411yescharacteristic
467C22×C43#57611yescharacteristic
468C22×C43#57711yescharacteristic
469C2×D43—21no—
470C2×D43—21no—
471C2×D43—21no—
472C2×D43—21no—
473C2×D43—21no—
474C2×D43—42no—
475C2×D43—42no—
476C2×D43—41no—
477C2×D43—41no—
478C2×D43—41no—
479C2×D43—162no—
480C2×D43C2×#10412yes—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485C4×C43—42no—
486C4×C43—42no—
487C4×C43—41no—
488C4×C43—41no—
489Dic43—21no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—42no—
495Dic43—42no—
496Dic43—41no—
497Dic43—41no—
498Dic43—41no—
499Dic43C2×#10412yes—
500#3519—431no—
501#2974—431no—
502#2275—431no—
503#1509—431no—
504#1507—431no—
505#1507D4311yescharacteristic, complemented
506#1505—431no—
507#1504—431no—
508#1504—431no—
509#1502—431no—
510#1501—431no—
511#1501—431no—
512#1500—431no—
513C2×#327—431no—
514C2×#327—431no—
515C2×C43—21no—
516C2×C43—21no—
517C2×C43—22no—
518C2×C43—41no—
519C2×C43—81no—
520C2×C43—81no—
521C2×C43#288311yescharacteristic
522C2×C43#289711yescharacteristic
523C2×C43C22×#10411yescharacteristic
524D43—22no—
525D43—41no—
526D43—81no—
527#555—431no—
528#554—431no—
529#553—431no—
530#553—431no—
531#553—861no—
532#550—431no—
533#546—431no—
534#546—431no—
535#546—861no—
536#546—861no—
537D42—431no—
538D42—861no—
539#540—861no—
540#538—861no—
541#538—861no—
542#532—431no—
543#529—431no—
544#525—431no—
545#525—431no—
546C2×#121—431no—
547C2×#121C2×D4311yescharacteristic
548#518—861no—
549C2×C4×D4—431no—
550C2×C4×D4—861no—
551#436—861no—
552#435—861no—
553#435—861no—
554C8×D4—861no—
555#432—431no—
556#431—431no—
557#407—431no—
558#407C2×D4311yescharacteristic, complemented
559C2×C22⋊C8—431no—
560C2×C22⋊C8—431no—
561C4×C4⋊C4—431no—
562C4×C4⋊C4—861no—
563C4×C22⋊C4—431no—
564C4×C22⋊C4—861no—
565C4×C22⋊C4—861no—
566C4×C22⋊C4C2×D4311yescharacteristic, complemented
567#376—431no—
568C2×#95—431no—
569C2×#95—431no—
570#328—431no—
571#328—431no—
572#328—431no—
573#328—431no—
574#327—431no—
575#327—431no—
576#327—431no—
577#327—431no—
578#327—431no—
579#327—431no—
580#327—431no—
581#327—431no—
582#327C2×D4311yescharacteristic
583#327C2×D4311yescharacteristic
584#327C2×D4311yescharacteristic, complemented
585#327C2×D4311yescharacteristic, complemented
586C43#1754711yescharacteristic, complemented, Sylow
587C2×#41—431no—
588C2×#41—431no—
589C2×#41—861no—
590C22×D4—21no—
591C22×D4—431no—
592C22×D4—431no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4C4×D4311yescharacteristic, complemented
596C23×C4—431no—
597C23×C4—861no—
598C23×C4—861no—
599C23×C4C22×D4311yescharacteristic
600C2×M16—21no—
601C2×M16—861no—
602C22×C8—861no—
603C22×C8—861no—
604C4⋊Q8—431no—
605#127—431no—
606#127—861no—
607#126—861no—
608#126—861no—
609#126—861no—
610#125—431no—
611#125—861no—
612#124—431no—
613#124—861no—
614#124—861no—
615#124—861no—
616#123—861no—
617#123—861no—
618#123—861no—
619#123—861no—
620#123—861no—
621#123—861no—
622#123—861no—
623C22⋊Q8—431no—
624C22⋊Q8—431no—
625C22⋊Q8—431no—
626C22⋊Q8—861no—
627C22⋊Q8—861no—
628#121—21no—
629#121—21no—
630#121—431no—
631#121—431no—
632#121—431no—
633#121—431no—
634#121—431no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#121—861no—
644#121—861no—
645#121—861no—
646#121C4×D4311yescharacteristic, complemented
647#121C4×D4311yescharacteristic, complemented
648#121C22×D4311yescharacteristic
649#121C22×D4311yescharacteristic
650#120—861no—
651#120—861no—
652#120—861no—
653#120—861no—
654#120—861no—
655#120—861no—
656C4×Q8—431no—
657C4×D4—431no—
658C4×D4—431no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—431no—
664C4×D4—431no—
665C4×D4—431no—
666C4×D4—431no—
667C4×D4—431no—
668C4×D4—861no—
669C4×D4—861no—
670C4×D4—861no—
671C4×D4—861no—
672C4×D4—868no—
673C4×D4—861no—
674C4×D4—861no—
675C4×D4—861no—
676C4×D4—861no—
677C4×D4—861no—
678C4×D4—861no—
679#117—431no—
680#117—431no—
681#117—861no—
682#117—861no—
683C2×C4⋊C4—431no—
684C2×C4⋊C4—431no—
685C2×C4⋊C4—861no—
686C2×C4⋊C4C4×D4311yescharacteristic, complemented
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—431no—
690C2×C22⋊C4—431no—
691C2×C22⋊C4—861no—
692C2×C22⋊C4—861no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C42—21no—
696C2×C42—431no—
697C2×C42—861no—
698C2×C42—861no—
699C2×C42—861no—
700C4⋊C8—861no—
701C4⋊C8—861no—
702C22⋊C8—21no—
703C22⋊C8—431no—
704C22⋊C8—431no—
705C22⋊C8—861no—
706C22⋊C8—861no—
707C22⋊C8—861no—
708C22⋊C8C22×D4311yescharacteristic
709C22⋊C8C22×D4311yescharacteristic
710#97—861no—
711C4×C8—861no—
712#95—431no—
713#95—431no—
714#95—861no—
715#95—861no—
716#95—861no—
717#95C22×D4311yescharacteristic
718#95C22×D4311yescharacteristic
719C24—21no—
720C24—431no—
721C24—861no—
722C24D4×D4311yescharacteristic
723#41—3441no—
724#41—3441no—
725#41—3441no—
726#41—3441no—
727C2×Q8—431no—
728C2×Q8—861no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—431no—
738C2×D4—431no—
739C2×D4—431no—
740C2×D4—431no—
741C2×D4—431no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4—864no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—861no—
750C2×D4—861no—
751C2×D4—861no—
752C2×D4—861no—
753C2×D4—3441no—
754C2×D4—3441no—
755C2×D4—3441no—
756C2×D4—1724no—
757C2×D4C2×C4×D4311yescharacteristic
758C2×D4C2×C4×D4311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—81no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—864no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—864no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—3441no—
781C22×C4—3441no—
782C22×C4—3441no—
783C22×C4—3441no—
784C22×C4—3441no—
785C22×C4C2×C4×D4311yescharacteristic
786C22×C4C2×C4×D4311yescharacteristic
787C22×C4D4×D4311yescharacteristic
788C22×C4D4×D4311yescharacteristic
789C22×C4D4×D4311yescharacteristic
790C22×C4C23×D4311yescharacteristic
791M16—81no—
792M16—3441no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—861no—
796C2×C8—861no—
797C2×C8—3441no—
798C2×C8—3441no—
799C4⋊C4—21no—
800C4⋊C4—431no—
801C4⋊C4—431no—
802C4⋊C4—431no—
803C4⋊C4—431no—
804C4⋊C4—431no—
805C4⋊C4—431no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—864no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4C2×C4×D4311yescharacteristic
816C4⋊C4C2×C4×D4311yescharacteristic
817C22⋊C4—24no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—431no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—431no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—864no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—861no—
840C22⋊C4—861no—
841C22⋊C4—861no—
842C22⋊C4—861no—
843C22⋊C4—861no—
844C22⋊C4—861no—
845C22⋊C4—861no—
846C42—81no—
847C42—431no—
848C42—431no—
849C42—431no—
850C42—431no—
851C42—861no—
852C42—861no—
853C42—864no—
854C42—861no—
855C42—3441no—
856C42—3441no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—431no—
867C23—431no—
868C23—862no—
869C23—861no—
870C23—861no—
871C23—861no—
872C23—3441no—
873C23—3441no—
874C23—1721no—
875C23—1722no—
876C23C22⋊C4×D4311yescharacteristic
877C23C22⋊C4×D4311yescharacteristic
878C23C2×D4×D4311yescharacteristic
879Q8—3441no—
880Q8—1721no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—434no—
891D4—862no—
892D4—862no—
893D4—862no—
894D4—3441no—
895D4—3441no—
896D4—3441no—
897D4—3441no—
898D4—3441no—
899D4—3441no—
900D4—1721no—
901D4—1722no—
902D4—1722no—
903D4—1722no—
904D4—1721no—
905D4—1721no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—431no—
922C2×C4—431no—
923C2×C4—431no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—862no—
928C2×C4—861no—
929C2×C4—861no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—861no—
933C2×C4—861no—
934C2×C4—861no—
935C2×C4—3441no—
936C2×C4—3441no—
937C2×C4—3441no—
938C2×C4—3444no—
939C2×C4—3441no—
940C2×C4—3441no—
941C2×C4—3444no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1722no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4C22⋊C4×D4311yescharacteristic
953C2×C4C22⋊C4×D4311yescharacteristic
954C2×C4C22×C4×D4311yescharacteristic
955C2×C4C2×D4×D4311yescharacteristic
956C8—41no—
957C8—41no—
958C8—1721no—
959C8—1721no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—162no—
976C22—432no—
977C22—861no—
978C22—861no—
979C22—861no—
980C22—861no—
981C22—861no—
982C22—1722no—
983C22—1722no—
984C22—1721no—
985C22—1721no—
986C22—1721no—
987C22—6882no—
988C22#104×D4312yes—
989C22C2×C22⋊C4×D4311yescharacteristic
990C22#1458370311yescharacteristic
991C22#1458370911yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—432no—
1001C4—861no—
1002C4—861no—
1003C4—861no—
1004C4—861no—
1005C4—861no—
1006C4—1722no—
1007C4—1722no—
1008C4—1721no—
1009C4—1721no—
1010C4—1721no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—862no—
1018C2—3441no—
1019C2—1721no—
1020C2#1914305311yescharacteristic
1021C2#1914312011yescharacteristic
1022C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1507C2
socleC22×C43C22×C22⋊C4
prime radical#19148621C2
cosocleC22×C4×C43C24
hypercenter#1507D43
hypocenterC43#17547
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19136954C2semidirect
4. #19133117C2semidirect
5. #19133109C2semidirect
6. #19133101C2semidirect
7. #19133100C2semidirect
8. #19133096C2semidirect
9. #19133088C2semidirect
10. #19133084C2semidirect
11. #19133083C2semidirect
12. #19133078C2semidirect
13. C2×#14582633C2semidirect
14. #327×D43C2semidirect
15. C43×#1507C2semidirect
16. #14583613C4semidirect
17. #14583604C4semidirect
18. #14583597C4semidirect
19. #14583596C4semidirect
21. #14583567C4semidirect
22. #14583546C4semidirect
24. #14583543C4semidirect
27. D4×C22⋊D43C4semidirect
43. #14582953C22semidirect
44. #14582949C22semidirect
45. #14582861C22semidirect
46. C2×C22⋊(C43⋊C8)C22semidirect
47. C22⋊C8×D43C22semidirect
49. #14582750C22semidirect
52. #14582746C22semidirect
53. #14582744C22semidirect
54. C2×C43⋊#95C22semidirect
55. #95×D43C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
64. #14582633C22semidirect
65. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#407C22semidirect
70. C4×C22⋊C4×C43C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
75. C2×#10621898C2×C4semidirect
77. C2×#10621900C2×C4semidirect
81. C2×D4×D43C2×C4semidirect
88. #13063324C2×C4semidirect
90. #13063321C2×C4semidirect
94. #13063316C2×C4semidirect
97. #13063312C2×C4semidirect
107. #13063305C2×C4semidirect
109. #13063304C2×C4semidirect
112. #13063300C2×C4semidirect
114. #13063299C2×C4semidirect
126. #13063296C2×C4semidirect
127. #13063296C2×C4semidirect
134. #13063290C2×C4semidirect
137. D4×Dic43C2×C4semidirect
138. D4×Dic43C2×C4semidirect
139. #13063287C2×C4semidirect
157. #13063284C2×C4semidirect
158. #13063283C2×C4semidirect
163. C4⋊C4×D43C2×C4semidirect
189. C22×D4×C43C2×C4semidirect
194. #121×C43C2×C4semidirect
195. #121×C43C2×C4semidirect
198. C2×C4⋊C4×C43C2×C4semidirect
505. #1507D43semidirect
558. #407C2×D43semidirect
566. C4×C22⋊C4C2×D43semidirect
584. #327C2×D43semidirect
585. #327C2×D43semidirect
586. C43#17547semidirect
595. C22×D4C4×D43semidirect
646. #121C4×D43semidirect
647. #121C4×D43semidirect
686. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486212
#191436312
#191369542
#191331172
#191331092
#191331012
#191331002
#191330962
#191330882
#191330842
#191330832
#191330782
C2×#145826332
#327×D432
C43×#15072
#1754743