Finite Group Databasebeta

← #25107938

Subgroups — #25107938

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2#19137288C211yesmaximal, characteristic, complemented
3#19135470C211yesmaximal, characteristic, complemented
4#19135460C211yesmaximal, characteristic, complemented
5#19135295C211yesmaximal, characteristic, complemented
6#19135281C211yesmaximal, characteristic, complemented
7#19135219C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134917C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2309C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic, complemented
20#14583033C418yescomplemented
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic, complemented
30C2×#13063245C2211yescharacteristic, complemented
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063236C2211yescharacteristic, complemented
34C2×C4×C43⋊C8C2211yescharacteristic, complemented
35#14582801C2211yescharacteristic, complemented
36#14582799—21no—
37#14582797C2211yescharacteristic, complemented
38#14582789—21no—
39#14582775—21no—
40#14582770—21no—
41#14582759C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic, complemented
43#14582661C2211yescharacteristic, complemented
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582654C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49C23×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#390—21no—
53C43×#390—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#379—21no—
59C43×#379—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621882—41no—
64C2×#10621882—41no—
65C2×#10621882—41no—
66C2×#10621882—41no—
67C2×#10621882C2×C414yes—
68C2×#10621882C2×C414yes—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063299—22no—
74#13063299C2×C414yes—
75C4×D172—41no—
76C4×D172—41no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87#13063258—41no—
88#13063256—41no—
89#13063246—41no—
90#13063246—41no—
91#13063246—41no—
92#13063246—41no—
93#13063246C2×C414yescomplemented
94#13063246C2×C414yescomplemented
95#13063245—41no—
96#13063245—41no—
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)C2×C414yescomplemented
99#13063236—41no—
100C4×C43⋊C8—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C25×C43—21no—
105C22×D4×C43—21no—
106C22×D4×C43—22no—
107C22×D4×C43—41no—
108C22×D4×C43—41no—
109C22×D4×C43—41no—
110C22×D4×C43—41no—
111C22×D4×C43C2×C414yescomplemented
112C22×D4×C43C2311yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115#117×C43—41no—
116#117×C43—41no—
117#117×C43—41no—
118#117×C43—41no—
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—24no—
140C24×C43—42no—
141C24×C43—42no—
142C24×C43—81no—
143C24×C43—81no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43C2×D411yescharacteristic
147C23×D43—21no—
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
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—21no—
158C2×D4×C43—21no—
159C2×D4×C43—44no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—44no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43C22×C412yes—
166C2×D4×C43C22×C412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43#4112yes—
180C22×C4×C43C2411yescharacteristic
181C2×C22⋊D43—24no—
182C2×C22⋊D43—81no—
183C2×C22⋊D43—81no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C22×C412yes—
193C2×C4×D43—42no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—81no—
206C22⋊C4×C43—81no—
207C22⋊C4×C43—81no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43—81no—
210C22⋊C4×C43—81no—
211C22⋊C4×C43—81no—
212C22⋊C4×C43—81no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—42no—
218C22⋊Dic43—81no—
219#10621882—44no—
220#10621882—44no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224(C2×D43)⋊C4—81no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C22×C412yes—
231Dic43⋊C4—81no—
232C4×Dic43—81no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C22×C412yes—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—48no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43—84no—
271C23×C43—84no—
272C23×C43C4×D412yes—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—48no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43C4×D412yes—
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C22⋊D43—84no—
322C2×Dic43—22no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331D172—22no—
332D172—22no—
333D172—41no—
334D172—41no—
335C4×D43—84no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340#22056—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—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—816no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43C2×C4×D411yescharacteristic
364C22×C43#53411yescharacteristic
365C22×C43#53511yescharacteristic
366C22×C43#57611yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57611yescharacteristic
369C22×C43#57711yescharacteristic
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C4×C43—22no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43#51811yescharacteristic
385C4×C43#51811yescharacteristic
386C4×C43#53811yescharacteristic
387C4×C43#53811yescharacteristic
388Dic43—42no—
389Dic43—81no—
390Dic43—81no—
391C2×#447—431no—
392#2324—431no—
393#2309D4311yescharacteristic, complemented
394#1972—431no—
395#1970—431no—
396#1936—431no—
397#1934—431no—
398#1926—431no—
399#1925—431no—
400#1879—431no—
401#1879—431no—
402#1875—431no—
403#1854—431no—
404#1786—431no—
405#1750—431no—
406C2×C43—42no—
407C2×C43—82no—
408C2×C43—82no—
409C2×C43#232111yescharacteristic
410C2×C43#294611yescharacteristic
411C2×C43#294811yescharacteristic
412C2×C43#319811yescharacteristic
413C2×C43#319911yescharacteristic
414C2×C43#322011yescharacteristic
415C2×C43#322411yescharacteristic
416D43—82no—
417C23×D4C2×D4311yescharacteristic
418C22×D8—431no—
419C22×D8—431no—
420C2×#121—431no—
421C2×C4×D4—431no—
422C2×#117C2×D4311yescharacteristic
423C2×#117C2×D4311yescharacteristic
424#447—438no—
425C2×#107—431no—
426C2×#106—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×#97—431no—
438C2×C4×C8—431no—
439#390—21no—
440#390—21no—
441#390—431no—
442#390—861no—
443#390C2×D4311yescharacteristic
444#390C2×D4311yescharacteristic
445#390C2×D4311yescharacteristic
446#390C2×D4311yescharacteristic
447#389—431no—
448#388—861no—
449#386—861no—
450#385—861no—
451#380—431no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340—431no—
459#336—431no—
460#336—431no—
461C43#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—431no—
470C22×D4—861no—
471C22×D4C4×D4314yescomplemented
472C22×D4C22×D4311yescharacteristic
473C22×D4C22×D4311yescharacteristic
474C23×C4—861no—
475C23×C4C22×D4311yescharacteristic
476C2×D8—434no—
477C2×D8—434no—
478C2×D8—1721no—
479C2×D8—1721no—
480C2×D8—1721no—
481C2×D8—1721no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—431no—
486#121—434no—
487#121—862no—
488C4×D4—1721no—
489C4×D4—1721no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4C22⋊D4311yescharacteristic
499C2×C4⋊C4C22⋊D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4C22⋊D4311yescharacteristic
517C2×C22⋊C4C22⋊D4311yescharacteristic
518C2×C42—21no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521C2×C42C22×D4311yescharacteristic
522#107—1721no—
523#106—1721no—
524#102—434no—
525#102—434no—
526#102—1721no—
527#102—1721no—
528#102—1721no—
529#102—1721no—
530#102—1721no—
531#102—1721no—
532C22⋊C8—434no—
533C22⋊C8—862no—
534#97—1721no—
535C4×C8—1721no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—861no—
549C24C2×C22⋊D4311yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—3441no—
575C2×D4—3441no—
576C2×D4C2×C4×D4312yes—
577C2×D4C2×C4×D4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—1722no—
590C22×C4C2×C4×D4312yes—
591C22×C4#1062189812yes—
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598D8—1724no—
599D8—1724no—
600C2×C8—432no—
601C2×C8—432no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—432no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—3441no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—864no—
637C22⋊C4—3441no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—1722no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—3441no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—862no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23C4×C22⋊D4312yes—
682C23C22×C22⋊D4311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—862no—
693D4—862no—
694D4—3444no—
695D4—1721no—
696D4—1721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—862no—
722C2×C4—3444no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4C4×C22⋊D4312yes—
732C2×C4C22×C4×D4311yescharacteristic
733C2×C4C2×#1062189811yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337011yescharacteristic
737C2×C4#1306337011yescharacteristic
738C8—862no—
739C8—862no—
740C8—1721no—
741C8—1721no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—3441no—
765C22—3441no—
766C22—3441no—
767C22—3441no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22C2×C4×C22⋊D4311yescharacteristic
772C22#1458345811yescharacteristic
773C22#1458346611yescharacteristic
774C22#1458370211yescharacteristic
775C22#1458370211yescharacteristic
776C22#1458370211yescharacteristic
777C22#1458371011yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—3441no—
786C4—3441no—
787C4—1722no—
788C4#1458337211yescharacteristic
789C4#1458337211yescharacteristic
790C4#1458348711yescharacteristic
791C4#1458348711yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—3442no—
796C2#1913725311yescharacteristic
797C2#1914342711yescharacteristic
798C2#1914344511yescharacteristic
799C2#1914544711yescharacteristic
800C2#1914545611yescharacteristic
801C2#1914564511yescharacteristic
802C2#1914568911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2309C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenter#2309D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #19137288C2semidirect
3. #19135470C2semidirect
4. #19135460C2semidirect
5. #19135295C2semidirect
6. #19135281C2semidirect
7. #19135219C2semidirect
8. #19135212C2semidirect
9. #19134946C2semidirect
10. #19134946C2semidirect
11. #19134917C2semidirect
12. #19134794C2semidirect
13. #19134526C2semidirect
14. #19134361C2semidirect
15. C43×#2309C2semidirect
19. C2×C4×D172C22semidirect
20. #14583033C4semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
29. C2×#13063245C22semidirect
30. C2×#13063245C22semidirect
33. C2×#13063236C22semidirect
34. C2×C4×C43⋊C8C22semidirect
35. #14582801C22semidirect
37. #14582797C22semidirect
42. C4×C4⋊Dic43C22semidirect
43. #14582661C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582654C22semidirect
48. #14582654C22semidirect
93. #13063246C2×C4semidirect
94. #13063246C2×C4semidirect
98. C22⋊(C43⋊C8)C2×C4semidirect
111. C22×D4×C43C2×C4semidirect
393. #2309D43semidirect
461. C43#22056semidirect
471. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
#191372882
#191354702
#191354602
#191352952
#191352812
#191352192
#191352122
#191349462
#191349172
#191347942
#191345262
#191343612
C43×#23092
#2205643