Finite Group Databasebeta

← #25130778

Subgroups — #25130778

Order 11008.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583588C211yesmaximal, characteristic
2C2×#14583205C211yesmaximal, characteristic, complemented
3C2×#14583005C211yesmaximal, characteristic, complemented
4#19139519C211yesmaximal, characteristic
5#19135800C211yesmaximal, characteristic, complemented
6#19135791C211yesmaximal, characteristic, complemented
7#19135606C211yesmaximal, characteristic, complemented
8#19135605C211yesmaximal, characteristic, complemented
9#19135562C211yesmaximal, characteristic, complemented
10#19135391C211yesmaximal, characteristic
11#19134907C211yesmaximal, characteristic, complemented
12#19134901C211yesmaximal, characteristic, complemented
13#19134786C211yesmaximal, characteristic, complemented
14#19134599C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17#14583588—24no—
18#14583588—24no—
19C2×#13063318—21no—
20C2×#13063317—21no—
21C2×#13063316C2211yescharacteristic
22C2×#13063307—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063304C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063282—21no—
31C2×C4⋊C4×D43C2211yescharacteristic
32#14583205—24no—
33#14583005—24no—
34C2×#13063256C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582823—21no—
47#14582822—21no—
48#14582799—21no—
49#14582796—21no—
50#14582768C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43D411yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×Dic172—22no—
69C2×Dic172—22no—
70C2×Dic172—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063318—28no—
74#13063317—28no—
75#13063316—22no—
76#13063316D414yes—
77#13063307—28no—
78#13063305—22no—
79#13063305—22no—
80#13063305—22no—
81#13063305—41no—
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304—41no—
86#13063290—22no—
87#13063290—22no—
88#13063290—22no—
89#13063290D414yes—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92#13063282—28no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
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⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4D411yescharacteristic
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119#13063256—22no—
120Dic43⋊C8—22no—
121#13063250—22no—
122#13063250—41no—
123#13063248—22no—
124#13063248—22no—
125#13063248—22no—
126#13063248—41no—
127C22⋊(C43⋊C8)—41no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8—41no—
130#13063235—22no—
131C43⋊#95—21no—
132C23×C4×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135#117×C43—22no—
136#117×C43—22no—
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C42×C43—21no—
144#107×C43—22no—
145#106×C43—22no—
146C22⋊C8×C43—22no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
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×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—41no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×C4×D43—24no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86C2×D412yes—
192C2×Dic86#4112yes—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43#4112yes—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C2×D412yes—
206C4⋊C4×C43C2×D412yes—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—81no—
209C42×C43—24no—
210C22⋊Dic43—24no—
211C22⋊Dic43—22no—
212C22⋊Dic43—42no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—81no—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—24no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43C2×D412yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228Dic43⋊C4—22no—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231Dic43⋊C4—42no—
232Dic43⋊C4—81no—
233C4×Dic43—24no—
234C4×Dic43—42no—
235C4×Dic43C2×D412yes—
236C4×Dic43C2×D412yes—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243Dic172—28no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43C22×D411yescharacteristic
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43#13712yes—
259C2×C4×C43—22no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C22⋊D43—44no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
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—41no—
304C2×Dic43#12012yes—
305C2×Dic43#12012yes—
306C4×D43—48no—
307C4×D43—41no—
308C4×D43—41no—
309C4×D43—41no—
310C4×D43—41no—
311Dic86—22no—
312Dic86—22no—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317Dic86—41no—
318Dic86—41no—
319C8×C43—22no—
320C8×C43—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#24139—431nomaximal, Sylow
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43C2×#12011yescharacteristic
332C22×C43#54611yescharacteristic
333C22×C43#54711yescharacteristic
334C22×C43C2×#13711yescharacteristic
335C22×C43#57511yescharacteristic
336C22×C43#57711yescharacteristic
337C22×C43#57811yescharacteristic
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C4×C43—41no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43—81no—
349C4×C43—81no—
350C4×C43#52511yescharacteristic
351C4×C43#53711yescharacteristic
352C4×C43#54811yescharacteristic
353C4×C43#55011yescharacteristic
354Dic43—22no—
355Dic43—22no—
356Dic43—42no—
357Dic43—42no—
358Dic43—41no—
359Dic43—42no—
360Dic43—81no—
361C2×#552—431no—
362C2×#479—431no—
363C2×#441—431no—
364#2538—431no—
365#2036—431no—
366#2035—431no—
367#2001—431no—
368#2001—431no—
369#1992—431no—
370#1955—431no—
371#1873—431no—
372#1872—431no—
373#1854D4311yescharacteristic, complemented
374#1853—431no—
375#1803—431no—
376C2×C43—81no—
377C2×C43#240711yescharacteristic
378C2×C43#300711yescharacteristic
379C2×C43#301311yescharacteristic
380C2×C43#331211yescharacteristic
381C2×C43#331711yescharacteristic
382C2×C43#334411yescharacteristic
383C2×C43#334911yescharacteristic
384D43—42no—
385C22×Q16—431no—
386#552—864no—
387#552—864no—
388C2×#126—861no—
389C2×#125—431no—
390C2×#125—861no—
391C2×#123—861no—
392C2×C22⋊Q8—431no—
393C2×C22⋊Q8—431no—
394C2×C22⋊Q8—431no—
395C2×C22⋊Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×Q8—431no—
398C2×C4×D4—431no—
399C2×#117—861no—
400C2×#117C2×D4311yescharacteristic
401C22×C4⋊C4—431no—
402#479—864no—
403#441—864no—
404C2×#107C2×D4311yescharacteristic
405C2×#106—431no—
406C2×#106C2×D4311yescharacteristic
407C2×C4⋊C8—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417C2×C22⋊C8C2×D4311yescharacteristic
418C2×#97—431no—
419#396—861no—
420#396—861no—
421#390—861no—
422#389—861no—
423#384—431no—
424#380—431no—
425#380C2×D4311yescharacteristic
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340C2×D4311yescharacteristic
431#340C2×D4311yescharacteristic
432C43#2413911yescharacteristic, complemented, Sylow
433C22×Q8—431no—
434C22×Q8—431no—
435C22×D4—431no—
436C23×C4—431no—
437C23×C4—861no—
438C23×C4C22×D4311yescharacteristic
439C2×Q16—862no—
440C2×Q16—862no—
441C2×Q16—862no—
442C22×C8—431no—
443C22×C8—431no—
444C22×C8C22×D4311yescharacteristic
445C22×C8C22×D4311yescharacteristic
446#126—868no—
447#125—434no—
448#125—868no—
449#125—862no—
450#123—868no—
451C22⋊Q8—862no—
452C22⋊Q8—862no—
453C22⋊Q8—862no—
454C22⋊Q8—862no—
455C22⋊Q8—862no—
456C22⋊Q8—862no—
457C22⋊Q8—1721no—
458C22⋊Q8—1721no—
459C4×Q8—434no—
460C4×Q8—862no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×D4—862no—
464C4×D4—862no—
465#117—22no—
466#117—22no—
467#117—868no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—862no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—862no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C42—21no—
498C2×C42—431no—
499C2×C42—861no—
500C2×C42—861no—
501#107—22no—
502#106—22no—
503#106—862no—
504C4⋊C8—862no—
505#103—862no—
506#103—862no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#103—1721no—
511C22⋊C8—22no—
512C22⋊C8—862no—
513C22⋊C8—1721no—
514C22⋊C8—1721no—
515#97—862no—
516#95—21no—
517#95—861no—
518C24—431no—
519C24D4×D4311yescharacteristic
520C2×Q8—432no—
521C2×Q8—432no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×D4—862no—
533C2×D4—862no—
534C2×D4—1721no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—864no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563Q16—868no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8#1062189812yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—432no—
583C4⋊C4—862no—
584C4⋊C4—864no—
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—3441no—
594C4⋊C4—1722no—
595C4⋊C4—1722no—
596C4⋊C4—1722no—
597C4⋊C4—1722no—
598C4⋊C4D4×D4312yes—
599C4⋊C4D4×D4312yes—
600C22⋊C4—24no—
601C22⋊C4—81no—
602C22⋊C4—862no—
603C22⋊C4—864no—
604C22⋊C4—862no—
605C22⋊C4—864no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—24no—
610C42—432no—
611C42—432no—
612C42—864no—
613C42—1722no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—432no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23C2×D4×D4311yescharacteristic
629Q8—862no—
630Q8—862no—
631Q8—862no—
632Q8—862no—
633Q8—1721no—
634Q8—1721no—
635Q8—1721no—
636Q8—1721no—
637D4—1724no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—861no—
666C2×C4—862no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—1728no—
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×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C2×D4×D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4C2×#1062189811yescharacteristic
687C2×C4#1306337111yescharacteristic
688C2×C4#1306337311yescharacteristic
689C8—22no—
690C8—41no—
691C8—1721no—
692C8—1721no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—862no—
701C22—862no—
702C22—862no—
703C22—1721no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22#120×D4311yescharacteristic
708C22#1458354111yescharacteristic
709C22#1458355011yescharacteristic
710C22#137×D4311yescharacteristic
711C22#1458369611yescharacteristic
712C22#1458370911yescharacteristic
713C22#1458371311yescharacteristic
714C4—41no—
715C4—42no—
716C4—42no—
717C4—81no—
718C4—81no—
719C4—862no—
720C4—862no—
721C4—3441no—
722C4—1721no—
723C4—1722no—
724C4—1722no—
725C4—1722no—
726C4#1458340811yescharacteristic
727C4#1458347911yescharacteristic
728C4#1458355911yescharacteristic
729C4#1458357011yescharacteristic
730C2—81no—
731C2—1722no—
732C2#1913793911yescharacteristic
733C2#1914385211yescharacteristic
734C2#1914390811yescharacteristic
735C2#1914664911yescharacteristic
736C2#1914671911yescharacteristic
737C2#1914705111yescharacteristic
738C2#1914712111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1854D43
hypocenterC43#24139
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#14583205C2semidirect
3. C2×#14583005C2semidirect
5. #19135800C2semidirect
6. #19135791C2semidirect
7. #19135606C2semidirect
8. #19135605C2semidirect
9. #19135562C2semidirect
11. #19134907C2semidirect
12. #19134901C2semidirect
13. #19134786C2semidirect
14. #19134599C2semidirect
15. C43×#1854C2semidirect
373. #1854D43semidirect
432. C43#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145832052
C2×#145830052
#191395192
#191358002
#191357912
#191356062
#191356052
#191355622
#191353912
#191349072
#191349012
#191347862
#191345992
C43×#18542
#2413943