Finite Group Databasebeta

← #25002166

Subgroups — #25002166

Order 11008.

1370 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic43C211yesmaximal, characteristic
2C22×#13063249C211yesmaximal, characteristic
3C2×#14582662C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic
5C2×#14582653C211yesmaximal, characteristic
6#19132824C211yesmaximal, characteristic
7C22×#103×C43C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C2×Q8×Dic43—22no—
10C2×Q8×Dic43—22no—
11C2×Q8×Dic43—22no—
12C2×Q8×Dic43—22no—
13C2×Q8×Dic43—22no—
14C2×Q8×Dic43C414yescomplemented
15C22×C4⋊Dic43—21no—
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4×Dic43—21no—
19C22×C4×Dic43C2211yescharacteristic
20C2×#13063249—22no—
21C2×#13063249—22no—
22C2×#13063249C414yescomplemented
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25#14582662—22no—
26#14582661—22no—
27#14582653—22no—
28C23×Q8×C43C2211yescharacteristic
29C23×C8×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C2×#103×C43—22no—
32C2×#103×C43—22no—
33C2×#103×C43C414yescomplemented
34C23×Dic43—21no—
35C23×Dic43—21no—
36C23×Dic43D411yescharacteristic
37C23×Dic43D411yescharacteristic
38C22×C43⋊C8—21no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42C22×C43⋊C8—21no—
43C22×C43⋊C8—21no—
44C22×C43⋊C8C2×C412yes—
45Q8×Dic43—28no—
46Q8×Dic43—28no—
47Q8×Dic43—28no—
48Q8×Dic43—28no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—24no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43C2×C412yes—
61C2×C4⋊Dic43C2×C412yes—
62C2×C4⋊Dic43D412yes—
63C2×C4⋊Dic43D412yes—
64C2×C4×Dic43—24no—
65C2×C4×Dic43—24no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43C2×C412yes—
72C2×C4×Dic43D412yes—
73#13063249—28no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C22×Q8×C43—21no—
77C22×Q8×C43—21no—
78C22×Q8×C43—21no—
79C22×Q8×C43—21no—
80C22×Q8×C43—21no—
81C22×Q8×C43—21no—
82C22×Q8×C43—21no—
83C22×Q8×C43C2×C412yes—
84C22×Q8×C43C2×C412yes—
85C22×Q8×C43C2×C412yes—
86C22×Q8×C43D412yes—
87C22×Q8×C43D412yes—
88C22×Q8×C43D412yes—
89C22×Q8×C43Q812yes—
90C23×C4×C43—21no—
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C22×C8×C43—21no—
94C22×C8×C43—21no—
95C22×C8×C43—21no—
96C22×C8×C43—21no—
97C22×C8×C43—21no—
98C22×C8×C43—21no—
99C22×C8×C43C2×C412yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2×C412yes—
106#103×C43—28no—
107C24×C43C2×D411yescharacteristic
108C2×Q8×C43—22no—
109C2×Q8×C43—22no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—22no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43C4214yes—
130C2×Q8×C43C22⋊C414yes—
131C2×Q8×C43C22⋊C414yes—
132C2×Q8×C43C22⋊C414yes—
133C2×Q8×C43C4⋊C414yes—
134C2×Q8×C43C4⋊C414yes—
135C2×Q8×C43C4⋊C414yes—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43—41no—
147C22×C4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×Q811yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C22×C4×C43#4111yescharacteristic
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—41no—
179C22×Dic43—41no—
180C22×Dic43—41no—
181C22×Dic43—41no—
182C22×Dic43—41no—
183C22×Dic43—41no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186C22×Dic43—41no—
187C22×Dic43—41no—
188C22×Dic43C22⋊C412yes—
189C22×Dic43C22⋊C412yes—
190C22×Dic43SD1612yes—
191C22×Dic43Q1612yes—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C2×C8×C43—22no—
195C2×C8×C43—41no—
196C2×C8×C43—41no—
197C2×C8×C43—41no—
198C2×C8×C43—41no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊Dic43—216no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43—22no—
208C4⋊Dic43—22no—
209C4⋊Dic43—41no—
210C4⋊Dic43—41no—
211C4⋊Dic43C22⋊C414yes—
212C4×Dic43—216no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—41no—
221C2×C43⋊C8—41no—
222C2×C43⋊C8—41no—
223C2×C43⋊C8—41no—
224C23×C43C2×C22⋊C411yescharacteristic
225C23×C43C4×D411yescharacteristic
226C23×C43C4×D411yescharacteristic
227C23×C43#12011yescharacteristic
228C23×C43#12011yescharacteristic
229C23×C43#12111yescharacteristic
230C23×C43C22⋊Q811yescharacteristic
231C23×C43C2×SD1611yescharacteristic
232C23×C43C2×Q1611yescharacteristic
233C23×C43#13511yescharacteristic
234C23×C43#13511yescharacteristic
235C23×C43AGL(1,ℤ/8)11yescharacteristic
236C23×C43#13711yescharacteristic
237C23×C43#13711yescharacteristic
238C23×C43#13711yescharacteristic
239Q8×C43—24no—
240Q8×C43—24no—
241Q8×C43—24no—
242Q8×C43—24no—
243Q8×C43—24no—
244Q8×C43—24no—
245Q8×C43—24no—
246Q8×C43#9518yescomplemented
247C2×C4×C43—24no—
248C2×C4×C43—24no—
249C2×C4×C43—24no—
250C2×C4×C43—24no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—81no—
258C2×C4×C43—81no—
259C2×C4×C43—81no—
260C2×C4×C43—81no—
261C2×C4×C43C2×C4211yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C4⋊C411yescharacteristic
267C2×C4×C43C2×C4⋊C411yescharacteristic
268C2×C4×C43C2×C4⋊C411yescharacteristic
269C2×C4×C43#11711yescharacteristic
270C2×C4×C43#11711yescharacteristic
271C2×C4×C43C4×D411yescharacteristic
272C2×C4×C43C4×D411yescharacteristic
273C2×C4×C43C4×D411yescharacteristic
274C2×C4×C43C4×D411yescharacteristic
275C2×C4×C43C4×D411yescharacteristic
276C2×C4×C43C4×D411yescharacteristic
277C2×C4×C43#12011yescharacteristic
278C2×C4×C43#12011yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43C22⋊Q811yescharacteristic
283C2×C4×C43C22⋊Q811yescharacteristic
284C2×C4×C43C22⋊Q811yescharacteristic
285C2×C4×C43#12311yescharacteristic
286C2×C4×C43#12311yescharacteristic
287C2×C4×C43#12311yescharacteristic
288C2×C4×C43#12311yescharacteristic
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—24no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—81no—
313C2×Dic43—81no—
314C2×Dic43—81no—
315C2×Dic43—81no—
316C2×Dic43#10314yescomplemented
317C8×C43—42no—
318C43⋊C8—42no—
319#10789—431nomaximal, Sylow
320C22×C43C4×C22⋊C411yescharacteristic
321C22×C43#37911yescharacteristic
322C22×C43#38011yescharacteristic
323C22×C43#38511yescharacteristic
324C22×C43#38511yescharacteristic
325C22×C43#38611yescharacteristic
326C22×C43#38611yescharacteristic
327C22×C43C2×#10311yescharacteristic
328C22×C43#41611yescharacteristic
329C22×C43#41711yescharacteristic
330C22×C43#41911yescharacteristic
331C22×C43C4×SD1611yescharacteristic
332C22×C43C4×SD1611yescharacteristic
333C22×C43C4×Q1611yescharacteristic
334C22×C43C4×Q1611yescharacteristic
335C22×C43#44011yescharacteristic
336C22×C43#44011yescharacteristic
337C22×C43#44111yescharacteristic
338C22×C43#44111yescharacteristic
339C22×C43#44811yescharacteristic
340C22×C43#44811yescharacteristic
341C22×C43#44911yescharacteristic
342C22×C43#44911yescharacteristic
343C22×C43#45111yescharacteristic
344C22×C43#45111yescharacteristic
345C22×C43#45211yescharacteristic
346C22×C43#45211yescharacteristic
347C22×C43#46011yescharacteristic
348C22×C43#46211yescharacteristic
349C22×C43#46411yescharacteristic
350C22×C43#46411yescharacteristic
351C22×C43#47511yescharacteristic
352C22×C43#47711yescharacteristic
353C22×C43#47911yescharacteristic
354C22×C43#47911yescharacteristic
355C4×C43—28no—
356C4×C43—82no—
357C4×C43C2×#9511yescharacteristic
358C4×C43C4×C22⋊C411yescharacteristic
359C4×C43#38011yescharacteristic
360C4×C43#38111yescharacteristic
361C4×C43#38511yescharacteristic
362C4×C43#38511yescharacteristic
363C4×C43#38611yescharacteristic
364C4×C43#38611yescharacteristic
365Dic43—24no—
366Dic43—42no—
367Dic43—44no—
368Dic43—82no—
369C22×C4×Q8—431no—
370C22×#103—431no—
371C22×#103D4311yescharacteristic
372C2×#340—431no—
373C2×#340—431no—
374C2×#336—431no—
375C4⋊#95—431no—
376C2×C43C22⋊#9511yescharacteristic
377C2×C43C4×#10311yescharacteristic
378C2×C43#176311yescharacteristic
379C2×C43#178711yescharacteristic
380C2×C43#178811yescharacteristic
381C2×C43#180311yescharacteristic
382C2×C43#180511yescharacteristic
383C2×C43#186311yescharacteristic
384C2×C43#186311yescharacteristic
385C2×C43#186511yescharacteristic
386C2×C43#186511yescharacteristic
387C2×C43#187811yescharacteristic
388C2×C43#187811yescharacteristic
389C2×C43#188011yescharacteristic
390C2×C43#188011yescharacteristic
391C23×Q8C2×D4311yescharacteristic
392C23×C8—431no—
393C23×C8C2×D4311yescharacteristic
394C2×C4×Q8—434no—
395C2×C4×Q8—862no—
396C2×C4×Q8—862no—
397C2×C4×Q8—862no—
398C2×C4×Q8—862no—
399C2×C4×Q8—862no—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—861no—
403C22×C4⋊C4C2×D4311yescharacteristic
404C22×C42—431no—
405C22×C42—861no—
406C2×#103—22no—
407C2×#103—22no—
408C2×#103—434no—
409C2×#103—862no—
410C2×#103—862no—
411C2×#103Dic4314yescomplemented
412C2×#95—861no—
413C2×#95—861no—
414#340—862no—
415#340—862no—
416#336—862no—
417C43#1078911yescharacteristic, complemented, Sylow
418C22×Q8—21no—
419C22×Q8—21no—
420C22×Q8—21no—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8Dic8612yes—
426C22×Q8C4×D4312yes—
427C22×Q8C4×D4312yes—
428C22×Q8D17212yes—
429C22×Q8C2×Dic4312yes—
430C22×Q8C22⋊D4312yes—
431C22×Q8C22⋊D4312yes—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—861no—
437C23×C4—861no—
438C23×C4C22×D4311yescharacteristic
439C22×C8—21no—
440C22×C8—21no—
441C22×C8—21no—
442C22×C8—21no—
443C22×C8—21no—
444C22×C8—21no—
445C22×C8—432no—
446C22×C8—861no—
447C22×C8—861no—
448C22×C8—861no—
449C22×C8—861no—
450C22×C8—861no—
451C22×C8—861no—
452C22×C8C2×Dic4312yes—
453C4×Q8—868no—
454C4×Q8—868no—
455C4×Q8—868no—
456C4×Q8—868no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—432no—
463C2×C4⋊C4—432no—
464C2×C4⋊C4—432no—
465C2×C4⋊C4—432no—
466C2×C4⋊C4—864no—
467C2×C4⋊C4—864no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4C2×Dic4312yes—
478C2×C42—432no—
479C2×C42—432no—
480C2×C42—864no—
481C2×C42—864no—
482C2×C42—864no—
483C2×C42—861no—
484C2×C42—861no—
485C2×C42—861no—
486C2×C42—861no—
487#103—28no—
488#103—868no—
489#95—1722no—
490#95—1722no—
491C24D4×D4311yescharacteristic
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8C4×Dic4314yes—
514C2×Q8Dic43⋊C414yes—
515C2×Q8Dic43⋊C414yes—
516C2×Q8C4⋊Dic4314yes—
517C2×Q8(C2×D43)⋊C414yes—
518C2×Q8(C2×D43)⋊C414yes—
519C2×Q8C22⋊Dic4314yes—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—432no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—861no—
545C22×C4—862no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—862no—
552C22×C4—1721no—
553C22×C4—1721no—
554C22×C4—1721no—
555C22×C4—1721no—
556C22×C4—1721no—
557C22×C4—1721no—
558C22×C4—1721no—
559C22×C4—1721no—
560C22×C4—1721no—
561C22×C4—1721no—
562C22×C4C2×Dic8611yescharacteristic
563C22×C4C2×C4×D4311yescharacteristic
564C22×C4C2×C4×D4311yescharacteristic
565C22×C4C2×D17211yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4D4×D4311yescharacteristic
568C22×C4D4×D4311yescharacteristic
569C22×C4#1062190011yescharacteristic
570C22×C4#1062190011yescharacteristic
571C22×C4#1062190011yescharacteristic
572C22×C4#1062190011yescharacteristic
573C22×C4C22×Dic4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C2×C22⋊D4311yescharacteristic
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—862no—
584C2×C8—862no—
585C2×C8—862no—
586C2×C8—1721no—
587C2×C8—1721no—
588C2×C8—1721no—
589C2×C8—1721no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—434no—
595C4⋊C4—8616no—
596C4⋊C4—862no—
597C4⋊C4—862no—
598C4⋊C4—862no—
599C4⋊C4—862no—
600C4⋊C4—862no—
601C4⋊C4—1721no—
602C4⋊C4—1721no—
603C42—8616no—
604C42—862no—
605C42—862no—
606C42—862no—
607C42—862no—
608C23C22⋊C4×D4311yescharacteristic
609C23(C22⋊D43)⋊C411yescharacteristic
610C23D4×Dic4311yescharacteristic
611C23#1306329311yescharacteristic
612C23#1306329511yescharacteristic
613C23#1306329711yescharacteristic
614C23#1306330211yescharacteristic
615C23SD16×D4311yescharacteristic
616C23Q16×D4311yescharacteristic
617C23#1306334611yescharacteristic
618C23#1306334811yescharacteristic
619C23#1306335211yescharacteristic
620C23#1306335411yescharacteristic
621C23#1306335711yescharacteristic
622C23#1306335711yescharacteristic
623Q8—24no—
624Q8—24no—
625Q8—24no—
626Q8—24no—
627Q8—24no—
628Q8—24no—
629Q8—24no—
630Q8C43⋊#9518yescomplemented
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—434no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—864no—
655C2×C4—862no—
656C2×C4—3441no—
657C2×C4—3441no—
658C2×C4—3441no—
659C2×C4—3441no—
660C2×C4—1722no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4—1721no—
664C2×C4—1722no—
665C2×C4—1721no—
666C2×C4—1722no—
667C2×C4—1721no—
668C2×C4—1722no—
669C2×C4—1721no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4C2×C4×Dic4311yescharacteristic
674C2×C4C22⋊C4×D4311yescharacteristic
675C2×C4C2×(C2×D43)⋊C411yescharacteristic
676C2×C4C2×(C2×D43)⋊C411yescharacteristic
677C2×C4C2×C22⋊Dic4311yescharacteristic
678C2×C4C2×Dic43⋊C411yescharacteristic
679C2×C4C2×Dic43⋊C411yescharacteristic
680C2×C4C2×C4⋊Dic4311yescharacteristic
681C2×C4#1306328111yescharacteristic
682C2×C4#1306328111yescharacteristic
683C2×C4(C22⋊D43)⋊C411yescharacteristic
684C2×C4(C22⋊D43)⋊C411yescharacteristic
685C2×C4(C22⋊D43)⋊C411yescharacteristic
686C2×C4D4×Dic4311yescharacteristic
687C2×C4D4×Dic4311yescharacteristic
688C2×C4D4×Dic4311yescharacteristic
689C2×C4#1306329311yescharacteristic
690C2×C4#1306329511yescharacteristic
691C2×C4#1306329711yescharacteristic
692C2×C4#1306329711yescharacteristic
693C2×C4#1306329711yescharacteristic
694C2×C4#1306330211yescharacteristic
695C2×C4#1306330211yescharacteristic
696C2×C4#1306330211yescharacteristic
697C2×C4#1306330611yescharacteristic
698C2×C4#1306330611yescharacteristic
699C2×C4#1306330911yescharacteristic
700C2×C4#1306330911yescharacteristic
701C8—42no—
702C8—1722no—
703C22C22⋊C4×Dic4311yescharacteristic
704C22#1458275411yescharacteristic
705C22#1458275711yescharacteristic
706C22#1458277111yescharacteristic
707C22#1458277411yescharacteristic
708C22#1458277611yescharacteristic
709C22#1458277911yescharacteristic
710C22#103×D4311yescharacteristic
711C22#1458289411yescharacteristic
712C22#1458289911yescharacteristic
713C22#1458290611yescharacteristic
714C22#1458298411yescharacteristic
715C22SD16×Dic4311yescharacteristic
716C22#1458299111yescharacteristic
717C22Q16×Dic4311yescharacteristic
718C22#1458300011yescharacteristic
719C22#1458300211yescharacteristic
720C22#1458300311yescharacteristic
721C22#1458300611yescharacteristic
722C22#1458303611yescharacteristic
723C22#1458303911yescharacteristic
724C22#1458304311yescharacteristic
725C22#1458304711yescharacteristic
726C22#1458305311yescharacteristic
727C22#1458305611yescharacteristic
728C22#1458306011yescharacteristic
729C22#1458306411yescharacteristic
730C22#1458309711yescharacteristic
731C22#1458310711yescharacteristic
732C22#1458311911yescharacteristic
733C22#1458312311yescharacteristic
734C22#1458318211yescharacteristic
735C22#1458319211yescharacteristic
736C22#1458320411yescharacteristic
737C22#1458320811yescharacteristic
738C4—28no—
739C4—82no—
740C4—864no—
741C4—3442no—
742C4—1722no—
743C4—1724no—
744C4C2×C43⋊#9511yescharacteristic
745C4C22⋊C4×Dic4311yescharacteristic
746C4#1458275711yescharacteristic
747C4#1458276011yescharacteristic
748C4#1458277111yescharacteristic
749C4#1458277411yescharacteristic
750C4#1458277611yescharacteristic
751C4#1458277911yescharacteristic
752C2#1913281711yescharacteristic
753C2#103×Dic4311yescharacteristic
754C2#1913442711yescharacteristic
755C2#1913452811yescharacteristic
756C2#1913453411yescharacteristic
757C2#1913459811yescharacteristic
758C2#1913460811yescharacteristic
759C2#1913484711yescharacteristic
760C2#1913485111yescharacteristic
761C2#1913486111yescharacteristic
762C2#1913486511yescharacteristic
763C2#1913493411yescharacteristic
764C2#1913493811yescharacteristic
765C2#1913494811yescharacteristic
766C2#1913495211yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC22×#103×C43C2
socle, prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC22×#103D43
hypocenterC43#10789
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
14. C2×Q8×Dic43C4semidirect
22. C2×#13063249C4semidirect
33. C2×#103×C43C4semidirect
246. Q8×C43#95semidirect
316. C2×Dic43#103semidirect
411. C2×#103Dic43semidirect
417. C43#10789semidirect
630. Q8C43⋊#95semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic432
C22×#130632492
C2×#145826622
C2×#145826612
C2×#145826532
#191328242
C22×#103×C432
#1078943