Finite Group Databasebeta

← #25116919

Subgroups — #25116919

Order 11008.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583035C211yesmaximal, characteristic
2C2×#14583012C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic, complemented
4#19137609C211yesmaximal, characteristic, complemented
5C22⋊C4×D172C211yesmaximal, characteristic, complemented
6#19135471C211yesmaximal, characteristic, complemented
7#19135292C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135023C211yesmaximal, characteristic, complemented
10#19134942C211yesmaximal, characteristic, complemented
11#19134942C211yesmaximal, characteristic, complemented
12#19134859C211yesmaximal, characteristic, complemented
13#19134790C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C43×#1752C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic, complemented
23C2×(C22⋊D43)⋊C4—21no—
24C22×C4⋊Dic43C2211yescharacteristic
25C2×C22⋊C4×D43—21no—
26#14583035C418yescomplemented
27#14583012—24no—
28C2×#13063257C2211yescharacteristic, complemented
29C2×#13063257C2211yescharacteristic, complemented
30C2×#13063247—24no—
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic, complemented
42#14582797C2211yescharacteristic, complemented
43#14582791—21no—
44#14582777—21no—
45#14582777—21no—
46#14582776—21no—
47#14582773—21no—
48#14582759C2211yescharacteristic
49#14582754—21no—
50C4×C4⋊Dic43C2211yescharacteristic, complemented
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×D172—22no—
64C22×D172—22no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2×C414yescomplemented
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C2×D344—22no—
79C2×D344—22no—
80C2×D344—41no—
81C2×D344—41no—
82C2×D344C2×C414yescomplemented
83C2×D344C2×C414yescomplemented
84#13063299—22no—
85#13063299C2×C414yescomplemented
86C4×D172—22no—
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—41no—
90C4×D172—41no—
91C4×D172—41no—
92(C22⋊D43)⋊C4—44no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—41no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—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—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C22⋊C4×D43—44no—
114C2×C4×Dic43—21no—
115#13063257—22no—
116#13063257—41no—
117#13063247—22no—
118#13063247—22no—
119#13063247—22no—
120#13063247—22no—
121#13063247—41no—
122#13063247C2×C414yescomplemented
123#13063247C2×C414yescomplemented
124#13063247D414yescomplemented
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C23×C4×C43C2311yescharacteristic
129C22×C8×C43—22no—
130C22×C8×C43—22no—
131C22×C8×C43—41no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C22⋊C8×C43C2×C414yescomplemented
141#97×C43—22no—
142#97×C43—41no—
143#95×C43D411yescharacteristic
144#95×C43D411yescharacteristic
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—24no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43—42no—
154C23×D43—81no—
155C23×D43—81no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43#4112yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—24no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—42no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—81no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—24no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—28no—
194C2×D172—42no—
195C2×D172—42no—
196C2×D172—44no—
197C2×D172—44no—
198C2×D172—44no—
199C2×D172C22×C412yes—
200C2×D172C22×C412yes—
201C2×D172C22×C412yes—
202C2×D172C2×D412yes—
203C2×D172#4112yes—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—81no—
211C2×C4×D43—81no—
212C2×C4×D43—81no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—44no—
223C2×C8×C43C22×C412yes—
224C2×C8×C43C22×C412yes—
225C2×C8×C43C2×D412yes—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—22no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—21no—
232C22⋊Dic43—42no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—42no—
240(C2×D43)⋊C4—81no—
241(C2×D43)⋊C4—81no—
242(C2×D43)⋊C4—81no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—42no—
252C4⋊Dic43C22×C412yes—
253C4⋊Dic43C2×D412yes—
254Dic43⋊C4—42no—
255C4×Dic43—42no—
256D344—28no—
257D344—44no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43C4×D412yes—
263C23×C43AGL(1,ℤ/8)12yes—
264C23×C43AGL(1,ℤ/8)12yes—
265C23×C43C22×D411yescharacteristic
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—48no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—48no—
289C22×D43—84no—
290C22×D43—84no—
291C22×D43—84no—
292C22×D43—84no—
293C22×D43—84no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
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—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43C4×D412yes—
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C22⋊D43—48no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—84no—
336D172—22no—
337D172—22no—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—22no—
343D172—48no—
344D172—41no—
345D172—41no—
346D172—41no—
347D172—41no—
348D172C4×D414yescomplemented
349C4×D43—84no—
350C4×D43—84no—
351C4×D43—84no—
352C8×C43—22no—
353C8×C43—22no—
354C8×C43—22no—
355C8×C43—41no—
356#22858—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43#44214yescomplemented
364C22×C43C2×C4×D411yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43#54611yescharacteristic
367C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C43#57611yescharacteristic
370C22×C43#57711yescharacteristic
371C2×D43—24no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—816no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C2×D43—81no—
393C4×C43—22no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43—41no—
398C4×C43C2×C4×D411yescharacteristic
399C4×C43#51811yescharacteristic
400C4×C43#54611yescharacteristic
401C4×C43#55111yescharacteristic
402Dic43—42no—
403Dic43—42no—
404Dic43—81no—
405Dic43—81no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
409C22×#102—431no—
410#2361—431no—
411D4×C22⋊C4—431no—
412#1972—431no—
413#1936—431no—
414#1926—431no—
415#1893—431no—
416#1879—431no—
417#1879—431no—
418#1864—431no—
419#1853—431no—
420#1762—431no—
421#1752D4311yescharacteristic, complemented
422C2×C43—24no—
423C2×C43#235811yescharacteristic
424C2×C43C2×#44211yescharacteristic
425C2×C43#294611yescharacteristic
426C2×C43#326411yescharacteristic
427C2×C43#326511yescharacteristic
428C2×C43#330611yescharacteristic
429C2×C43#331811yescharacteristic
430D43—44no—
431D43—82no—
432D43—82no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8—431no—
436C23×C8C2×D4311yescharacteristic
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C22⋊C4—861no—
444#447—438no—
445#442—864no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—864no—
457C2×C22⋊C8C2×D4311yescharacteristic
458C2×#97C2×D4311yescharacteristic, complemented
459C2×#97C2×D4311yescharacteristic, complemented
460#390—431no—
461#390—431no—
462#390—431no—
463#389—431no—
464#388—861no—
465#386—861no—
466#386—861no—
467#386—861no—
468#385—861no—
469#380—431no—
470#379—861no—
471C4×C4⋊C4—431no—
472C4×C22⋊C4C2×D4311yescharacteristic
473#340—431no—
474#340—431no—
475#340—431no—
476#340—431no—
477#336C2×D4311yescharacteristic, complemented
478#336C2×D4311yescharacteristic, complemented
479C43#2285811yescharacteristic, complemented, Sylow
480C25—861no—
481C22×D4—434no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—862no—
486C22×D4—862no—
487C22×D4—861no—
488C22×D4—861no—
489C22×D4—862no—
490C22×D4—1721no—
491C22×D4—1721no—
492C23×C4—861no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—862no—
500C2×D8—862no—
501C2×D8—1721no—
502C2×D8—1721no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510#121—434no—
511#121—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1721no—
516C4×D4—1721no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—862no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—1721no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—1724no—
540C2×C22⋊C4D17211yescharacteristic
541C2×C22⋊C4D17211yescharacteristic
542C2×C42—861no—
543C2×C42C22×D4311yescharacteristic
544C2×C42C22×D4311yescharacteristic
545#106—862no—
546#106—1721no—
547#102—434no—
548#102—434no—
549#102—434no—
550#102—862no—
551#102—862no—
552#102—862no—
553#102—862no—
554#102—1721no—
555C22⋊C8C4×D4314yescomplemented
556#97—22no—
557#97—41no—
558#95—861no—
559#95—861no—
560#95—861no—
561#95D17211yescharacteristic
562#95D17211yescharacteristic
563C24—861no—
564C24—864no—
565C24—861no—
566C24—861no—
567C24—3441no—
568C24—3441no—
569C24—1722no—
570C24—1722no—
571C24—1722no—
572C24—1722no—
573C24C2×D17211yescharacteristic
574C2×D4—432no—
575C2×D4—432no—
576C2×D4—432no—
577C2×D4—432no—
578C2×D4—432no—
579C2×D4—868no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—1724no—
596C2×D4—1724no—
597C2×D4—1724no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4—1722no—
601C2×D4—1722no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4—3441no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4C2×C4×D4312yes—
624C22×C4C2×D17211yescharacteristic
625C22×C4C2×D17211yescharacteristic
626C22×C4C2×D17211yescharacteristic
627C22×C4C2×D17211yescharacteristic
628C22×C4C2×D17211yescharacteristic
629C22×C4#1062189812yes—
630C22×C4C23×D4311yescharacteristic
631D8—868no—
632D8—1724no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8C2×C4×D4312yes—
644C2×C8C2×C4×D4312yes—
645C2×C8D4×D4312yes—
646C4⋊C4—432no—
647C4⋊C4—432no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—1722no—
657C4⋊C4—1722no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—864no—
661C22⋊C4—3441no—
662C22⋊C4—3441no—
663C22⋊C4—3441no—
664C22⋊C4—1722no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—1722no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—862no—
685C23—3444no—
686C23—3444no—
687C23—3444no—
688C23—3444no—
689C23—3444no—
690C23—1728no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23—1728no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23C4×D17212yes—
709C23#1306335312yes—
710C23#1306335312yes—
711C23C22×D17211yescharacteristic
712D4—434no—
713D4—862no—
714D4—862no—
715D4—862no—
716D4—862no—
717D4—862no—
718D4—862no—
719D4—862no—
720D4—1728no—
721D4—1728no—
722D4—1721no—
723D4—1721no—
724D4—1721no—
725D4—1721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—3444no—
749C2×C4—3444no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4C4×D17212yes—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4311yescharacteristic
767C2×C4C2×#1062189811yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337111yescharacteristic
770C8—22no—
771C8—22no—
772C8—22no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—864no—
781C22—34416no—
782C22—3441no—
783C22—3441no—
784C22—3441no—
785C22—3441no—
786C22—3441no—
787C22—3441no—
788C22—3441no—
789C22—3441no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22#1458301214yescomplemented
803C22C2×C4×D17211yescharacteristic
804C22D4×D17211yescharacteristic
805C22#1458354411yescharacteristic
806C22C2×#1306335311yescharacteristic
807C22C2×#1306335311yescharacteristic
808C22#1458370411yescharacteristic
809C22#1458371111yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—3441no—
816C4—3441no—
817C4—3441no—
818C4—1722no—
819C4—1722no—
820C4C4×D4×D4311yescharacteristic
821C4#1458337111yescharacteristic
822C4#1458353911yescharacteristic
823C4#1458357311yescharacteristic
824C2—24no—
825C2—3442no—
826C2—3442no—
827C2—1724no—
828C2#1913757711yescharacteristic
829C2C2×#1458301211yescharacteristic
830C2#1914342911yescharacteristic
831C2#1914608011yescharacteristic
832C2#1914609511yescharacteristic
833C2#1914655811yescharacteristic
834C2#1914673811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1752C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1752D43
hypocenterC43#22858
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×#14583012C2semidirect
3. C22×#13063247C2semidirect
4. #19137609C2semidirect
5. C22⋊C4×D172C2semidirect
6. #19135471C2semidirect
7. #19135292C2semidirect
8. #19135223C2semidirect
9. #19135023C2semidirect
10. #19134942C2semidirect
11. #19134942C2semidirect
12. #19134859C2semidirect
13. #19134790C2semidirect
14. #19134421C2semidirect
15. C43×#1752C2semidirect
22. C2×C4×D172C22semidirect
26. #14583035C4semidirect
28. C2×#13063257C22semidirect
29. C2×#13063257C22semidirect
37. C2×#13063247C22semidirect
38. C2×#13063247C22semidirect
41. #14582801C22semidirect
42. #14582797C22semidirect
50. 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
69. C22×D172C2×C4semidirect
82. C2×D344C2×C4semidirect
83. C2×D344C2×C4semidirect
85. #13063299C2×C4semidirect
122. #13063247C2×C4semidirect
123. #13063247C2×C4semidirect
124. #13063247D4semidirect
140. C22⋊C8×C43C2×C4semidirect
348. D172C4×D4semidirect
363. C22×C43#442semidirect
421. #1752D43semidirect
458. C2×#97C2×D43semidirect
459. C2×#97C2×D43semidirect
477. #336C2×D43semidirect
478. #336C2×D43semidirect
479. C43#22858semidirect
555. C22⋊C8C4×D43semidirect
802. C22#14583012semidirect

Maximal subgroups

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

subgroupindex
C2×#145830352
C2×#145830122
C22×#130632472
#191376092
C22⋊C4×D1722
#191354712
#191352922
#191352232
#191350232
#191349422
#191348592
#191347902
#191344212
C43×#17522
#2285843