Finite Group Databasebeta

← #25149686

Subgroups — #25149686

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×#14583211C211yesmaximal, characteristic, complemented
3C2×#14583144C211yesmaximal, characteristic, complemented
4#19138009C211yesmaximal, characteristic
5#19135922C211yesmaximal, characteristic, complemented
6#19135799C211yesmaximal, characteristic, complemented
7#19135729C211yesmaximal, characteristic, complemented
8#19135598C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134889C211yesmaximal, characteristic, complemented
12#19134850C211yesmaximal, characteristic, complemented
13#19134783C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583604—24no—
19#14583604—24no—
20C2×#13063324C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063304—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063303—21no—
26C2×#13063296C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14583211—24no—
33#14583144—24no—
34C2×#13063259C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063258C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43#14582815—21no—
44#14582807—21no—
45#14582802—21no—
46#14582802C2211yescharacteristic
47#14582798C2211yescharacteristic
48#14582787—21no—
49#14582759C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43D411yescharacteristic
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—41no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063324—22no—
78#13063324—22no—
79#13063315—28no—
80#13063305—22no—
81#13063305D414yescomplemented
82#13063304—28no—
83#13063304—22no—
84#13063304—22no—
85#13063303—28no—
86#13063296—22no—
87#13063296—22no—
88#13063290—22no—
89#13063290—22no—
90C4×C22⋊D43—28no—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93#13063283—22no—
94#13063283—41no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
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×D43D414yescomplemented
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43D411yescharacteristic
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#13063259—22no—
120#13063258—22no—
121#13063258—22no—
122#13063250—22no—
123#13063250—41no—
124#13063248—22no—
125#13063246—22no—
126C22⋊(C43⋊C8)—22no—
127(C2×D43)⋊C8—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C22×D4×C43—21no—
131C22×D4×C43C2311yescharacteristic
132C23×C4×C43—21no—
133C23×C4×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#121×C43—22no—
137#121×C43—41no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145#102×C43—22no—
146#102×C43—22no—
147C22⋊C8×C43—41no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C22×C4×C43—24no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
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—81no—
171C22×C4×C43—81no—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—81no—
179C2×C22⋊D43—81no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—24no—
192C2×C4×D43—81no—
193C2×C4×D43—81no—
194C2×C4×D43C2×D412yes—
195C2×C4×D43C2×D412yes—
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—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C4⋊C4×C43—24no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43C2×D412yes—
216C4⋊C4×C43C2×D412yes—
217C4⋊C4×C43#4112yes—
218C22⋊C4×C43—42no—
219C22⋊Dic43—24no—
220C22⋊Dic43—22no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225#10621883—44no—
226(C2×D43)⋊C4—24no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—42no—
229C4⋊Dic43—21no—
230C4⋊Dic43—24no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—81no—
236C4⋊Dic43C2×D412yes—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—22no—
242C4×Dic43—24no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—42no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8#4112yes—
252#10621872—44no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43#13712yes—
267C23×C43C22×D411yescharacteristic
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43#12012yes—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—84no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
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—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—84no—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C432−1+411yescharacteristic
303C22⋊D43—28no—
304C22⋊D43—84no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43#12012yes—
325C2×Dic43#13712yes—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—84no—
331Dic86—22no—
332Dic86—22no—
333Dic86—41no—
334Dic86—41no—
335Dic86—84no—
336C8×C43—41no—
337C8×C43—41no—
338C43⋊C8—22no—
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×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43C2×#12011yescharacteristic
356C22×C43#54611yescharacteristic
357C22×C43#54711yescharacteristic
358C22×C43C2×#13711yescharacteristic
359C22×C43C2×#13711yescharacteristic
360C22×C43#57611yescharacteristic
361C22×C43#57611yescharacteristic
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C4×C43—41no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43#53211yescharacteristic
374C4×C43#53711yescharacteristic
375C4×C43#54611yescharacteristic
376C4×C43#54711yescharacteristic
377Dic43—22no—
378Dic43—22no—
379Dic43—42no—
380Dic43—41no—
381Dic43—42no—
382Dic43—81no—
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#1874D4311yescharacteristic, complemented
394#1873—431no—
395#1870—431no—
396#1863—431no—
397#1852—431no—
398#1736—431no—
399C2×C43—42no—
400C2×C43—161no—
401C2×C43#243011yescharacteristic
402C2×C43#300411yescharacteristic
403C2×C43#300811yescharacteristic
404C2×C43#331411yescharacteristic
405C2×C43#333311yescharacteristic
406C2×C43#334611yescharacteristic
407C2×C43#335711yescharacteristic
408D43—42no—
409C22×SD16—431no—
410C22×M16—431no—
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×#121C2×D4311yescharacteristic
421C2×C4×Q8—431no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C2×#117—431no—
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×#102C2×D4311yescharacteristic
437C2×#102C2×D4311yescharacteristic
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8C2×D4311yescharacteristic
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#340—431no—
451#340—431no—
452#340C2×D4311yescharacteristic
453#340C2×D4311yescharacteristic
454#336—431no—
455#336—431no—
456C43#2555911yescharacteristic, complemented, Sylow
457C22×Q8—431no—
458C22×Q8—861no—
459C22×D4—21no—
460C22×D4—431no—
461C22×D4—861no—
462C22×D4C22×D4311yescharacteristic
463C23×C4—21no—
464C23×C4—431no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—1721no—
470C2×M16—862no—
471C2×M16—862no—
472C2×M16—1721no—
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—862no—
484C22⋊Q8—862no—
485C22⋊Q8—868no—
486#121—22no—
487#121—41no—
488#121—862no—
489#121—862no—
490C4×Q8—862no—
491C4×Q8—862no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—868no—
495#117—862no—
496#117—1721no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
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—431no—
526C2×C42—861no—
527C2×C42—861no—
528#107—862no—
529#107—862no—
530#107—862no—
531#103—862no—
532#103—862no—
533#103—1721no—
534#102—22no—
535#102—22no—
536#102—862no—
537C22⋊C8—41no—
538C22⋊C8—862no—
539C22⋊C8—862no—
540#95—861no—
541#95—861no—
542C24—21no—
543C24—431no—
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—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—81no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—862no—
566C2×D4—3441no—
567C2×D4—3441no—
568C2×D4—1722no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—431no—
586C22×C4—864no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—3441no—
596C22×C4—3441no—
597C22×C4D4×D4311yescharacteristic
598C22×C4C23×D4311yescharacteristic
599SD16—1724no—
600M16—1724no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—432no—
618C4⋊C4—864no—
619C4⋊C4—862no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—3441no—
630C4⋊C4#1062189812yes—
631C4⋊C4D4×D4312yes—
632C4⋊C4D4×D4312yes—
633C22⋊C4—42no—
634C22⋊C4—862no—
635C22⋊C4—864no—
636C22⋊C4—862no—
637C22⋊C4—864no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—864no—
644C42—861no—
645C42—861no—
646C42—1722no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—432no—
661C23—861no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23#1306335412yes—
668C23C2×D4×D4311yescharacteristic
669Q8—862no—
670Q8—862no—
671Q8—3444no—
672Q8—1721no—
673Q8—1721no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—868no—
680D4—3444no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—861no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—3444no—
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—1721no—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C2×D4×D4311yescharacteristic
726C2×C4#41×D4311yescharacteristic
727C2×C4C2×#1062189811yescharacteristic
728C2×C4#1306337011yescharacteristic
729C2×C4#1306337211yescharacteristic
730C8—41no—
731C8—41no—
732C8—862no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—862no—
749C22—862no—
750C22—862no—
751C22—1721no—
752C22—1721no—
753C22—1721no—
754C22—1721no—
755C22#120×D4311yescharacteristic
756C22#1458353911yescharacteristic
757C22#1458354711yescharacteristic
758C22#137×D4311yescharacteristic
759C22C2×#1306335411yescharacteristic
760C22#1458370011yescharacteristic
761C22#1458370311yescharacteristic
762C4—41no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—862no—
767C4—862no—
768C4—3441no—
769C4—3441no—
770C4—1722no—
771C4—1721no—
772C4—1722no—
773C4#1458344611yescharacteristic
774C4#1458347811yescharacteristic
775C4#1458354611yescharacteristic
776C4#1458355411yescharacteristic
777C2—42no—
778C2—161no—
779C2—1722no—
780C2#1913820211yescharacteristic
781C2#1914382611yescharacteristic
782C2#1914385811yescharacteristic
783C2#1914667211yescharacteristic
784C2#1914692911yescharacteristic
785C2#1914707811yescharacteristic
786C2#1914721411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radical#19138009C2
hypercenter#1874D43
hypocenterC43#25559
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#14583604C2semidirect
2. C2×#14583211C2semidirect
3. C2×#14583144C2semidirect
5. #19135922C2semidirect
6. #19135799C2semidirect
7. #19135729C2semidirect
8. #19135598C2semidirect
9. #19134947C2semidirect
10. #19134906C2semidirect
11. #19134889C2semidirect
12. #19134850C2semidirect
13. #19134783C2semidirect
14. #19134313C2semidirect
15. C43×#1874C2semidirect
81. #13063305D4semidirect
106. C4⋊C4×D43D4semidirect
393. #1874D43semidirect
456. C43#25559semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145832112
C2×#145831442
#191380092
#191359222
#191357992
#191357292
#191355982
#191349472
#191349062
#191348892
#191348502
#191347832
#191343132
C43×#18742
#2555943