Finite Group Databasebeta

← #25147337

Subgroups — #25147337

Order 11008.

1018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583139C211yesmaximal, characteristic, complemented
2C2×#14583107C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D43C211yesmaximal, characteristic
4#19139545C211yesmaximal, characteristic
5#19139514C211yesmaximal, characteristic
6#19135800C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135602C211yesmaximal, characteristic, complemented
10#19135395C211yesmaximal, characteristic, complemented
11#19135350C211yesmaximal, characteristic, complemented
12#19135018C211yesmaximal, characteristic, complemented
13#19135015C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#467C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063301C2211yescharacteristic
22C2×#13063301C2211yescharacteristic
23C2×Q8×Dic43C2211yescharacteristic
24C2×C4×C22⋊D43C2211yescharacteristic
25#14583139—24no—
26#14583107—24no—
27C8×C22⋊D43—24no—
28C2×#13063258C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582835—21no—
40#14582834—21no—
41#14582822—21no—
42#14582821—21no—
43#14582799—21no—
44#14582799—21no—
45#14582794—21no—
46#14582768—21no—
47#14582768C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C43×#467—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C2×C8×D43—22no—
72C2×C8×D43—22no—
73C2×C8×D43—41no—
74#13063323—22no—
75#13063323—22no—
76#13063305—22no—
77#13063305—41no—
78#13063304—22no—
79#13063304—41no—
80#13063301—22no—
81#13063301—22no—
82#13063301—41no—
83#13063301—41no—
84Q8×Dic43—22no—
85Q8×Dic43—22no—
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112#13063258—22no—
113Dic43⋊C8D414yes—
114#13063250—22no—
115#13063250—22no—
116#13063249—22no—
117#13063249—22no—
118#13063249—41no—
119#13063248—41no—
120C22⋊(C43⋊C8)—22no—
121(C2×D43)⋊C8—22no—
122C8×Dic43—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×Q8×C43C2311yescharacteristic
127C22×Q8×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C2×Q16×C43—22no—
130C2×Q16×C43—22no—
131C2×Q16×C43—41no—
132C22×C8×C43—22no—
133C22×C8×C43—22no—
134C22×C8×C43—41no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43—41no—
140C22⋊Q8×C43—41no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147#107×C43—22no—
148#103×C43—22no—
149#103×C43D414yescomplemented
150C24×C43C2×D411yescharacteristic
151C23×D43C2×D411yescharacteristic
152C2×Q8×C43—21no—
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—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43C2×D412yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43Q1614yescomplemented
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198Q16×C43—44no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—44no—
204C2×C8×C43C2×D412yes—
205C2×C8×C43C2×D412yes—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—42no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43C2×D412yes—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊Dic43—22no—
215C22⋊Dic43—42no—
216C22⋊Dic43—81no—
217#10621885—44no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—81no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230C4⋊Dic43#4112yes—
231Dic43⋊C4—22no—
232Dic43⋊C4—42no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238Dic43⋊C4—81no—
239C4×Dic43—42no—
240C4×Dic43—42no—
241C4×Dic43C2×D412yes—
242C4×Dic43#4112yes—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8C2×D412yes—
249C8×D43—44no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43C2×Q1612yes—
257C23×C43C22×D411yescharacteristic
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43C2×Q1612yes—
265Q8×C43—22no—
266Q8×C43—22no—
267Q8×C43—41no—
268Q8×C43—41no—
269Q8×C43—41no—
270Q8×C43—41no—
271Q8×C43—41no—
272Q8×C43—41no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C22⋊D43—28no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—21no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43#12112yes—
317C2×Dic43#12112yes—
318C2×Dic43C2×Q1612yes—
319C2×Dic43#13512yes—
320C4×D43—41no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—41no—
324Dic86—41no—
325Dic86—41no—
326Dic86—41no—
327Dic86—41no—
328C8×C43—22no—
329C8×C43—22no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332#25386—431nomaximal, Sylow
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43C2×#12111yescharacteristic
341C22×C43D4211yescharacteristic
342C22×C43#54611yescharacteristic
343C22×C43C22×Q1611yescharacteristic
344C22×C43C2×#13511yescharacteristic
345C22×C43#57711yescharacteristic
346C22×C43#57811yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—41no—
354C4×C43—41no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43#53211yescharacteristic
360C4×C43#54011yescharacteristic
361C4×C43D4211yescharacteristic
362C4×C43#55011yescharacteristic
363Dic43—22no—
364Dic43—41no—
365Dic43—42no—
366Dic43—81no—
367Dic43—81no—
368Dic43—81no—
369Dic43#46714yescomplemented
370C2×#467—431no—
371C2×#467D4311yescharacteristic, complemented
372C2×#462—431no—
373C2×C8×D4—431no—
374#2542—431no—
375#2538—431no—
376#2036—431no—
377#2036—431no—
378#2001—431no—
379#2001—431no—
380#1956—431no—
381#1947—431no—
382#1892—431no—
383#1892—431no—
384C4×#103—431no—
385C2×C43—42no—
386C2×C43#242811yescharacteristic
387C2×C43C2×#46711yescharacteristic
388C2×C43#306311yescharacteristic
389C2×C43#328411yescharacteristic
390C2×C43D4×Q1611yescharacteristic
391C2×C43#329911yescharacteristic
392C2×C43#330211yescharacteristic
393D43—42no—
394C22×Q16—431no—
395C22×Q16C2×D4311yescharacteristic
396C23×C8—431no—
397C23×C8C2×D4311yescharacteristic
398C2×C4⋊Q8—431no—
399C2×C22⋊Q8—431no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—431no—
402C2×C22⋊Q8—431no—
403C2×C22⋊Q8C2×D4311yescharacteristic
404C2×C22⋊Q8C2×D4311yescharacteristic
405C2×C4×Q8—431no—
406C2×C4×D4—431no—
407#467—24no—
408#467—864no—
409#462—864no—
410C8×D4—864no—
411C2×#107—431no—
412C2×#107C2×D4311yescharacteristic
413C2×C4⋊C8—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103C2×D4311yescharacteristic
421C2×#103C2×D4311yescharacteristic
422C2×C22⋊C8—431no—
423C2×C22⋊C8—431no—
424C2×C4×C8—431no—
425#399—861no—
426#399—861no—
427#396—861no—
428#396—861no—
429#390—861no—
430#390—861no—
431#389—861no—
432#384—431no—
433#384—861no—
434#380—431no—
435#380—431no—
436C4×C4⋊C4—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441C43#2538611yescharacteristic, complemented, Sylow
442C22×Q8—431no—
443C22×Q8C22×D4311yescharacteristic
444C22×Q8C22×D4311yescharacteristic
445C22×D4—431no—
446C23×C4—431no—
447C23×C4C22×D4311yescharacteristic
448C2×Q16—22no—
449C2×Q16—22no—
450C2×Q16—41no—
451C2×Q16—862no—
452C2×Q16—862no—
453C2×Q16—1721no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—41no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8—1721no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C4⋊Q8—862no—
465C4⋊Q8—862no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—41no—
469C22⋊Q8—41no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C22⋊Q8—862no—
473C22⋊Q8—862no—
474C22⋊Q8—1721no—
475C22⋊Q8—1721no—
476C22⋊Q8—1721no—
477C22⋊Q8—1721no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×D4—862no—
481C4×D4—862no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C42—431no—
510C2×C42—861no—
511C2×C42—861no—
512#107—22no—
513#107—862no—
514C4⋊C8—434no—
515#103—22no—
516#103—862no—
517#103—862no—
518#103—862no—
519#103—862no—
520#103—1721no—
521#103—1721no—
522#103C22⋊D4314yescomplemented
523C22⋊C8—862no—
524C22⋊C8—862no—
525C4×C8—862no—
526#95—861no—
527#95—861no—
528#95—861no—
529C24—431no—
530C24D4×D4311yescharacteristic
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8C2×C22⋊D4312yes—
549C2×D4—434no—
550C2×D4—862no—
551C2×D4—862no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4D4×D4311yescharacteristic
576C22×C4C23×D4311yescharacteristic
577Q16—44no—
578Q16—1724no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8—432no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—1724no—
591C2×C8D4×D4312yes—
592C2×C8C2×C22⋊D4312yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—432no—
599C4⋊C4—862no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—3441no—
606C4⋊C4—1722no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C4⋊C4C2×C22⋊D4312yes—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—3441no—
620C22⋊C4—3441no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C42—432no—
626C42—432no—
627C42—1722no—
628C42—1722no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—432no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23Q16×D4312yes—
643C23C2×D4×D4311yescharacteristic
644Q8—22no—
645Q8—22no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—1721no—
653Q8—1721no—
654Q8—1721no—
655Q8—1721no—
656D4—868no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—862no—
685C2×C4—861no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4C2×D4×D4311yescharacteristic
702C2×C4C22×C22⋊D4311yescharacteristic
703C2×C4#41×D4311yescharacteristic
704C2×C4#41×D4311yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337011yescharacteristic
707C8—22no—
708C8—22no—
709C8—862no—
710C8—1721no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—1721no—
722C22—1721no—
723C22—1721no—
724C22—1721no—
725C22#121×D4311yescharacteristic
726C22D4×C22⋊D4311yescharacteristic
727C22#1458353811yescharacteristic
728C22C2×Q16×D4311yescharacteristic
729C22#135×D4311yescharacteristic
730C22#1458370611yescharacteristic
731C22#1458371211yescharacteristic
732C4—42no—
733C4—41no—
734C4—42no—
735C4—81no—
736C4—81no—
737C4—434no—
738C4—862no—
739C4—3441no—
740C4—3441no—
741C4—3441no—
742C4—1722no—
743C4—1721no—
744C4#1458344511yescharacteristic
745C4#1458349911yescharacteristic
746C4D4×C22⋊D4311yescharacteristic
747C4#1458356711yescharacteristic
748C2—42no—
749C2—1722no—
750C2#1913818011yescharacteristic
751C2#467×D4311yescharacteristic
752C2#1914428511yescharacteristic
753C2#1914631911yescharacteristic
754C2Q16×C22⋊D4311yescharacteristic
755C2#1914646611yescharacteristic
756C2#1914650711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#467D43
hypocenterC43#25386
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#14583139C2semidirect
2. C2×#14583107C2semidirect
6. #19135800C2semidirect
7. #19135795C2semidirect
8. #19135603C2semidirect
9. #19135602C2semidirect
10. #19135395C2semidirect
11. #19135350C2semidirect
12. #19135018C2semidirect
13. #19135015C2semidirect
14. #103×Dic43C2semidirect
15. C2×C43×#467C2semidirect
149. #103×C43D4semidirect
178. C2×C22⋊D43Q16semidirect
369. Dic43#467semidirect
371. C2×#467D43semidirect
441. C43#25386semidirect
522. #103C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831392
C2×#145831072
C2×C8×C22⋊D432
#191395452
#191395142
#191358002
#191357952
#191356032
#191356022
#191353952
#191353502
#191350182
#191350152
#103×Dic432
C2×C43×#4672
#2538643