Finite Group Databasebeta

← #25105708

Subgroups — #25105708

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C2×#14582866C211yesmaximal, characteristic, complemented
3#19135031C211yesmaximal, characteristic, complemented
4#19135026C211yesmaximal, characteristic, complemented
5#19135021C211yesmaximal, characteristic, complemented
6#19135016C211yesmaximal, characteristic, complemented
7#19134917C211yesmaximal, characteristic, complemented
8#19134912C211yesmaximal, characteristic, complemented
9#19134907C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134683C211yesmaximal, characteristic, complemented
12#19134679C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic, complemented
14#19134533C211yesmaximal, characteristic, complemented
15C43×#2311C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19#14583477—24no—
20#14583477C418yescomplemented
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063301—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063297—21no—
27C2×#13063297—21no—
28C2×#13063296—21no—
29C22×C4⋊Dic43C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38#14582866—24no—
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C43×#391—21no—
55C43×#390—21no—
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yescomplemented
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C2×#10621877—22no—
76C2×#10621877—41no—
77C2×#10621877—41no—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—41no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063304—22no—
86#13063304—22no—
87#13063304C2×C414yes—
88#13063304C2×C414yescomplemented
89#13063301—28no—
90#13063299—22no—
91#13063299—22no—
92#13063299C2×C414yes—
93#13063299C2×C414yescomplemented
94#13063297—28no—
95#13063297—28no—
96#13063296—28no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43C2×C414yescomplemented
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108#13063248—41no—
109#13063248—41no—
110#13063248—41no—
111#13063248—41no—
112#13063245—41no—
113#13063245—41no—
114#13063245—41no—
115#13063245—41no—
116C22⋊(C43⋊C8)—22no—
117C22⋊(C43⋊C8)—22no—
118C22⋊(C43⋊C8)—22no—
119C22⋊(C43⋊C8)—22no—
120C2×#41×C43—41no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C2×#41×C43—41no—
124C2×#41×C43C2×C414yes—
125C2×#41×C43D414yes—
126C22×Q8×C43D411yescharacteristic
127C22×D4×C43D411yescharacteristic
128C22×D4×C43D411yescharacteristic
129C22×D4×C43D411yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134#117×C43—41no—
135#117×C43—41no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—41no—
138C2×C4⋊C4×C43—41no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43—21no—
149#95×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153C24×C43C2×D411yescharacteristic
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C23×D43—21no—
157#41×C43—44no—
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161C2×Q8×C43—41no—
162C2×Q8×C43—41no—
163C2×Q8×C43C22⋊C414yes—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43—41no—
167C2×D4×C43—41no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43C22⋊C414yes—
171C2×D4×C43C22⋊C414yes—
172C2×D4×C43C22⋊C414yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—42no—
190C22×C4×C43—81no—
191C22×C4×C43—81no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C22×C412yes—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—81no—
216C22×Dic43—81no—
217#10621898—44no—
218#10621898—44no—
219#10621898—44no—
220#10621898—44no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172C22×C412yes—
227C2×C4×D43—24no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86C22×C412yes—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—81no—
247C22⋊C4×C43—81no—
248C22⋊C4×C43—81no—
249C22⋊C4×C43—81no—
250C42×C43—42no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43C22×C412yes—
259C4⋊Dic43C22×C412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262#10621877—44no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—44no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C2×C22⋊C412yes—
296C23×C43C2×C22⋊C412yes—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305Q8×C43—44no—
306D4×C43—44no—
307D4×C43—44no—
308D4×C43—44no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—84no—
340C2×C4×C43C2×C22⋊C412yes—
341C2×C4×C43C2×C22⋊C412yes—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C22⋊D43—48no—
350C22⋊D43—84no—
351C22⋊D43—84no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—84no—
362D172—22no—
363D172—22no—
364D172—41no—
365D172—41no—
366C4×D43—48no—
367Dic86—22no—
368Dic86—22no—
369Dic86—41no—
370Dic86—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#21772—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43C22×C22⋊C411yescharacteristic
398C22×C43#53411yescharacteristic
399C22×C43#53411yescharacteristic
400C22×C43#57611yescharacteristic
401C22×C43#57711yescharacteristic
402C22×C43#57711yescharacteristic
403C22×C43#57811yescharacteristic
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—81no—
408C2×D43—81no—
409C2×D43—81no—
410C2×D43—81no—
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—81no—
415C4×C43—81no—
416C4×C43—81no—
417C4×C43—81no—
418C4×C43#51811yescharacteristic
419C4×C43#51811yescharacteristic
420C4×C43#53411yescharacteristic
421C4×C43#53411yescharacteristic
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425C2×#537—431no—
426C2×#408—431no—
427#2311D4311yescharacteristic, complemented
428#1895—431no—
429#1894—431no—
430#1893—431no—
431#1892—431no—
432#1875—431no—
433#1874—431no—
434#1873—431no—
435#1872—431no—
436#1824—431no—
437#1823—431no—
438#1788—431no—
439#1788—431no—
440C2×C43—42no—
441C2×C43—42no—
442C2×C43—42no—
443C2×C43#230811yescharacteristic
444C2×C43#289711yescharacteristic
445C2×C43#289811yescharacteristic
446C2×C43#319811yescharacteristic
447C2×C43#320111yescharacteristic
448C2×C43#320311yescharacteristic
449C2×C43#320411yescharacteristic
450D43—82no—
451C22×#41—431no—
452C22×#41C2×D4311yescharacteristic
453C22×M16—431no—
454C23×C8—431no—
455#537—438no—
456#537—864no—
457C2×C22⋊Q8—431no—
458C2×C22⋊Q8—431no—
459C2×C22⋊Q8—861no—
460C2×#121—431no—
461C2×#121—431no—
462C2×#121—861no—
463C2×#121—861no—
464C2×#121—861no—
465C2×#117C2×D4311yescharacteristic
466C22×C4⋊C4—431no—
467C22×C4⋊C4C2×D4311yescharacteristic
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476#408—864no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481#391—21no—
482#390—21no—
483#386—21no—
484#386—21no—
485#380C2×D4311yescharacteristic
486#380C2×D4311yescharacteristic
487#380C2×D4311yescharacteristic
488#380C2×D4311yescharacteristic
489#340—431no—
490#340—431no—
491#340—431no—
492#340—431no—
493#340—431no—
494#340—431no—
495#340—431no—
496#340—431no—
497C43#2177211yescharacteristic, complemented, Sylow
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—434no—
503C2×#41—862no—
504C2×#41—1721no—
505C2×#41—1721no—
506C2×#41—1721no—
507C2×#41—1721no—
508C2×#41C4×D4314yes—
509C2×#41D17214yes—
510C22×Q8—431no—
511C22×Q8C22⋊D4311yescharacteristic
512C22×D4—431no—
513C22×D4—861no—
514C22×D4—861no—
515C22×D4—861no—
516C22×D4C22⋊D4311yescharacteristic
517C22×D4C22⋊D4311yescharacteristic
518C22×D4C22⋊D4311yescharacteristic
519C23×C4—21no—
520C23×C4—861no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523C23×C4C22×D4311yescharacteristic
524C23×C4C22×D4311yescharacteristic
525C2×M16—862no—
526C2×M16—1721no—
527C2×M16—1721no—
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—862no—
533C22×C8—1721no—
534C22×C8—1721no—
535C22⋊Q8—434no—
536C22⋊Q8—434no—
537C22⋊Q8—868no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540#121—434no—
541#121—434no—
542#121—868no—
543#121—868no—
544#121—868no—
545#121—862no—
546#121—862no—
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—434no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—862no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—21no—
573#103—1721no—
574#103—1721no—
575#103—1721no—
576#103—1721no—
577#102—1721no—
578#102—1721no—
579#102—1721no—
580#102—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—862no—
584C22⋊C8—862no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—861no—
590C24C2×C22⋊D4311yescharacteristic
591C24C2×C22⋊D4311yescharacteristic
592C24C2×C22⋊D4311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—1724no—
598#41—1724no—
599#41—1724no—
600#41—1724no—
601C2×Q8—41no—
602C2×Q8—41no—
603C2×Q8—432no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8(C2×D43)⋊C414yes—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—432no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—3441no—
626C2×D4—3441no—
627C2×D4—3441no—
628C2×D4—3441no—
629C2×D4—1722no—
630C2×D4—1722no—
631C2×D4(C2×D43)⋊C414yes—
632C2×D4(C2×D43)⋊C414yes—
633C2×D4(C2×D43)⋊C414yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—81no—
652C22×C4—81no—
653C22×C4—864no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—864no—
658C22×C4—3441no—
659C22×C4—3441no—
660C22×C4—1722no—
661C22×C4—1722no—
662C22×C4C2×C4×D4312yes—
663C22×C4C2×C4×D4312yes—
664C22×C4C2×C4×D4312yes—
665C22×C4C2×D17212yes—
666C22×C4C2×D17212yes—
667C22×C4C2×D17212yes—
668C22×C4C2×C22⋊D4311yescharacteristic
669C22×C4C2×C22⋊D4311yescharacteristic
670C22×C4C2×C22⋊D4311yescharacteristic
671C22×C4C23×D4311yescharacteristic
672M16—1724no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—1724no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—862no—
731C23—1721no—
732C23—1721no—
733C23—1721no—
734C23—1721no—
735C23—1721no—
736C23—1721no—
737C23C2×(C2×D43)⋊C412yes—
738C23C2×(C2×D43)⋊C412yes—
739C23C2×(C2×D43)⋊C412yes—
740C23C22×C22⋊D4311yescharacteristic
741Q8—44no—
742Q8—862no—
743Q8—862no—
744Q8—1721no—
745Q8—1721no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—862no—
750D4—862no—
751D4—3444no—
752D4—3444no—
753D4—1728no—
754D4—1721no—
755D4—1721no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—3444no—
791C2×C4—1728no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4C2×(C2×D43)⋊C412yes—
799C2×C4C2×(C2×D43)⋊C412yes—
800C2×C4C2×(C2×D43)⋊C412yes—
801C2×C4C22×C4×D4311yescharacteristic
802C2×C4C22×D17211yescharacteristic
803C2×C4#1306337011yescharacteristic
804C2×C4#1306337011yescharacteristic
805C2×C4#1306337011yescharacteristic
806C2×C4#1306337011yescharacteristic
807C8—1721no—
808C8—1721no—
809C8—1721no—
810C8—1721no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—3441no—
833C22—3441no—
834C22—3441no—
835C22—3441no—
836C22—1722no—
837C22—1722no—
838C22—1722no—
839C22C22×(C2×D43)⋊C411yescharacteristic
840C22#1458345811yescharacteristic
841C22#1458345811yescharacteristic
842C22#1458370211yescharacteristic
843C22#1458370711yescharacteristic
844C22#1458371011yescharacteristic
845C22#1458371411yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—1722no—
854C4—1722no—
855C4—1722no—
856C4#1458337211yescharacteristic
857C4#1458337211yescharacteristic
858C4#1458346111yescharacteristic
859C4#1458346111yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—3442no—
864C2#1913717011yescharacteristic
865C2#1914311811yescharacteristic
866C2#1914312511yescharacteristic
867C2#1914544711yescharacteristic
868C2#1914547711yescharacteristic
869C2#1914549211yescharacteristic
870C2#1914550111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
cosocleC22×C4×C43C24
hypercenter#2311D43
hypocenterC43#21772
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#14582866C2semidirect
3. #19135031C2semidirect
4. #19135026C2semidirect
5. #19135021C2semidirect
6. #19135016C2semidirect
7. #19134917C2semidirect
8. #19134912C2semidirect
9. #19134907C2semidirect
10. #19134902C2semidirect
11. #19134683C2semidirect
12. #19134679C2semidirect
13. #19134533C2semidirect
14. #19134533C2semidirect
15. C43×#2311C2semidirect
20. #14583477C4semidirect
67. C2×#10621898C2×C4semidirect
88. #13063304C2×C4semidirect
93. #13063299C2×C4semidirect
99. C2×C4⋊Dic43C2×C4semidirect
427. #2311D43semidirect
497. C43#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145828662
#191350312
#191350262
#191350212
#191350162
#191349172
#191349122
#191349072
#191349022
#191346832
#191346792
#191345332
C43×#23112
#2177243