Finite Group Databasebeta

← #25112832

Subgroups — #25112832

Order 11008.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic
3#19137491C211yesmaximal, characteristic
4#19135554C211yesmaximal, characteristic, complemented
5#19135541C211yesmaximal, characteristic, complemented
6#19135015C211yesmaximal, characteristic, complemented
7#19134903C211yesmaximal, characteristic, complemented
8#19134899C211yesmaximal, characteristic, complemented
9#19134684C211yesmaximal, characteristic, complemented
10#19134683C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582662C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1892C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17#14583607—24no—
18#14583607C418yescomplemented
19C2×#13063324C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063305—21no—
22C2×#13063302—21no—
23C2×#13063301C2211yescharacteristic
24C2×Q8×Dic43C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C8×C22⋊D43—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582796—21no—
40#14582773—21no—
41#14582771—21no—
42#14582768C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×C22⋊D43D411yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C2×C8×D43—22no—
72C2×C8×D43—22no—
73C2×C8×D43—41no—
74#13063324—22no—
75#13063324C2×C414yescomplemented
76#13063315—28no—
77#13063305—28no—
78#13063302—28no—
79#13063301—22no—
80#13063301C2×C414yescomplemented
81Q8×Dic43—22no—
82Q8×Dic43C2×C414yescomplemented
83C4×C22⋊D43C2×C414yes—
84C4×C22⋊D43D414yes—
85(C22⋊D43)⋊C4—28no—
86(C22⋊D43)⋊C4—44no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2×C414yescomplemented
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—41no—
108C4⋊C4×D43C2×C414yescomplemented
109C2×C22⋊Dic43D411yescharacteristic
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063249—22no—
118#13063249—41no—
119C22⋊(C43⋊C8)—22no—
120(C2×D43)⋊C8—22no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×Q8×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43—22no—
127C22×C8×C43—22no—
128C22×C8×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43C2×C414yescomplemented
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139#103×C43—22no—
140#103×C43—41no—
141#95×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43C22⋊C414yes—
163C2×C22⋊D43SD1614yes—
164C2×C22⋊D43Q1614yes—
165C22×Dic43—24no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—42no—
171C22×Dic43—42no—
172C22×Dic43—81no—
173C22×Dic43—81no—
174C22×Dic43—81no—
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—24no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—81no—
186C2×C4×D43—81no—
187C2×C4×D43—81no—
188C2×C4×D43C22×C412yes—
189C2×C4×D43C2×D412yes—
190C2×Dic86—24no—
191C2×Dic86—81no—
192C2×Dic86—81no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—44no—
199C2×C8×C43#4112yes—
200C4⋊C4×C43—24no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43C22×C412yes—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—42no—
209C22⋊Dic43C22⋊C414yes—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4C22⋊C414yes—
213C4⋊Dic43—24no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—42no—
221C4⋊Dic43C22×C412yes—
222C4⋊Dic43C22×C412yes—
223C4⋊Dic43#4112yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229Dic43⋊C4—81no—
230Dic43⋊C4C22⋊C414yes—
231C4×Dic43—24no—
232C4×Dic43—42no—
233C4×Dic43C22×C412yes—
234C4×Dic43C2×D412yes—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C8×D43—44no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43C2×C22⋊C412yes—
247C23×C43C2×SD1612yes—
248C23×C43C2×Q1612yes—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43C2×C22⋊C412yes—
255C22×D43C2×SD1612yes—
256C22×D43C2×Q1612yes—
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—41no—
260Q8×C43—41no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43C2×C22⋊C412yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C22⋊D43#103116yescomplemented
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—84no—
304C2×Dic43—84no—
305C2×Dic43C2×C22⋊C412yes—
306C2×Dic43C2×C22⋊C412yes—
307C2×Dic43C2×C22⋊C412yes—
308C2×Dic43C2×SD1612yes—
309C2×Dic43C2×Q1612yes—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—84no—
315C4×D43—84no—
316Dic86—84no—
317C8×C43—22no—
318C8×C43—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#22487—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43C2×#10314yes—
329C22×C43C22×C22⋊C411yescharacteristic
330C22×C43#54611yescharacteristic
331C22×C43#54711yescharacteristic
332C22×C43C22×SD1611yescharacteristic
333C22×C43C22×Q1611yescharacteristic
334C22×C43#57611yescharacteristic
335C22×C43#57711yescharacteristic
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43C2×#10314yes—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—81no—
347C4×C43—81no—
348C4×C43C4×#4111yescharacteristic
349C4×C43#52011yescharacteristic
350C4×C43#54611yescharacteristic
351C4×C43#54711yescharacteristic
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—42no—
356Dic43—42no—
357Dic43—81no—
358Dic43C2×#10314yes—
359C2×#554—431no—
360C2×C8×D4—431no—
361D4×C4⋊C4—431no—
362#1990—431no—
363#1987—431no—
364#1892—431no—
365#1892D4311yescharacteristic, complemented
366#1872—431no—
367#1872—431no—
368#1824—431no—
369#1824—431no—
370#1803—431no—
371C4×#103—431no—
372C2×#340—431no—
373C2×#340—431no—
374C2×C43—24no—
375C2×C43#233911yescharacteristic
376C2×C43C22×#10311yescharacteristic
377C2×C43#289711yescharacteristic
378C2×C43#329511yescharacteristic
379C2×C43#329911yescharacteristic
380C2×C43#333511yescharacteristic
381C2×C43#333811yescharacteristic
382D43—24no—
383C23×C8—431no—
384C23×C8C2×D4311yescharacteristic
385#554—438no—
386#554—864no—
387C2×C4⋊Q8—431no—
388C2×#125—861no—
389C2×C22⋊Q8—431no—
390C2×C22⋊Q8—861no—
391C2×C22⋊Q8—861no—
392C2×C22⋊Q8C2×D4311yescharacteristic
393C2×C4×Q8—431no—
394C2×C4×D4—431no—
395C2×C4×D4—861no—
396C2×C4×D4—861no—
397C22×C4⋊C4—431no—
398C22×C4⋊C4—431no—
399C22×C4⋊C4—431no—
400C22×C4⋊C4—431no—
401C8×D4—864no—
402C2×C4⋊C8—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103C2×D4311yescharacteristic
406C2×#103C2×D4311yescharacteristic
407C2×C22⋊C8—431no—
408C2×C22⋊C8—431no—
409C2×C4×C8—431no—
410#389—861no—
411#385—861no—
412#385—861no—
413#384—431no—
414#380—431no—
415#380C2×D4311yescharacteristic
416C4×C4⋊C4—431no—
417#340—431no—
418#340—431no—
419#340—431no—
420#340—431no—
421#340—431no—
422#340—431no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340C2×D4311yescharacteristic
428#340C2×D4311yescharacteristic
429C43#2248711yescharacteristic, complemented, Sylow
430C22×Q8—861no—
431C22×Q8C22×D4311yescharacteristic
432C22×D4—431no—
433C23×C4—431no—
434C23×C4—861no—
435C23×C4—861no—
436C23×C4—861no—
437C23×C4—861no—
438C23×C4C22×D4311yescharacteristic
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8—431no—
443C22×C8—431no—
444C22×C8—862no—
445C22×C8—862no—
446C22×C8—1721no—
447C22×C8C22×D4311yescharacteristic
448C22×C8C22×D4311yescharacteristic
449C4⋊Q8—434no—
450C4⋊Q8—862no—
451#125—868no—
452C22⋊Q8—22no—
453C22⋊Q8—434no—
454C22⋊Q8—868no—
455C22⋊Q8—868no—
456C22⋊Q8—862no—
457C22⋊Q8C4×D4314yescomplemented
458C4×Q8—434no—
459C4×Q8—862no—
460C4×D4—434no—
461C4×D4—434no—
462C4×D4—868no—
463C4×D4—1724no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—434no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—434no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—862no—
473C2×C4⋊C4—862no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—1721no—
486C2×C4⋊C4—1721no—
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—431no—
497C2×C42—861no—
498C2×C42—861no—
499C4⋊C8—862no—
500#103—22no—
501#103—41no—
502#103—862no—
503#103—1721no—
504C22⋊C8—862no—
505C22⋊C8—862no—
506C4×C8—862no—
507#95—21no—
508#95—861no—
509#95—861no—
510C24—431no—
511C24D4×D4311yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—864no—
518C2×Q8—3441no—
519C2×Q8—3441no—
520C2×Q8C2×C4×D4312yes—
521C2×D4—434no—
522C2×D4—434no—
523C2×D4—434no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—431no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—864no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—864no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—3441no—
548C22×C4—3441no—
549C22×C4—3441no—
550C22×C4—3441no—
551C22×C4—3441no—
552C22×C4—3441no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4C2×C4×D4312yes—
558C22×C4D4×D4311yescharacteristic
559C22×C4D4×D4312yes—
560C22×C4C23×D4311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—44no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—1724no—
574C2×C8#1062190012yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—434no—
582C4⋊C4—432no—
583C4⋊C4—432no—
584C4⋊C4—432no—
585C4⋊C4—864no—
586C4⋊C4—864no—
587C4⋊C4—864no—
588C4⋊C4—864no—
589C4⋊C4—864no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—3441no—
596C4⋊C4—1722no—
597C4⋊C4—1722no—
598C4⋊C4—1722no—
599C4⋊C4C2×C4×D4312yes—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—434no—
603C22⋊C4—434no—
604C22⋊C4—864no—
605C22⋊C4—1722no—
606C42—432no—
607C42—432no—
608C42—864no—
609C42—1722no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—432no—
615C23—432no—
616C23—432no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23C22⋊C4×D4312yes—
622C23SD16×D4312yes—
623C23Q16×D4312yes—
624C23C2×D4×D4311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—3444no—
630D4—4316no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—432no—
650C2×C4—432no—
651C2×C4—432no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—861no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—3444no—
666C2×C4—3444no—
667C2×C4—3444no—
668C2×C4—3444no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4C22⋊C4×D4312yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4#41×D4311yescharacteristic
682C2×C4C2×#1062190011yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337211yescharacteristic
685C8—22no—
686C8—41no—
687C8—1721no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—434no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22—862no—
700C22—862no—
701C22—862no—
702C22#103×D4314yes—
703C22C2×C22⋊C4×D4311yescharacteristic
704C22#1458353811yescharacteristic
705C22#1458354911yescharacteristic
706C22C2×SD16×D4311yescharacteristic
707C22C2×Q16×D4311yescharacteristic
708C22#1458370111yescharacteristic
709C22#1458370611yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—81no—
714C4—81no—
715C4—434no—
716C4—862no—
717C4—862no—
718C4—3441no—
719C4—1722no—
720C4—1722no—
721C4—1722no—
722C4C4×#1062190011yescharacteristic
723C4#1458337811yescharacteristic
724C4#1458353611yescharacteristic
725C4#1458354711yescharacteristic
726C2—24no—
727C2—864no—
728C2#1913742111yescharacteristic
729C2C2×#103×D4311yescharacteristic
730C2#1914311711yescharacteristic
731C2#1914641411yescharacteristic
732C2#1914646611yescharacteristic
733C2#1914694711yescharacteristic
734C2#1914698411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1892C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1892D43
hypocenterC43#22487
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. #19135554C2semidirect
5. #19135541C2semidirect
6. #19135015C2semidirect
7. #19134903C2semidirect
8. #19134899C2semidirect
9. #19134684C2semidirect
10. #19134683C2semidirect
11. #19134598C2semidirect
12. #103×Dic43C2semidirect
13. C2×#14582662C2semidirect
14. #340×D43C2semidirect
15. C43×#1892C2semidirect
18. #14583607C4semidirect
75. #13063324C2×C4semidirect
80. #13063301C2×C4semidirect
82. Q8×Dic43C2×C4semidirect
93. C2×C4⋊Dic43C2×C4semidirect
108. C4⋊C4×D43C2×C4semidirect
132. C22⋊Q8×C43C2×C4semidirect
286. C22⋊D43#103semidirect
365. #1892D43semidirect
429. C43#22487semidirect
457. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×C8×C22⋊D432
#191374912
#191355542
#191355412
#191350152
#191349032
#191348992
#191346842
#191346832
#191345982
#103×Dic432
C2×#145826622
#340×D432
C43×#18922
#2248743