Finite Group Databasebeta

← #25106414

Subgroups — #25106414

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583482C211yesmaximal, characteristic
2#19137208C211yesmaximal, characteristic, complemented
3#19137192C211yesmaximal, characteristic, complemented
4#19135578C212yesmaximal, complemented
5#19135429C212yesmaximal, complemented
6#19135047C212yesmaximal, complemented
7#19135045C212yesmaximal, complemented
8#19134583C211yesmaximal, characteristic, complemented
9#19134580C211yesmaximal, characteristic, complemented
10#19134580C211yesmaximal, characteristic, complemented
11C43×#1799C211yesmaximal, characteristic, complemented
12#14583482—22no—
13#14583482—22no—
14#14583482—22no—
15#14583482—22no—
16C2×#13063320C411yescharacteristic, complemented
17C2×#13063319C411yescharacteristic, complemented
18C2×#13063313C411yescharacteristic, complemented
19C2×#13063311C411yescharacteristic, complemented
20C2×#13063310C411yescharacteristic, complemented
21C2×#13063308C411yescharacteristic, complemented
22C2×#13063302C2211yescharacteristic
23C2×#13063299C411yescharacteristic, complemented
24C2×#13063298C411yescharacteristic, complemented
25C2×#13063297C2211yescharacteristic
26C2×#13063295C2211yescharacteristic
27C2×#13063293C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C2×C22⋊C4×D43C2212yes—
31C2×#13063240C2212yes—
32C2×#13063239C2212yes—
33C2×#13063239C2212yes—
34#14582791—22no—
35#14582789—22no—
36#14582773—22no—
37#14582770—22no—
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582757C2212yes—
41#14582754C2212yes—
42C22⋊C4×Dic43C2212yes—
43#14582666C2212yes—
44#14582665C2212yes—
45#14582665C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C2×#99×C43C2212yes—
48C43×#380C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C43×#342C2212yes—
51C24×D43C2311yescharacteristic
52C22×Dic86C2×C411yescharacteristic, complemented
53C22×D172C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43C2×C411yescharacteristic
57C22×C22⋊D43C2×C411yescharacteristic, complemented
58C22×C22⋊D43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C22×C4×D43—22no—
61C22×C4×D43C2×C411yescharacteristic, complemented
62#13063320—22no—
63#13063320—22no—
64#13063319—22no—
65#13063319—22no—
66#13063313—22no—
67#13063313—22no—
68#13063311—22no—
69#13063311—22no—
70#13063310—22no—
71#13063310—22no—
72#13063308—22no—
73#13063308—22no—
74#13063302—22no—
75#13063302—22no—
76#13063299—22no—
77#13063299—22no—
78#13063298—22no—
79#13063298—22no—
80#13063297—22no—
81#13063297—22no—
82#13063295—22no—
83#13063295—22no—
84#13063293—22no—
85#13063293—22no—
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89C4×C22⋊D43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C411yescharacteristic, complemented
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4C2×C411yescharacteristic, complemented
95C2×Dic43⋊C4C2×C411yescharacteristic, complemented
96C2×Dic43⋊C4C2×C411yescharacteristic, complemented
97C2×Dic43⋊C4C2×C411yescharacteristic, complemented
98C2×C22⋊Dic43C2×C411yescharacteristic, complemented
99C2×C22⋊Dic43C2312yes—
100C2×C22⋊Dic43C2312yes—
101C2×C22⋊Dic43C2311yescharacteristic
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
114C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
115C2×(C2×D43)⋊C4D412yes—
116C2×(C2×D43)⋊C4D412yes—
117C2×(C2×D43)⋊C4D412yes—
118C2×(C2×D43)⋊C4D412yes—
119C22⋊C4×D43—42no—
120C22⋊C4×D43—42no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43C2×C411yescharacteristic, complemented
123#13063240—42no—
124#13063239—42no—
125#13063239—42no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43C2×C411yescharacteristic, complemented
132C23×C4×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2312yes—
143C2×C22⋊C4×C43C2311yescharacteristic
144C2×C42×C43C2×C411yescharacteristic, complemented
145#99×C43—42no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C22×C411yescharacteristic
149C24×C43C2411yescharacteristic
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—81no—
155C23×D43—81no—
156C23×D43C22×C411yescharacteristic
157C23×D43C22×C411yescharacteristic
158C23×D43C22×C411yescharacteristic
159C23×D43C2×D412yes—
160C23×D43C2×D412yes—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C2×C22⋊D43—22no—
183C2×C22⋊D43—21no—
184C2×C22⋊D43—21no—
185C2×C22⋊D43—21no—
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—81no—
192C2×C22⋊D43—81no—
193C2×C22⋊D43—81no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—81no—
197C22×Dic43C22×C411yescharacteristic
198C22×Dic43C22×C411yescharacteristic
199C22×Dic43C22×C411yescharacteristic
200C22×Dic43C22×C411yescharacteristic
201C22×Dic43C22×C411yescharacteristic
202C22×Dic43C2×D412yes—
203C22×Dic43C2×D412yes—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—81no—
207C2×D172—81no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—44no—
211C2×C4×D43—82no—
212C2×C4×D43—82no—
213C2×C4×D43—81no—
214C2×Dic86—22no—
215C2×Dic86—81no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—81no—
219C4⋊C4×C43—81no—
220C22⋊C4×C43—21no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—21no—
223C22⋊C4×C43—21no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—22no—
228C42×C43—21no—
229C42×C43—21no—
230C22⋊Dic43—22no—
231C22⋊Dic43—21no—
232C22⋊Dic43—21no—
233C22⋊Dic43—22no—
234C22⋊Dic43—22no—
235C22⋊Dic43—22no—
236C22⋊Dic43—22no—
237(C2×D43)⋊C4—21no—
238(C2×D43)⋊C4—21no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—22no—
242(C2×D43)⋊C4—22no—
243(C2×D43)⋊C4—22no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4—82no—
246(C2×D43)⋊C4—82no—
247(C2×D43)⋊C4C22⋊C412yes—
248(C2×D43)⋊C4C22⋊C412yes—
249(C2×D43)⋊C4C22⋊C412yes—
250(C2×D43)⋊C4C22⋊C412yes—
251(C2×D43)⋊C4C22⋊C412yes—
252(C2×D43)⋊C4C22⋊C412yes—
253(C2×D43)⋊C4C22⋊C412yes—
254(C2×D43)⋊C4C22⋊C412yes—
255C4⋊Dic43—22no—
256C4⋊Dic43—81no—
257C4⋊Dic43—81no—
258Dic43⋊C4—21no—
259Dic43⋊C4—21no—
260Dic43⋊C4—22no—
261Dic43⋊C4—22no—
262Dic43⋊C4—22no—
263Dic43⋊C4—82no—
264C4×Dic43—21no—
265C4×Dic43—21no—
266C4×Dic43—82no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43C23×C411yescharacteristic
275C23×C43C22×D411yescharacteristic
276C23×C43C22×D411yescharacteristic
277C23×C43H(5,𝔽2)11yescharacteristic
278C23×C43H(5,𝔽2)11yescharacteristic
279C23×C432−1+411yescharacteristic
280C23×C432−1+411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—82no—
303C22×D43—82no—
304C22×D43—82no—
305C22×D43—82no—
306C22×D43C2×C22⋊C412yes—
307C22×D43C2×C22⋊C412yes—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—81no—
332C2×C4×C43—81no—
333C2×C4×C43C2×C22⋊C411yescharacteristic
334C2×C4×C43C2×C22⋊C411yescharacteristic
335C2×C4×C43C2×C22⋊C411yescharacteristic
336C2×C4×C43C2×C22⋊C411yescharacteristic
337C22⋊D43—41no—
338C22⋊D43—41no—
339C22⋊D43—41no—
340C22⋊D43—41no—
341C22⋊D43—82no—
342C22⋊D43—82no—
343C22⋊D43—82no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43—42no—
360C2×Dic43—42no—
361C2×Dic43C2×C22⋊C412yes—
362C2×Dic43C2×C22⋊C412yes—
363D172—82no—
364D172—82no—
365C4×D43—81no—
366C4×D43—81no—
367C4×D43—88no—
368Dic86—82no—
369#21876—431nomaximal, Sylow
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43C22×C22⋊C411yescharacteristic
386C22×C43#52011yescharacteristic
387C22×C43#52011yescharacteristic
388C22×C43#53511yescharacteristic
389C22×C43#53611yescharacteristic
390C22×C43#53711yescharacteristic
391C22×C43#53711yescharacteristic
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—22no—
398C2×D43—44no—
399C2×D43—44no—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—41no—
403C2×D43—82no—
404C2×D43—82no—
405C2×D43—81no—
406C2×D43—81no—
407C2×D43—81no—
408C2×D43—81no—
409C2×D43—81no—
410C2×D43—81no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—82no—
419C4×C43—82no—
420Dic43—22no—
421Dic43—22no—
422Dic43—41no—
423Dic43—41no—
424Dic43—41no—
425Dic43—82no—
426Dic43—82no—
427C2×#538—431no—
428#2315—431no—
429#2312—431no—
430#1996—432no—
431#1964—432no—
432#1898—432no—
433#1898—432no—
434#1799—431no—
435#1799—431no—
436#1799—431no—
437#1799D4311yescharacteristic, complemented
438C2×C43—21no—
439C2×C43—21no—
440C2×C43—21no—
441C2×C43—21no—
442C2×C43—21no—
443C2×C43—21no—
444C2×C43—81no—
445C2×C43#231111yescharacteristic
446C2×C43#288311yescharacteristic
447C2×C43#288311yescharacteristic
448D43—42no—
449D43—42no—
450D43—81no—
451#538—862no—
452#538—862no—
453#538—862no—
454#538—862no—
455C2×#126—431no—
456C2×#126—431no—
457C2×#124—431no—
458C2×#124—431no—
459C2×#123—431no—
460C2×#123—431no—
461C2×C22⋊Q8—431no—
462C2×#121—431no—
463C2×#121—431no—
464C2×#121—431no—
465C2×#120—431no—
466C2×#120—431no—
467C2×C4×D4—431no—
468C2×C4×D4C2×D4311yescharacteristic
469C22×C22⋊C4—431no—
470C22×C22⋊C4—432no—
471C2×#99—432no—
472C2×#99—432no—
473C2×#99—432no—
474C2×#99C2×D4312yes—
475#388—862no—
476#388—862no—
477#385—862no—
478#385—862no—
479#380—431no—
480#380—431no—
481#380—432no—
482#380C2×D4311yescharacteristic
483#380C2×D4311yescharacteristic
484#379—432no—
485C4×C22⋊C4—432no—
486#342—432no—
487#342—432no—
488#342—432no—
489#342C2×D4312yes—
490C43#2187611yescharacteristic, complemented, Sylow
491C25—431no—
492C22×Q8—431no—
493C22×D4—431no—
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—431no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4C22×D4311yescharacteristic
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—862no—
503C23×C4C4×D4311yescharacteristic, complemented
504C23×C4C22×D4311yescharacteristic
505#126—862no—
506#126—862no—
507#126—862no—
508#126—862no—
509#124—862no—
510#124—862no—
511#124—862no—
512#124—862no—
513#123—862no—
514#123—862no—
515#123—862no—
516#123—862no—
517C22⋊Q8—862no—
518C22⋊Q8—862no—
519#121—862no—
520#121—862no—
521#121—862no—
522#121—862no—
523#121—862no—
524#121—862no—
525#120—862no—
526#120—862no—
527#120—862no—
528#120—862no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—862no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4C4×D4311yescharacteristic, complemented
548C2×C22⋊C4—431no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—432no—
553C2×C22⋊C4—432no—
554C2×C22⋊C4—432no—
555C2×C22⋊C4—432no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—431no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—431no—
563C2×C22⋊C4—431no—
564C2×C22⋊C4—432no—
565C2×C22⋊C4—432no—
566C2×C22⋊C4—862no—
567C2×C22⋊C4—862no—
568C2×C22⋊C4—862no—
569C2×C22⋊C4—1722no—
570C2×C22⋊C4—1722no—
571C2×C22⋊C4C4×D4311yescharacteristic, complemented
572C2×C22⋊C4C22×D4312yes—
573C2×C22⋊C4C22×D4312yes—
574C2×C22⋊C4C22×D4311yescharacteristic
575C2×C42—431no—
576C2×C42—862no—
577C2×C42C4×D4311yescharacteristic, complemented
578#99—42no—
579#99—1722no—
580#99—1722no—
581#99—1722no—
582#95—21no—
583#95—21no—
584#95—862no—
585#95—862no—
586#95—861no—
587#95—861no—
588C24—431no—
589C24—431no—
590C24—432no—
591C24—432no—
592C24—431no—
593C24—861no—
594C24—861no—
595C24—861no—
596C24—861no—
597C24—3441no—
598C24—3441no—
599C24C2×C4×D4311yescharacteristic
600C24C23×D4311yescharacteristic
601C2×Q8—862no—
602C2×Q8—3441no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—3441no—
621C2×D4—3441no—
622C2×D4—3441no—
623C2×D4—3441no—
624C2×D4—3441no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—3442no—
643C22×C4—3442no—
644C22×C4—3441no—
645C22×C4—3441no—
646C22×C4—1724no—
647C22×C4C2×C4×D4311yescharacteristic
648C22×C4C2×C4×D4311yescharacteristic
649C22×C4C2×C4×D4311yescharacteristic
650C22×C4C2×C4×D4311yescharacteristic
651C22×C4C2×C4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4D4×D4311yescharacteristic
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—81no—
659C4⋊C4—81no—
660C4⋊C4—862no—
661C4⋊C4—862no—
662C4⋊C4—862no—
663C4⋊C4—862no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—3442no—
667C4⋊C4—3441no—
668C4⋊C4—3441no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—432no—
678C22⋊C4—432no—
679C22⋊C4—432no—
680C22⋊C4—432no—
681C22⋊C4—432no—
682C22⋊C4—432no—
683C22⋊C4—432no—
684C22⋊C4—432no—
685C22⋊C4—862no—
686C22⋊C4—862no—
687C22⋊C4—862no—
688C22⋊C4—862no—
689C22⋊C4—862no—
690C22⋊C4—862no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—862no—
696C22⋊C4—862no—
697C22⋊C4—862no—
698C22⋊C4—862no—
699C22⋊C4—3442no—
700C22⋊C4—3442no—
701C22⋊C4—1724no—
702C42—21no—
703C42—21no—
704C42—861no—
705C42—861no—
706C42—3442no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—432no—
715C23—432no—
716C23—861no—
717C23—861no—
718C23—861no—
719C23—861no—
720C23—862no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—861no—
725C23—861no—
726C23—861no—
727C23—3442no—
728C23—3442no—
729C23—3442no—
730C23—3442no—
731C23—1722no—
732C23—1722no—
733C23—1721no—
734C23—1721no—
735C23—1721no—
736C23—1721no—
737C23—1722no—
738C23—1722no—
739C23—1721no—
740C23—1721no—
741C23C22×C4×D4311yescharacteristic
742C23C2×D4×D4311yescharacteristic
743C23C2×D4×D4311yescharacteristic
744C23#1306337011yescharacteristic
745C23#1306337111yescharacteristic
746C23#1306337211yescharacteristic
747C23#1306337311yescharacteristic
748Q8—3442no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—3442no—
754D4—3442no—
755D4—3442no—
756D4—3442no—
757D4—3442no—
758D4—1721no—
759D4—1721no—
760D4—1721no—
761D4—1721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—432no—
784C2×C4—432no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—3441no—
791C2×C4—3441no—
792C2×C4—3448no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1722no—
798C2×C4—1722no—
799C2×C4—1722no—
800C2×C4—1722no—
801C2×C4—1722no—
802C2×C4—1722no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4C22⋊C4×D4311yescharacteristic
806C2×C4C22⋊C4×D4311yescharacteristic
807C2×C4C22⋊C4×D4311yescharacteristic
808C2×C4C22⋊C4×D4311yescharacteristic
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—81no—
823C22—81no—
824C22—862no—
825C22—862no—
826C22—862no—
827C22—862no—
828C22—862no—
829C22—862no—
830C22—3441no—
831C22—3441no—
832C22—3442no—
833C22—3442no—
834C22—3441no—
835C22—3441no—
836C22—3441no—
837C22—3441no—
838C22—1724no—
839C22—1724no—
840C22—1721no—
841C22—1721no—
842C22—1721no—
843C22C2×C22⋊C4×D4311yescharacteristic
844C22#1458337911yescharacteristic
845C22#1458338011yescharacteristic
846C22#1458346511yescharacteristic
847C22#1458347211yescharacteristic
848C22#1458347811yescharacteristic
849C22#1458347911yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—82no—
858C4—82no—
859C4—862no—
860C4—862no—
861C4—3442no—
862C4—3442no—
863C4—1721no—
864C4—1721no—
865C4—1721no—
866C2—21no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—81no—
873C2—3441no—
874C2—1722no—
875C2—1722no—
876C2#1913718411yescharacteristic
877C2#1914305311yescharacteristic
878C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1799C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583482C2
cosocleC24×C43C24
hypercenter#1799D43
hypocenterC43#21876
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19137208C2semidirect
3. #19137192C2semidirect
4. #19135578C2semidirect
5. #19135429C2semidirect
6. #19135047C2semidirect
7. #19135045C2semidirect
8. #19134583C2semidirect
9. #19134580C2semidirect
10. #19134580C2semidirect
11. C43×#1799C2semidirect
16. C2×#13063320C4semidirect
17. C2×#13063319C4semidirect
18. C2×#13063313C4semidirect
19. C2×#13063311C4semidirect
20. C2×#13063310C4semidirect
21. C2×#13063308C4semidirect
23. C2×#13063299C4semidirect
24. C2×#13063298C4semidirect
52. C22×Dic86C2×C4semidirect
57. C22×C22⋊D43C2×C4semidirect
61. C22×C4×D43C2×C4semidirect
92. C2×C4⋊Dic43C2×C4semidirect
94. C2×Dic43⋊C4C2×C4semidirect
95. C2×Dic43⋊C4C2×C4semidirect
96. C2×Dic43⋊C4C2×C4semidirect
97. C2×Dic43⋊C4C2×C4semidirect
98. C2×C22⋊Dic43C2×C4semidirect
113. C2×(C2×D43)⋊C4C2×C4semidirect
114. C2×(C2×D43)⋊C4C2×C4semidirect
122. C2×C4×Dic43C2×C4semidirect
131. C23×C4×C43C2×C4semidirect
139. C2×C4⋊C4×C43C2×C4semidirect
140. C2×C22⋊C4×C43C2×C4semidirect
144. C2×C42×C43C2×C4semidirect
437. #1799D43semidirect
490. C43#21876semidirect
503. C23×C4C4×D43semidirect
547. C2×C4⋊C4C4×D43semidirect
571. C2×C22⋊C4C4×D43semidirect
577. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834822
#191372082
#191371922
#191355782
#191354292
#191350472
#191350452
#191345832
#191345802
C43×#17992
#2187643