Finite Group Databasebeta

← #25063759

Subgroups — #25063759

Order 11008.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582863C211yesmaximal, characteristic, complemented
3#19133114C212yesmaximal, complemented
4#19133110C212yesmaximal, complemented
5#19133097C214yesmaximal, complemented
6#19133084C214yesmaximal, complemented
7C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C411yescharacteristic, complemented
9C22×#10621877—21no—
10#14583410—21no—
11#14583410—21no—
12#14583410—21no—
13#14583410—21no—
14#14583410C412yescomplemented
15#14583410C412yescomplemented
16#14583410C2212yes—
17#14583410C2212yes—
18C2×#13063308—21no—
19C2×#13063304C411yescharacteristic, complemented
20C2×#13063304C2211yescharacteristic
21C2×#13063299C411yescharacteristic, complemented
22C2×#13063299C2211yescharacteristic
23C2×#13063294—21no—
24C2×C4×C22⋊D43—21no—
25C2×C4×C22⋊D43—21no—
26C2×#13063284C411yescharacteristic, complemented
27#14582863—21no—
28#14582863—21no—
29#14582863C2212yes—
30#14582863C2212yescomplemented
31C2×C22⋊(C43⋊C8)—21no—
32C2×C22⋊(C43⋊C8)C2212yescomplemented
33#14582635C2218yescomplemented
34#14582632C2218yescomplemented
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43—21no—
37C22×C42×C43—21no—
38C4×C22⋊C4×C43—21no—
39C4×C22⋊C4×C43—21no—
40C4×C22⋊C4×C43C2212yes—
41C4×C22⋊C4×C43C2212yescomplemented
42C2×#95×C43C2212yescomplemented
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—44no—
46C2×#10621898C2×C412yes—
47C2×#10621898C2×C412yescomplemented
48C22×Dic86C2×C411yescharacteristic, complemented
49C22×D172C2×C411yescharacteristic, complemented
50C22×C22⋊D43—21no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C4×D43—21no—
54C2×#10621877—22no—
55C2×#10621877—22no—
56C2×#10621877—44no—
57C22×C43⋊C8—22no—
58#13063308—22no—
59#13063308—22no—
60#13063308—22no—
61#13063308—22no—
62#13063304—21no—
63#13063304—21no—
64#13063304—21no—
65#13063304—21no—
66#13063304C2×C412yes—
67#13063304C2×C412yescomplemented
68#13063304C2×C412yescomplemented
69#13063304C2312yes—
70#13063299—21no—
71#13063299—21no—
72#13063299—21no—
73#13063299—21no—
74#13063299C2×C412yes—
75#13063299C2×C412yescomplemented
76#13063299C2×C412yescomplemented
77#13063299C2312yes—
78#13063294—22no—
79#13063294—22no—
80#13063294—22no—
81#13063294—22no—
82C4×C22⋊D43—22no—
83C4×C22⋊D43—22no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90#13063284—21no—
91#13063284—21no—
92#13063284C2×C412yes—
93#13063284C2×C412yescomplemented
94C2×C4⋊Dic43C2×C411yescharacteristic, complemented
95C2×C4⋊Dic43C2×C411yescharacteristic, complemented
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C22⋊(C43⋊C8)—22no—
105C22⋊(C43⋊C8)—22no—
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)C2314yes—
108C25×C43D411yescharacteristic
109C23×C4×C43—22no—
110C23×C4×C43—44no—
111C23×C4×C43C2×C411yescharacteristic
112C23×C4×C43C2×C411yescharacteristic
113C23×C4×C43C2×C411yescharacteristic
114C23×C4×C43C2×C411yescharacteristic
115C23×C4×C43D411yescharacteristic
116C23×C4×C43D411yescharacteristic
117C23×C4×C43D411yescharacteristic
118C23×C4×C43D411yescharacteristic
119C23×C4×C43D411yescharacteristic
120C23×C4×C43D411yescharacteristic
121C23×C4×C43D411yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—28no—
126C2×C22⋊C4×C43—22no—
127C2×C22⋊C4×C43—22no—
128C2×C42×C43—22no—
129C2×C42×C43—22no—
130C2×C42×C43—44no—
131#95×C43—22no—
132#95×C43C2314yes—
133C24×C43—24no—
134C24×C43—42no—
135C24×C43—42no—
136C24×C43C22⋊C411yescharacteristic
137C24×C43C22⋊C411yescharacteristic
138C24×C43C22⋊C411yescharacteristic
139C24×C43C22⋊C411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C23×D43—21no—
144C22×C4×C43—24no—
145C22×C4×C43—24no—
146C22×C4×C43—24no—
147C22×C4×C43—28no—
148C22×C4×C43—24no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—44no—
153C22×C4×C43—44no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43C22⋊C411yescharacteristic
163C22×C4×C43C22⋊C411yescharacteristic
164C22×C4×C43C22⋊C411yescharacteristic
165C22×C4×C43C22⋊C411yescharacteristic
166C22×C4×C43C22⋊C411yescharacteristic
167C22×C4×C43C22⋊C411yescharacteristic
168C22×C4×C43C22⋊C411yescharacteristic
169C22×C4×C43C22⋊C411yescharacteristic
170C22×C4×C43C22⋊C411yescharacteristic
171C22×C4×C43C22⋊C411yescharacteristic
172C22×C4×C43C22⋊C411yescharacteristic
173C22×C4×C43C22⋊C411yescharacteristic
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C22×C411yescharacteristic
179C22×C4×C43C22×C411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—44no—
197C2×C22⋊D43—44no—
198C2×C22⋊D43—44no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202#10621898—44no—
203#10621898—44no—
204#10621898—44no—
205#10621898—44no—
206C2×D172—21no—
207C2×D172—42no—
208C2×D172C22×C412yes—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—44no—
212C2×Dic86—21no—
213C2×Dic86—42no—
214C2×Dic86C22×C412yes—
215C22⋊C4×C43—28no—
216C22⋊C4×C43—28no—
217C42×C43—44no—
218C42×C43—44no—
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C22×C412yes—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237C4×Dic43—22no—
238C4×Dic43—22no—
239#10621877—44no—
240#10621877—44no—
241C2×C43⋊C8—24no—
242C2×C43⋊C8—44no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—416no—
264C23×C43#10414yes—
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C2×C22⋊C411yescharacteristic
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C2×C22⋊C411yescharacteristic
269C23×C43C2×C22⋊C411yescharacteristic
270C23×C43C2×C22⋊C411yescharacteristic
271C23×C43C22×D411yescharacteristic
272C22×D43—22no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—28no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—44no—
305C2×C4×C43—416no—
306C2×C4×C43—44no—
307C2×C4×C43#9914yes—
308C2×C4×C43C2×C22⋊C411yescharacteristic
309C2×C4×C43C2×C22⋊C411yescharacteristic
310C2×C4×C43C2×C22⋊C411yescharacteristic
311C2×C4×C43C2×C22⋊C411yescharacteristic
312C2×C4×C43C2×C22⋊C411yescharacteristic
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C22⋊D43—44no—
317C22⋊D43—44no—
318C22⋊D43—44no—
319C22⋊D43—44no—
320C22⋊D43—44no—
321C22⋊D43—44no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328D172—42no—
329D172—42no—
330C4×D43—44no—
331C4×D43—44no—
332Dic86—42no—
333Dic86—42no—
334C43⋊C8—44no—
335#17542—431nomaximal, Sylow
336C22×C43—28no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—44no—
354C22×C43—44no—
355C22×C43—44no—
356C22×C43—44no—
357C22×C43—44no—
358C22×C43—44no—
359C22×C43C2×#9912yes—
360C22×C43C2×#10412yes—
361C22×C43C2×#10412yes—
362C22×C43C2×#10412yes—
363C22×C43C22×C22⋊C411yescharacteristic
364C22×C43#57512yes—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—84no—
369C4×C43—21no—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—21no—
375C4×C43—48no—
376C4×C43C2×#9912yes—
377C4×C43C2×#9912yes—
378Dic43—42no—
379Dic43—42no—
380Dic43—42no—
381C2×#525—431no—
382C2×#407—431no—
383C2×C4×C22⋊C4D4311yescharacteristic, complemented
384#1508—432no—
385#1507—432no—
386#1504—434no—
387#1501—434no—
388C2×C43—22no—
389C2×C43—22no—
390C2×C43—22no—
391C2×C43—22no—
392C2×C43—22no—
393C2×C43—41no—
394C2×C43—41no—
395C2×C43C22×#9911yescharacteristic
396C2×C43#289611yescharacteristic
397C2×C43C22×#10411yescharacteristic
398D43—82no—
399C22×#41—431no—
400C24×C4C2×D4311yescharacteristic
401C22×M16—861no—
402#525—432no—
403#525—432no—
404#525—432no—
405#525—432no—
406#525—861no—
407#525—861no—
408#525—861no—
409#525—861no—
410C2×#123—861no—
411C2×C22⋊Q8—431no—
412C2×C22⋊Q8—431no—
413C2×#121—431no—
414C2×#121—431no—
415C2×#120—861no—
416C2×C4×D4—861no—
417C2×C4×D4—861no—
418C2×#117—431no—
419C22×C22⋊C4—21no—
420C22×C42—21no—
421#407—432no—
422#407—432no—
423#407—861no—
424#407—861no—
425C2×C22⋊C8—432no—
426C2×C22⋊C8—861no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2×D4312yes—
430C4×C22⋊C4C2×D4312yescomplemented
431C2×#95C2×D4312yescomplemented
432#328—438no—
433#327—438no—
434C43#1754211yescharacteristic, complemented, Sylow
435C25C22⋊D4311yescharacteristic
436C2×#41—432no—
437C2×#41—432no—
438C2×#41—861no—
439C2×#41—861no—
440C2×#41—1724no—
441C22×Q8—431no—
442C22×D4—431no—
443C22×D4—861no—
444C22×D4—861no—
445C22×D4—861no—
446C23×C4—22no—
447C23×C4—44no—
448C23×C4—861no—
449C23×C4C4×D4311yescharacteristic
450C23×C4C4×D4311yescharacteristic
451C23×C4C4×D4311yescharacteristic
452C23×C4C4×D4311yescharacteristic
453C23×C4D17211yescharacteristic
454C23×C4D17211yescharacteristic
455C23×C4D17211yescharacteristic
456C23×C4D17211yescharacteristic
457C23×C4C22⋊D4311yescharacteristic
458C23×C4C22⋊D4311yescharacteristic
459C23×C4C22⋊D4311yescharacteristic
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4311yescharacteristic
462C23×C4C22×D4311yescharacteristic
463C2×M16—862no—
464C2×M16—862no—
465C2×M16—1724no—
466C22×C8—862no—
467#123—862no—
468#123—862no—
469#123—862no—
470#123—862no—
471C22⋊Q8—432no—
472C22⋊Q8—432no—
473C22⋊Q8—432no—
474C22⋊Q8—432no—
475C22⋊Q8—861no—
476C22⋊Q8—861no—
477C22⋊Q8—861no—
478C22⋊Q8—861no—
479#121—432no—
480#121—432no—
481#121—432no—
482#121—432no—
483#121—861no—
484#121—861no—
485#121—861no—
486#121—861no—
487#120—862no—
488#120—862no—
489#120—862no—
490#120—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—862no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—862no—
498C4×D4—862no—
499#117—432no—
500#117—432no—
501#117—861no—
502#117—861no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C22⋊C4—28no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—44no—
518C2×C42—861no—
519C22⋊C8—434no—
520C22⋊C8—862no—
521C22⋊C8—862no—
522C22⋊C8—862no—
523#95—22no—
524#95C22×D4314yes—
525C24—24no—
526C24—42no—
527C24—42no—
528C24—861no—
529C24(C2×D43)⋊C411yescharacteristic
530C24(C2×D43)⋊C411yescharacteristic
531C24(C2×D43)⋊C411yescharacteristic
532C24(C2×D43)⋊C411yescharacteristic
533C24C2×C22⋊D4311yescharacteristic
534C24C2×C22⋊D4311yescharacteristic
535C24C2×C22⋊D4311yescharacteristic
536#41—1724no—
537#41—1724no—
538#41—1724no—
539#41—1724no—
540C2×Q8—432no—
541C2×Q8—861no—
542C2×Q8—1722no—
543C2×D4—432no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—862no—
548C2×D4—862no—
549C2×D4—862no—
550C2×D4—861no—
551C2×D4—1722no—
552C2×D4—1724no—
553C2×D4—1724no—
554C2×D4—1724no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—28no—
559C22×C4—24no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—1724no—
579C22×C4(C2×D43)⋊C411yescharacteristic
580C22×C4(C2×D43)⋊C411yescharacteristic
581C22×C4(C2×D43)⋊C411yescharacteristic
582C22×C4(C2×D43)⋊C411yescharacteristic
583C22×C4(C2×D43)⋊C411yescharacteristic
584C22×C4(C2×D43)⋊C411yescharacteristic
585C22×C4(C2×D43)⋊C411yescharacteristic
586C22×C4(C2×D43)⋊C411yescharacteristic
587C22×C4(C2×D43)⋊C411yescharacteristic
588C22×C4(C2×D43)⋊C411yescharacteristic
589C22×C4(C2×D43)⋊C411yescharacteristic
590C22×C4(C2×D43)⋊C411yescharacteristic
591C22×C4C2×C4×D4311yescharacteristic
592C22×C4C2×C4×D4311yescharacteristic
593C22×C4C2×C4×D4311yescharacteristic
594C22×C4C2×C4×D4311yescharacteristic
595C22×C4C2×C4×D4311yescharacteristic
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4C2×D17211yescharacteristic
600C22×C4C2×D17211yescharacteristic
601C22×C4C2×D17211yescharacteristic
602C22×C4C2×D17211yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C23×D4311yescharacteristic
607M16—1724no—
608M16—1724no—
609C2×C8—864no—
610C2×C8—1724no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—862no—
616C4⋊C4—862no—
617C4⋊C4—862no—
618C4⋊C4—862no—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—862no—
622C22⋊C4—862no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—862no—
627C22⋊C4—862no—
628C22⋊C4—862no—
629C22⋊C4—862no—
630C22⋊C4—862no—
631C42—44no—
632C42—44no—
633C42—862no—
634C42—862no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—416no—
656C23—862no—
657C23—1722no—
658C23—1722no—
659C23—1722no—
660C23#1306325314yes—
661C23C2×(C2×D43)⋊C411yescharacteristic
662C23C2×(C2×D43)⋊C411yescharacteristic
663C23C2×(C2×D43)⋊C411yescharacteristic
664C23C2×(C2×D43)⋊C411yescharacteristic
665C23C2×(C2×D43)⋊C411yescharacteristic
666C23C2×(C2×D43)⋊C411yescharacteristic
667C23C22×C22⋊D4311yescharacteristic
668Q8—1722no—
669Q8—1722no—
670D4—1722no—
671D4—1724no—
672D4—1724no—
673D4—1724no—
674D4—1724no—
675D4—1724no—
676D4—1724no—
677D4—1722no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—44no—
707C2×C4—416no—
708C2×C4—44no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—1724no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1724no—
717C2×C4#1306323914yes—
718C2×C4C2×(C2×D43)⋊C411yescharacteristic
719C2×C4C2×(C2×D43)⋊C411yescharacteristic
720C2×C4C2×(C2×D43)⋊C411yescharacteristic
721C2×C4C2×(C2×D43)⋊C411yescharacteristic
722C2×C4C2×(C2×D43)⋊C411yescharacteristic
723C2×C4C2×(C2×D43)⋊C411yescharacteristic
724C2×C4C22×C4×D4311yescharacteristic
725C2×C4C22×D17211yescharacteristic
726C8—1724no—
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—3444no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22C2×#1306323912yes—
755C22C2×#1306325312yes—
756C22C2×#1306325312yes—
757C22C2×#1306325312yes—
758C22C22×(C2×D43)⋊C411yescharacteristic
759C22#1458369712yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—48no—
767C4—1722no—
768C4—1722no—
769C4—1722no—
770C4C2×#1306323912yes—
771C4C2×#1306323912yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—3442no—
780C2C22×#1306323911yescharacteristic
781C2#1914311211yescharacteristic
782C2C22×#1306325311yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×C22⋊C4×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#17542
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14582863C2semidirect
3. #19133114C2semidirect
4. #19133110C2semidirect
5. #19133097C2semidirect
6. #19133084C2semidirect
7. C2×C4×C22⋊C4×C43C2semidirect
8. C22×#10621898C4semidirect
14. #14583410C4semidirect
15. #14583410C4semidirect
19. C2×#13063304C4semidirect
21. C2×#13063299C4semidirect
26. C2×#13063284C4semidirect
30. #14582863C22semidirect
32. C2×C22⋊(C43⋊C8)C22semidirect
33. #14582635C22semidirect
34. #14582632C22semidirect
41. C4×C22⋊C4×C43C22semidirect
42. C2×#95×C43C22semidirect
47. C2×#10621898C2×C4semidirect
48. C22×Dic86C2×C4semidirect
49. C22×D172C2×C4semidirect
67. #13063304C2×C4semidirect
68. #13063304C2×C4semidirect
75. #13063299C2×C4semidirect
76. #13063299C2×C4semidirect
93. #13063284C2×C4semidirect
94. C2×C4⋊Dic43C2×C4semidirect
95. C2×C4⋊Dic43C2×C4semidirect
383. C2×C4×C22⋊C4D43semidirect
430. C4×C22⋊C4C2×D43semidirect
431. C2×#95C2×D43semidirect
434. C43#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145828632
#191331142
#191331102
#191330972
#191330842
C2×C4×C22⋊C4×C432
#1754243