Finite Group Databasebeta

← #25102316

Subgroups — #25102316

Order 11008.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19137288C211yesmaximal, characteristic, complemented
5#19134943C211yesmaximal, characteristic, complemented
6#19134943C211yesmaximal, characteristic, complemented
7#19134917C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic, complemented
9#19134842C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic, complemented
11#19134526C211yesmaximal, characteristic, complemented
12#19134420C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C2×C43×#518C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic, complemented
20#14583033C418yescomplemented
21#14583009—24no—
22C4×#10621882—24no—
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063256C2211yescharacteristic, complemented
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic, complemented
32C2×#13063245C2211yescharacteristic, complemented
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063236C2211yescharacteristic, complemented
36C2×C4×C43⋊C8C2211yescharacteristic, complemented
37#14582801C2211yescharacteristic, complemented
38#14582799—21no—
39#14582797C2211yescharacteristic, complemented
40#14582789—21no—
41#14582775—21no—
42#14582770—21no—
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51C23×D4×C43C2211yescharacteristic
52C43×#518—24no—
53C43×#518—24no—
54C2×C4×D4×C43—21no—
55C2×C4×D4×C43—21no—
56C2×C4×D4×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×#117×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C22×C22⋊C4×C43—21no—
63C22×C22⋊C4×C43—21no—
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882C2×C414yescomplemented
72C2×#10621882C2×C414yescomplemented
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063299—22no—
78#13063299C2×C414yescomplemented
79C4×D172—22no—
80C4×D172—22no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91#13063258—22no—
92#13063256—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246C2×C414yescomplemented
98#13063246C2×C414yescomplemented
99#13063245—22no—
100#13063245—22no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)C2×C414yescomplemented
103#13063236—22no—
104C4×C43⋊C8—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C25×C43—21no—
109C22×D4×C43—22no—
110C22×D4×C43—22no—
111C22×D4×C43—22no—
112C22×D4×C43—22no—
113C22×D4×C43—21no—
114C22×D4×C43—22no—
115C22×D4×C43C2×C414yescomplemented
116C22×D4×C43C2311yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C23×C4×C43—21no—
120C23×C4×C43—21no—
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C4×D4×C43—28no—
124C4×D4×C43—28no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43D414yescomplemented
132C4×D4×C43D414yescomplemented
133#117×C43—22no—
134#117×C43—22no—
135#117×C43—22no—
136#117×C43—22no—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C4⋊C4×C43D411yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—28no—
142C2×C22⋊C4×C43—28no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152C2×C42×C43C2311yescharacteristic
153C24×C43—24no—
154C24×C43—24no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—24no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43C2×D411yescharacteristic
163C23×D43—21no—
164C2×D4×C43—24no—
165C2×D4×C43—28no—
166C2×D4×C43—28no—
167C2×D4×C43—24no—
168C2×D4×C43—28no—
169C2×D4×C43—28no—
170C2×D4×C43—24no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C412yes—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C2×D412yes—
180C2×D4×C43C2×D412yes—
181C2×D4×C43#4112yes—
182C2×D4×C43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—24no—
188C22×C4×C43—24no—
189C22×C4×C43—24no—
190C22×C4×C43—24no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—81no—
194C22×C4×C43—81no—
195C22×C4×C43—81no—
196C22×C4×C43—81no—
197C22×C4×C43—81no—
198C22×C4×C43—81no—
199C22×C4×C43—81no—
200C22×C4×C43—81no—
201C22×C4×C43C22×C412yes—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43#4112yes—
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43—81no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22×C412yes—
221C2×C4×D43—42no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C2×D412yes—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—24no—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—24no—
237C42×C43—24no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43C2×D412yes—
241C42×C43C2×D412yes—
242C22⋊Dic43—81no—
243#10621882—28no—
244#10621882—28no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—42no—
247(C2×D43)⋊C4—81no—
248(C2×D43)⋊C4—81no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43C22×C412yes—
255Dic43⋊C4—81no—
256C4×Dic43—81no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C412yes—
268C2×C43⋊C8C22×C412yes—
269C23×C43—216no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—21no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—84no—
291C23×C43—84no—
292C23×C43—84no—
293C23×C43—84no—
294C23×C43—84no—
295C23×C43—84no—
296C23×C43C4×D412yes—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305D4×C43—216no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43C4×D414yes—
313D4×C43C4×D414yes—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—84no—
337C2×C4×C43—84no—
338C2×C4×C43—84no—
339C2×C4×C43—84no—
340C2×C4×C43C4×D412yes—
341C2×C4×C43#12012yes—
342C2×C4×C43#12012yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C22⋊D43—84no—
350C2×Dic43—22no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359D172—22no—
360D172—22no—
361D172—41no—
362D172—41no—
363C4×D43—84no—
364C43⋊C8—22no—
365C43⋊C8—22no—
366C43⋊C8—41no—
367C43⋊C8—41no—
368#21458—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—24no—
373C22×C43—24no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—816no—
391C22×C43C2×C4×D411yescharacteristic
392C22×C43C2×#12011yescharacteristic
393C22×C43#52511yescharacteristic
394C22×C43#57611yescharacteristic
395C22×C43#57611yescharacteristic
396C22×C43#57611yescharacteristic
397C22×C43#57711yescharacteristic
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C2×D43—81no—
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—22no—
408C4×C43—41no—
409C4×C43—42no—
410C4×C43—41no—
411C4×C43—42no—
412C4×C43C2×C4×D411yescharacteristic
413C4×C43C2×C4×D411yescharacteristic
414C4×C43#52511yescharacteristic
415C4×C43#52511yescharacteristic
416Dic43—42no—
417Dic43—81no—
418Dic43—81no—
419C2×#518D4311yescharacteristic, complemented
420C2×#447—431no—
421C2×#442—431no—
422C2×C4×D8—431no—
423#2324—431no—
424#1879—431no—
425#1879—431no—
426#1875—431no—
427#1864—431no—
428#1862—431no—
429#1854—431no—
430#1786—431no—
431#1762—431no—
432C4×#102—431no—
433#1750—431no—
434C2×C43—42no—
435C2×C43—44no—
436C2×C43—44no—
437C2×C43C4×#12011yescharacteristic
438C2×C43#294611yescharacteristic
439C2×C43#294811yescharacteristic
440C2×C43#300811yescharacteristic
441C2×C43#301211yescharacteristic
442C2×C43#311811yescharacteristic
443C2×C43#312211yescharacteristic
444D43—82no—
445C23×D4C2×D4311yescharacteristic
446C22×D8—431no—
447C22×D8—431no—
448C2×#121—431no—
449#518—24no—
450#518—24no—
451C2×C4×D4—21no—
452C2×C4×D4—21no—
453C2×C4×D4—431no—
454C2×C4×D4C2×D4311yescharacteristic
455C2×C4×D4C2×D4311yescharacteristic
456C2×C4×D4C2×D4311yescharacteristic
457C2×C4×D4C2×D4311yescharacteristic
458C2×#117C2×D4311yescharacteristic
459C2×#117C2×D4311yescharacteristic
460C22×C22⋊C4—21no—
461C22×C22⋊C4—21no—
462#447—438no—
463#442—864no—
464C4×D8—864no—
465C2×#107—431no—
466C2×#106—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×C22⋊C8—431no—
476C2×C22⋊C8—431no—
477C2×#97—431no—
478C2×C4×C8—431no—
479#390—431no—
480#390—861no—
481#389—431no—
482#388—861no—
483#386—861no—
484#385—861no—
485#380—431no—
486C4×C4⋊C4—431no—
487#340—431no—
488#340—431no—
489#340—431no—
490#340—431no—
491#336—431no—
492#336—431no—
493C43#2145811yescharacteristic, complemented, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4C4×D4314yescomplemented
504C22×D4C22×D4311yescharacteristic
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×D8—434no—
513C2×D8—434no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8—862no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—431no—
522#121—434no—
523#121—862no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4C22⋊D4314yescomplemented
535C4×D4C22⋊D4314yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4C22⋊D4311yescharacteristic
545C2×C4⋊C4C22⋊D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4C22⋊D4311yescharacteristic
561C2×C22⋊C4C22⋊D4311yescharacteristic
562C2×C42—21no—
563C2×C42—861no—
564C2×C42C22×D4311yescharacteristic
565C2×C42C22×D4311yescharacteristic
566#107—862no—
567#106—862no—
568#102—434no—
569#102—434no—
570#102—862no—
571#102—862no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—862no—
576C22⋊C8—434no—
577C22⋊C8—862no—
578#97—862no—
579C4×C8—862no—
580#95—861no—
581#95—861no—
582#95—861no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—81no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—861no—
593C24C2×C22⋊D4311yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—432no—
608C2×D4—864no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—3441no—
615C2×D4—3441no—
616C2×D4C2×C4×D4312yes—
617C2×D4C2×C4×D4312yes—
618C2×D4#1062189812yes—
619C2×D4#1062189812yes—
620C2×D4C2×C22⋊D4312yes—
621C2×D4C2×C22⋊D4312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—1722no—
646C22×C4C2×C4×D4312yes—
647C22×C4#1062189812yes—
648C22×C4C2×C22⋊D4311yescharacteristic
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654D8—868no—
655D8—868no—
656C2×C8—432no—
657C2×C8—432no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—432no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—3441no—
679C4⋊C4C2×C22⋊D4312yes—
680C4⋊C4C2×C22⋊D4312yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—1722no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—3441no—
697C42C2×C22⋊D4312yes—
698C42C2×C22⋊D4312yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—862no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23C4×C22⋊D4312yes—
734C23C22×C22⋊D4311yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—862no—
743D4—862no—
744D4—3444no—
745D4—1721no—
746D4—1721no—
747D4C4×C22⋊D4314yes—
748D4C4×C22⋊D4314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—862no—
776C2×C4—3444no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4C4×C22⋊D4312yes—
786C2×C4#1306329412yes—
787C2×C4#1306329412yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C22×C22⋊D4311yescharacteristic
790C2×C4C22×C22⋊D4311yescharacteristic
791C2×C4C2×#1062189811yescharacteristic
792C2×C4C2×#1062189811yescharacteristic
793C2×C4C2×#1062189811yescharacteristic
794C8—862no—
795C8—862no—
796C8—1721no—
797C8—1721no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—816no—
820C22—3441no—
821C22—3441no—
822C22—3441no—
823C22—3441no—
824C22—1722no—
825C22—1722no—
826C22—1722no—
827C22C2×C4×C22⋊D4311yescharacteristic
828C22C2×#1306329411yescharacteristic
829C22#1458341011yescharacteristic
830C22#1458370211yescharacteristic
831C22#1458370211yescharacteristic
832C22#1458370211yescharacteristic
833C22#1458371011yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—42no—
839C4—41no—
840C4—42no—
841C4—3441no—
842C4—3441no—
843C4—1722no—
844C4C2×C4×C22⋊D4311yescharacteristic
845C4C2×C4×C22⋊D4311yescharacteristic
846C4#1458341011yescharacteristic
847C4#1458341011yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—3442no—
852C2C4×#1306329411yescharacteristic
853C2#1914342711yescharacteristic
854C2#1914344511yescharacteristic
855C2#1914386311yescharacteristic
856C2#1914389911yescharacteristic
857C2#1914477911yescharacteristic
858C2#1914483811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#518C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenterC2×#518D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19137288C2semidirect
5. #19134943C2semidirect
6. #19134943C2semidirect
7. #19134917C2semidirect
8. #19134856C2semidirect
9. #19134842C2semidirect
10. #19134794C2semidirect
11. #19134526C2semidirect
12. #19134420C2semidirect
13. C4×#13063246C2semidirect
14. #19134361C2semidirect
15. C2×C43×#518C2semidirect
19. C2×C4×D172C22semidirect
20. #14583033C4semidirect
23. C2×#13063258C22semidirect
24. C2×#13063256C22semidirect
31. C2×#13063245C22semidirect
32. C2×#13063245C22semidirect
35. C2×#13063236C22semidirect
36. C2×C4×C43⋊C8C22semidirect
37. #14582801C22semidirect
39. #14582797C22semidirect
44. C4×C4⋊Dic43C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582654C22semidirect
50. #14582654C22semidirect
71. C2×#10621882C2×C4semidirect
72. C2×#10621882C2×C4semidirect
78. #13063299C2×C4semidirect
97. #13063246C2×C4semidirect
98. #13063246C2×C4semidirect
102. C22⋊(C43⋊C8)C2×C4semidirect
115. C22×D4×C43C2×C4semidirect
131. C4×D4×C43D4semidirect
132. C4×D4×C43D4semidirect
419. C2×#518D43semidirect
493. C43#21458semidirect
503. C22×D4C4×D43semidirect
534. C4×D4C22⋊D43semidirect
535. C4×D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
C2×#145830092
C2×C4×#106218822
#191372882
#191349432
#191349172
#191348562
#191348422
#191347942
#191345262
#191344202
C4×#130632462
#191343612
C2×C43×#5182
#2145843