Finite Group Databasebeta

← #25101950

Subgroups — #25101950

Order 11008.

1318 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583482C211yesmaximal, characteristic
2#19137190C211yesmaximal, characteristic, complemented
3#19136947C211yesmaximal, characteristic, complemented
4#19135578C212yesmaximal, complemented
5#19135429C212yesmaximal, complemented
6#19135047C212yesmaximal, complemented
7#19135045C212yesmaximal, complemented
8C4×#13063239C211yesmaximal, characteristic, complemented
9C4×#13063239C211yesmaximal, characteristic, complemented
10C4×#13063240C211yesmaximal, characteristic, complemented
11C4×#99×C43C211yesmaximal, 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#14582790—22no—
35#14582788—22no—
36#14582757C2212yes—
37#14582754C2212yes—
38C22⋊C4×Dic43C2212yes—
39C4×(C2×D43)⋊C4—22no—
40C4×C22⋊Dic43C2211yescharacteristic
41C4×C22⋊Dic43C2211yescharacteristic
42#14582746—22no—
43#14582666C2212yes—
44#14582665C2212yes—
45#14582665C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C2×#99×C43C2212yes—
48C4×C22⋊C4×C43C2211yescharacteristic
49C4×C22⋊C4×C43C2211yescharacteristic
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⋊Dic43C2×C411yescharacteristic, complemented
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4C2×C411yescharacteristic, complemented
93C2×Dic43⋊C4C2×C411yescharacteristic, complemented
94C2×Dic43⋊C4C2×C411yescharacteristic, complemented
95C2×Dic43⋊C4C2×C411yescharacteristic, complemented
96C2×C22⋊Dic43C2×C411yescharacteristic, complemented
97C2×C22⋊Dic43C2312yes—
98C2×C22⋊Dic43C2311yescharacteristic
99C2×C22⋊Dic43C2312yes—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
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, complemented
112C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
113C2×(C2×D43)⋊C4D412yes—
114C2×(C2×D43)⋊C4D412yes—
115C2×(C2×D43)⋊C4D412yes—
116C2×(C2×D43)⋊C4D412yes—
117C22⋊C4×D43—24no—
118C22⋊C4×D43—24no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43C2×C411yescharacteristic, complemented
123#13063240—24no—
124#13063239—24no—
125#13063239—24no—
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×C43C2×C411yescharacteristic, complemented
138C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C43C2312yes—
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43C2312yes—
142C2×C42×C43—21no—
143C2×C42×C43—21no—
144C2×C42×C43C2×C411yescharacteristic, complemented
145#99×C43—24no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C22×C411yescharacteristic
149C24×C43C2411yescharacteristic
150C23×D43—22no—
151C23×D43—22no—
152C23×D43—81no—
153C23×D43—81no—
154C23×D43C22×C411yescharacteristic
155C23×D43C22×C411yescharacteristic
156C23×D43C22×C411yescharacteristic
157C23×D43C2×D412yes—
158C23×D43C2×D412yes—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—81no—
168C22×C4×C43—81no—
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C2×C22⋊D43—22no—
179C2×C22⋊D43—21no—
180C2×C22⋊D43—21no—
181C2×C22⋊D43—22no—
182C2×C22⋊D43—22no—
183C2×C22⋊D43—22no—
184C2×C22⋊D43—22no—
185C2×C22⋊D43—81no—
186C2×C22⋊D43—81no—
187C2×C22⋊D43—81no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—81no—
191C22×Dic43C22×C411yescharacteristic
192C22×Dic43C22×C411yescharacteristic
193C22×Dic43C22×C411yescharacteristic
194C22×Dic43C22×C411yescharacteristic
195C22×Dic43C22×C411yescharacteristic
196C22×Dic43C2×D412yes—
197C22×Dic43C2×D412yes—
198C2×D172—22no—
199C2×D172—22no—
200C2×D172—81no—
201C2×D172—81no—
202C2×C4×D43—28no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—82no—
206C2×C4×D43—82no—
207C2×C4×D43—81no—
208C2×Dic86—22no—
209C2×Dic86—81no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—21no—
215C22⋊C4×C43—21no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43#4114yes—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—81no—
223C42×C43—81no—
224C22⋊Dic43—22no—
225C22⋊Dic43—21no—
226C22⋊Dic43—21no—
227C22⋊Dic43—22no—
228C22⋊Dic43—22no—
229C22⋊Dic43—22no—
230C22⋊Dic43#4114yes—
231(C2×D43)⋊C4—28no—
232(C2×D43)⋊C4—21no—
233(C2×D43)⋊C4—21no—
234(C2×D43)⋊C4—22no—
235(C2×D43)⋊C4—22no—
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—82no—
240(C2×D43)⋊C4—82no—
241(C2×D43)⋊C4C22⋊C412yes—
242(C2×D43)⋊C4C22⋊C412yes—
243(C2×D43)⋊C4C22⋊C412yes—
244(C2×D43)⋊C4C22⋊C412yes—
245(C2×D43)⋊C4C22⋊C412yes—
246(C2×D43)⋊C4C22⋊C412yes—
247(C2×D43)⋊C4C22⋊C412yes—
248(C2×D43)⋊C4C22⋊C412yes—
249C4⋊Dic43—22no—
250Dic43⋊C4—21no—
251Dic43⋊C4—21no—
252Dic43⋊C4—22no—
253Dic43⋊C4—22no—
254Dic43⋊C4—22no—
255Dic43⋊C4—82no—
256C4×Dic43—21no—
257C4×Dic43—21no—
258C4×Dic43—82no—
259C4×Dic43—81no—
260C4×Dic43—81no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43C23×C411yescharacteristic
269C23×C43C22×D411yescharacteristic
270C23×C43C22×D411yescharacteristic
271C23×C43C2×#4112yes—
272C23×C43C2×#4112yes—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—24no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—84no—
294C22×D43—84no—
295C22×D43C2×C22⋊C412yes—
296C22×D43C2×C22⋊C412yes—
297D4×C43—42no—
298D4×C43—42no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—24no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—81no—
319C2×C4×C43—81no—
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—82no—
327C22⋊D43—82no—
328C22⋊D43—82no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—24no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43C2×C22⋊C412yes—
347C2×Dic43C2×C22⋊C412yes—
348D172—82no—
349D172—82no—
350C4×D43—81no—
351C4×D43—81no—
352C4×D43—88no—
353Dic86—82no—
354#21422—431nomaximal, Sylow
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43C22×C22⋊C411yescharacteristic
369C22×C43C4×#4111yescharacteristic
370C22×C43C4×#4111yescharacteristic
371C22×C43#52512yes—
372C22×C43#53212yes—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—44no—
380C2×D43—44no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—84no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C2×D43—81no—
390C2×D43—81no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—21no—
394C4×C43—21no—
395C4×C43—44no—
396C4×C43—41no—
397C4×C43—41no—
398C4×C43—41no—
399C4×C43—82no—
400Dic43—22no—
401Dic43—22no—
402Dic43—44no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406Dic43—82no—
407C2×#538—431no—
408#2312—431no—
409#2273—431no—
410#1996—432no—
411#1964—432no—
412#1898—432no—
413#1898—432no—
414C4×#99—431no—
415C4×#99—431no—
416C4×#99—431no—
417C4×#99D4311yescharacteristic, complemented
418C2×C43—22no—
419C2×C43—22no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43—81no—
423C2×C43#229711yescharacteristic
424C2×C43#288311yescharacteristic
425C2×C43#288311yescharacteristic
426D43—42no—
427D43—42no—
428D43—81no—
429#538—862no—
430#538—862no—
431#538—862no—
432#538—862no—
433C2×#126—431no—
434C2×#126—431no—
435C2×#124—431no—
436C2×#124—431no—
437C2×#123—431no—
438C2×#123—431no—
439C2×C22⋊Q8—431no—
440C2×#121—431no—
441C2×#121—431no—
442C2×#121—431no—
443C2×#120—431no—
444C2×#120—431no—
445C2×C4×D4—431no—
446C2×C4×D4C2×D4311yescharacteristic
447C22×C22⋊C4—431no—
448C22×C22⋊C4—432no—
449C2×#99—432no—
450C2×#99—432no—
451C2×#99—432no—
452C2×#99C2×D4312yes—
453#388—862no—
454#388—862no—
455#380—432no—
456#379—432no—
457C4×C22⋊C4—431no—
458C4×C22⋊C4—431no—
459C4×C22⋊C4—432no—
460C4×C22⋊C4—862no—
461C4×C22⋊C4—862no—
462C4×C22⋊C4C2×D4311yescharacteristic
463C4×C22⋊C4C2×D4311yescharacteristic
464#342—432no—
465#342—432no—
466#342—432no—
467#342C2×D4312yes—
468C43#2142211yescharacteristic, complemented, Sylow
469C25—431no—
470C22×Q8—431no—
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—431no—
474C22×D4—431no—
475C22×D4—431no—
476C22×D4—431no—
477C22×D4C22×D4311yescharacteristic
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—862no—
481C23×C4C4×D4311yescharacteristic, complemented
482C23×C4C22×D4311yescharacteristic
483#126—862no—
484#126—862no—
485#126—862no—
486#126—862no—
487#124—862no—
488#124—862no—
489#124—862no—
490#124—862no—
491#123—862no—
492#123—862no—
493#123—862no—
494#123—862no—
495C22⋊Q8—862no—
496C22⋊Q8—862no—
497#121—862no—
498#121—862no—
499#121—862no—
500#121—862no—
501#121—862no—
502#121—862no—
503#120—862no—
504#120—862no—
505#120—862no—
506#120—862no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—861no—
512C4×D4—861no—
513C4×D4—861no—
514C4×D4—861no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—862no—
521C2×C4⋊C4C4×D4311yescharacteristic, complemented
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—432no—
527C2×C22⋊C4—432no—
528C2×C22⋊C4—432no—
529C2×C22⋊C4—432no—
530C2×C22⋊C4—432no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—431no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—432no—
540C2×C22⋊C4—864no—
541C2×C22⋊C4—862no—
542C2×C22⋊C4—864no—
543C2×C22⋊C4—862no—
544C2×C22⋊C4—862no—
545C2×C22⋊C4C4×D4311yescharacteristic, complemented
546C2×C22⋊C4C22×D4312yes—
547C2×C22⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4C22×D4312yes—
549C2×C42—21no—
550C2×C42—21no—
551C2×C42—431no—
552C2×C42—862no—
553C2×C42—861no—
554C2×C42—861no—
555C2×C42C4×D4311yescharacteristic, complemented
556#99—24no—
557#99—864no—
558#99—864no—
559#99—864no—
560#95—21no—
561#95—21no—
562#95—862no—
563#95—862no—
564#95—861no—
565#95—861no—
566C24—431no—
567C24—431no—
568C24—432no—
569C24—432no—
570C24—431no—
571C24—862no—
572C24—862no—
573C24—3441no—
574C24—3441no—
575C24C2×C4×D4311yescharacteristic
576C24C23×D4311yescharacteristic
577C2×Q8—862no—
578C2×Q8—3441no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—3441no—
593C2×D4—3441no—
594C2×D4—3441no—
595C2×D4—3441no—
596C2×D4—3441no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—432no—
606C22×C4—432no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—868no—
611C22×C4—862no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—862no—
615C22×C4—3442no—
616C22×C4—3442no—
617C22×C4—3441no—
618C22×C4—3441no—
619C22×C4C2×C4×D4311yescharacteristic
620C22×C4C2×C4×D4311yescharacteristic
621C22×C4C2×C4×D4311yescharacteristic
622C22×C4C2×C4×D4311yescharacteristic
623C22×C4C2×C4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—862no—
631C4⋊C4—862no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—3442no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—432no—
645C22⋊C4—432no—
646C22⋊C4—432no—
647C22⋊C4—432no—
648C22⋊C4—432no—
649C22⋊C4—432no—
650C22⋊C4—432no—
651C22⋊C4—432no—
652C22⋊C4—434no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—868no—
659C22⋊C4—862no—
660C22⋊C4—861no—
661C22⋊C4—861no—
662C22⋊C4—862no—
663C22⋊C4—861no—
664C22⋊C4—861no—
665C22⋊C4—862no—
666C22⋊C4—862no—
667C22⋊C4—3442no—
668C22⋊C4—3442no—
669C22⋊C4#1062189814yes—
670C42—21no—
671C42—21no—
672C42—81no—
673C42—81no—
674C42—861no—
675C42—861no—
676C42—3441no—
677C42—3441no—
678C42—3442no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—432no—
687C23—432no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—864no—
693C23—862no—
694C23—862no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—3444no—
699C23—3444no—
700C23—1722no—
701C23—1722no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23—1722no—
707C23—1722no—
708C23—1721no—
709C23—1721no—
710C23C22×C4×D4311yescharacteristic
711C23C2×D4×D4311yescharacteristic
712C23C2×D4×D4311yescharacteristic
713C23#41×D4312yes—
714C23C2×#1062189812yes—
715Q8—3442no—
716D4—42no—
717D4—42no—
718D4—3442no—
719D4—3442no—
720D4—3442no—
721D4—3442no—
722D4—3442no—
723D4—1722no—
724D4—1722no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—24no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—864no—
754C2×C4—3441no—
755C2×C4—3441no—
756C2×C4—3448no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4C22⋊C4×D4311yescharacteristic
769C2×C4C22⋊C4×D4311yescharacteristic
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22⋊C4×D4311yescharacteristic
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—81no—
784C22—81no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—862no—
789C22—862no—
790C22—862no—
791C22—3441no—
792C22—3441no—
793C22—3444no—
794C22—3441no—
795C22—3441no—
796C22—3441no—
797C22—3441no—
798C22—1724no—
799C22—1724no—
800C22—1721no—
801C22—1721no—
802C22—1721no—
803C22C2×C22⋊C4×D4311yescharacteristic
804C22#1458336711yescharacteristic
805C22C4×#1062189811yescharacteristic
806C22#1458340812yes—
807C22#1458344612yes—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C4—862no—
818C4—862no—
819C4—3442no—
820C4—1724no—
821C4—1721no—
822C4—1721no—
823C4—1721no—
824C2—22no—
825C2—22no—
826C2—21no—
827C2—21no—
828C2—81no—
829C2—3441no—
830C2—1722no—
831C2—1722no—
832C2#1913708111yescharacteristic
833C2#1914305311yescharacteristic
834C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583482C2
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43#21422
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #19137190C2semidirect
3. #19136947C2semidirect
4. #19135578C2semidirect
5. #19135429C2semidirect
6. #19135047C2semidirect
7. #19135045C2semidirect
8. C4×#13063239C2semidirect
9. C4×#13063239C2semidirect
10. C4×#13063240C2semidirect
11. C4×#99×C43C2semidirect
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
90. C2×C4⋊Dic43C2×C4semidirect
92. C2×Dic43⋊C4C2×C4semidirect
93. C2×Dic43⋊C4C2×C4semidirect
94. C2×Dic43⋊C4C2×C4semidirect
95. C2×Dic43⋊C4C2×C4semidirect
96. C2×C22⋊Dic43C2×C4semidirect
111. C2×(C2×D43)⋊C4C2×C4semidirect
112. C2×(C2×D43)⋊C4C2×C4semidirect
122. C2×C4×Dic43C2×C4semidirect
131. C23×C4×C43C2×C4semidirect
137. C2×C4⋊C4×C43C2×C4semidirect
138. C2×C22⋊C4×C43C2×C4semidirect
144. C2×C42×C43C2×C4semidirect
417. C4×#99D43semidirect
468. C43#21422semidirect
481. C23×C4C4×D43semidirect
521. C2×C4⋊C4C4×D43semidirect
545. C2×C22⋊C4C4×D43semidirect
555. 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
#191371902
#191369472
#191355782
#191354292
#191350472
#191350452
C4×#130632392
C4×#130632402
C4×#99×C432
#2142243