Finite Group Databasebeta

← #25116859

Subgroups — #25116859

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583052C211yesmaximal, characteristic
2C2×#14583001C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic
4#19137598C211yesmaximal, characteristic, complemented
5C22⋊C4×D172C211yesmaximal, characteristic
6#19135476C211yesmaximal, characteristic, complemented
7#19135292C211yesmaximal, characteristic, complemented
8#19135216C211yesmaximal, characteristic, complemented
9#19135018C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134845C211yesmaximal, characteristic, complemented
13#19134785C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C43×#1752C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic, complemented
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C2×C22⋊C4×D43—21no—
25#14583052C418yescomplemented
26#14583001—24no—
27C2×#13063259C2211yescharacteristic, complemented
28C2×#13063259C2211yescharacteristic, complemented
29C2×#13063250C2211yescharacteristic, complemented
30C2×#13063250C2211yescharacteristic, complemented
31C2×#13063247—24no—
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38#14582805C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582797C2211yescharacteristic, complemented
42#14582796—21no—
43#14582786—21no—
44#14582777—21no—
45#14582777—21no—
46#14582771—21no—
47#14582759C2211yescharacteristic
48#14582754—21no—
49C4×C4⋊Dic43C2211yescharacteristic, complemented
50C22⋊C4×Dic43—21no—
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55C23×C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic, complemented
58C2×#97×C43C2211yescharacteristic, complemented
59C4×C22⋊C4×C43C2211yescharacteristic
60C43×#336C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—21no—
67C22×D172—22no—
68C22×D172—41no—
69C22×D172—41no—
70C22×D172C2×C414yes—
71C22×D172C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C2×#10621873—22no—
77C2×#10621873—22no—
78C2×#10621873—41no—
79C2×#10621873—41no—
80C2×#10621873C2×C414yescomplemented
81C2×#10621873C2×C414yescomplemented
82#13063304—22no—
83#13063304C2×C414yescomplemented
84C4×Dic86—22no—
85C4×Dic86—41no—
86C4×D172—22no—
87C4×D172—22no—
88C4×D172—41no—
89C4×D172—41no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C22⋊C4×D43—44no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112#13063259—22no—
113#13063259—41no—
114#13063250—22no—
115#13063250—41no—
116#13063247—22no—
117#13063247—22no—
118#13063247—22no—
119#13063247C2×C414yescomplemented
120#13063247C2×C414yescomplemented
121#13063247D414yes—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43—22no—
129C22×C8×C43—22no—
130C22×C8×C43—41no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C22⋊C8×C43C2×C414yescomplemented
140#97×C43—22no—
141#97×C43—41no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C23×D43—21no—
147C23×D43—24no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—81no—
153C23×D43—81no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4112yes—
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—42no—
173C22×Dic43—42no—
174C22×Dic43—81no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—24no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—28no—
185C2×D172—42no—
186C2×D172—42no—
187C2×D172—44no—
188C2×D172—44no—
189C2×D172—44no—
190C2×D172C22×C412yes—
191C2×D172C22×C412yes—
192C2×D172C2×D412yes—
193C2×D172#4112yes—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43—81no—
199C2×C4×D43—81no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86C22×C412yes—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—44no—
216C2×C8×C43C22×C412yes—
217C2×C8×C43C22×C412yes—
218C2×C8×C43C2×D412yes—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—24no—
226C22⋊Dic43—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—81no—
232(C2×D43)⋊C4—81no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—42no—
242C4⋊Dic43C22×C412yes—
243C4⋊Dic43C2×D412yes—
244Dic43⋊C4—24no—
245Dic43⋊C4—42no—
246Dic43⋊C4—81no—
247C4×Dic43—42no—
248C4×Dic43—81no—
249#10621873—28no—
250#10621873—44no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43C4×D412yes—
256C23×C43AGL(1,ℤ/8)12yes—
257C23×C43#13712yes—
258C23×C43C22×D411yescharacteristic
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—48no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—48no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43C4×D412yes—
299C2×C4×C43C23×C411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
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—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—84no—
324D172—22no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—22no—
329D172—48no—
330D172—41no—
331D172—41no—
332D172C4×D414yes—
333C4×D43—84no—
334C4×D43—84no—
335Dic86—22no—
336Dic86—22no—
337Dic86—41no—
338Dic86—41no—
339C8×C43—22no—
340C8×C43—22no—
341C8×C43—22no—
342C8×C43—41no—
343#22854—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43#44014yescomplemented
351C22×C43C2×C4×D411yescharacteristic
352C22×C43D4211yescharacteristic
353C22×C43#54611yescharacteristic
354C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C43C2×#13711yescharacteristic
356C22×C43#57611yescharacteristic
357C22×C43#57711yescharacteristic
358C2×D43—24no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—816no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C4×C43—22no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43C2×C4×D411yescharacteristic
379C4×C43#51811yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#55111yescharacteristic
382Dic43—42no—
383Dic43—42no—
384Dic43—42no—
385Dic43—81no—
386Dic43—81no—
387Dic43—81no—
388C2×#450—431no—
389C2×#440—431no—
390C22×#102—431no—
391#2360—431no—
392D4×C22⋊C4—431no—
393#1973—431no—
394#1936—431no—
395#1925—431no—
396#1892—431no—
397#1880—431no—
398#1877—431no—
399#1862—431no—
400#1852—431no—
401#1762—431no—
402#1752D4311yescharacteristic, complemented
403C2×C43—24no—
404C2×C43#235811yescharacteristic
405C2×C43C2×#44011yescharacteristic
406C2×C43#294611yescharacteristic
407C2×C43#326411yescharacteristic
408C2×C43#326611yescharacteristic
409C2×C43#331011yescharacteristic
410C2×C43#331411yescharacteristic
411D43—44no—
412D43—82no—
413C23×D4—431no—
414C22×SD16—431no—
415C22×SD16—431no—
416C23×C8C2×D4311yescharacteristic
417C2×C22⋊Q8—431no—
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C22×C4⋊C4—431no—
422C22×C22⋊C4—861no—
423#450—438no—
424#440—864no—
425C2×#107—431no—
426C2×#107—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#102—864no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97C2×D4311yescharacteristic, complemented
438C2×#97C2×D4311yescharacteristic, complemented
439#391—431no—
440#390—431no—
441#390—431no—
442#389—431no—
443#389—861no—
444#387—861no—
445#386—861no—
446#386—861no—
447#385—861no—
448#380—431no—
449#379—861no—
450C4×C4⋊C4—431no—
451C4×C22⋊C4—861no—
452C4×C22⋊C4C2×D4311yescharacteristic
453#340—431no—
454#340—431no—
455#340—431no—
456#340—431no—
457#336C2×D4311yescharacteristic, complemented
458#336C2×D4311yescharacteristic, complemented
459C43#2285411yescharacteristic, complemented, Sylow
460C25—861no—
461C22×Q8—431no—
462C22×D4—434no—
463C22×D4—431no—
464C22×D4—431no—
465C22×D4—862no—
466C22×D4—862no—
467C22×D4—861no—
468C22×D4—862no—
469C22×D4—1721no—
470C22×D4—1721no—
471C23×C4—861no—
472C23×C4—861no—
473C23×C4—861no—
474C23×C4C22×D4311yescharacteristic
475C2×SD16—434no—
476C2×SD16—434no—
477C2×SD16—862no—
478C2×SD16—862no—
479C2×SD16—1721no—
480C2×SD16—1721no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C22⋊Q8—434no—
489C22⋊Q8—862no—
490C4×Q8—862no—
491C4×Q8—1721no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—1721no—
495C4×D4—1721no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—1721no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—1724no—
516C2×C22⋊C4D17211yescharacteristic
517C2×C22⋊C4D17211yescharacteristic
518C2×C42—861no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521C2×C42C22×D4311yescharacteristic
522#107—862no—
523#107—1721no—
524#103—862no—
525#103—1721no—
526#102—434no—
527#102—434no—
528#102—434no—
529#102—862no—
530#102—862no—
531#102—862no—
532C22⋊C8C4×D4314yescomplemented
533#97—22no—
534#97—41no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539#95—861no—
540#95D17211yescharacteristic
541#95D17211yescharacteristic
542C24—861no—
543C24—864no—
544C24—861no—
545C24—3441no—
546C24—3441no—
547C24—1722no—
548C24—1722no—
549C24—1722no—
550C24—1722no—
551C24C2×D17211yescharacteristic
552C2×Q8—432no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×D4—432no—
559C2×D4—432no—
560C2×D4—432no—
561C2×D4—432no—
562C2×D4—868no—
563C2×D4—864no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—1724no—
573C2×D4—1724no—
574C2×D4—1724no—
575C2×D4—1722no—
576C2×D4—1722no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—3441no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4C2×C4×D4312yes—
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4C2×D17211yescharacteristic
600C22×C4C2×D17211yescharacteristic
601C22×C4C2×D17211yescharacteristic
602C22×C4#1062189812yes—
603C22×C4C23×D4311yescharacteristic
604SD16—868no—
605SD16—1724no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C2×C4×D4312yes—
617C2×C8C2×C4×D4312yes—
618C2×C8D4×D4312yes—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—3441no—
631C4⋊C4—1722no—
632C4⋊C4—1722no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—864no—
636C22⋊C4—3441no—
637C22⋊C4—3441no—
638C22⋊C4—1722no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—3441no—
648C42—1722no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—3444no—
658C23—3444no—
659C23—3444no—
660C23—3444no—
661C23—3444no—
662C23—1728no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—1728no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23C4×D17212yes—
675C23#1306335312yes—
676C23#1306335812yes—
677C23C22×D17211yescharacteristic
678Q8—862no—
679Q8—862no—
680Q8—1721no—
681Q8—1721no—
682D4—434no—
683D4—862no—
684D4—862no—
685D4—862no—
686D4—862no—
687D4—862no—
688D4—1728no—
689D4—1721no—
690D4—1721no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—3444no—
713C2×C4—3444no—
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×C4C4×D17212yes—
731C2×C4C22×C4×D4311yescharacteristic
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4#41×D4311yescharacteristic
734C2×C4C2×#1062189811yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337111yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—864no—
748C22—34416no—
749C22—3441no—
750C22—3441no—
751C22—3441no—
752C22—3441no—
753C22—1722no—
754C22—1722no—
755C22—1722no—
756C22—1722no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22#1458300114yescomplemented
763C22C2×C4×D17211yescharacteristic
764C22D4×D17211yescharacteristic
765C22#1458354411yescharacteristic
766C22C2×#1306335311yescharacteristic
767C22C2×#1306335811yescharacteristic
768C22#1458370411yescharacteristic
769C22#1458371111yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—3441no—
776C4—3441no—
777C4—3441no—
778C4—1722no—
779C4—1722no—
780C4—1722no—
781C4C4×D4×D4311yescharacteristic
782C4#1458337111yescharacteristic
783C4#1458353911yescharacteristic
784C4#1458357311yescharacteristic
785C2—24no—
786C2—3442no—
787C2—1724no—
788C2#1913757711yescharacteristic
789C2C2×#1458300111yescharacteristic
790C2#1914342911yescharacteristic
791C2#1914608011yescharacteristic
792C2#1914611011yescharacteristic
793C2#1914661811yescharacteristic
794C2#1914667811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1752C2
socleC23×C43C22×D4
prime radicalC23×D172C22
cosocleC22×C4×C43C24
hypercenter#1752D43
hypocenterC43#22854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#14583001C2semidirect
4. #19137598C2semidirect
6. #19135476C2semidirect
7. #19135292C2semidirect
8. #19135216C2semidirect
9. #19135018C2semidirect
10. #19134949C2semidirect
11. #19134928C2semidirect
12. #19134845C2semidirect
13. #19134785C2semidirect
14. #19134421C2semidirect
15. C43×#1752C2semidirect
20. C2×C4×Dic86C22semidirect
25. #14583052C4semidirect
27. C2×#13063259C22semidirect
28. C2×#13063259C22semidirect
29. C2×#13063250C22semidirect
30. C2×#13063250C22semidirect
38. #14582805C22semidirect
41. #14582797C22semidirect
49. C4×C4⋊Dic43C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
57. C2×#97×C43C22semidirect
58. C2×#97×C43C22semidirect
60. C43×#336C22semidirect
61. C43×#336C22semidirect
80. C2×#10621873C2×C4semidirect
81. C2×#10621873C2×C4semidirect
83. #13063304C2×C4semidirect
119. #13063247C2×C4semidirect
120. #13063247C2×C4semidirect
139. C22⋊C8×C43C2×C4semidirect
350. C22×C43#440semidirect
402. #1752D43semidirect
437. C2×#97C2×D43semidirect
438. C2×#97C2×D43semidirect
457. #336C2×D43semidirect
458. #336C2×D43semidirect
459. C43#22854semidirect
532. C22⋊C8C4×D43semidirect
762. C22#14583001semidirect

Maximal subgroups

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

subgroupindex
C2×#145830522
C2×#145830012
C22×#130632472
#191375982
C22⋊C4×D1722
#191354762
#191352922
#191352162
#191350182
#191349492
#191349282
#191348452
#191347852
#191344212
C43×#17522
#2285443