Finite Group Databasebeta

← #25149679

Subgroups — #25149679

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583604C211yesmaximal, characteristic, complemented
2C2×#14583212C211yesmaximal, characteristic, complemented
3C2×#14583145C211yesmaximal, characteristic, complemented
4#19138007C211yesmaximal, characteristic
5#19135922C211yesmaximal, characteristic, complemented
6#19135801C211yesmaximal, characteristic, complemented
7#19135730C211yesmaximal, characteristic, complemented
8#19135601C211yesmaximal, characteristic, complemented
9#19134951C211yesmaximal, characteristic, complemented
10#19134911C211yesmaximal, characteristic, complemented
11#19134907C211yesmaximal, characteristic, complemented
12#19134892C211yesmaximal, characteristic, complemented
13#19134850C211yesmaximal, characteristic, complemented
14#19134784C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17#14583604—24no—
18#14583604—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063305C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063303—21no—
25C2×#13063300C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31#14583212—24no—
32#14583145—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45#14582815—21no—
46#14582808—21no—
47#14582801—21no—
48#14582800C2211yescharacteristic
49#14582798C2211yescharacteristic
50#14582790—21no—
51#14582756C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×D172—21no—
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C22×C22⋊D43D411yescharacteristic
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C2×#10621873—22no—
72C2×#10621873—22no—
73C2×#10621873—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063324—22no—
77#13063324—22no—
78#13063315—28no—
79#13063305—22no—
80#13063305—22no—
81#13063304—28no—
82#13063304—22no—
83#13063304D414yescomplemented
84#13063303—28no—
85#13063300—22no—
86#13063300—41no—
87#13063299—22no—
88#13063299—22no—
89#13063290—22no—
90#13063290—22no—
91C4×C22⋊D43—28no—
92C4×C22⋊D43—22no—
93C4×C22⋊D43—22no—
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⋊C4D411yescharacteristic
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43D411yescharacteristic
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116#13063259—22no—
117#13063258—22no—
118#13063258—22no—
119#13063250—22no—
120#13063248—22no—
121#13063248—41no—
122#13063247—22no—
123#13063245—22no—
124#13063245—22no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—41no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C2×M16×C43—22no—
133C2×M16×C43—22no—
134C2×M16×C43—41no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#117×C43—22no—
138#117×C43—41no—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43D414yescomplemented
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43—21no—
150C23×D43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—24no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—81no—
161C22×C4×C43—81no—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—42no—
185C2×D172—42no—
186C2×D172—81no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—24no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—24no—
202C2×Dic86—81no—
203C2×Dic86—81no—
204C2×Dic86C2×D412yes—
205M16×C43—44no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43#4112yes—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43C2×D412yes—
219C4⋊C4×C43C2×D412yes—
220C4⋊C4×C43#4112yes—
221C22⋊C4×C43—42no—
222C42×C43—42no—
223C22⋊Dic43—24no—
224C22⋊Dic43—22no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—81no—
231(C2×D43)⋊C4—81no—
232C4⋊Dic43—24no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—81no—
237C4⋊Dic43C2×D412yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—22no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252#10621873—44no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43#12012yes—
260C23×C43C22×D411yescharacteristic
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43#13712yes—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
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×C43—41no—
293C2×C4×C43—84no—
294C2×C4×C43#12012yes—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C432−1+411yescharacteristic
301C22⋊D43—28no—
302C22⋊D43—84no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43#13712yes—
321D172—41no—
322D172—41no—
323D172—41no—
324D172—41no—
325D172—84no—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—84no—
331Dic86—22no—
332Dic86—22no—
333Dic86—41no—
334Dic86—41no—
335Dic86—84no—
336C8×C43—22no—
337C8×C43—41no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340#25559—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43C2×#12011yescharacteristic
349C22×C43#54611yescharacteristic
350C22×C43#54711yescharacteristic
351C22×C43C2×#13711yescharacteristic
352C22×C43C2×#13711yescharacteristic
353C22×C43#57611yescharacteristic
354C22×C43#57611yescharacteristic
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—81no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C4×C43—22no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43—81no—
374C4×C43#53211yescharacteristic
375C4×C43#53711yescharacteristic
376C4×C43#54611yescharacteristic
377C4×C43#54711yescharacteristic
378Dic43—22no—
379Dic43—42no—
380Dic43—41no—
381Dic43—41no—
382Dic43—42no—
383Dic43—81no—
384C2×#554—431no—
385C2×#480—431no—
386C2×#468—431no—
387#2414—431no—
388#2057—431no—
389#2036—431no—
390#2023—431no—
391#2000—431no—
392#1880—431no—
393#1874—431no—
394#1873—431no—
395#1870—431no—
396#1863—431no—
397#1852—431no—
398#1736D4311yescharacteristic, complemented
399C2×C43—42no—
400C2×C43#243011yescharacteristic
401C2×C43#300411yescharacteristic
402C2×C43#300811yescharacteristic
403C2×C43#331411yescharacteristic
404C2×C43#333311yescharacteristic
405C2×C43#334611yescharacteristic
406C2×C43#335711yescharacteristic
407D43—42no—
408D43—161no—
409C22×SD16—431no—
410C22×M16C2×D4311yescharacteristic
411#554—864no—
412#554—864no—
413C2×C4⋊Q8—431no—
414C2×#125—861no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8—861no—
419C2×#121—431no—
420C2×#121—431no—
421C2×C4×Q8—431no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C2×#117C2×D4311yescharacteristic
425C22×C4⋊C4—431no—
426C22×C4⋊C4C2×D4311yescharacteristic
427#480—864no—
428#468—864no—
429C2×#107—431no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441#394—861no—
442#392—861no—
443#390—431no—
444#390—861no—
445#389—431no—
446#388—861no—
447#380—431no—
448#340—431no—
449#340—431no—
450#340C2×D4311yescharacteristic
451#340C2×D4311yescharacteristic
452#340C2×D4311yescharacteristic
453#340C2×D4311yescharacteristic
454#336—431no—
455#336—431no—
456C43#2555911yescharacteristic, complemented, Sylow
457C22×Q8—431no—
458C22×Q8—861no—
459C22×D4—431no—
460C22×D4—431no—
461C22×D4—861no—
462C22×D4—861no—
463C23×C4—21no—
464C23×C4—431no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—1721no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—41no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477C4⋊Q8—862no—
478C4⋊Q8—862no—
479#125—868no—
480C22⋊Q8—434no—
481C22⋊Q8—862no—
482C22⋊Q8—868no—
483C22⋊Q8—868no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486#121—862no—
487#121—862no—
488#121—862no—
489#121—1721no—
490C4×Q8—862no—
491C4×Q8—862no—
492C4×D4—868no—
493C4×D4—862no—
494C4×D4—862no—
495#117—22no—
496#117—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—862no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4D17214yescomplemented
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—861no—
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×C42—21no—
526C2×C42—431no—
527C2×C42—861no—
528#107—862no—
529#107—862no—
530#107—862no—
531#103—862no—
532#103—862no—
533#103—1721no—
534#102—862no—
535#102—862no—
536#102—862no—
537C22⋊C8—862no—
538C22⋊C8—862no—
539C22⋊C8—1721no—
540#95—861no—
541#95—861no—
542C24—431no—
543C24—861no—
544C24D4×D4311yescharacteristic
545C2×Q8—432no—
546C2×Q8—864no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—3441no—
553C2×Q8—3441no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—862no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—3441no—
564C2×D4—3441no—
565C2×D4—3441no—
566C2×D4—1722no—
567C2×D4—1722no—
568C2×D4—1722no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—864no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—3441no—
594C22×C4—3441no—
595C22×C4C2×D17212yes—
596C22×C4D4×D4311yescharacteristic
597C22×C4D4×D4312yes—
598C22×C4C23×D4311yescharacteristic
599SD16—1724no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8#1062189812yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—432no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—862no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—3441no—
630C4⋊C4C2×D17212yes—
631C4⋊C4C2×D17212yes—
632C4⋊C4#1062189812yes—
633C22⋊C4—42no—
634C22⋊C4—864no—
635C22⋊C4—862no—
636C22⋊C4—864no—
637C22⋊C4—862no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—42no—
644C42—864no—
645C42—861no—
646C42—861no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—432no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23—1721no—
661C23—1721no—
662C23—1721no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23#1306329512yes—
668C23C2×D4×D4311yescharacteristic
669Q8—862no—
670Q8—862no—
671Q8—3444no—
672Q8—1721no—
673Q8—1721no—
674D4—868no—
675D4—3444no—
676D4—3444no—
677D4—1721no—
678D4—1721no—
679D4—1721no—
680D4—1721no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—84no—
700C2×C4—432no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—862no—
704C2×C4—861no—
705C2×C4—862no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—3444no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
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#1306329512yes—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C22×D17211yescharacteristic
726C2×C4C2×#1062189811yescharacteristic
727C2×C4C2×#1062189811yescharacteristic
728C2×C4#1306337011yescharacteristic
729C2×C4#1306337311yescharacteristic
730C8—22no—
731C8—41no—
732C8—1721no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—862no—
742C22—862no—
743C22—862no—
744C22—3441no—
745C22—3441no—
746C22—3441no—
747C22—3441no—
748C22—3441no—
749C22—3441no—
750C22—3441no—
751C22—1721no—
752C22—1721no—
753C22—1721no—
754C22—1721no—
755C22C2×#1306329511yescharacteristic
756C22#1458353911yescharacteristic
757C22#1458355011yescharacteristic
758C22#137×D4311yescharacteristic
759C22#137×D4311yescharacteristic
760C22#1458370311yescharacteristic
761C22#1458370311yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—81no—
767C4—862no—
768C4—3441no—
769C4—1721no—
770C4—1722no—
771C4—1721no—
772C4—1722no—
773C4#1458344911yescharacteristic
774C4#1458348011yescharacteristic
775C4#1458353911yescharacteristic
776C4#1458355011yescharacteristic
777C2—42no—
778C2—1722no—
779C2—6881no—
780C2#1913820511yescharacteristic
781C2#1914383111yescharacteristic
782C2#1914386411yescharacteristic
783C2#1914667711yescharacteristic
784C2#1914692911yescharacteristic
785C2#1914708111yescharacteristic
786C2#1914721711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radical#19138007C2
hypercenter#1736D43
hypocenterC43#25559
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C2×#14583604C2semidirect
2. C2×#14583212C2semidirect
3. C2×#14583145C2semidirect
5. #19135922C2semidirect
6. #19135801C2semidirect
7. #19135730C2semidirect
8. #19135601C2semidirect
9. #19134951C2semidirect
10. #19134911C2semidirect
11. #19134907C2semidirect
12. #19134892C2semidirect
13. #19134850C2semidirect
14. #19134784C2semidirect
15. C43×#1736C2semidirect
83. #13063304D4semidirect
141. C2×C4⋊C4×C43D4semidirect
398. #1736D43semidirect
456. C43#25559semidirect
510. C2×C4⋊C4D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145832122
C2×#145831452
#191380072
#191359222
#191358012
#191357302
#191356012
#191349512
#191349112
#191349072
#191348922
#191348502
#191347842
C43×#17362
#2555943