Finite Group Databasebeta

← #25144105

Subgroups — #25144105

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583121C211yesmaximal, characteristic, complemented
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14583038C211yesmaximal, characteristic
4C2×C4×#10621884C211yesmaximal, characteristic, complemented
5#19138172C211yesmaximal, characteristic
6#19135976C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135777C211yesmaximal, characteristic
9#19135688C211yesmaximal, characteristic, complemented
10#19135455C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134936C211yesmaximal, characteristic, complemented
13#19134932C211yesmaximal, characteristic, complemented
14#19134849C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24#14583121—24no—
25#14583055—24no—
26#14583038—24no—
27C4×#10621884—24no—
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582828—21no—
43#14582814—21no—
44#14582805C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582775—21no—
47#14582758—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C23×Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#391—21no—
56C43×#391—21no—
57C43×#391C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#380—21no—
60C43×#380C2211yescharacteristic
61C4×C22⋊C4×C43—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—41no—
73C2×#10621884—22no—
74C2×#10621884—22no—
75C2×#10621884—22no—
76C2×#10621884—22no—
77C2×#10621884—41no—
78C2×#10621884D414yes—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063313—22no—
84#13063313—41no—
85#13063304—22no—
86#13063304—41no—
87#13063299—22no—
88#13063299—41no—
89C4×D172—22no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100#13063258—41no—
101#13063256—22no—
102C4⋊(C43⋊C8)—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249D414yescomplemented
107#13063248—22no—
108#13063248—41no—
109#13063245—22no—
110#13063245—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C22×Q8×C43—22no—
118C22×Q8×C43—22no—
119C22×Q8×C43—21no—
120C22×Q8×C43—22no—
121C22×Q8×C43—22no—
122C22×Q8×C43—41no—
123C22×Q8×C43—41no—
124C22×Q8×C43C2311yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128C4×Q8×C43—22no—
129C4×Q8×C43—22no—
130C4×Q8×C43—41no—
131C4×Q8×C43—41no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43D411yescharacteristic
139C2×C42×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C23×D43—21no—
152C2×Q8×C43—24no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—42no—
162C2×Q8×C43—42no—
163C2×Q8×C43—44no—
164C2×Q8×C43—44no—
165C2×Q8×C43—44no—
166C2×Q8×C43—44no—
167C2×Q8×C43C2×D412yes—
168C2×Q8×C43C2×D412yes—
169C2×Q8×C43#4112yes—
170C2×Q8×C43#4112yes—
171C22×C4×C43—24no—
172C22×C4×C43—21no—
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—42no—
183C22×C4×C43—42no—
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—42no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—81no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172C2×D412yes—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—81no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43—42no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—42no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C42×C43—42no—
225C42×C43—42no—
226C22⋊Dic43—42no—
227#10621885—44no—
228#10621885—44no—
229#10621884—28no—
230#10621884—44no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—42no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—42no—
240Dic43⋊C4—81no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8C2×D412yes—
252C2×C43⋊C8C2×D412yes—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43#13512yes—
260C23×C43C22×D411yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—48no—
274Q8×C43—41no—
275Q8×C43—41no—
276Q8×C43#12114yes—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—48no—
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—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43#13712yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C2×C4×C43H(5,𝔽2)11yescharacteristic
315C22⋊D43—84no—
316C2×Dic43—22no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325D172—22no—
326D172—22no—
327D172—41no—
328D172—41no—
329C4×D43—84no—
330Dic86—41no—
331Dic86—41no—
332Dic86—41no—
333Dic86—41no—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#25157—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43#52511yescharacteristic
347C22×C43D4211yescharacteristic
348C22×C43D4211yescharacteristic
349C22×C43C2×#13511yescharacteristic
350C22×C43C2×#13711yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—24no—
361C4×C43—22no—
362C4×C43—41no—
363C4×C43—42no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—81no—
368C4×C43—81no—
369C4×C43C2×#12111yescharacteristic
370C4×C43#53811yescharacteristic
371C4×C43#54611yescharacteristic
372C4×C43#54611yescharacteristic
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376C2×#464—431no—
377C2×#451—431no—
378C2×#448—431no—
379C2×C4×SD16—431no—
380#2427—431no—
381Q8×C22⋊C4D4311yescharacteristic, complemented
382#2066—431no—
383#2035—431no—
384#2033—431no—
385#2015—431no—
386#1969—431no—
387#1923—431no—
388#1878—431no—
389#1877—431no—
390#1863—431no—
391C2×C43—42no—
392C2×C43#242411yescharacteristic
393C2×C43#310811yescharacteristic
394C2×C43#312111yescharacteristic
395C2×C43#326611yescharacteristic
396C2×C43#327611yescharacteristic
397C2×C43#328211yescharacteristic
398C2×C43#328511yescharacteristic
399D43—82no—
400C23×Q8C2×D4311yescharacteristic
401C22×Q16—431no—
402C22×Q16—431no—
403C22×SD16—431no—
404C22×SD16—431no—
405C2×#124—431no—
406C2×C22⋊Q8—431no—
407C2×#121—431no—
408C2×C4×Q8C2×D4311yescharacteristic
409C2×C4×Q8C2×D4311yescharacteristic
410C2×C4×D4—431no—
411#464—864no—
412#451—864no—
413#448—864no—
414C4×SD16—864no—
415C2×#107—431no—
416C2×#106—431no—
417C2×C4⋊C8—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×C22⋊C8—431no—
427C2×C22⋊C8—431no—
428C2×C4×C8—431no—
429#397—861no—
430#394—861no—
431#391—21no—
432#391—21no—
433#391—431no—
434#391C2×D4311yescharacteristic
435#391C2×D4311yescharacteristic
436#389—431no—
437#386—861no—
438#380—21no—
439#380—861no—
440#380C2×D4311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2×D4311yescharacteristic
443#340—431no—
444#340—431no—
445#336—431no—
446#336—431no—
447C43#2515711yescharacteristic, complemented, Sylow
448C22×Q8—22no—
449C22×Q8—22no—
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—41no—
454C22×Q8—41no—
455C22×Q8—431no—
456C22×Q8C22×D4311yescharacteristic
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—21no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×Q16—862no—
464C2×Q16—862no—
465C2×Q16—862no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×Q16—1721no—
469C2×SD16—434no—
470C2×SD16—862no—
471C2×SD16—862no—
472C2×SD16—862no—
473C2×SD16—862no—
474C2×SD16—1721no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479#124—862no—
480#124—1721no—
481C22⋊Q8—862no—
482C22⋊Q8—1721no—
483#121—862no—
484#121—1721no—
485C4×Q8—22no—
486C4×Q8—22no—
487C4×Q8—41no—
488C4×Q8—41no—
489C4×D4—862no—
490C4×D4—1721no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4C22⋊D4311yescharacteristic
506C2×C22⋊C4C22⋊D4311yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42C22×D4311yescharacteristic
510C2×C42C22×D4311yescharacteristic
511#107—1721no—
512#106—862no—
513C4⋊C8—862no—
514#103—434no—
515#103—862no—
516#103—862no—
517#103—862no—
518#103—862no—
519#103—1721no—
520#102—862no—
521#102—862no—
522C22⋊C8—862no—
523C22⋊C8—862no—
524C4×C8—862no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—861no—
531#95—861no—
532#95—861no—
533#95C22⋊D4311yescharacteristic
534#95C22⋊D4311yescharacteristic
535C24—861no—
536C24C2×C22⋊D4311yescharacteristic
537C2×Q8—24no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—44no—
549C2×Q8—44no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8#1062189812yes—
559C2×Q8#1062189812yes—
560C2×Q8D4×D4312yes—
561C2×Q8D4×D4312yes—
562C2×D4—432no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—3441no—
569C2×D4—1722no—
570C2×D4—1722no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C23×D4311yescharacteristic
596Q16—1724no—
597Q16—1724no—
598SD16—868no—
599SD16—1724no—
600C2×C8—432no—
601C2×C8—432no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—432no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—3441no—
623C4⋊C4—1722no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—1722no—
628C22⋊C4—1722no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—42no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—862no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23#1306334512yes—
652C23C22×C22⋊D4311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—48no—
659Q8—41no—
660Q8—41no—
661Q8—1721no—
662Q8—1721no—
663Q8—1721no—
664Q8—1721no—
665Q8#1306329814yes—
666D4—862no—
667D4—862no—
668D4—3444no—
669D4—1721no—
670D4—1721no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—48no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
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—862no—
703C2×C4—3444no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4#1306335612yes—
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×#1062189811yescharacteristic
716C2×C4C2×#1062189811yescharacteristic
717C2×C4#1306337011yescharacteristic
718C2×C4#1306337011yescharacteristic
719C8—862no—
720C8—862no—
721C8—1721no—
722C8—1721no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—3441no—
731C22—3441no—
732C22—3441no—
733C22—3441no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22#1458341011yescharacteristic
738C22D4×C22⋊D4311yescharacteristic
739C22D4×C22⋊D4311yescharacteristic
740C22C2×#1306334511yescharacteristic
741C22C2×#1306335611yescharacteristic
742C22#1458370711yescharacteristic
743C22#1458371411yescharacteristic
744C4—24no—
745C4—22no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—3441no—
754C4—3441no—
755C4—1722no—
756C4C2×#1306329811yescharacteristic
757C4#1458348711yescharacteristic
758C4#1458353911yescharacteristic
759C4#1458353911yescharacteristic
760C2—42no—
761C2—3442no—
762C2#1913813111yescharacteristic
763C2#1914467511yescharacteristic
764C2#1914482411yescharacteristic
765C2#1914610611yescharacteristic
766C2#1914624111yescharacteristic
767C2#1914630311yescharacteristic
768C2#1914633211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingQ8×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterQ8×C22⋊C4D43
hypocenterC43#25157
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583121C2semidirect
2. C2×#14583055C2semidirect
4. C2×C4×#10621884C2semidirect
6. #19135976C2semidirect
7. #19135791C2semidirect
9. #19135688C2semidirect
10. #19135455C2semidirect
11. #19135203C2semidirect
12. #19134936C2semidirect
13. #19134932C2semidirect
14. #19134849C2semidirect
15. Q8×C22⋊C4×C43C2semidirect
106. #13063249D4semidirect
381. Q8×C22⋊C4D43semidirect
447. C43#25157semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
C2×#145830552
C2×#145830382
C2×C4×#106218842
#191381722
#191359762
#191357912
#191357772
#191356882
#191354552
#191352032
#191349362
#191349322
#191348492
Q8×C22⋊C4×C432
#2515743