Finite Group Databasebeta

← #25147531

Subgroups — #25147531

Order 11008.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583127C211yesmaximal, characteristic, complemented
2C2×#14583102C211yesmaximal, characteristic, complemented
3C2×#14582968C211yesmaximal, characteristic, complemented
4#19139545C211yesmaximal, characteristic, complemented
5#19139494C211yesmaximal, characteristic
6#19135800C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135598C211yesmaximal, characteristic, complemented
9#19135595C211yesmaximal, characteristic, complemented
10#19135413C211yesmaximal, characteristic, complemented
11#19135360C211yesmaximal, characteristic, complemented
12#19135028C211yesmaximal, characteristic, complemented
13#19135015C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C2×C43×#468C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063301C2211yescharacteristic
22C2×#13063296C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×C4×C22⋊D43C2211yescharacteristic
25#14583127—24no—
26#14583102—24no—
27#14582968—24no—
28C2×#13063256C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39#14582835—21no—
40#14582834—21no—
41#14582827—21no—
42#14582807—21no—
43#14582799—21no—
44#14582779—21no—
45#14582776—21no—
46#14582768—21no—
47#14582764C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C43×#468—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C23×Dic43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—22no—
74C2×C8×D43—22no—
75C2×C8×D43—41no—
76#13063323—22no—
77#13063323—22no—
78#13063305—22no—
79#13063305—41no—
80#13063304—22no—
81#13063304—41no—
82#13063301—22no—
83#13063301—41no—
84#13063296—22no—
85#13063296—41no—
86D4×Dic43—22no—
87D4×Dic43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4D411yescharacteristic
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
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)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110#13063256—22no—
111Dic43⋊C8D414yescomplemented
112#13063250—22no—
113#13063250—22no—
114#13063249—22no—
115#13063249—41no—
116#13063248—41no—
117#13063246—22no—
118C22⋊(C43⋊C8)—22no—
119(C2×D43)⋊C8—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×Q8×C43C2311yescharacteristic
127C22×D4×C43—21no—
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C2×SD16×C43—22no—
131C2×SD16×C43—22no—
132C2×SD16×C43—41no—
133C2×M16×C43—22no—
134C2×M16×C43—22no—
135C2×M16×C43—41no—
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43—41no—
140#121×C43—22no—
141#121×C43—41no—
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#102×C43D414yescomplemented
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C23×D43C2×D411yescharacteristic
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×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—81no—
167C2×D4×C43C2×D412yes—
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×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—41no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—81no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—42no—
190C22×Dic43—81no—
191C22×Dic43—81no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207SD16×C43—44no—
208M16×C43—44no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43C2×D412yes—
214C2×C8×C43C2×D412yes—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—42no—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊Dic43—22no—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225C22⋊Dic43—42no—
226C22⋊Dic43—81no—
227#10621883—44no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—81no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—42no—
238C4⋊Dic43#4112yes—
239Dic43⋊C4—22no—
240Dic43⋊C4—42no—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244C4×Dic43—42no—
245C4×Dic43C2×D412yes—
246C4×Dic43#4112yes—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8C2×D412yes—
253C8×D43—44no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43C22×D411yescharacteristic
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43#13712yes—
276Q8×C43—41no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43—41no—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—84no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C22⋊D43—44no—
308C22⋊D43—84no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—84no—
329C2×Dic43#12112yes—
330C2×Dic43#12112yes—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335Dic86—41no—
336Dic86—41no—
337Dic86—41no—
338Dic86—41no—
339C8×C43—22no—
340C8×C43—22no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343#25400—431nomaximal, Sylow
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43C2×#12111yescharacteristic
359C22×C43D4211yescharacteristic
360C22×C43#54611yescharacteristic
361C22×C43C2×#13711yescharacteristic
362C22×C43#57511yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57711yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43#53211yescharacteristic
377C4×C43#54011yescharacteristic
378C4×C43D4211yescharacteristic
379C4×C43#55011yescharacteristic
380Dic43—22no—
381Dic43—22no—
382Dic43—41no—
383Dic43—42no—
384Dic43—81no—
385Dic43—81no—
386Dic43—81no—
387C2×#468D4311yescharacteristic, complemented
388C2×#465—431no—
389C2×#461—431no—
390C2×#435—431no—
391#2542—431no—
392#2535—431no—
393#2036—431no—
394#2035—431no—
395#2000—431no—
396#2000—431no—
397#1960—431no—
398#1949—431no—
399#1894—431no—
400#1892—431no—
401#1762—431no—
402C2×C43—81no—
403C2×C43—82no—
404C2×C43#242811yescharacteristic
405C2×C43#305611yescharacteristic
406C2×C43#305711yescharacteristic
407C2×C43#326611yescharacteristic
408C2×C43#326711yescharacteristic
409C2×C43#330711yescharacteristic
410C2×C43#332011yescharacteristic
411D43—42no—
412C22×SD16—431no—
413C22×SD16C2×D4311yescharacteristic
414C22×M16C2×D4311yescharacteristic
415C23×C8—431no—
416C2×C4⋊Q8—431no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—431no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8C2×D4311yescharacteristic
421C2×#121—431no—
422C2×#121C2×D4311yescharacteristic
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425#468—24no—
426#465—864no—
427#461—864no—
428#435—864no—
429C2×#107C2×D4311yescharacteristic
430C2×#106—431no—
431C2×C4⋊C8—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103C2×D4311yescharacteristic
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×#97—431no—
443#399—861no—
444#399—861no—
445#397—861no—
446#392—861no—
447#390—861no—
448#386—861no—
449#386—861no—
450#384—861no—
451#382—431no—
452#380—431no—
453#380—431no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340—431no—
459C43#2540011yescharacteristic, complemented, Sylow
460C22×Q8—431no—
461C22×Q8C22×D4311yescharacteristic
462C22×D4—21no—
463C22×D4—431no—
464C22×D4—861no—
465C22×D4C22×D4311yescharacteristic
466C23×C4—431no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—41no—
472C2×SD16—862no—
473C2×SD16—862no—
474C2×SD16—1721no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—41no—
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—862no—
481C22×C8—862no—
482C22×C8—1721no—
483C22×C8C22×D4311yescharacteristic
484C22×C8C22×D4311yescharacteristic
485C4⋊Q8—862no—
486C4⋊Q8—862no—
487C22⋊Q8—22no—
488C22⋊Q8—41no—
489C22⋊Q8—862no—
490C22⋊Q8—862no—
491C22⋊Q8—862no—
492C22⋊Q8—1721no—
493C22⋊Q8—1721no—
494C22⋊Q8—1721no—
495#121—22no—
496#121—41no—
497#121—862no—
498#121—1721no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—862no—
502C4×D4—862no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C42—431no—
527C2×C42—861no—
528#107—22no—
529#106—862no—
530C4⋊C8—434no—
531#103—22no—
532#103—862no—
533#103—862no—
534#103—862no—
535#103—1721no—
536#103—1721no—
537#102—862no—
538#102C22⋊D4314yescomplemented
539C22⋊C8—862no—
540C22⋊C8—862no—
541#97—862no—
542#95—861no—
543#95—861no—
544#95—861no—
545#95—861no—
546#95—861no—
547C24—21no—
548C24—431no—
549C24D4×D4311yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—3441no—
573C2×D4—1721no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4C2×C22⋊D4312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—3441no—
600C22×C4—3441no—
601C22×C4—1722no—
602C22×C4D4×D4311yescharacteristic
603C22×C4C23×D4311yescharacteristic
604SD16—44no—
605SD16—1724no—
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—432no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—1724no—
618C2×C8D4×D4312yes—
619C2×C8C2×C22⋊D4312yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—432no—
625C4⋊C4—862no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—1722no—
632C4⋊C4—1722no—
633C4⋊C4—1722no—
634C4⋊C4—1722no—
635C4⋊C4—1722no—
636C4⋊C4C2×C22⋊D4312yes—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—862no—
640C22⋊C4—862no—
641C22⋊C4—3441no—
642C22⋊C4—3441no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C42—432no—
649C42—432no—
650C42—1722no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—432no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23C2×D4×D4311yescharacteristic
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—1721no—
678Q8—1721no—
679Q8—1721no—
680Q8—1721no—
681D4—22no—
682D4—22no—
683D4—41no—
684D4—41no—
685D4—84no—
686D4—3444no—
687D4—1724no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
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—41no—
703C2×C4—41no—
704C2×C4—432no—
705C2×C4—432no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—862no—
713C2×C4—861no—
714C2×C4—3444no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C22×C22⋊D4311yescharacteristic
732C2×C4#41×D4311yescharacteristic
733C2×C4#41×D4311yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C8—22no—
737C8—22no—
738C8—862no—
739C8—1721no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22#121×D4311yescharacteristic
762C22D4×C22⋊D4311yescharacteristic
763C22#1458353811yescharacteristic
764C22#137×D4311yescharacteristic
765C22#1458369511yescharacteristic
766C22#1458370811yescharacteristic
767C22#1458370911yescharacteristic
768C4—42no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—862no—
773C4—862no—
774C4—3441no—
775C4—3441no—
776C4—3441no—
777C4—1722no—
778C4—1721no—
779C4#1458344511yescharacteristic
780C4#1458349911yescharacteristic
781C4D4×C22⋊D4311yescharacteristic
782C4#1458356711yescharacteristic
783C2—81no—
784C2—82no—
785C2—1722no—
786C2#1913818011yescharacteristic
787C2#1914422011yescharacteristic
788C2#1914423211yescharacteristic
789C2#1914609911yescharacteristic
790C2#1914611411yescharacteristic
791C2#1914656611yescharacteristic
792C2#1914676111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#468C2
socleC23×C43C22×D4
prime radical#19139494C2
hypercenterC2×#468D43
hypocenterC43#25400
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#14583127C2semidirect
2. C2×#14583102C2semidirect
3. C2×#14582968C2semidirect
4. #19139545C2semidirect
6. #19135800C2semidirect
7. #19135788C2semidirect
8. #19135598C2semidirect
9. #19135595C2semidirect
10. #19135413C2semidirect
11. #19135360C2semidirect
12. #19135028C2semidirect
13. #19135015C2semidirect
14. #19134422C2semidirect
15. C2×C43×#468C2semidirect
111. Dic43⋊C8D4semidirect
149. #102×C43D4semidirect
387. C2×#468D43semidirect
459. C43#25400semidirect
538. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831272
C2×#145831022
C2×#145829682
#191395452
#191394942
#191358002
#191357882
#191355982
#191355952
#191354132
#191353602
#191350282
#191350152
#191344222
C2×C43×#4682
#2540043