Finite Group Databasebeta

← #25105716

Subgroups — #25105716

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
2#19137187C211yesmaximal, characteristic, complemented
3#19135033C211yesmaximal, characteristic, complemented
4#19135028C211yesmaximal, characteristic, complemented
5#19135023C211yesmaximal, characteristic, complemented
6#19135018C211yesmaximal, characteristic, complemented
7#19134915C211yesmaximal, characteristic, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#19134905C211yesmaximal, characteristic, complemented
10#19134900C211yesmaximal, characteristic, complemented
11#19134686C211yesmaximal, characteristic, complemented
12#19134682C211yesmaximal, characteristic, complemented
13#19134536C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic, complemented
15C2×C43×#408C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583477—24no—
18#14583477C418yescomplemented
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063301—21no—
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063297—21no—
26C2×#13063296—21no—
27C2×#13063284C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38#14582806—21no—
39#14582802—21no—
40#14582779—21no—
41#14582779—21no—
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×#41×C43C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C43×#408—24no—
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
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—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76#13063304—22no—
77#13063304—22no—
78#13063304C2×C414yes—
79#13063304C2×C414yescomplemented
80#13063301—28no—
81#13063299—22no—
82#13063299—22no—
83#13063299C2×C414yes—
84#13063299C2×C414yescomplemented
85#13063297—28no—
86#13063297—28no—
87#13063296—28no—
88#13063284—41no—
89#13063284—41no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43—41no—
95C2×C4⋊Dic43C2×C414yescomplemented
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114#13063250—41no—
115#13063250—41no—
116#13063250—41no—
117#13063250—41no—
118#13063247—41no—
119#13063247—41no—
120#13063247—41no—
121#13063247—41no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C2×#41×C43—41no—
129C2×#41×C43—41no—
130C2×#41×C43C2×C414yes—
131C2×#41×C43D414yes—
132C22×Q8×C43D411yescharacteristic
133C22×D4×C43D411yescharacteristic
134C22×D4×C43D411yescharacteristic
135C22×D4×C43D411yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×M16×C43—22no—
140C2×M16×C43—41no—
141C2×M16×C43—41no—
142C22×C8×C43—22no—
143C22×C8×C43—41no—
144C22×C8×C43—41no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22⋊C8×C43—22no—
150C22⋊C8×C43—22no—
151C22⋊C8×C43—22no—
152C22⋊C8×C43—22no—
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×C43C22×C412yes—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C22×C412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—81no—
201C2×C22⋊D43—81no—
202C2×C22⋊D43—81no—
203C2×C22⋊D43—81no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—42no—
213C22×Dic43—81no—
214C22×Dic43—81no—
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—
236M16×C43—44no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—44no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252C22⋊Dic43—42no—
253C22⋊Dic43—81no—
254C22⋊Dic43—81no—
255C22⋊Dic43—81no—
256C22⋊Dic43—81no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259C4⋊Dic43—24no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—42no—
271C4⋊Dic43C22×C412yes—
272C4⋊Dic43C22×C412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275C4×Dic43—42no—
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×C43C2×C22⋊C412yes—
328C2×C4×C43C2×C22⋊C412yes—
329C2×C4×C43C2×C22⋊C412yes—
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C22⋊D43—48no—
337C22⋊D43—84no—
338C22⋊D43—84no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—84no—
361C2×Dic43—84no—
362D172—22no—
363D172—22no—
364D172—41no—
365D172—41no—
366C4×D43—48no—
367Dic86—22no—
368Dic86—22no—
369Dic86—41no—
370Dic86—41no—
371C8×C43—41no—
372C8×C43—41no—
373C8×C43—41no—
374C8×C43—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#51811yescharacteristic
415C4×C43#51811yescharacteristic
416C4×C43#53411yescharacteristic
417C4×C43#53411yescharacteristic
418Dic43—42no—
419Dic43—42no—
420Dic43—42no—
421Dic43—81no—
422Dic43—81no—
423Dic43—81no—
424Dic43—81no—
425C2×#537—431no—
426C2×#408D4311yescharacteristic, complemented
427#2311—431no—
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×M16C2×D4311yescharacteristic
454C23×C8C2×D4311yescharacteristic
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×#117—431no—
466C22×C4⋊C4—431no—
467C22×C4⋊C4—431no—
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—24no—
477C2×C22⋊C8C2×D4311yescharacteristic
478C2×C22⋊C8C2×D4311yescharacteristic
479C2×C22⋊C8C2×D4311yescharacteristic
480C2×C22⋊C8C2×D4311yescharacteristic
481#391—861no—
482#390—861no—
483#386—861no—
484#386—861no—
485#380—431no—
486#380—431no—
487#380—431no—
488#380—431no—
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×#41C22⋊D4314yes—
510C22×Q8—431no—
511C22×Q8D17211yescharacteristic
512C22×D4—431no—
513C22×D4—861no—
514C22×D4—861no—
515C22×D4—861no—
516C22×D4D17211yescharacteristic
517C22×D4D17211yescharacteristic
518C22×D4D17211yescharacteristic
519C23×C4—861no—
520C23×C4—861no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523C23×C4C22×D4311yescharacteristic
524C23×C4C22×D4311yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C22×D4311yescharacteristic
532C22×C8C22×D4311yescharacteristic
533C22×C8C22×D4311yescharacteristic
534C22×C8C22×D4311yescharacteristic
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—1721no—
548#117—1721no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—1721no—
562C2×C4⋊C4—1721no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—861no—
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—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—861no—
586#95—861no—
587#95—861no—
588#95—861no—
589C24—861no—
590C24C2×D17211yescharacteristic
591C24C2×D17211yescharacteristic
592C24C2×D17211yescharacteristic
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—864no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—864no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—3441no—
656C22×C4—3441no—
657C22×C4—3441no—
658C22×C4—3441no—
659C22×C4—1722no—
660C22×C4—1722no—
661C22×C4—1722no—
662C22×C4C2×C4×D4312yes—
663C22×C4C2×C4×D4312yes—
664C22×C4C2×C4×D4312yes—
665C22×C4C2×D17211yescharacteristic
666C22×C4C2×D17211yescharacteristic
667C22×C4C2×D17211yescharacteristic
668C22×C4C2×C22⋊D4312yes—
669C22×C4C2×C22⋊D4312yes—
670C22×C4C2×C22⋊D4312yes—
671C22×C4C23×D4311yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—432no—
687C4⋊C4—432no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—1722no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—3441no—
707C22⋊C4—3441no—
708C22⋊C4—3441no—
709C22⋊C4—3441no—
710C22⋊C4—1722no—
711C42—1722no—
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×D17211yescharacteristic
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—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—1728no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
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×C22⋊D4311yescharacteristic
803C2×C4#1306337011yescharacteristic
804C2×C4#1306337011yescharacteristic
805C2×C4#1306337011yescharacteristic
806C2×C4#1306337011yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
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#1458346111yescharacteristic
841C22#1458346111yescharacteristic
842C22#1458370411yescharacteristic
843C22#1458371111yescharacteristic
844C22#1458371111yescharacteristic
845C22#1458371611yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—3441no—
850C4—3441no—
851C4—3441no—
852C4—3441no—
853C4—1722no—
854C4—1722no—
855C4—1722no—
856C4#1458337211yescharacteristic
857C4#1458337211yescharacteristic
858C4#1458345811yescharacteristic
859C4#1458345811yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—3442no—
864C2#1913717011yescharacteristic
865C2#1914312211yescharacteristic
866C2#1914312911yescharacteristic
867C2#1914544911yescharacteristic
868C2#1914547911yescharacteristic
869C2#1914549711yescharacteristic
870C2#1914550711yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#408C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
cosocleC22×C4×C43C24
hypercenterC2×#408D43
hypocenterC43#21772
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #19137187C2semidirect
3. #19135033C2semidirect
4. #19135028C2semidirect
5. #19135023C2semidirect
6. #19135018C2semidirect
7. #19134915C2semidirect
8. #19134910C2semidirect
9. #19134905C2semidirect
10. #19134900C2semidirect
11. #19134686C2semidirect
12. #19134682C2semidirect
13. #19134536C2semidirect
14. #19134536C2semidirect
15. C2×C43×#408C2semidirect
18. #14583477C4semidirect
67. C2×#10621898C2×C4semidirect
79. #13063304C2×C4semidirect
84. #13063299C2×C4semidirect
95. C2×C4⋊Dic43C2×C4semidirect
426. C2×#408D43semidirect
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
#191371872
#191350332
#191350282
#191350232
#191350182
#191349152
#191349102
#191349052
#191349002
#191346862
#191346822
#191345362
C2×C43×#4082
#2177243