Finite Group Databasebeta

← #25102320

Subgroups — #25102320

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×#14583373C211yesmaximal, characteristic, complemented
2C2×#14583035C211yesmaximal, characteristic
3C2×#14583012C211yesmaximal, characteristic, complemented
4C2×C4×D344C211yesmaximal, characteristic, complemented
5#19137288C211yesmaximal, characteristic, complemented
6#19134942C211yesmaximal, characteristic, complemented
7#19134942C211yesmaximal, characteristic, complemented
8#19134915C211yesmaximal, characteristic, complemented
9#19134859C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134527C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20#14583373—24no—
21#14583373—24no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic, complemented
27C2×#13063287—21no—
28C2×#13063287—21no—
29C2×#13063284C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31C2×C22⋊C4×D43—21no—
32#14583035C418yescomplemented
33#14583012—24no—
34C4×D344—24no—
35C2×#13063259C2211yescharacteristic, complemented
36C2×#13063257C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic, complemented
44C2×#13063247C2211yescharacteristic, complemented
45#14582801C2211yescharacteristic, complemented
46#14582799—21no—
47#14582797C2211yescharacteristic, complemented
48#14582789—21no—
49#14582775—21no—
50#14582770—21no—
51#14582759C2211yescharacteristic
52C4×C4⋊Dic43C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582662C2211yescharacteristic, complemented
56#14582662C2211yescharacteristic, complemented
57C2×#117×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic, complemented
61C2×C4×C8×C43C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—22no—
70C22×D172—22no—
71C22×D172C2×C414yescomplemented
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43—21no—
80C22×C4×D43—21no—
81C2×D344—22no—
82C2×D344—22no—
83C2×D344—22no—
84C2×D344—22no—
85C2×D344C2×C414yescomplemented
86C2×D344C2×C414yescomplemented
87#13063299—22no—
88#13063299C2×C414yescomplemented
89C4×D172—22no—
90C4×D172—22no—
91C4×D172—22no—
92C4×D172—22no—
93C4×D172—22no—
94C4×D172—22no—
95C4×D172—22no—
96C4×D172—22no—
97C4×D172D414yescomplemented
98C4×D172D414yescomplemented
99#13063287—28no—
100#13063287—28no—
101#13063284—22no—
102#13063284—22no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×Dic43⋊C4—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C22⋊C4×D43—28no—
120C22⋊C4×D43—28no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123#13063259—22no—
124#13063257—22no—
125#13063247—22no—
126#13063247—22no—
127#13063247—22no—
128#13063247—22no—
129#13063247—22no—
130#13063247—22no—
131#13063247C2×C414yescomplemented
132#13063247C2×C414yescomplemented
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C23×C4×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141#117×C43—22no—
142#117×C43—22no—
143C2×C4⋊C4×C43D411yescharacteristic
144C2×C4⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C22⋊C8×C43—22no—
150C22⋊C8×C43C2×C414yescomplemented
151#97×C43—22no—
152C4×C8×C43—22no—
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—24no—
159C23×D43—21no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43—81no—
163C23×D43—81no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43C22×C412yes—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—24no—
177C2×C22⋊D43—81no—
178C2×C22⋊D43—81no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C2×D172—24no—
185C2×D172—24no—
186C2×D172—28no—
187C2×D172—28no—
188C2×D172—24no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—28no—
196C2×D172—28no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172C22×C412yes—
203C2×D172C22×C412yes—
204C2×D172C22×C412yes—
205C2×D172C2×D412yes—
206C2×D172C2×D412yes—
207C2×D172#4112yes—
208C2×D172#4112yes—
209C2×C4×D43—24no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—42no—
214C2×C4×D43—81no—
215C2×C4×D43—81no—
216C2×C4×D43—81no—
217C2×C4×D43—81no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43—81no—
221C2×C4×D43—81no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43C22×C412yes—
235C2×C8×C43C22×C412yes—
236C4⋊C4×C43—22no—
237C4⋊C4×C43—22no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—22no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43C2×D412yes—
243C42×C43C2×D412yes—
244C22⋊Dic43—24no—
245C22⋊Dic43—81no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—42no—
252(C2×D43)⋊C4—81no—
253(C2×D43)⋊C4—81no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43C22×C412yes—
262C4⋊Dic43C2×D412yes—
263C4⋊Dic43C2×D412yes—
264Dic43⋊C4—81no—
265C4×Dic43—24no—
266C4×Dic43—81no—
267D344—28no—
268D344—28no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43C4×D412yes—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—216no—
284C22×D43—22no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—84no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—84no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43C4×D412yes—
322C2×C4×C43#12012yes—
323C2×C4×C43#12012yes—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C22⋊D43—84no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346D172—216no—
347D172—22no—
348D172—22no—
349D172—22no—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—41no—
356D172—41no—
357D172C4×D414yes—
358D172C4×D414yes—
359C4×D43—84no—
360C4×D43—84no—
361C4×D43—84no—
362C4×D43—84no—
363C4×D43—84no—
364C8×C43—22no—
365C8×C43—22no—
366C8×C43—41no—
367C8×C43—41no—
368#21458—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43C2×C4×D411yescharacteristic
377C22×C43C2×#12011yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57611yescharacteristic
382C22×C43#57711yescharacteristic
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—816no—
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—41no—
410C4×C43C2×C4×D411yescharacteristic
411C4×C43C2×C4×D411yescharacteristic
412C4×C43#52511yescharacteristic
413C4×C43#52511yescharacteristic
414Dic43—42no—
415Dic43—42no—
416Dic43—42no—
417Dic43—81no—
418Dic43—81no—
419C2×#518—431no—
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#1750D4311yescharacteristic, complemented
434C2×C43—42no—
435C2×C43C4×#12011yescharacteristic
436C2×C43#294611yescharacteristic
437C2×C43#294811yescharacteristic
438C2×C43#300811yescharacteristic
439C2×C43#301211yescharacteristic
440C2×C43#311811yescharacteristic
441C2×C43#312211yescharacteristic
442D43—44no—
443D43—44no—
444D43—82no—
445C23×D4—431no—
446C22×D8—431no—
447C22×D8—431no—
448C2×#121—431no—
449#518—864no—
450#518—864no—
451C2×C4×D4—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—431no—
456C2×C4×D4—861no—
457C2×C4×D4—861no—
458C2×#117—431no—
459C2×#117C2×D4311yescharacteristic
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
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⋊C8C2×D4311yescharacteristic
476C2×C22⋊C8C2×D4311yescharacteristic
477C2×#97C2×D4311yescharacteristic, complemented
478C2×C4×C8C2×D4311yescharacteristic, complemented
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#336C2×D4311yescharacteristic, complemented
492#336C2×D4311yescharacteristic, complemented
493C43#2145811yescharacteristic, complemented, Sylow
494C25—861no—
495C22×D4—434no—
496C22×D4—431no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—862no—
500C22×D4—862no—
501C22×D4—862no—
502C22×D4—862no—
503C22×D4—861no—
504C22×D4—861no—
505C22×D4—862no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—861no—
509C23×C4—861no—
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×C8C22×D4311yescharacteristic
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522#121—434no—
523#121—862no—
524C4×D4—434no—
525C4×D4—434no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—868no—
531C4×D4—868no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4—862no—
535C4×D4—862no—
536#117—22no—
537#117—22no—
538#117—862no—
539#117—862no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4D17211yescharacteristic
547C2×C4⋊C4D17211yescharacteristic
548C2×C22⋊C4—868no—
549C2×C22⋊C4—868no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4D17211yescharacteristic
561C2×C22⋊C4D17211yescharacteristic
562C2×C42—861no—
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—22no—
577C22⋊C8C4×D4314yescomplemented
578#97—22no—
579C4×C8—22no—
580#95—861no—
581#95—861no—
582#95—861no—
583C24—864no—
584C24—864no—
585C24—864no—
586C24—861no—
587C24—861no—
588C24—861no—
589C24—3441no—
590C24—3441no—
591C24—3441no—
592C24—3441no—
593C24C2×D17211yescharacteristic
594C2×D4—432no—
595C2×D4—432no—
596C2×D4—432no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—432no—
601C2×D4—868no—
602C2×D4—868no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—868no—
606C2×D4—868no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—3441no—
621C2×D4—3441no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—864no—
627C22×C4—864no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—864no—
632C22×C4—864no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—3441no—
636C22×C4—3441no—
637C22×C4—3441no—
638C22×C4—3441no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—3441no—
642C22×C4—3441no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—1722no—
646C22×C4C2×C4×D4312yes—
647C22×C4C2×D17211yescharacteristic
648C22×C4C2×D17211yescharacteristic
649C22×C4C2×D17211yescharacteristic
650C22×C4C2×D17211yescharacteristic
651C22×C4C2×D17211yescharacteristic
652C22×C4#1062189812yes—
653C22×C4C23×D4311yescharacteristic
654D8—868no—
655D8—868no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×C4×D4312yes—
667C2×C8C2×C4×D4312yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—432no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—3441no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—1722no—
693C42—21no—
694C42—21no—
695C42—864no—
696C42—3441no—
697C42D4×D4312yes—
698C42D4×D4312yes—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—8616no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—3444no—
714C23—3444no—
715C23—3444no—
716C23—3444no—
717C23—3444no—
718C23—3444no—
719C23—1721no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23C4×D17212yes—
734C23C22×D17211yescharacteristic
735D4—434no—
736D4—434no—
737D4—8616no—
738D4—862no—
739D4—862no—
740D4—862no—
741D4—862no—
742D4—862no—
743D4—862no—
744D4—862no—
745D4—862no—
746D4—3444no—
747D4—1721no—
748D4—1721no—
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—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—3444no—
769C2×C4—3444no—
770C2×C4—3444no—
771C2×C4—3444no—
772C2×C4—3444no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
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×D17212yes—
786C2×C4#1306329512yes—
787C2×C4#1306329512yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4#41×D4311yescharacteristic
792C2×C4#41×D4311yescharacteristic
793C2×C4C2×#1062189811yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—864no—
806C22—864no—
807C22—34416no—
808C22—3441no—
809C22—3441no—
810C22—3441no—
811C22—3441no—
812C22—1722no—
813C22—1722no—
814C22—1722no—
815C22—1722no—
816C22—1722no—
817C22—1722no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22—1722no—
827C22C2×C4×D17211yescharacteristic
828C22C2×#1306329511yescharacteristic
829C22#1458341111yescharacteristic
830C22#1458370411yescharacteristic
831C22#1458370411yescharacteristic
832C22#1458370411yescharacteristic
833C22#1458371111yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—41no—
839C4—3441no—
840C4—3441no—
841C4—1722no—
842C4—1722no—
843C4—1722no—
844C4C4×D4×D4311yescharacteristic
845C4C4×D4×D4311yescharacteristic
846C4#1458340811yescharacteristic
847C4#1458340811yescharacteristic
848C2—42no—
849C2—3442no—
850C2—1724no—
851C2—1724no—
852C2C4×#1306329511yescharacteristic
853C2#1914342911yescharacteristic
854C2#1914344811yescharacteristic
855C2#1914386511yescharacteristic
856C2#1914390211yescharacteristic
857C2#1914478111yescharacteristic
858C2#1914483911yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#14583373C2semidirect
3. C2×#14583012C2semidirect
4. C2×C4×D344C2semidirect
5. #19137288C2semidirect
6. #19134942C2semidirect
7. #19134942C2semidirect
8. #19134915C2semidirect
9. #19134859C2semidirect
10. #19134845C2semidirect
11. #19134796C2semidirect
12. #19134527C2semidirect
13. #19134421C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1750C2semidirect
26. C2×C4×D172C22semidirect
32. #14583035C4semidirect
35. C2×#13063259C22semidirect
36. C2×#13063257C22semidirect
43. C2×#13063247C22semidirect
44. C2×#13063247C22semidirect
45. #14582801C22semidirect
47. #14582797C22semidirect
52. C4×C4⋊Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582662C22semidirect
56. #14582662C22semidirect
60. C2×#97×C43C22semidirect
61. C2×C4×C8×C43C22semidirect
62. C43×#336C22semidirect
63. C43×#336C22semidirect
71. C22×D172C2×C4semidirect
85. C2×D344C2×C4semidirect
86. C2×D344C2×C4semidirect
88. #13063299C2×C4semidirect
97. C4×D172D4semidirect
98. C4×D172D4semidirect
131. #13063247C2×C4semidirect
132. #13063247C2×C4semidirect
150. C22⋊C8×C43C2×C4semidirect
433. #1750D43semidirect
477. C2×#97C2×D43semidirect
478. C2×C4×C8C2×D43semidirect
491. #336C2×D43semidirect
492. #336C2×D43semidirect
493. C43#21458semidirect
577. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833732
C2×#145830352
C2×#145830122
C2×C4×D3442
#191372882
#191349422
#191349152
#191348592
#191348452
#191347962
#191345272
#191344212
C4×#130632472
C43×#17502
#2145843